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Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet
Accepted Manuscript
Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet K. Warncke, S. Gepperth, B. Sauer, A. Sadiki, J. Janicka, R. Koch, H.-J. Bauer PII: DOI: Reference:
S0301-9322(15)30214-7 10.1016/j.ijmultiphaseflow.2016.12.010 IJMF 2536
To appear in:
International Journal of Multiphase Flow
Received date: Revised date: Accepted date:
19 December 2015 1 December 2016 10 December 2016
Please cite this article as: K. Warncke, S. Gepperth, B. Sauer, A. Sadiki, J. Janicka, R. Koch, H.-J. Bauer, Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet, International Journal of Multiphase Flow (2017), doi: 10.1016/j.ijmultiphaseflow.2016.12.010
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Highlights • Identical breakup phenomena are observed in experiment and simulation
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• Ligament and bag formation in the vicinity of the atomizing edge
• Efficient characterization of the liquid sheet by tracking the phase interface • 3D-DNS data is analyzed as seen from the top corresponding to shadow images
• Droplet size distributions provided by eDNS are in good agreement with
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the experiment
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Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet
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K. Warnckea,∗, S. Gepperthb , B. Sauera , A. Sadikia , J. Janickaa , R. Kochb , H.-J. Bauerb a Department
of Energy and Power Plant Technology, Technische Universität Darmstadt, 64287 Darmstadt, Jovanka-Bontschits-Straße 2, Germany b Institut für Thermische Strömungsmaschinen, Karlsruher Institut für Technologie, 76135 Karlsruhe, Kaiserstraße 12, Germany
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Abstract
The primary breakup of airblast atomization is governed by complex mechanisms and is still not well understood. In recent years high speed shadowgraphy experiments and Direct Numerical Simulations of prefilming airblast atomization have been performed independently. In this paper detailed results of a
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combined experimental and numerical study are presented. A single operating point of a planar prefilming airblast atomizer is investigated, based on a spatial resolution of 10 µm and a consistent analysis of the liquid film in both the exper-
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imental and the numerical studies. For the analysis the three-dimensional DNS data is projected on a plane, corresponding to the data obtained by shadowgraphy. The experiment is characterized by back light illumination in conjunction
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with particle and ligament tracking velocimetry. A Depth of Field correction is applied to further improve the measurement accuracy. For the numerical inves-
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tigation the embedded DNS approach is utilized: The primary breakup region is simulated with a highly resolved DNS, embedded in a coarser Large Eddy Simulation. The comparison comprises a phenomenological discussion of the
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disintegration process and quantitative results. Distributions for the breakup length, the liquid film deformation velocity, the droplet sizes and velocities are presented. The results are in good agreement and confirm the applicability of ∗ Corresponding
author. Tel. +49 6151 1628906; fax +49 6151 28900 Email address: [email protected] (K. Warncke)
Preprint submitted to International Journal of Multiphase Flow
February 3, 2017
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the embedded DNS and the particle and ligament tracking velocimetry for the analysis of the primary breakup of airblast atomization. Shadowgraphy, embedded DNS, aircraft engine, primary
atomization, ligament tracking, droplet tracking 1. Introduction
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Keywords:
The air traffic has doubled every 15 years since the 1970s and is expected to continue this growth for at least the next 15 years (Airbus (2013); Boeing
(2013)). The Advisory Council of Aeronauctical Research in Europe defined
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emissions targets for the year 2020: CO2 reduction about 50 % per passenger kilometer, NOx reduction about 80 % and noise reduction about 50 % compared
to the year 2000 (ACARE (2010)). Similar targets were defined by the US aviation industry (NSaTC (2010)).
To reach these emission targets, lean combustion technologies need to be
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integrated in future aircraft engines (Wilfert et al. (2007)). For lean combustion high quality fuel atomization is required to ensure a stable combustion in every operating condition during a flight. Prefilming airblast atomizers are used in
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aircraft engines to atomize the liquid fuel. Here, a thin liquid fuel film is formed on a prefilmer and disintegrated by coflowing air streams. To effectively control
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the atomization an improved understanding of the breakup process is required. A major limitation in understanding these flow systems is a detailed insight into the initial atomization step, the primary breakup. Especially, the impact
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of modified geometry and operating parameters is highly demanded to improve the design of combustion chambers. The investigation of the primary breakup is challenging as the geometries
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of airblast atomizers are complex and the two-phase flow is characterized by high Weber and Reynolds numbers. To capture the temporal evolution of the liquid film in experimental or numerical investigations high resolutions in time and space are mandatory. In addition, the spatial domain belonging to primary breakup is large compared to the breakup of a liquid jet. Wheras a liquid jet 2
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is typically injected with a high velocity in a stagnant environment, the velocity of an airblasted sheet is at least one order of magnitude smaller than the coflow air velocity. As a result breakup time and breakup length are extended.
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Furthermore, compared to other atomizer designs like flat sheet or jet atomizers, where the dominant instability mechanisms have already been identified
(Marmottant and Villermaux (2004); Fuster et al. (2013)), no such fundamental understanding exists for prefilming airblast atomizers.
Since the idea of an airblast atomizer was first introduced by Lefebvre and
Miller (1966) many experimental investigations have been carried out to under-
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stand the physical processes of the atomization of the liquid film at the atomizing edge. Most of the research did focus on the investigation of the spray charac-
teristic downstream of the atomizer. By applying laser optical measurement systems the key parameters affecting the breakup process were identified. The most pronounced effect on the droplet sizes comes from the mean air velocity within the atomizer. An increase in mean air velocity results in increased aero-
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dynamic forces that reduce the droplet sizes (Lefebvre (1980); Jasuja (1981); Sattelmayer and Wittig (1986); Aigner and Wittig (1988); Beck et al. (1991);
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Bhayaraju et al. (2005)). Additionally, it could be observed that an increase in air pressure reduces the droplet size (Rizkalla and Lefebvre (1975); Lefebvre (1980); Brandt et al. (1996); Bhayaraju et al. (2005); Jasuja (2006)). A reverse
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effect on the Sauter Mean Diameter has the increase in the surface tension of the liquid (Lefebvre (1980); Aigner and Wittig (1988); Brandt et al. (1998)). The
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liquid viscosity on the other hand has only a minor effect on the droplet size as long as its value is small, which is the case for aero engine fuels (Sattelmayer and Wittig (1986); Jasuja (1981)). A still controversial discussed parameter is
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the liquid film thickness. Some researchers observed that an increase in liquid film thickness is accompanied by an increase in the Sauter Mean Diameter (ElShanawany and Lefebvre (1980); Lefebvre (1980); Rizk and Lefebvre (1983)). Other investigations could not identify this behavior and reported that a change in the film thickness has no effect on the droplet size due to a decoupling of the film disintegration process and the film thickness at the atomizing edge. The 3
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reason is an observed accumulation of the liquid film at the atomizing edge prior to the primary atomization of this accumulation (Sattelmayer and Wittig (1986); Aigner and Wittig (1988); Brandt et al. (1996); Müller et al. (2005);
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Gepperth et al. (2013); Bärow et al. (2015)). Therefore, the atomizing edge thickness and air flow structures in the vicinity of the atomizing edge will affect the size of droplets (Gepperth et al. (2012); Braun et al. (2015)).
In order to describe the atomization process analytically, Chaussonnet et al.
(2013) presented an approach that transfers the instabilities observed in co-
flowing atomizer configurations to the breakup of prefilming airblast atomizers.
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To include the accumulation of the liquid at the atomizing edge and its effect on the dominant instability mechanism, the atomization edge thickness is included in the calculation of the transverse instability (Chaussonnet et al. (2013)). However, without detailed numerical investigations it is impossible to identify the responsible atomization instability in prefilming airblast atomizers. To investigate the primary breakup numerically, Direct Numerical Simula-
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tions (DNS) are a suitable approach as all scales are resolved. The Volume of Fluid (VOF) and the Level Set (LS) are well-established methods to repro-
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duce the physics of the immiscible fluids and to transport the interface between them. In several numerical studies the phenomena of airblast atomization are analyzed by computing the breakup of a planar liquid sheet directly injected in
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two coflowing air streams. In this configuration no prefilmer is present. Considering this configuration the study by Couderc and Estivalezes (2005) focused on
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the validation of global sheet oscillations against experimental results, utilizing a 2-D DNS combined with a LS approach. Villedieu et al. (2013) applied a compressible two-fluid model and compared the oscillation frequency and the
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breakup length of the liquid sheet to experimental data. Pringuey and Cant (2014) performed a three-dimensional Large Eddy Simulation (LES) to prove the applicability of the Robust Conservative Level Set (RCLS) method to airblast atomization. This method allows an improved mass conservation of the LS method and is based on the Conservative Level Set by Olsson and Kreiss (2005); Olsson et al. (2007). The injection of a liquid sheet into a stagnant environment 4
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was investigated by Sander and Weigand (2008) using different injection nozzles and liquid inflow profiles. For the simulations DNS with VOF was combined. Other studies focus on the liquid wall film disturbed by the air stream above,
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either with a 2-D RANS solver (Hashmi et al. (2010) or a 3-D DNS combined with a LS-VOF approach (Berlemont et al. (2012)). The 2-D LES simulations
by Volz et al. (2015) focused on the film thickness and were validated against experimental results.
To describe the full atomization process, including primary and secondary breakup, the coupling of an Eulerian multiphase solver with Lagrangian Particle
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Tracking (LPT) is another field of research. Here, small droplets generated by the primary breakup are transferred to a mass point description and tracked by
a Lagrangian solver (Ling and Zaleski (2014); Zuzio et al. (2013)). In contrast to these methods a meshless approach, called Smoothed Particle Hydrodynamics (SPH), is applied by Hoefler et al. (2013); Braun et al. (2015) to simulate primary breakup.
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Although several numerical and experimental studies have been performed, a combined investigation considering the liquid wall film on top of the prefilmer
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and the subsequent disintegration is still a missing link. This paper fills this gap and presents a numerical and experimental investigation of a planar prefilming airblast atomizer, establishing a first basis for identifying the dominating
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breakup mechanisms. The study is based on an identical operating point and consistent geometrical conditions of the prefilmer. Further, an identical analy-
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sis procedure is applied to the experimental and numerical data, facilitating a reliable comparison of quantitative results, e.g. the breakup length. In order to capture the complex physical processes involved in the primary
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breakup of a liquid film in the experiment, sophisticated laser optical diagnostics are used. In combination with a generic atomizer design a highly resolved temporal as well as spacial investigation is possible. For statistically reliable data of droplet sizes and velocities as well as the ligament formation process, an adapted particle and ligament tracking velocimetry setup is used (Müller et al. (2006, 2007)). It was extended by a Depth of Field (DoF) correction algorithm 5
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to increase the measurement accuracy (Gepperth et al. (2012)). Furthermore, a three dimensional high speed shadowgraphy technique is applied for investigating the various temporal and spatial quantities observed during primary
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breakup, leading to a profound understanding of this process. This enables the unique opportunity for accurate quantitative and qualitative comparisons to data obtained by the numerical simulation.
For the simulation the embedded DNS approach is applied as introduced by Sauer (2014) for the primary breakup of airblast atomization. With eDNS a highly resolved 3D-DNS is applied to the breakup region, embedded in a
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LES. High quality boundary conditions are generated by the LES and mapped to the DNS domain. Sauer proved the applicability of the concept using a generic planar prefilming atomizer and six operating points, including cruise and altitude relight conditions.
The paper is organized as follows: the experimental investigation including set-up, diagnostics and post-processing steps are presented followed by the
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numerical investigation. The embedded DNS methodology and numerical setup are explained. Additionaly, the post-procesing of the DNS data focusing
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on an analysis consistent with the experiment, is presented. Furthermore, the selected operating conditions are described. Afterwards, the results of the primary breakup are shown, the following discussion being divided into two sec-
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tions. First, the physical phenomena observed both experimentally and numerically are compared considering also the temporal evolution of the liquid sheet.
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Second, quantitative results of the liquid sheet and the droplets generated by primary breakup are validated against each other.
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2. Experimental Investigation The measurements have been conducted at the spray test rig at the Institut
für Thermische Strömungsmaschinen (ITS). The air is supplied by a radial compressor with a maximum mass flow of 200 g/s. The air mass flow is measured via an air mass flow meter. To ensure a homogeneous velocity field, a mixer, a flow
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straightener and a nozzle are positioned upstream of the test section (Fig. 1). To capture the relevant flow parameters, pressure and temperature probes are connected to the mixing unit. Details on the test rig can be found in Gepperth
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et al. (2010); Müller et al. (2006); Müller (2015). 2.1. Test section
In order to enhance the optical accessibility, the test section itself is a two-
dimensional abstraction of an axis-symmetric airblast atomizer (Fig. 1(a)). It consists of four wall segments and the prefilming surface. The air emerging
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from the mixer is split into two air streams that pass the prefilmer on each side. Inside the prefilmer, a cavity used as a continuous feed for the test liquids is located. The liquid is ejected through a set of 50 equidistant distributed holes
with a diameter of 0.5 mm each (Fig. 1(b)). The air shear causes the liquid to form a uniform thin film flowing in the z-direction. It was ensured that no film dryout was occurring during the experiments. The liquid flow through the test
2.2. Diagnostics
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section is controlled by a mass flow meter/controller.
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The experimental observation of the film disintegration process and the measurement of the non-spherical droplets and structures as well as the ligaments
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attached to the atomizer is very challenging. For this reason, previous experimental studies focused on the development of an efficient an reliable measurement technique for the observation of the primary breakup (Gepperth et al.
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(2012); Müller et al. (2006); Müller (2015)). To derive statistically robust results of the ligament structures and droplet sizes, an efficient algorithm based on
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the particle and ligament tracking velocimetry was developed by Müller (2015). The algorithm of Müller (2015) has been extended by a Depth of Field (DoF) correction to further increase the measurement accuracy. Additionally, high speed images are recorded to gain a detailed insight to the
physical processes causing the film disintegration into ligaments and droplets.
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grid
l = 47
21.6 5
46
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test section
h = 0.23
8.1
y
prefilmer honeycomb inlet nozzle 65
70.5
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(a) Inlet and generic airblast atomizer
z
x
cavity
liquid inlet
liquid inlet
69.5
ejection holes
x
b = 50 96
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z
y
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wetted area
(b) Prefilmer of the generic airblast atomizer
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Figure 1: Experimental setup (all units are represented in mm)
2.2.1. Particle and ligament tracking velocimetry
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For the detailed investigation of the liquid film atomization process, a combined method of particle and ligament tracking velocimetry has been used. The technique is based on back light illumination of a measurement volume (shad-
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owgraphy) with a double-pulsed laser. The field of view is 12 mm in the zdirection and 16 mm in the y-direction. The spatial resolution is 10 µm. Details on the optical setup and the measurement system can be found in Gepperth et al. (2010, 2012). The key advantage of this technique is that information about the accumulated liquid at the atomizing edge and the generated droplets
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are gathered at the same time. A schematic view of the liquid accumulation at the atomizing edge is shown in Fig. 2. The droplets do not need to be spherical as it is the case with Phase-Doppler-Anemometry (Tropea and Damaschke
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(2000); Tropea (2011)). In addition, it is possible to measure the velocity of both, droplets and liquid accumulation at the same time. This is a disadvantage of commercially available shadow sizing systems where only the droplet
velocity can be measured. The information about the liquid structure and the initial particles is of particular interest in the primary atomization region near
the atomizer edge. This helps to link the produced droplets near the atomizer which the droplets are generated.
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edge to the deformation of the liquid accumulation at the atomizing edge by
film flow
air flow
accumulated liquid
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air flow
droplets
z
x
prefilmer
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Figure 2: Liquid accumulation at the atomizing edge
The software for the post-processing has previously been developed at ITS
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(Kapulla et al. (2008); Müller et al. (2006); Müller (2015)). The post-processing routine can be divided in four major tasks. First, a grey scale analysis of
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the recorded double frame images is performed. In this step, a threshold is calculated based on the image intensity distribution. By means of this threshold, the pixel array of the image is than split into background and object. In the
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second step, a contouring algorithm is applied. This algorithm detects connected structures based on the grey scale level in step one. It further divides the detected areas into the accumulated liquid at the atomizer edge and droplets. Afterwards, a sphere or ellipse is fitted to the accepted droplets and their size is corrected by a Depth of Field correction (section 2.2.2) based on the work
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of Kim and Kim (1994); Lee and Kim (2004); Castanet et al. (2013). This
0 1 2 3
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0 Y [mm]
5
Pstr maxima
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Lstr
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Z [mm]
correction leads to a significant increase of the measurement accuracy.
(a) Detected liquid accumulation and ligaments
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Z [mm]
4
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10
0 Y [mm]
5
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(b) Detected droplets and corresponding velocity com-
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ponents
Figure 3: Detected liquid accumulation and droplets after data processing
The third step is the calculation of the droplet velocities in the yz-plane. As a
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first estimation a velocity field is calculated based on an ordinary PIV algorithm. Due to the intensity distribution and the huge span of possible droplet sizes, this algorithm produces inaccurate and multiple velocity vectors for each droplet. Therefore, a least square fitting algorithm that uses the estimated velocity field as a ’first guess’ and the detected droplet positions for frame one and two is used
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to calculate the displacement and based on the inter framing time the velocity for each droplet (Müller (2015)). In the last step, the geometrical parameters of the accumulated liquid are
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recorded. The blue line in Fig. 3(a) indicates the perimeter of the accumulated liquid, Pstr . The red dots along the perimeter represent the maximum elon-
gation of the liquid accumulation in the streamwise direction. Based on the
position of the atomizing edge and the detected maxima, the breakup length of the ligaments Lstr can be derived. In addition, the detected liquid accumulation
at the atomizing edge of subsequent temporal frames is used to calculate the
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streamwise deformation velocity udef,str of the liquid.
For the present test case, a set of 300 double frame images was post-processed. A processed double frame image is shown in Fig. 3(b), including the raw image, liquid accumulation (blue and red lines), droplets (blue and red ellipses) and the calculated droplet velocities (green arrows). The lengths of the arrows indicate the velocity magnitude and the arrow head points into the direction in which
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the droplet moves. The atomizing edge is represented by the dashed red line. 2.2.2. Depth of Field (DoF) correction
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The back light technique as previously discussed usually does not give a sharp edge of all interesting objects in every part of the image. This is due to
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the fact that lenses can only be focused to the so called focal plane. Objects located at exactly this position are accurately captured on the camera chip. If the object moves closer or further away from this focal plane it moves ’out-of-
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focus’ and can no longer be detected accurately. The region in which an object can be considered as accurately detected is the depth of field. In an optical
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setup this depth of field is dependent on the f-number and the focal distance of the lens, the distance between camera and object as well as the physical pixel size of the CCD chip. In the present study, it was important to capture a wide range of possible droplet sizes, starting from droplets with tenth of microns up to droplets with more than one millimetre. To accurately detect small droplets of less than 60 µm, a large magnification is needed. To achieve this magnification, 11
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spacer rings were inserted between the lens and the camera. This leads to a
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reduction in the depth of field.
(a) Calibrated droplet diameter as a function (b) Calibrated droplet diameter as a function of the out-of-focus position and reference di- of the out-of-focus position and reference diameter
ameter
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1.4
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1.6
x = 0 [mm] x = 1 [mm] x = 2 [mm] x = 4 [mm] x = 8 [mm]
1.2
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Dmeas/Dref [mm]
1.8
1
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0.8
0.020.1 0.2 0.3 0.4 0.5 Dref [mm]
1
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(c) Non-dimensional sizing accuracy for different out-of-focus positions
Figure 4: Calibrated droplet diameter as a function of the out-of-focus position and reference
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diameter
On the other hand, the field of view has to have a certain size in order to
be able to track the liquid accumulation for a sufficient length. This leads to a limited resolution of 10 µm per pixel. With such a setup, a constant intensity threshold of 80 %, as it is used in the present investigations, leads to an over estimation of the droplet sizes (Kapulla et al. (2008)). Therefore, a calibration 12
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is mandatory. In the present study a calibration target was used. Due to the accurate manufacturing process, the spherical dots are highly resolved, both in size and shape. The calibration plate consists of four different areas and covers
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dot sizes between 10 µm to 2000 µm. The calibration process itself has to be carried out with the exact same settings (laser power, laser dye, diffuser plate, etc.) that are used for the spray measurements. Therefore, a set of calibration images has been recorded prior to every measurement sequence. The calibration plate was positioned on a 1D traverse system and scanned along the x-direction.
A set of 30 calibration images was recorded for every out-of-focus plane for the
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range of ± 10 mm at every 500 µm. The positive direction refers to a movement
of the calibration plate closer to the camera. A summary of the optical settings can be found in Tab. 1.
Table 1: Characteristic parameters of the optical configuration
Parameter resolution
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field of view
Unit
Value
mm2
16 × 12
µm/pixel
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f-number (f /#)
10 16
focal length
mm
105
calibration planes
mm
−10 to 10
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no. of images per plain
30
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The same post-processing algorithm as discussed previously for the mea-
surements was used for the analysis of the calibration data sets, but with one difference: in addition to the earlier described detection and ellipse fitting pro-
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cess, an additional computation is performed. The detected dot positions are correlated to the known positions of the dots on the calibration plate. The reference diameter of the calibration dot is then compared to the measured dot size. This procedure is repeated for every out-of-focus plane and a diameter calibration matrix (Fig. 4) is derived. In Fig. 4 the color corresponds to the measured
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dot size. The information on the interdependency between the measured and the real dot size can be applied in exactly the same way to the measured droplet sizes during the experiment. It can be seen from Figs. 4(a) and 4(b), that an
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almost perfect symmetrical function for the measured dot size over the reference dot size along the x-positions is derived. Details of the difference between measured and detected dot sizes (Fig. 4(c)) reveal the same tendency. Due to the setup and chosen threshold, the diameters are consequently predicted as being
too large. This error increases by moving away from the focal plane. The error in prediction of droplets smaller than 60 µm drastically changes which is likely
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to be due to the optical setup. However, it can be seen that this behaviour sets a limit to the detectable droplet size depending on the out-of-focus position.
Based on these investigations, the diameter correction is a tool that enables the correct diameter measurement of a droplet at an out-of-focus position. However, in a typical setup, as it is used for experimental spray investigations, it is not possible to predict the out-of-focus position of each droplet a priori. Con-
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sequently, a correction of the droplet diameters cannot be performed based on these predictions. A second parameter is needed to define the out-of-focus posi-
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tion for each measured droplet. The intensity gradient at the outer edge of each detected object can usually be used. The mean value of the intensity gradient of every boundary pixel for each dot is calculated and normalized by the median
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intensity of the image. This normalized intensity gradient per pixel will be referred to as int/pixel. Using this gradient for every dot on the calibration plate
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and in every out-of-focus position, it is possible to create a second calibration matrix for the gradient values (Fig. 5). The color scale refers to the measured mean intensity gradient of each detected dot. Again, the actual gradient values
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were only measured for the available dot sizes. The points between the measured dots sizes are linearly interpolated. The gradient and diameter matrixes both show the same behaviour. They are both symmetrical to the yz-plane at x =0 mm. The gradient becomes smaller when moving further away from the focal plane. It can be seen, that for small droplets a peak in the gradient matrix can be seen before the gradient values rapidly decrease. This behaviour is due 14
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to the experimental setup for the present investigation. The minimum gradient
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value for the evaluation of each diameter class was set to 0.05 int/pixel.
(a) Calibrated normalised intensity gradients (b) Calibrated droplet diameter as a function as a function of the out-of-focus position and of the out-of-focus position and reference direference diameter 2D
ameter 3D
Figure 5: Calibrated normalised intensity gradients as a function of the out-of-focus position
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and reference diameter
In the measurements for every droplet the normalized intensity gradient and the corresponding measured droplet diameter are known. These two values can
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be superposed with the two calibration matrices (Fig. 4(b) and Fig. 5(b)) and the real droplet diameter can be calculated. By applying this methodology,
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the calculation can be done without knowing the exact droplet position in the measurement volume. The calculation principle is schematically illustrated in Fig. 6. The interdependency between the measured and the reference diameter
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are represented by the grey lines. The numbers in the corresponding fields represent the size of the measured diameter. The black lines and associated values
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in the dark fields correspond to the interdependency between the normalized intensity gradient and the real droplet diameter. Both calibration values are symmetrical to the yz-plane at x =0 mm. Therefore, two possible solutions for the real droplet diameter for each combination of measured droplet size and gradient exist. These are given by the two intersection points A and B. Finally, the real droplet diameter in the measurement is calculated by the mean of the 15
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determined droplet diameter from the two intersection points. The limiting 10
0.05
0.08
intersection A
0.17 0.14 0.11
intersection B 0.08
1
−5
0.20
2
0
0.11 0.14 0.17 0.20
0.5
1
1.5 2 Dref [mm]
2.5
3
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−10
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3
x−direction [mm]
2.5
2
1.5
1
0.5
5
Figure 6: Calculation of the real droplet diameter based on the normalized intensity gradient and the measured droplet diameter
parameter for the application of this algorithm is the size of the measurement
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volume and therefore the lower detectable gradient boundary. In the presented case, this restricts the droplet detection to approximately ± 9 mm in the di-
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rection of the optical axis, which has been demonstrated to be well within the range needed for properly studying primary atomization.
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2.2.3. Measurement uncertainty The measurement uncertainty has been determined using the approach given by Kline and McClintock (1953). The uncertainty of the mean air velocity can
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be estimated to 3 %. The uncertainty of the liquid mass flow is less than 0.5 %.
Due to the enhanced calibration and post-processing procedure, the error in
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measuring the droplet size and velocity is estimated to be less than 4 %. In summary, the maximum uncertainties for the measurements are about 7 %.
2.2.4. High speed shadowgraphy The film flow and the primary breakup process have been recorded with two high speed video cameras at 7 kHz at a spatial resolution of 13.89 µm. The field 16
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of view was set to approximately 14.2 × 14.2mm. Therefore, the utilization of two cameras enables the recording of the liquid film disintegration process simultaneously from two angles shifted by 90◦ . For capturing the high speed breakup
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processes the exposure time was reduced to 1 µs, minimizing the blurring effect of fast deforming structures and droplets. For the operating condition a total of
5.000 images are recorded. The measurement volume is illuminated using two 500 W halogen spotlights. The spotlights are mounted opposite of the cameras. 3. Numerical Investigation
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The numerical simulation in this paper is based on the embedded DNS (eDNS) concept. Sauer (2014) introduced this numerical concept for the primary breakup of airblast atomization and proved its applicability by simulating six different operating points. For a detailed validation of the numerical concept with experimental results a further operating point is investigated in the present
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study. A short overview of the numerical approach is given in the following section, more details can be found in Sauer (2014). The idea of the eDNS concept is to apply a DNS only to a small region
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of interest embedded in a larger and coarser LES. For simulating the primary breakup of an airblasted liquid sheet, the DNS domain can be reduced to the primary breakup region, as illustrated in Fig. 7. A key issue of the concept is
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the generation of high quality boundary conditions for the embedded domain
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by the LES.
Figure 7: The embedded DNS domain for an annular airblast atomizer
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Figure 8: Geometry simplification of the airblast atomizer
The planar configuration, considered here, represents a geometry simplification of the annular atomizer as illustrated in Fig. 8. The application of the
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eDNS approach to the planar airblast atomizer is shown in Fig. 9. The embedded domain comprises a planar prefilmer lip and the atomization region. An
air flow inlet is sited each above and below the prefilmer. The values of the velocity field for the air inlets are generated by a single-phase LES of a turbulent channel. They are extracted on a plane normal to the channel wall at each LES time step and mapped to both air inlets. For the lower air inlet the sign of
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the y-component is inverted accounting for the boundary layer induced by the bottom side of the prefilmer. As time step and grid size of the LES are coarser
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than in the DNS a linear interpolation in time and space is applied to map the data. The data are defined as transient Dirichlet boundary conditions for each individual time step. The turbulent fluctuations are directly transferred to the
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DNS domain.
Figure 9: Application of the eDNS concept to a planar airblast atomizer
The application of the transient velocity data to the DNS domain enables an
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investigation of the primary breakup with realistic boundary conditions. Fig. 10 illustrates the evolution of an airblasted liquid film for two different air inflow types: a fully developed turbulent channel flow and a laminar inflow correspondadded in the latter case. Mean velocity profile
3.0 ms
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4.0 ms
5.0 ms
Time varying profile
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2.0 ms
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ing to the mean velocity profile of the same channel flow. No fluctuations are
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6.0 ms
Figure 10: Impact of the inlet boundary condition variation on the primary breakup. Gas phase: u = 50 m/s, ρ = 3.9 kg/m3 , ν = 4.7 × 10−6 m2 /s. Liquid phase: u = 0.5 m/s,
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ρ = 650 kg/m3 , ν = 2.9 × 10−6 m2 /s, σ = 0.0085 kg/s2 . Prefilmer: h = 50 µm.
The snapshots illustrate that turbulence plays a decisive role in the devel-
opment of the primary breakup regarding the characteristic of the dominating structures. Quantitative parameters as the breakup length or the breakup time are changed by the introduction of turbulence. By applying the embedded DNS 19
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concept, such influence of the turbulent flow is rationally accounted for and an improved transfer of the results to industrial airblast atomizers is possible. A detailed discussion about the impact of different inflow types on the primary
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breakup and the role of turbulence can be found in Sauer (2014). 3.1. Generation of transient inlet boundary conditions for the embedded domain
Due to its close proximity to the prefilmer, the air streams in the embedded domain are mainly affected by wall-related structures. A single-phase LES of a
turbulent channel is selected to generate the suitable velocity data. The quality
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of the generated inflow data influences directly the results of the two-phase DNS simulation.
With a LES the large scales are resolved whereas the small unresolved subgrid scales need to be modeled. This seperation is obtained by filtering of the Navier-Stokes equations, including the continuity Eq. (1) and the momentum Eq. (2), that are formulated with the velocity vector of the resolved scales U ,
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the gravitational vector g, the kinematic viscosity ν and the kinematic Pressure
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P.
(1)
∂U + ∇ · (U U ) = g − ∇P + ∇ · (ν∇U ) ∂t
(2)
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∇·U =0
Splitting the convective term of the momentum equation in a resolved and
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an unresolved part, (Eq. (3)), the residual stress tensor τ sgs is introduced to
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the momentum equation, as formulated in Eq. (4).
U U = U U + τ sgs
(3)
∂U + ∇ · (U U ) = g − ∇P + ∇ · (ν∇U ) − ∇ · τ sgs ∂t
(4)
2 T τ sgs − ksgs I = −νsgs (∇U + (∇U ) ) 3
(5)
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For modeling the subgrid scale stress the Boussinesq approximation is used (Eq. (5)). The turbulent viscosity νsgs and the turbulent kinetic energy ksgs of the subgrid scales are calculated from the One-Equation Eddy model by
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Yoshizawa and Horiuti (1985). Fig. 11 illustrates the turbulent channel flow domain which measures 2πδ
in streamwise x-direction, 2δ in wall-normal y-direction and πδ in spanwise z-direction (Moser et al. (1999)). In order that the height of the channel 2δ
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corresponds to the prefilmer experiment, δ measures 4 mm.
Figure 11: Geometry and grid of the turbulent channel
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A turbulent channel flow is dominated by small wall-related structures. To realize a highly resolved grid in the near-wall region but to limit the general number of grid points a zonal grid is used, refining the domain from the channel
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core to the walls. Sauer et al. (2016) compared the results of a coarse, a fine and a zonal LES to the results of a DNS by Moser et al. (1999) and proved the
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applicability of the zonal approach. Three different zones are distinguished: a core zone, a wall zone and a sandwiched zone in between them. The number of streamwise and spanwise grid points are doubled from zone to zone, starting
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with the core zone. Normal to the walls a simple gradient is applied concentrating more grid points close to the walls. The zonal boundaries are positioned at y + = 200 und y + = 420. Tab. 2 summarizes the non-dimensional grid spacings for each zone, formulated as ∆y + = ∆uτ /ν for the wall-normal distance. Due to + the grid-stretching in y-direction the minimum grid spacing ∆ymin is listed for
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+ the wall and the sandwiched zone, whereas the maximum grid spacing ∆ymax
is listed for the core zone. The grid points in x- and z-direction are equidistant distributed. For the streamwise and spanwise direction periodic boundary con-
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ditions are set. The sampling of the velocity data is started once a statistically stationary state of the flow is reached.
The described configuration has also been utilized in the turbulent channel
configuration by Sauer et al. (2016). There the primary breakup of an airblasted
liquid sheet under identical gas phase conditions, but different prefilmer geometry and liquid properties, has been investigated. A detailed discussion about can be found in the cited study.
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the velocity profiles and a validation against DNS results by Iwamoto (2002)
Table 2: Non-dimensional grid spacings for the turbulent channel. Reg = 13, 333, Reτ = 777. + ∆ymin
Wall zone
9.7
4.9
9.2
Sandwiched zone
19.4
17.0
18.5
Core zone
38.8
+ ∆ymax
49.1
∆z +
37.0
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∆x+
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3.2. Two-phase DNS of the primary breakup For simulating the liquid and the gaseous phase the two-phase solver Inter-
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FOAM of the opensource code OpenFOAM is used. Spyrou (2011) verified the functionality of the code by computing several test cases for the advection, the surface tension and the buoyancy force. In InterFOAM the Volume-of-Fluid
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(VOF) method is implemented to describe the phase interface. The VOF introduces a indicator function α representing the liquid volume
contained in a cell. The density ρ and the viscosity µ in a cell are formulated as a function of the volume fraction (Eq. (6) and Eq. (7)).
ρ = αρl + (1 − α)ρg 22
(6)
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(7)
µ = αµl + (1 − α)µg
The incompressible Navier-Stokes equations consist of the vectorial momen-
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tum advection Eq. (8) under the incompressibility constraint Eq. (9). In order
to find a mathematical description for two-phase flows, the surface tension effect appears as an external force into Eq. (8) ruled by the interface curvature κ. The curvature κ is determined by Eq. (10).
(8)
∇·U =0
(9)
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∂ρU + ∇ · (ρU U ) = ρg − ∇p + ∇ · [µ(∇U + (∇U )T )] + σκ∇α ∂t
∇α |∇α|
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κ = −∇ ·
∂α + ∇ · (U α) + ∇ · (U r α(1 − α)) = 0 ∂t
(10)
(11)
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The transient evolution of the indicator function of an incompressible flow field is described by the advection Eq. (11). The last term on the left side is only active in the proximity of the phase interface and represents an artificial
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compression term antagonizing numerical diffusion (Rusche (2002)). No geometrical recontruction of the phase interface is applied. The phase interface is
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smeared in a transition region from 0 to 1 and is not known exactly. The surface tension force in Eq. (8) cannot directly be determined. A volume force, that is effective in the transition region, is formulated instead. This method is known
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as the Continuum Surface Force (CSF) method by Brackbill et al. (1992). Fig. 12 illustrates the embedded DNS domain. The liquit fuel enters the
domain through a small slit, is transported along the prefilmer to the trailing edge and exposed to high shear forces induced by the coflowing air streams. The liquid accumulates at the trailing edge and is atomized downstream of the trailing edge. 23
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Figure 12: Computational domain of the planar prefilmer
The prefilmer thickness measures 200 µm and is increased by a factor of four
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compared to the preliminary simulations by Sauer (2014); Sauer et al. (2016). Down to a value of 100 µm the height of the trailing edge has a significant influence on the breakup length and breakup time (Braun et al. (2015)). To
capture the expected breakup length, the computational domain was additionally expanded from 4 mm to 6 mm in the streamwise direction. To keep the DNS domain as small as possible, the prefilmer length only measures 1 mm and
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is clearly smaller as in the experimental set up. This deviation is accepted, as the studies by Gepperth et al. (2012) have shown, that the prefilmer length has no significant impact on the disintegration process.
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The liquid fuel enters the domain with a constant velocity. The faces of the prefilmer are treated as walls with a no-slip condition. An outlet condition is
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assigned to the top, the bottom and the outlet of the domain enabling liquid structures to leave the domain. The total pressure is fixed at the outlets and recirculations are prevented by setting inflowing velocity components to zero.
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A slip condition is assigned to the lateral faces, the normal component is set to zero and the tangential components are initialized as zero gradients. The
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coflowing air next to the prefilmer is directly linked to the turbulent channel flow. The sampled velocity data during the LES is mapped onto the air inlets as transient Dirichlet boundary conditions. For the grid an equidistant grid spacing of 10 µm in all three directions is
realized. For the blocks downstream of the liquid inlet slit and the trailing edge a further refinement by a factor of two in y-direction is performed. Sauer et al. 24
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(2016) have shown that this grid resolution is suitable to resolve the smallest scales of turbulence, the Kolmogorov length scales lη , regarding the investigated operating point. In their study, the embedded DNS concept has been utilized
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to simulate the primary breakup in the same turbulent channel flow (Reg = 13, 333). The prefilmer thickness and the liquid properties were modified. The Kolmogorov length scale was found to be lη = 12 µm and the required minimum
grid spacing was identified as ∆xmin = 25 µm following Eq. (12) by Pope (2000).
The relation between the minimum required grid spacing in physical space and
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the Kolmogorov scales is quantified as ∆xmin π ≈ 2.1. = lη 1.5
(12)
A further aspect in the grid resolution assessment is the representation of small liquid structures and droplets, produced by the primary breakup. The findings by Sauer et al. (2016) show that an resolution of the entire liquid mass is hard to achieve due to the amount of small droplets. 80 % of the liquid
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mass have been resolved in their simulation utilizing the above mentioned grid resolution. A detailed discussion about the droplet representation on different
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grid sizes (20 µm and 10 µm) can be found in the cited study. For the operating point, investigated in this paper, the liquid structure resolution is discussed in section 6.2 and 6.3, directly linked to the quantitative results.
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The total number of cells amounts 84.41 millions. 14 ms physical time with a time step of 50 ns has been simulated. The highly resolved DNS was performed
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on 720 processors. A total of 540000 cpuh were consumed.
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3.3. Processing of DNS data Analogously to the experimental data processing, the analysis of the com-
puted results is splitted into the analysis of the accumulated liquid at the trailing edge and the analysis of droplets. For determining the number of droplets and their properties, a sampling
plane at the outlet is defined. According to a minimum volume fraction α in each cell, a connected liquid structure is detected by using an approach of Connected 25
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Component Labeling (CCL). The surface area of each droplet is quantified by the sum of all cells i containing liquid with the corresponding volume fraction αi and the grid sizes ∆yi and ∆zi (Eq. (13)). The droplet diameter is derived
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by assuming a circular area. Velocity data is extracted at each cell belonging to a droplet. The components of the droplet velocity Ud are further calculated as the mean value over the area of the droplet (Eq. (14)). This post-processing
routine is inspired by the algorithm presented by Grosshans and Fuchs (2011) and Herbert et al. (2008). Ad =
n X
αi ∆yi ∆zi
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i=1
Pn i=1 αi Ui Ud = P n i=1 αi
(13)
(14)
The analysis of the accumulated liquid at the trailing edge is challenging. An analysis at a fixed position, similar to the droplets, is not suitable as the
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liquid film oscillates and changes its shape and position from time step to time step. To determine characteristic sizes, like the breakup length and the streamwise deformation velocity, the position of the phase interface needs to be known.
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Therefore an post-processing algorithm has been developed, facilitating an automated analysis of the continuous liquid film.
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The procedure is illustrated in Fig. 13. Based on a predefined α-threshold the phase (liquid or gas) in a grid cell is determined. Corresponding to the identified phase each cell receives the label 1 (liquid) or 0 (gas). A view from
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the top, analogous to the shadowgraphy images, is generated by summing up the labels in x-direction. A sum exceeding 1 signifies that at this position a liquid phase would be observed from the top. A CCL algorithm is applied,
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identifying all liquid structures. A connectivity of 8 is utilized, checking for liquid in each neighboring cell. As only the accumulated liquid at the trailing edge is of interest, any other liquid structure, detected by the CCL, is deleted. Finally, the interface of the accumulated liquid is identified. The result is a one-dimensional plot of the phase interface, that enables an easy and efficient
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Figure 13: Reducing three-dimensional DNS data to a plot of the interface
analysis compared to the original three-dimensional DNS data. The described processing is applied for every time step. The subsequent procedure is reduced
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to the analysis of the recognized phase interface, similar to the experimental data processing. This way an identical definition of the breakup length and the deformation velocity for the experimental and numerical investigations is
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possible.
Reducing the huge amount of DNS data to single plots of the phase-interface
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enables a fast and efficient analysis. But in contrast, two disadvantages have to be mentioned: first, superimposed structures as seen from the top can not be distinguished and thus an overestimation of the liquid sheet expansion into the atomization region is possible. Secondly, the velocity data calculated by the DNS is not used. Both aspects could be avoided by identifying the accumulated liquid in the original DNS domain and extracting the velocity data in each cell 27
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belonging to the liquid sheet or its interface. However, due to the focus of this paper, the DNS data is here reduced, facilitating a more reliable comparison
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against the experimental results. 4. Operating Conditions
Real aircraft engine conditions are characterized by high Reynolds and Weber numbers providing highly turbulent flow conditions and finely atomized droplets. A detailed investigation requires a high resolution in time and space,
challenging for both simulations and experiments. For the present study a mod-
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erate operating point with a comparatively low Reynolds- and Weber number
has been selected. It corresponds to altitude relight conditions and enables an adequate resolution of the breakup events in both investigations. It is therefore suitable for a reliable comparison of the numerical and experimental results. The operating conditions are summarized in Tab. 3. The gas Reynolds num-
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ber Reg is formulated with the half height of the channel δ as Reg = ug δ/νg . Here, ug and νg describe the velocity and the kinematic viscosity of the gas 2
phase. The film weber number, W er,ht = ρg (ug − ul ) ht /σ, considers the in-
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fluence of the density of the gas phase ρg , the velocity difference between gas and liquid as well as the surface tension σ. As characteristic length the prefilmer trailing edge thickness is utilized due to its impact on the breakup length
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identified by Gepperth et al. (2012). To classify the atomization process the momentum flux ratio between gas and liquid phase (M = ρg u2g /ρl u2l ) is also
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specified.
In the afore mentioned study by Gepperth et al. (2012) the influence of dif-
ferent properties of several liquids has been investigated besides the influence of
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geometrical parameters like prefilmer length and trailing edge thickness. From the investigated liquids Shellsoll D70 with a low surface tension at ambient conditions has been selected. The surface tension plays a decisive role as it antagonizes the disintegration. When the surface tension force is low, the interface behaves less stable and breakup events occur faster. Therefore the size of the
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Table 3: Operating conditions
Unit
Value
Reg
13,333
W er,hl
21.4
ρl /ρg
636.4
M
16.0
Gas properties m/s
ug
kg/m
1.2
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ρg
50 3
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Parameter
m /s
1.50e-05
m/s2
0.5
kg/m3
770
m2 /s
2.03e-06
2
νg
Liquid properties ul ρl νl
kg/s
0.0275
mm2 /s
50
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V˙ /b
M
σ
2
numerical domain can be kept small in the present investigation. In addition
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the physical properties of Shellsoll D70 are close to those of aviation fuels. The liquid volume flow rate per unit length V˙ /b is kept constant at 50 mm2 /s
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during both the experiment and the simulation. At the liquid inlet slit of the DNS domain the velocity is set to 0.5 m/s. In contrast, the bulk air velocity of
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the air is 50 m/s. 5. Qualitative Results In Fig. 14 a snapshot of the disintegrating liquid film obtained by the shad-
owgraphy is shown. A red rectangle illustrates the cross section of the DNS domain in comparison to the experimental field of view. Due to the numerical 29
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effort, the DNS domain is smaller and actually reduced to the primary breakup region. The domain covers 1 mm upstream and 5 mm downstream of the prefilmer trailing edge in normal direction. In parallel to the trailing edge the
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domain measures 4 mm. In both investigations the following breakup process is observed: waves are formed on top of the prefilmer, transporting the liquid to the prefilmer trailing edge, where a reservoir is formed. Out of this reser-
voir elongated structures (ligaments) as well as bag like structures are formed, grow in size and finally break up into droplets. The droplets differ in their size,
small as well as big bulgy droplets are generated. During the atomization no
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dewetting of the prefilmer is observed.
Figure 14: Experimental field of view and the used image section of the size of the DNS
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domain for the comparison of the breakup phenomena
To visualize the breakup process, two different snapshot sequences are shown
in Fig. 15 and Fig. 16. The side- and topview of the experiment and the sim-
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ulation are shown. All image sections correspond to the dimensions of the numerical domain. The time lag between two numerical snapshots is 0.3 ms, which corresponds to every second high speed shadowgraphy image (frame rate 7 kHz). The time stamp of the first snapshot in Fig. 15 is set to 0 ms and serves as reference time.
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In the first sequence the formation of ligaments, arising from the liquid reservoir at the trailing edge, is visualized. The surface tension force can not counteract against the disintegration of the accumulated liquid so that the liquid
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starts to break up. Initial holes are formed and grow in time. Separated ligaments are left over, that are elongated deeper into the atomization region until parts of the ligaments are separated. In the experiment as well as in the simula-
tion varying ligament dimensions have been observed. Especially the maximum
length of single ligaments differs, a stable breakup length could not be identified. From the sideview of the numerical snapshots weak oscillations around
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the prefilmer (on the x-axis) are noticed. Thereby, a synchronous flapping of all ligaments along the prefilmer is not observed. This becomes apparent in the experimental sideview images, that capture a higher number of breakup events related to the increased experimental prefilmer width. The large variation in the ligament flapping leads to a strong overlapping and at least to a reduced sharpness of the sideview images.
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In the second sequence, starting at 2.9 ms, the ligaments have already been torn away. Out of the liquid reservoir a bag is formed by the gaseous flow,
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that increases particularly fast and finally bursts. The rim of the bubble-like structure is more stable and remains attached to the reservoir for a short time, before it disintegrates into ligaments or bigger droplets. The generation of
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bubbles occurs fast compared to the ligament formation in Fig. 15. From 2.9 ms to 3.1 ms the bag observed in the numerical snapshots has already been bursted
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and a second bag has started to develop close to the trailing edge. The same dynamic is noticed in the experiment: at 2.86 ms only the rim of the bag is
visual, at 3.43 ms a new bag is generated, that has already been bursted at
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3.72 ms. The disintegration of the bags or bubble-like structures results in the generation of multiple droplets and is more intensive compared to the ligament breakup. In conjunction with the formation of bags, strong oscillations around the prefilmer are visible. The investigations showed that the bags are formed alternating up- and downwards, according to an oscillation to the right and to the left in the sideview snapshots. However, similar to the ligaments this 31
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appears to be a stochastic process and flapping of all generated bags to the same side of the prefilmer with the same frequency is not observed. It should be noted that no continuous liquid sheet is developed behind the
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prefilmer. The bags and ligaments arise directly from the accumulated liquid at the trailing edge, flapping not in phase. As a consequence it is hard to identify
a global oscillation frequency as it is typical specified for flat sheet atomizer
designs. In addition, the bags and ligaments along the prefilmer do not start to
develop at the same time, whereby the spanwise spacing between ligaments or bags is changing permanently. The inter-ligament distance is strongly affected
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by separating or new arising ligaments and bags at varying positions.
With a momentum flux ratio of 16 the primary breakup of the analyzed operating point is located inside the torn sheet breakup regime according to the breakup regime classification by Fernandez (2010). The classification is oriented to the morphological aspects of the breakup instead of instability mechanisms. Fernandez specified a momentum flux ratio between 5 and 22 for the torn-sheet
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breakup. Typically, the liquid sheet is eventually torn away due to the shear effect by the gaseous flow. The generation of longitudinal streamwise ligaments,
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irregular shaped, and the formation of big bulgy droplets is also significant for the torn-sheet regime. Referring to the images in Fig. 15 and Fig. 16 a wide
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range of droplet sizes, including big bulgy droplets are generated.
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x
y
z
y
z
x
z
0.0 ms
0.3 ms
M
0.29 ms
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0.0 ms
z
0.6 ms
0.86 ms
0.9 ms
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0.57 ms
33 Figure 15: Disintegration sequence at the atomizing edge with ligament formation. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation
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x
y
z
y
z
z
2.9 ms
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2.86 ms
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3.1 ms
M
3.14 ms
x
z
3.4 ms
3.72 ms
3.7 ms
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3.43 ms
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Figure 16: Disintegration sequence at the atomizing edge with the formation of bag like structures. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation
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6. Quantitative Results Quantitative data are obtained in order to compare the numerical and experimental results. The accumulated liquid film at the trailing edge is characterized
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by its breakup length and its streamwise deformation velocity. The analysis pro-
cedure to extract those quantities is presented, providing a consistent definition for the numerical and experimental results. As the numerical results are linked
to a predefined threshold for the liquid volume fraction α (see section 3), the influence of this parameter on the numerical results is additionally discussed. Finally the droplet sizes and droplet velocities are compared. In addition to
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their mean values the distributions of all compared quantities are presented. 6.1. Characterization of the accumulated liquid
The analysis of the accumulated liquid is based on the phase interface. For the experimental investigation the analysis procedure is included in the software by Müller (2015), utilized for the post-processing of the shadowgraphy
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images. The analysis of the numerical results has been implemented in the post-processing routine introduced in section 3.3. Both algorithms follow the
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same procedure to determine the breakup length and the streamwise deformation velocity as described in the following section. The expansion of the liquid film into the atomization region is quantified by
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the length of ligaments, arising from the accumulated liquid. A single ligament length Lstr is defined as the distance between the ligament peak and the trailing
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edge of the prefilmer. The mean value of all ligament lengths is defined as the breakup length Lbu . Ligaments are identified as maxima of the phase interface plot. A central
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aspect is a well-defined choice of the detected maxima to suppress repeated counting of ligaments with a wrinkled contour. As a criterium a minimum distance between adjacent minima and maxima of 50 µm is predefined to obtain a more global behaviour, as illustrated in Fig. 17. The choice of the minimum distance is always a trade-off, as also small ligaments close to the trailing edge should be detected. 35
1
1
2
2
3
3
4
4
5
5
6 −2
−1
0 [mm]
1
2
6 −2
−1
0 [mm]
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0
[mm]
0
1
2
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[mm]
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(a)
(b)
Figure 17: Peak detection for the phase interface (a) and the effect of a minimum distance of 50 µm (b) for the analysed operating point
The breakup length is obtained as a mean value of several snapshots, using
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the current length of each ligament. This means a significant modification for the analysis of the numerical results in relation to previous studies by Sauer
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(2014), where the breakup length was defined as the maximum ligament length taken from a series of time steps. The analysis procedure has been started after the first breakup event occured.
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In case of the simulation ligaments attached to the sides of the numerical domain are not included in the analysis. Due to the slip condition, mentioned in section 3.2, these ligaments are prevented from breaking through the sides.
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In the simulation no significant deviation in the ligament development has been observed for ligaments in the vicinity of the sides or in the center of the domain,
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as the dominating expansion is in the streamwise direction. However, to avoid any errors, these ligaments are neglected. To determine the streamwise velocity of the continous liquid film in the
experiment the displacement of the phase interface between two timesteps is used. This approach is also adapted for the numerical results, providing an identical definition of the deformation velocity. The unique assignement of a 36
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specific interface point at two consecutive timesteps t1 and t2 is difficult due to variations in the wrikled contour or the seperation of liquid structures. In order to simplify the calculation, the determination of the displacement of each
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interface point is replaced by utilizing only the most remote interface point zmax per y-position at t1 and t2 . The streamwise deformation velocity at position yi is then calculated as udef,i = zmax,yi (t2 ) − zmax,yi (t1 )/(t2 − t1 ).
Fig. 18 illustrates the phase interface contour at two consecutive timesteps
and a cumulative distribution of the calculated velocities. Negative velocities indicate the separation of liquid structures (E1), whereas very high velocities
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indicate the expansion or movement of a ligament to the side, leading to an overestimation of the displacement at a close-by y-position (E2). The maximum velocity per frame or timestep is well represented by the 90 %-quantile, its mean
value of all timesteps provides the characteristic deformation velocity udef,str of
E2 Udef,i [m/s]
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E2
E1 N/N total
y [mm]
(a)
(b)
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z [mm]
E1
M
the investigated operating point.
Figure 18: Time displacement of the phase interface and ambiguities by its determination
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6.2. Breakup length and deformation velocity The breakup length Lbu and the deformation velocity udef,str determined
from the experiment and the DNS are summarized in Tab. 4. For their determination the phase interface position is required, that is found by a predefined liquid volume fraction (α = 0.5) in case of the simulation. In oder to study the 37
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sensitivity of the numerical results against α, additional thresholds have been utilized in the post-processing routine described in section 3.3. In Tab. 4 the numerical results for α = 0.5 and α = 0.01 are shown and compared to the
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experimental results. Table 4: Characteristic values for the accumulated liquid
α = 0.5
α = 0.01
Lbu [mm]
3.2
2.2
2.7
udef,str [m/s]
15.7
8.2
14.4
fbu [1/s]
4906.3
3727.3
5259.3
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Experiment
The breakup lengths of the DNS are a little smaller, albeit all breakup lengths are in the same order. For a better understanding of the determined
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values, the distribution of the ligament lengths is provided in Fig. 19. In the experiment a small amount of ligaments greater than the DNS domain (Lbu > 5 mm) are observed, leading to a greater breakup length. In the simulation the
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accumulated liquid reaches the outlet of the computational domain at no time step, the maximum ligament length measures 4.8 mm. Nevertheless, a reliable prediction of a maximum ligament length is difficult, due to the size of the
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numerical domain in streamwise direction. The long ligaments detected in the experiment are single structures, typically with a very thin connection to the
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liquid film. They appear occasional and can be detected by shadowgraphy due to a greater time period of recording. It is based on 300 frames with a time span of 100 ms between each frame. In contrast to that, the numerical results
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of 190 time steps with a time span of 20 µs are analyzed. Due to the numerical effort, the physical simulation time is kept short and a time span corresponding to the experiment is not feasible. The variation of the numerical threshold for the volume fraction implies
a displacement of the interface and has an effect on the numerical results by
38
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0.3
0.2
0.1
0 0
5 Lstr [mm]
0.2
0.1
0 0
10
Experiment Sim. α=0.01
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Experiment Sim. α=0.5 N/Ntotal
N/Ntotal
0.3
5 Lstr [mm]
10
Figure 19: Distribution of the ligament length 0.2
0.15
N/Ntotal
0.1 0.05
Experiment Sim. α=0.01
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total
0.15 N/N
0.2
Experiment Sim. α=0.5
0.1
0.05
0 0
20 40 Udef,str [m/s]
60
0 0
20 40 Udef,str [m/s]
60
M
Figure 20: Distribution of the deformation velocity
principle. As the grid resolution is small compared to ligament lengths the
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influence by the interface smearing is minor. Critical is the point of separation, when the connection between a ligament and the remaining accumulated liquid
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becomes very thin and is finally below the grid resolution. If α is reduced, the separating ligament is seen attached a few more timesteps, while it is further expanded in the streamwise direction. This effect is seen in the ligament length
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distribution for α = 0.01. The threshold is extremely low and illustrated as a lower bound. However, as illustrated in Fig. 21, the overall impact on the characteristic value for the breakup length is small. The deviation from Lbu (α =
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0.5) is smaller than ±7 % in the range of 0.1 < α < 0.9 and comparable to the experimental measurement uncertainty.
As specified in Tab. 4, a twice as high deformation velocity is measured
in the experiment in comparison to the DNS, if α = 0.5 is predefined for the phase interface. In contrast to the breakup length, a significant impact of the α39
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16
L [mm] bu
U
[m/s]
def
8
4
0
0.2
0.4
α
0.6
0.8
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12
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Figure 21: Sensitivity of breakup length and deformation velocity dependent on the liquid
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fraction α
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(a)
(b)
(c)
Figure 22: Representation of bubbles in the experiment (a) and the simulation with α=0.5
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(b) or α=0.05 (c)
threshold on the deformation velocity has been noticed, analyzing the numerical
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data. Reducing this threshold, the velocity distribution expands to greater velocities, assimilating the experimental distribution as shown in Fig. 20. The deformation velocity at several α-values is shown in Fig. 21. A moderate change
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for the deformation velocity is observed down to α = 0.2. Below this value, the velocity rises steeply, reaching a value of nearly 15 m/s at a liquid volume fraction of 1 %. It is presumed that the influence on the velocity can be attributed to an insuf-
ficient resolution of bubbles, arising from the accumulated liquid (see section 5).
40
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A typical bubble, observed during the experiment, is shown in Fig. 22(a). It is characterized by a thicker rim and a bag formed by a very thin liquid film. Typically, these bags rise faster than the rim into the atomization region and reach
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high velocities when they burst. In the simulation bag-like structures are also observed, but as the bags grow and the liquid sheet becomes thinner, a suitable resolution is hard to achieve. This is visualized in Fig. 22(b) and Fig. 22(c).
Considering a low threshold of α, the liquid film of a bubble is visible and higher velocities are observed.
As discussed in section 5 a global oscillation frequency is hard to determine
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as no continuous flapping sheet exists behind the trailing edge. As an alternative
the mean breakup frequency is calculated as a measure for the time distance between consecutive atomization events. It is directly obtained from the deformation velocity and the breakup length as fbu = udef /Lbu . For the analyzed operating point the frequency is in the range of 5000 1/s as specified in Tab. 4. Due to the variation of the deformation velocity for the DNS data only a range
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for the breakup frequency can be determined.
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6.3. Droplets
For the design of a combustion chamber the properties of the droplets generated by the airblast nozzle are a valuable information. The droplet size distribu-
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tions from the experiment and the simulation are shown in Fig. 23. The droplet diameters are obtained 5 mm downstream of the trailing edge, corresponding to the outlet position of the numerical domain. This analysis position differs
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from preliminary experimental studies by Gepperth et al. (2012), in which the entire field of view has been taken as a basis. The adaption improves the com-
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parability of the experimental and numerical results. Similar to the liquid film analysis two sets of numerical droplet data are compared to the experimental results: droplet data regarding a predefined α-threshold of 0.5 and a minor one (α = 0.03). In all three cases droplets with a diamteter up to 300 µm are observed (Fig. 23). For the numerical results a high number of small droplets in the 41
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range of a few micrometers is noticeable. For α = 0.03 the shape of the distribution differs strongly from the experimental results. Sauer et al. (2016) defined the liquid detected by this low threshold as the atomized mass that is not re-
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solved by the grid. This definition promotes the localization of small subgrid droplets, that are also not detectable by the experimental resolution. Experiment Sim. α=0.5 Sim. α=0.03
0.03 0.02 0.01 0 0
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PDF [1/µm]
0.04
100
200 dd [µm]
300
Figure 23: Droplet size distribution: Comparison between experiment and simulation
The knowledge of the smallest droplets generated by primary breakup is
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a fundamental problem caused by the resolution limit of numerical as well as experimental investigations. From the numerical simulation a determination of the liquid mass, that is not resolved by the numerical grid, is possible. As the
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VOF approach is mass conservative, the choice of the α-criterion defines how many mass is lost in the process. Each cell containing at least a volume fraction of α is taken into account for the droplet analysis. Droplets determined by
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α = 0.5 are defined as resolved droplets in this paper. For the quantification of the resolved liquid mass the droplet mass md at the outflow of the DNS
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domain is studied for varying α-values. In addition, the corresponding number of droplets Nd , passing through the outflow plane, is determined. The results
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are visualized in Fig. 24, normalized by their respective value taken at α = 0.01. The evaluation of the liquid mass depending on α shows that 80 % of the
total liquid mass are represented for α = 0.5. This mass is carried by 20 % of the liquid structures. It becomes evident that the large and mass carrying structures are resolved by the numerical grid, but that a resolution of the total liquid mass due to the huge amount of fine droplets is hard to achieve. Fig. 23,
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m /m d
d,total
N /N d
d,theo
1
0
0.2
0.4
α
0.6
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0.5
0.8
Figure 24: Small structure properties extracted at the eDNS outflow: droplet mass and number of droplets
which depicts the droplet distribution for α = 0.03, includes these fine droplets,
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not resolved, but estimated as atomized mass.
Comparing the numerical and experimental droplet data the definition of a minimum droplet size, detectable in both investigations, is useful. In the experiment the lower limit of a droplet diameter is 20 µm, assuming a resolution of a single droplet by two pixels. Neglecting all droplets with a diameter smaller
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than 20 µm for the numerical data, the droplet distributions in Fig 25(a) are obtained. A good agreement of numerical and experimental results is observed. As a resolution of 10 µm is already realized by the numerical grid, the choice of
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α has no specific influence.
0.03 0.02
0 0
Experiment Sim. α=0.5
0.15
0.01
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0.2
PDF [s/m]
Experiment Sim. α=0.5 Sim. α=0.03
PT
PDF [1/µm]
0.04
0.1 0.05
100
200 d [µm]
0 0
300
d
20
u [m/s]
40
60
x
(a)
(b)
Figure 25: Droplet distribution for diameter and streamwise velocity: Comparison between experiment and simulation
The droplet velocity distributions in the streamwise direction are shown in Fig. 25(b). The mean values of both investigations are of the same order, mea43
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suring 14.5 m/s for the experiment and 10.4 m/s for the simulation. Nevertheless a significant amount of droplets with a velocity above 15 m/s is observed in the experiment, leading to a wider distribution and a higher mean velocity as in
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the simulation. It is presumed that the insufficient numerical resolution of the bubbles leads to an underestimation of the droplet velocity in the vicinity of the atomizing edge. As the fast development of a bubble is not predicted completely (see section 6.2), a correct prediction of the droplet acceleration, induced by the bursting of bubbles, is also prevented.
80
40
150
300 dd [µm]
450
M
0 0
Experiment Simulation
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uz [m/s]
120
Figure 26: Scatter plot for the droplet diameter dd and the streamwise droplet velocity uz .
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A deeper insight into the droplet properties is obtained by the scatter plot of the droplet diameter and velocity in Fig. 26. Raw data is shown, including the small droplets (dd < 20 µm) in case of the simulation. In addition, high droplet
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velocities in the experimental data (50 - 115 m/s) that are found due to errors in the droplet detection algorithm, are not filtered. These high values correspond
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to a false detection of the same droplet in two consecutive images, leading to an overestimation in the droplet velocity. In the scatter plot a wider spread of the experimental droplet properties can be observed. This is due to a greater time
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period for the sampling, and therefore, a higher amount of samples compared to the simulation. Single droplets with a velocity up to 50 m/s are recorded as well as droplet diameters up to 500 µm. These droplets occur occasionally and
have no significant influence on the number based distributions. In contrast, the Sauter mean diameter (as a volume based quantity) is affected even by a small number of larger droplets. In the present study it measures 154.8 µm for the 44
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experiment and 128.1 µm for the simulation. To improve the statistics regarding very large droplets in the simulation, a greater simulation time is required. Nevertheless, comparing the number based distributions, a good agreement has
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been identified. 7. Conclusions
In this paper a detailed comparison of numerical and experimental results of the primary breakup of a prefilming airblast atomizer was presented. Particle and ligament tracking velocimetry based on back light illumination was applied
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in the experiment, whereas the embedded DNS methodology was utilized in the simulation. An operating point in the range of altitude relight conditions
has been studied. A detailed discussion of the observed breakup phenomena and quantitative results of the breakup length, the deformation velocity of the liquid accumulation, droplet sizes and droplet velocities demonstrated the com-
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parability of the results. To ensure a consistent definition of the characteristic dimensions in case of the liquid accumulation, the three-dimensional DNS data was reduced to the topview corresponding to the shadowgraphy images. There-
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fore, the same analysis procedure could be applied to the experimental and the numerical data. Both investigation methods provided a similar prediction of the primary breakup, but an underestimation of large ligaments and very large
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droplets could be identified for the simulation. As observed in the experiment, these liquid structures appear occasionally and have a minor effect regarding
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the total number of droplets or ligaments. The comparison clearly illustrates the challenges for the spatial resolution of a thin liquid film in the numerical investigation. Bubbles arising from the liquid reservoir at the trailing edge were
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insufficently resolved as they grow and the liquid film becomes thinner. A further grid refinement down to 5 µm is in the focus of a current study. For the comparison of the droplet data a minimum size of 20 µm was specified, cor-
responding to the resolution of the experiment. Based on this value a good agreement between numerical and experimental droplet data was found. The
45
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results confirm the applicability of both methods, offering a detailed insight in the phenomena of primary breakup during airblast atomization.
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Acknowledgment The authors would like to thank the German Research Foundation (DFG) for the financial support under the contract no. JA 544/39-1 and GRK 1344.
The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GSC Super-
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List of Figures Experimental setup (all units are represented in mm) . . . . . . .
8
2
Liquid accumulation at the atomizing edge . . . . . . . . . . . .
9
3
Detected liquid accumulation and droplets after data processing .
10
4
Calibrated droplet diameter as a function of the out-of-focus po-
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1
sition and reference diameter . . . . . . . . . . . . . . . . . . . . 5
12
Calibrated normalised intensity gradients as a function of the
out-of-focus position and reference diameter . . . . . . . . . . . . 6
15
Calculation of the real droplet diameter based on the normalized
16
7
The embedded DNS domain for an annular airblast atomizer . .
17
8
Geometry simplification of the airblast atomizer . . . . . . . . . .
18
9
Application of the eDNS concept to a planar airblast atomizer .
18
10
Impact of the inlet boundary condition variation on the pri-
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intensity gradient and the measured droplet diameter . . . . . . .
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mary breakup. Gas phase: u = 50 m/s, ρ = 3.9 kg/m3 , ν = 4.7 × 10−6 m2 /s. Liquid phase: u = 0.5 m/s, ρ = 650 kg/m3 ,
19
Geometry and grid of the turbulent channel . . . . . . . . . . . .
21
12
Computational domain of the planar prefilmer . . . . . . . . . . .
24
13
Reducing three-dimensional DNS data to a plot of the interface .
27
14
Experimental field of view and the used image section of the size
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.
11
ν = 2.9 × 10−6 m2 /s, σ = 0.0085 kg/s2 . Prefilmer: h = 50 µm.
of the DNS domain for the comparison of the breakup phenomena 30 Disintegration sequence at the atomizing edge with ligament for-
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15
mation. From left to right: Sideview experiment, topview exper-
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iment, topview simulation, sideview simulation . . . . . . . . . .
16
33
Disintegration sequence at the atomizing edge with the formation
of bag like structures. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation . . 17
34
Peak detection for the phase interface (a) and the effect of a minimum distance of 50 µm (b) for the analysed operating point
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18
Time displacement of the phase interface and ambiguities by its 37
19
Distribution of the ligament length . . . . . . . . . . . . . . . . .
39
20
Distribution of the deformation velocity . . . . . . . . . . . . . .
39
21
Sensitivity of breakup length and deformation velocity dependent
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determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
on the liquid fraction α . . . . . . . . . . . . . . . . . . . . . . . 22
Representation of bubbles in the experiment (a) and the simula-
tion with α=0.5 (b) or α=0.05 (c) . . . . . . . . . . . . . . . . . 23
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Droplet distribution for diameter and streamwise velocity: Comparison between experiment and simulation . . . . . . . . . . . .
26
42
Small structure properties extracted at the eDNS outflow: droplet mass and number of droplets . . . . . . . . . . . . . . . . . . . .
25
40
Droplet size distribution: Comparison between experiment and
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
40
43
Scatter plot for the droplet diameter dd and the streamwise droplet
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velocity uz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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List of Tables 1
Characteristic parameters of the optical configuration . . . . . .
2
Non-dimensional grid spacings for the turbulent channel. Reg =
13 22
3
Operating conditions . . . . . . . . . . . . . . . . . . . . . . . . .
29
4
Characteristic values for the accumulated liquid . . . . . . . . . .
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13, 333, Reτ = 777. . . . . . . . . . . . . . . . . . . . . . . . . . .
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Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet K. Warncke, S. Gepperth, B. Sauer, A. Sadiki, J. Janicka, R. Koch, H.-J. Bauer PII: DOI: Reference:
S0301-9322(15)30214-7 10.1016/j.ijmultiphaseflow.2016.12.010 IJMF 2536
To appear in:
International Journal of Multiphase Flow
Received date: Revised date: Accepted date:
19 December 2015 1 December 2016 10 December 2016
Please cite this article as: K. Warncke, S. Gepperth, B. Sauer, A. Sadiki, J. Janicka, R. Koch, H.-J. Bauer, Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet, International Journal of Multiphase Flow (2017), doi: 10.1016/j.ijmultiphaseflow.2016.12.010
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Highlights • Identical breakup phenomena are observed in experiment and simulation
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• Ligament and bag formation in the vicinity of the atomizing edge
• Efficient characterization of the liquid sheet by tracking the phase interface • 3D-DNS data is analyzed as seen from the top corresponding to shadow images
• Droplet size distributions provided by eDNS are in good agreement with
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the experiment
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Experimental and numerical investigation of the primary breakup of an airblasted liquid sheet
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K. Warnckea,∗, S. Gepperthb , B. Sauera , A. Sadikia , J. Janickaa , R. Kochb , H.-J. Bauerb a Department
of Energy and Power Plant Technology, Technische Universität Darmstadt, 64287 Darmstadt, Jovanka-Bontschits-Straße 2, Germany b Institut für Thermische Strömungsmaschinen, Karlsruher Institut für Technologie, 76135 Karlsruhe, Kaiserstraße 12, Germany
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Abstract
The primary breakup of airblast atomization is governed by complex mechanisms and is still not well understood. In recent years high speed shadowgraphy experiments and Direct Numerical Simulations of prefilming airblast atomization have been performed independently. In this paper detailed results of a
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combined experimental and numerical study are presented. A single operating point of a planar prefilming airblast atomizer is investigated, based on a spatial resolution of 10 µm and a consistent analysis of the liquid film in both the exper-
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imental and the numerical studies. For the analysis the three-dimensional DNS data is projected on a plane, corresponding to the data obtained by shadowgraphy. The experiment is characterized by back light illumination in conjunction
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with particle and ligament tracking velocimetry. A Depth of Field correction is applied to further improve the measurement accuracy. For the numerical inves-
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tigation the embedded DNS approach is utilized: The primary breakup region is simulated with a highly resolved DNS, embedded in a coarser Large Eddy Simulation. The comparison comprises a phenomenological discussion of the
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disintegration process and quantitative results. Distributions for the breakup length, the liquid film deformation velocity, the droplet sizes and velocities are presented. The results are in good agreement and confirm the applicability of ∗ Corresponding
author. Tel. +49 6151 1628906; fax +49 6151 28900 Email address: [email protected] (K. Warncke)
Preprint submitted to International Journal of Multiphase Flow
February 3, 2017
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the embedded DNS and the particle and ligament tracking velocimetry for the analysis of the primary breakup of airblast atomization. Shadowgraphy, embedded DNS, aircraft engine, primary
atomization, ligament tracking, droplet tracking 1. Introduction
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Keywords:
The air traffic has doubled every 15 years since the 1970s and is expected to continue this growth for at least the next 15 years (Airbus (2013); Boeing
(2013)). The Advisory Council of Aeronauctical Research in Europe defined
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emissions targets for the year 2020: CO2 reduction about 50 % per passenger kilometer, NOx reduction about 80 % and noise reduction about 50 % compared
to the year 2000 (ACARE (2010)). Similar targets were defined by the US aviation industry (NSaTC (2010)).
To reach these emission targets, lean combustion technologies need to be
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integrated in future aircraft engines (Wilfert et al. (2007)). For lean combustion high quality fuel atomization is required to ensure a stable combustion in every operating condition during a flight. Prefilming airblast atomizers are used in
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aircraft engines to atomize the liquid fuel. Here, a thin liquid fuel film is formed on a prefilmer and disintegrated by coflowing air streams. To effectively control
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the atomization an improved understanding of the breakup process is required. A major limitation in understanding these flow systems is a detailed insight into the initial atomization step, the primary breakup. Especially, the impact
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of modified geometry and operating parameters is highly demanded to improve the design of combustion chambers. The investigation of the primary breakup is challenging as the geometries
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of airblast atomizers are complex and the two-phase flow is characterized by high Weber and Reynolds numbers. To capture the temporal evolution of the liquid film in experimental or numerical investigations high resolutions in time and space are mandatory. In addition, the spatial domain belonging to primary breakup is large compared to the breakup of a liquid jet. Wheras a liquid jet 2
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is typically injected with a high velocity in a stagnant environment, the velocity of an airblasted sheet is at least one order of magnitude smaller than the coflow air velocity. As a result breakup time and breakup length are extended.
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Furthermore, compared to other atomizer designs like flat sheet or jet atomizers, where the dominant instability mechanisms have already been identified
(Marmottant and Villermaux (2004); Fuster et al. (2013)), no such fundamental understanding exists for prefilming airblast atomizers.
Since the idea of an airblast atomizer was first introduced by Lefebvre and
Miller (1966) many experimental investigations have been carried out to under-
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stand the physical processes of the atomization of the liquid film at the atomizing edge. Most of the research did focus on the investigation of the spray charac-
teristic downstream of the atomizer. By applying laser optical measurement systems the key parameters affecting the breakup process were identified. The most pronounced effect on the droplet sizes comes from the mean air velocity within the atomizer. An increase in mean air velocity results in increased aero-
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dynamic forces that reduce the droplet sizes (Lefebvre (1980); Jasuja (1981); Sattelmayer and Wittig (1986); Aigner and Wittig (1988); Beck et al. (1991);
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Bhayaraju et al. (2005)). Additionally, it could be observed that an increase in air pressure reduces the droplet size (Rizkalla and Lefebvre (1975); Lefebvre (1980); Brandt et al. (1996); Bhayaraju et al. (2005); Jasuja (2006)). A reverse
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effect on the Sauter Mean Diameter has the increase in the surface tension of the liquid (Lefebvre (1980); Aigner and Wittig (1988); Brandt et al. (1998)). The
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liquid viscosity on the other hand has only a minor effect on the droplet size as long as its value is small, which is the case for aero engine fuels (Sattelmayer and Wittig (1986); Jasuja (1981)). A still controversial discussed parameter is
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the liquid film thickness. Some researchers observed that an increase in liquid film thickness is accompanied by an increase in the Sauter Mean Diameter (ElShanawany and Lefebvre (1980); Lefebvre (1980); Rizk and Lefebvre (1983)). Other investigations could not identify this behavior and reported that a change in the film thickness has no effect on the droplet size due to a decoupling of the film disintegration process and the film thickness at the atomizing edge. The 3
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reason is an observed accumulation of the liquid film at the atomizing edge prior to the primary atomization of this accumulation (Sattelmayer and Wittig (1986); Aigner and Wittig (1988); Brandt et al. (1996); Müller et al. (2005);
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Gepperth et al. (2013); Bärow et al. (2015)). Therefore, the atomizing edge thickness and air flow structures in the vicinity of the atomizing edge will affect the size of droplets (Gepperth et al. (2012); Braun et al. (2015)).
In order to describe the atomization process analytically, Chaussonnet et al.
(2013) presented an approach that transfers the instabilities observed in co-
flowing atomizer configurations to the breakup of prefilming airblast atomizers.
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To include the accumulation of the liquid at the atomizing edge and its effect on the dominant instability mechanism, the atomization edge thickness is included in the calculation of the transverse instability (Chaussonnet et al. (2013)). However, without detailed numerical investigations it is impossible to identify the responsible atomization instability in prefilming airblast atomizers. To investigate the primary breakup numerically, Direct Numerical Simula-
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tions (DNS) are a suitable approach as all scales are resolved. The Volume of Fluid (VOF) and the Level Set (LS) are well-established methods to repro-
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duce the physics of the immiscible fluids and to transport the interface between them. In several numerical studies the phenomena of airblast atomization are analyzed by computing the breakup of a planar liquid sheet directly injected in
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two coflowing air streams. In this configuration no prefilmer is present. Considering this configuration the study by Couderc and Estivalezes (2005) focused on
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the validation of global sheet oscillations against experimental results, utilizing a 2-D DNS combined with a LS approach. Villedieu et al. (2013) applied a compressible two-fluid model and compared the oscillation frequency and the
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breakup length of the liquid sheet to experimental data. Pringuey and Cant (2014) performed a three-dimensional Large Eddy Simulation (LES) to prove the applicability of the Robust Conservative Level Set (RCLS) method to airblast atomization. This method allows an improved mass conservation of the LS method and is based on the Conservative Level Set by Olsson and Kreiss (2005); Olsson et al. (2007). The injection of a liquid sheet into a stagnant environment 4
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was investigated by Sander and Weigand (2008) using different injection nozzles and liquid inflow profiles. For the simulations DNS with VOF was combined. Other studies focus on the liquid wall film disturbed by the air stream above,
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either with a 2-D RANS solver (Hashmi et al. (2010) or a 3-D DNS combined with a LS-VOF approach (Berlemont et al. (2012)). The 2-D LES simulations
by Volz et al. (2015) focused on the film thickness and were validated against experimental results.
To describe the full atomization process, including primary and secondary breakup, the coupling of an Eulerian multiphase solver with Lagrangian Particle
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Tracking (LPT) is another field of research. Here, small droplets generated by the primary breakup are transferred to a mass point description and tracked by
a Lagrangian solver (Ling and Zaleski (2014); Zuzio et al. (2013)). In contrast to these methods a meshless approach, called Smoothed Particle Hydrodynamics (SPH), is applied by Hoefler et al. (2013); Braun et al. (2015) to simulate primary breakup.
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Although several numerical and experimental studies have been performed, a combined investigation considering the liquid wall film on top of the prefilmer
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and the subsequent disintegration is still a missing link. This paper fills this gap and presents a numerical and experimental investigation of a planar prefilming airblast atomizer, establishing a first basis for identifying the dominating
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breakup mechanisms. The study is based on an identical operating point and consistent geometrical conditions of the prefilmer. Further, an identical analy-
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sis procedure is applied to the experimental and numerical data, facilitating a reliable comparison of quantitative results, e.g. the breakup length. In order to capture the complex physical processes involved in the primary
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breakup of a liquid film in the experiment, sophisticated laser optical diagnostics are used. In combination with a generic atomizer design a highly resolved temporal as well as spacial investigation is possible. For statistically reliable data of droplet sizes and velocities as well as the ligament formation process, an adapted particle and ligament tracking velocimetry setup is used (Müller et al. (2006, 2007)). It was extended by a Depth of Field (DoF) correction algorithm 5
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to increase the measurement accuracy (Gepperth et al. (2012)). Furthermore, a three dimensional high speed shadowgraphy technique is applied for investigating the various temporal and spatial quantities observed during primary
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breakup, leading to a profound understanding of this process. This enables the unique opportunity for accurate quantitative and qualitative comparisons to data obtained by the numerical simulation.
For the simulation the embedded DNS approach is applied as introduced by Sauer (2014) for the primary breakup of airblast atomization. With eDNS a highly resolved 3D-DNS is applied to the breakup region, embedded in a
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LES. High quality boundary conditions are generated by the LES and mapped to the DNS domain. Sauer proved the applicability of the concept using a generic planar prefilming atomizer and six operating points, including cruise and altitude relight conditions.
The paper is organized as follows: the experimental investigation including set-up, diagnostics and post-processing steps are presented followed by the
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numerical investigation. The embedded DNS methodology and numerical setup are explained. Additionaly, the post-procesing of the DNS data focusing
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on an analysis consistent with the experiment, is presented. Furthermore, the selected operating conditions are described. Afterwards, the results of the primary breakup are shown, the following discussion being divided into two sec-
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tions. First, the physical phenomena observed both experimentally and numerically are compared considering also the temporal evolution of the liquid sheet.
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Second, quantitative results of the liquid sheet and the droplets generated by primary breakup are validated against each other.
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2. Experimental Investigation The measurements have been conducted at the spray test rig at the Institut
für Thermische Strömungsmaschinen (ITS). The air is supplied by a radial compressor with a maximum mass flow of 200 g/s. The air mass flow is measured via an air mass flow meter. To ensure a homogeneous velocity field, a mixer, a flow
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straightener and a nozzle are positioned upstream of the test section (Fig. 1). To capture the relevant flow parameters, pressure and temperature probes are connected to the mixing unit. Details on the test rig can be found in Gepperth
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et al. (2010); Müller et al. (2006); Müller (2015). 2.1. Test section
In order to enhance the optical accessibility, the test section itself is a two-
dimensional abstraction of an axis-symmetric airblast atomizer (Fig. 1(a)). It consists of four wall segments and the prefilming surface. The air emerging
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from the mixer is split into two air streams that pass the prefilmer on each side. Inside the prefilmer, a cavity used as a continuous feed for the test liquids is located. The liquid is ejected through a set of 50 equidistant distributed holes
with a diameter of 0.5 mm each (Fig. 1(b)). The air shear causes the liquid to form a uniform thin film flowing in the z-direction. It was ensured that no film dryout was occurring during the experiments. The liquid flow through the test
2.2. Diagnostics
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section is controlled by a mass flow meter/controller.
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The experimental observation of the film disintegration process and the measurement of the non-spherical droplets and structures as well as the ligaments
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attached to the atomizer is very challenging. For this reason, previous experimental studies focused on the development of an efficient an reliable measurement technique for the observation of the primary breakup (Gepperth et al.
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(2012); Müller et al. (2006); Müller (2015)). To derive statistically robust results of the ligament structures and droplet sizes, an efficient algorithm based on
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the particle and ligament tracking velocimetry was developed by Müller (2015). The algorithm of Müller (2015) has been extended by a Depth of Field (DoF) correction to further increase the measurement accuracy. Additionally, high speed images are recorded to gain a detailed insight to the
physical processes causing the film disintegration into ligaments and droplets.
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grid
l = 47
21.6 5
46
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test section
h = 0.23
8.1
y
prefilmer honeycomb inlet nozzle 65
70.5
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(a) Inlet and generic airblast atomizer
z
x
cavity
liquid inlet
liquid inlet
69.5
ejection holes
x
b = 50 96
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z
y
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wetted area
(b) Prefilmer of the generic airblast atomizer
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Figure 1: Experimental setup (all units are represented in mm)
2.2.1. Particle and ligament tracking velocimetry
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For the detailed investigation of the liquid film atomization process, a combined method of particle and ligament tracking velocimetry has been used. The technique is based on back light illumination of a measurement volume (shad-
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owgraphy) with a double-pulsed laser. The field of view is 12 mm in the zdirection and 16 mm in the y-direction. The spatial resolution is 10 µm. Details on the optical setup and the measurement system can be found in Gepperth et al. (2010, 2012). The key advantage of this technique is that information about the accumulated liquid at the atomizing edge and the generated droplets
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are gathered at the same time. A schematic view of the liquid accumulation at the atomizing edge is shown in Fig. 2. The droplets do not need to be spherical as it is the case with Phase-Doppler-Anemometry (Tropea and Damaschke
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(2000); Tropea (2011)). In addition, it is possible to measure the velocity of both, droplets and liquid accumulation at the same time. This is a disadvantage of commercially available shadow sizing systems where only the droplet
velocity can be measured. The information about the liquid structure and the initial particles is of particular interest in the primary atomization region near
the atomizer edge. This helps to link the produced droplets near the atomizer which the droplets are generated.
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edge to the deformation of the liquid accumulation at the atomizing edge by
film flow
air flow
accumulated liquid
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air flow
droplets
z
x
prefilmer
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Figure 2: Liquid accumulation at the atomizing edge
The software for the post-processing has previously been developed at ITS
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(Kapulla et al. (2008); Müller et al. (2006); Müller (2015)). The post-processing routine can be divided in four major tasks. First, a grey scale analysis of
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the recorded double frame images is performed. In this step, a threshold is calculated based on the image intensity distribution. By means of this threshold, the pixel array of the image is than split into background and object. In the
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second step, a contouring algorithm is applied. This algorithm detects connected structures based on the grey scale level in step one. It further divides the detected areas into the accumulated liquid at the atomizer edge and droplets. Afterwards, a sphere or ellipse is fitted to the accepted droplets and their size is corrected by a Depth of Field correction (section 2.2.2) based on the work
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of Kim and Kim (1994); Lee and Kim (2004); Castanet et al. (2013). This
0 1 2 3
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0 Y [mm]
5
Pstr maxima
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Lstr
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Z [mm]
correction leads to a significant increase of the measurement accuracy.
(a) Detected liquid accumulation and ligaments
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Z [mm]
4
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10
0 Y [mm]
5
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(b) Detected droplets and corresponding velocity com-
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ponents
Figure 3: Detected liquid accumulation and droplets after data processing
The third step is the calculation of the droplet velocities in the yz-plane. As a
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first estimation a velocity field is calculated based on an ordinary PIV algorithm. Due to the intensity distribution and the huge span of possible droplet sizes, this algorithm produces inaccurate and multiple velocity vectors for each droplet. Therefore, a least square fitting algorithm that uses the estimated velocity field as a ’first guess’ and the detected droplet positions for frame one and two is used
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to calculate the displacement and based on the inter framing time the velocity for each droplet (Müller (2015)). In the last step, the geometrical parameters of the accumulated liquid are
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recorded. The blue line in Fig. 3(a) indicates the perimeter of the accumulated liquid, Pstr . The red dots along the perimeter represent the maximum elon-
gation of the liquid accumulation in the streamwise direction. Based on the
position of the atomizing edge and the detected maxima, the breakup length of the ligaments Lstr can be derived. In addition, the detected liquid accumulation
at the atomizing edge of subsequent temporal frames is used to calculate the
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streamwise deformation velocity udef,str of the liquid.
For the present test case, a set of 300 double frame images was post-processed. A processed double frame image is shown in Fig. 3(b), including the raw image, liquid accumulation (blue and red lines), droplets (blue and red ellipses) and the calculated droplet velocities (green arrows). The lengths of the arrows indicate the velocity magnitude and the arrow head points into the direction in which
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the droplet moves. The atomizing edge is represented by the dashed red line. 2.2.2. Depth of Field (DoF) correction
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The back light technique as previously discussed usually does not give a sharp edge of all interesting objects in every part of the image. This is due to
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the fact that lenses can only be focused to the so called focal plane. Objects located at exactly this position are accurately captured on the camera chip. If the object moves closer or further away from this focal plane it moves ’out-of-
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focus’ and can no longer be detected accurately. The region in which an object can be considered as accurately detected is the depth of field. In an optical
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setup this depth of field is dependent on the f-number and the focal distance of the lens, the distance between camera and object as well as the physical pixel size of the CCD chip. In the present study, it was important to capture a wide range of possible droplet sizes, starting from droplets with tenth of microns up to droplets with more than one millimetre. To accurately detect small droplets of less than 60 µm, a large magnification is needed. To achieve this magnification, 11
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spacer rings were inserted between the lens and the camera. This leads to a
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reduction in the depth of field.
(a) Calibrated droplet diameter as a function (b) Calibrated droplet diameter as a function of the out-of-focus position and reference di- of the out-of-focus position and reference diameter
ameter
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1.4
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1.6
x = 0 [mm] x = 1 [mm] x = 2 [mm] x = 4 [mm] x = 8 [mm]
1.2
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Dmeas/Dref [mm]
1.8
1
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0.8
0.020.1 0.2 0.3 0.4 0.5 Dref [mm]
1
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(c) Non-dimensional sizing accuracy for different out-of-focus positions
Figure 4: Calibrated droplet diameter as a function of the out-of-focus position and reference
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diameter
On the other hand, the field of view has to have a certain size in order to
be able to track the liquid accumulation for a sufficient length. This leads to a limited resolution of 10 µm per pixel. With such a setup, a constant intensity threshold of 80 %, as it is used in the present investigations, leads to an over estimation of the droplet sizes (Kapulla et al. (2008)). Therefore, a calibration 12
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is mandatory. In the present study a calibration target was used. Due to the accurate manufacturing process, the spherical dots are highly resolved, both in size and shape. The calibration plate consists of four different areas and covers
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dot sizes between 10 µm to 2000 µm. The calibration process itself has to be carried out with the exact same settings (laser power, laser dye, diffuser plate, etc.) that are used for the spray measurements. Therefore, a set of calibration images has been recorded prior to every measurement sequence. The calibration plate was positioned on a 1D traverse system and scanned along the x-direction.
A set of 30 calibration images was recorded for every out-of-focus plane for the
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range of ± 10 mm at every 500 µm. The positive direction refers to a movement
of the calibration plate closer to the camera. A summary of the optical settings can be found in Tab. 1.
Table 1: Characteristic parameters of the optical configuration
Parameter resolution
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field of view
Unit
Value
mm2
16 × 12
µm/pixel
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f-number (f /#)
10 16
focal length
mm
105
calibration planes
mm
−10 to 10
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no. of images per plain
30
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The same post-processing algorithm as discussed previously for the mea-
surements was used for the analysis of the calibration data sets, but with one difference: in addition to the earlier described detection and ellipse fitting pro-
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cess, an additional computation is performed. The detected dot positions are correlated to the known positions of the dots on the calibration plate. The reference diameter of the calibration dot is then compared to the measured dot size. This procedure is repeated for every out-of-focus plane and a diameter calibration matrix (Fig. 4) is derived. In Fig. 4 the color corresponds to the measured
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dot size. The information on the interdependency between the measured and the real dot size can be applied in exactly the same way to the measured droplet sizes during the experiment. It can be seen from Figs. 4(a) and 4(b), that an
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almost perfect symmetrical function for the measured dot size over the reference dot size along the x-positions is derived. Details of the difference between measured and detected dot sizes (Fig. 4(c)) reveal the same tendency. Due to the setup and chosen threshold, the diameters are consequently predicted as being
too large. This error increases by moving away from the focal plane. The error in prediction of droplets smaller than 60 µm drastically changes which is likely
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to be due to the optical setup. However, it can be seen that this behaviour sets a limit to the detectable droplet size depending on the out-of-focus position.
Based on these investigations, the diameter correction is a tool that enables the correct diameter measurement of a droplet at an out-of-focus position. However, in a typical setup, as it is used for experimental spray investigations, it is not possible to predict the out-of-focus position of each droplet a priori. Con-
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sequently, a correction of the droplet diameters cannot be performed based on these predictions. A second parameter is needed to define the out-of-focus posi-
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tion for each measured droplet. The intensity gradient at the outer edge of each detected object can usually be used. The mean value of the intensity gradient of every boundary pixel for each dot is calculated and normalized by the median
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intensity of the image. This normalized intensity gradient per pixel will be referred to as int/pixel. Using this gradient for every dot on the calibration plate
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and in every out-of-focus position, it is possible to create a second calibration matrix for the gradient values (Fig. 5). The color scale refers to the measured mean intensity gradient of each detected dot. Again, the actual gradient values
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were only measured for the available dot sizes. The points between the measured dots sizes are linearly interpolated. The gradient and diameter matrixes both show the same behaviour. They are both symmetrical to the yz-plane at x =0 mm. The gradient becomes smaller when moving further away from the focal plane. It can be seen, that for small droplets a peak in the gradient matrix can be seen before the gradient values rapidly decrease. This behaviour is due 14
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to the experimental setup for the present investigation. The minimum gradient
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value for the evaluation of each diameter class was set to 0.05 int/pixel.
(a) Calibrated normalised intensity gradients (b) Calibrated droplet diameter as a function as a function of the out-of-focus position and of the out-of-focus position and reference direference diameter 2D
ameter 3D
Figure 5: Calibrated normalised intensity gradients as a function of the out-of-focus position
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and reference diameter
In the measurements for every droplet the normalized intensity gradient and the corresponding measured droplet diameter are known. These two values can
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be superposed with the two calibration matrices (Fig. 4(b) and Fig. 5(b)) and the real droplet diameter can be calculated. By applying this methodology,
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the calculation can be done without knowing the exact droplet position in the measurement volume. The calculation principle is schematically illustrated in Fig. 6. The interdependency between the measured and the reference diameter
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are represented by the grey lines. The numbers in the corresponding fields represent the size of the measured diameter. The black lines and associated values
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in the dark fields correspond to the interdependency between the normalized intensity gradient and the real droplet diameter. Both calibration values are symmetrical to the yz-plane at x =0 mm. Therefore, two possible solutions for the real droplet diameter for each combination of measured droplet size and gradient exist. These are given by the two intersection points A and B. Finally, the real droplet diameter in the measurement is calculated by the mean of the 15
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determined droplet diameter from the two intersection points. The limiting 10
0.05
0.08
intersection A
0.17 0.14 0.11
intersection B 0.08
1
−5
0.20
2
0
0.11 0.14 0.17 0.20
0.5
1
1.5 2 Dref [mm]
2.5
3
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−10
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3
x−direction [mm]
2.5
2
1.5
1
0.5
5
Figure 6: Calculation of the real droplet diameter based on the normalized intensity gradient and the measured droplet diameter
parameter for the application of this algorithm is the size of the measurement
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volume and therefore the lower detectable gradient boundary. In the presented case, this restricts the droplet detection to approximately ± 9 mm in the di-
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rection of the optical axis, which has been demonstrated to be well within the range needed for properly studying primary atomization.
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2.2.3. Measurement uncertainty The measurement uncertainty has been determined using the approach given by Kline and McClintock (1953). The uncertainty of the mean air velocity can
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be estimated to 3 %. The uncertainty of the liquid mass flow is less than 0.5 %.
Due to the enhanced calibration and post-processing procedure, the error in
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measuring the droplet size and velocity is estimated to be less than 4 %. In summary, the maximum uncertainties for the measurements are about 7 %.
2.2.4. High speed shadowgraphy The film flow and the primary breakup process have been recorded with two high speed video cameras at 7 kHz at a spatial resolution of 13.89 µm. The field 16
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of view was set to approximately 14.2 × 14.2mm. Therefore, the utilization of two cameras enables the recording of the liquid film disintegration process simultaneously from two angles shifted by 90◦ . For capturing the high speed breakup
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processes the exposure time was reduced to 1 µs, minimizing the blurring effect of fast deforming structures and droplets. For the operating condition a total of
5.000 images are recorded. The measurement volume is illuminated using two 500 W halogen spotlights. The spotlights are mounted opposite of the cameras. 3. Numerical Investigation
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The numerical simulation in this paper is based on the embedded DNS (eDNS) concept. Sauer (2014) introduced this numerical concept for the primary breakup of airblast atomization and proved its applicability by simulating six different operating points. For a detailed validation of the numerical concept with experimental results a further operating point is investigated in the present
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study. A short overview of the numerical approach is given in the following section, more details can be found in Sauer (2014). The idea of the eDNS concept is to apply a DNS only to a small region
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of interest embedded in a larger and coarser LES. For simulating the primary breakup of an airblasted liquid sheet, the DNS domain can be reduced to the primary breakup region, as illustrated in Fig. 7. A key issue of the concept is
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the generation of high quality boundary conditions for the embedded domain
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by the LES.
Figure 7: The embedded DNS domain for an annular airblast atomizer
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Figure 8: Geometry simplification of the airblast atomizer
The planar configuration, considered here, represents a geometry simplification of the annular atomizer as illustrated in Fig. 8. The application of the
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eDNS approach to the planar airblast atomizer is shown in Fig. 9. The embedded domain comprises a planar prefilmer lip and the atomization region. An
air flow inlet is sited each above and below the prefilmer. The values of the velocity field for the air inlets are generated by a single-phase LES of a turbulent channel. They are extracted on a plane normal to the channel wall at each LES time step and mapped to both air inlets. For the lower air inlet the sign of
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the y-component is inverted accounting for the boundary layer induced by the bottom side of the prefilmer. As time step and grid size of the LES are coarser
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than in the DNS a linear interpolation in time and space is applied to map the data. The data are defined as transient Dirichlet boundary conditions for each individual time step. The turbulent fluctuations are directly transferred to the
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DNS domain.
Figure 9: Application of the eDNS concept to a planar airblast atomizer
The application of the transient velocity data to the DNS domain enables an
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investigation of the primary breakup with realistic boundary conditions. Fig. 10 illustrates the evolution of an airblasted liquid film for two different air inflow types: a fully developed turbulent channel flow and a laminar inflow correspondadded in the latter case. Mean velocity profile
3.0 ms
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4.0 ms
5.0 ms
Time varying profile
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2.0 ms
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ing to the mean velocity profile of the same channel flow. No fluctuations are
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6.0 ms
Figure 10: Impact of the inlet boundary condition variation on the primary breakup. Gas phase: u = 50 m/s, ρ = 3.9 kg/m3 , ν = 4.7 × 10−6 m2 /s. Liquid phase: u = 0.5 m/s,
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ρ = 650 kg/m3 , ν = 2.9 × 10−6 m2 /s, σ = 0.0085 kg/s2 . Prefilmer: h = 50 µm.
The snapshots illustrate that turbulence plays a decisive role in the devel-
opment of the primary breakup regarding the characteristic of the dominating structures. Quantitative parameters as the breakup length or the breakup time are changed by the introduction of turbulence. By applying the embedded DNS 19
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concept, such influence of the turbulent flow is rationally accounted for and an improved transfer of the results to industrial airblast atomizers is possible. A detailed discussion about the impact of different inflow types on the primary
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breakup and the role of turbulence can be found in Sauer (2014). 3.1. Generation of transient inlet boundary conditions for the embedded domain
Due to its close proximity to the prefilmer, the air streams in the embedded domain are mainly affected by wall-related structures. A single-phase LES of a
turbulent channel is selected to generate the suitable velocity data. The quality
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of the generated inflow data influences directly the results of the two-phase DNS simulation.
With a LES the large scales are resolved whereas the small unresolved subgrid scales need to be modeled. This seperation is obtained by filtering of the Navier-Stokes equations, including the continuity Eq. (1) and the momentum Eq. (2), that are formulated with the velocity vector of the resolved scales U ,
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the gravitational vector g, the kinematic viscosity ν and the kinematic Pressure
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P.
(1)
∂U + ∇ · (U U ) = g − ∇P + ∇ · (ν∇U ) ∂t
(2)
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∇·U =0
Splitting the convective term of the momentum equation in a resolved and
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an unresolved part, (Eq. (3)), the residual stress tensor τ sgs is introduced to
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the momentum equation, as formulated in Eq. (4).
U U = U U + τ sgs
(3)
∂U + ∇ · (U U ) = g − ∇P + ∇ · (ν∇U ) − ∇ · τ sgs ∂t
(4)
2 T τ sgs − ksgs I = −νsgs (∇U + (∇U ) ) 3
(5)
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For modeling the subgrid scale stress the Boussinesq approximation is used (Eq. (5)). The turbulent viscosity νsgs and the turbulent kinetic energy ksgs of the subgrid scales are calculated from the One-Equation Eddy model by
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Yoshizawa and Horiuti (1985). Fig. 11 illustrates the turbulent channel flow domain which measures 2πδ
in streamwise x-direction, 2δ in wall-normal y-direction and πδ in spanwise z-direction (Moser et al. (1999)). In order that the height of the channel 2δ
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corresponds to the prefilmer experiment, δ measures 4 mm.
Figure 11: Geometry and grid of the turbulent channel
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A turbulent channel flow is dominated by small wall-related structures. To realize a highly resolved grid in the near-wall region but to limit the general number of grid points a zonal grid is used, refining the domain from the channel
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core to the walls. Sauer et al. (2016) compared the results of a coarse, a fine and a zonal LES to the results of a DNS by Moser et al. (1999) and proved the
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applicability of the zonal approach. Three different zones are distinguished: a core zone, a wall zone and a sandwiched zone in between them. The number of streamwise and spanwise grid points are doubled from zone to zone, starting
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with the core zone. Normal to the walls a simple gradient is applied concentrating more grid points close to the walls. The zonal boundaries are positioned at y + = 200 und y + = 420. Tab. 2 summarizes the non-dimensional grid spacings for each zone, formulated as ∆y + = ∆uτ /ν for the wall-normal distance. Due to + the grid-stretching in y-direction the minimum grid spacing ∆ymin is listed for
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+ the wall and the sandwiched zone, whereas the maximum grid spacing ∆ymax
is listed for the core zone. The grid points in x- and z-direction are equidistant distributed. For the streamwise and spanwise direction periodic boundary con-
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ditions are set. The sampling of the velocity data is started once a statistically stationary state of the flow is reached.
The described configuration has also been utilized in the turbulent channel
configuration by Sauer et al. (2016). There the primary breakup of an airblasted
liquid sheet under identical gas phase conditions, but different prefilmer geometry and liquid properties, has been investigated. A detailed discussion about can be found in the cited study.
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the velocity profiles and a validation against DNS results by Iwamoto (2002)
Table 2: Non-dimensional grid spacings for the turbulent channel. Reg = 13, 333, Reτ = 777. + ∆ymin
Wall zone
9.7
4.9
9.2
Sandwiched zone
19.4
17.0
18.5
Core zone
38.8
+ ∆ymax
49.1
∆z +
37.0
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∆x+
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3.2. Two-phase DNS of the primary breakup For simulating the liquid and the gaseous phase the two-phase solver Inter-
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FOAM of the opensource code OpenFOAM is used. Spyrou (2011) verified the functionality of the code by computing several test cases for the advection, the surface tension and the buoyancy force. In InterFOAM the Volume-of-Fluid
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(VOF) method is implemented to describe the phase interface. The VOF introduces a indicator function α representing the liquid volume
contained in a cell. The density ρ and the viscosity µ in a cell are formulated as a function of the volume fraction (Eq. (6) and Eq. (7)).
ρ = αρl + (1 − α)ρg 22
(6)
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(7)
µ = αµl + (1 − α)µg
The incompressible Navier-Stokes equations consist of the vectorial momen-
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tum advection Eq. (8) under the incompressibility constraint Eq. (9). In order
to find a mathematical description for two-phase flows, the surface tension effect appears as an external force into Eq. (8) ruled by the interface curvature κ. The curvature κ is determined by Eq. (10).
(8)
∇·U =0
(9)
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∂ρU + ∇ · (ρU U ) = ρg − ∇p + ∇ · [µ(∇U + (∇U )T )] + σκ∇α ∂t
∇α |∇α|
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κ = −∇ ·
∂α + ∇ · (U α) + ∇ · (U r α(1 − α)) = 0 ∂t
(10)
(11)
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The transient evolution of the indicator function of an incompressible flow field is described by the advection Eq. (11). The last term on the left side is only active in the proximity of the phase interface and represents an artificial
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compression term antagonizing numerical diffusion (Rusche (2002)). No geometrical recontruction of the phase interface is applied. The phase interface is
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smeared in a transition region from 0 to 1 and is not known exactly. The surface tension force in Eq. (8) cannot directly be determined. A volume force, that is effective in the transition region, is formulated instead. This method is known
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as the Continuum Surface Force (CSF) method by Brackbill et al. (1992). Fig. 12 illustrates the embedded DNS domain. The liquit fuel enters the
domain through a small slit, is transported along the prefilmer to the trailing edge and exposed to high shear forces induced by the coflowing air streams. The liquid accumulates at the trailing edge and is atomized downstream of the trailing edge. 23
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Figure 12: Computational domain of the planar prefilmer
The prefilmer thickness measures 200 µm and is increased by a factor of four
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compared to the preliminary simulations by Sauer (2014); Sauer et al. (2016). Down to a value of 100 µm the height of the trailing edge has a significant influence on the breakup length and breakup time (Braun et al. (2015)). To
capture the expected breakup length, the computational domain was additionally expanded from 4 mm to 6 mm in the streamwise direction. To keep the DNS domain as small as possible, the prefilmer length only measures 1 mm and
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is clearly smaller as in the experimental set up. This deviation is accepted, as the studies by Gepperth et al. (2012) have shown, that the prefilmer length has no significant impact on the disintegration process.
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The liquid fuel enters the domain with a constant velocity. The faces of the prefilmer are treated as walls with a no-slip condition. An outlet condition is
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assigned to the top, the bottom and the outlet of the domain enabling liquid structures to leave the domain. The total pressure is fixed at the outlets and recirculations are prevented by setting inflowing velocity components to zero.
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A slip condition is assigned to the lateral faces, the normal component is set to zero and the tangential components are initialized as zero gradients. The
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coflowing air next to the prefilmer is directly linked to the turbulent channel flow. The sampled velocity data during the LES is mapped onto the air inlets as transient Dirichlet boundary conditions. For the grid an equidistant grid spacing of 10 µm in all three directions is
realized. For the blocks downstream of the liquid inlet slit and the trailing edge a further refinement by a factor of two in y-direction is performed. Sauer et al. 24
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(2016) have shown that this grid resolution is suitable to resolve the smallest scales of turbulence, the Kolmogorov length scales lη , regarding the investigated operating point. In their study, the embedded DNS concept has been utilized
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to simulate the primary breakup in the same turbulent channel flow (Reg = 13, 333). The prefilmer thickness and the liquid properties were modified. The Kolmogorov length scale was found to be lη = 12 µm and the required minimum
grid spacing was identified as ∆xmin = 25 µm following Eq. (12) by Pope (2000).
The relation between the minimum required grid spacing in physical space and
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the Kolmogorov scales is quantified as ∆xmin π ≈ 2.1. = lη 1.5
(12)
A further aspect in the grid resolution assessment is the representation of small liquid structures and droplets, produced by the primary breakup. The findings by Sauer et al. (2016) show that an resolution of the entire liquid mass is hard to achieve due to the amount of small droplets. 80 % of the liquid
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mass have been resolved in their simulation utilizing the above mentioned grid resolution. A detailed discussion about the droplet representation on different
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grid sizes (20 µm and 10 µm) can be found in the cited study. For the operating point, investigated in this paper, the liquid structure resolution is discussed in section 6.2 and 6.3, directly linked to the quantitative results.
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The total number of cells amounts 84.41 millions. 14 ms physical time with a time step of 50 ns has been simulated. The highly resolved DNS was performed
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on 720 processors. A total of 540000 cpuh were consumed.
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3.3. Processing of DNS data Analogously to the experimental data processing, the analysis of the com-
puted results is splitted into the analysis of the accumulated liquid at the trailing edge and the analysis of droplets. For determining the number of droplets and their properties, a sampling
plane at the outlet is defined. According to a minimum volume fraction α in each cell, a connected liquid structure is detected by using an approach of Connected 25
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Component Labeling (CCL). The surface area of each droplet is quantified by the sum of all cells i containing liquid with the corresponding volume fraction αi and the grid sizes ∆yi and ∆zi (Eq. (13)). The droplet diameter is derived
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by assuming a circular area. Velocity data is extracted at each cell belonging to a droplet. The components of the droplet velocity Ud are further calculated as the mean value over the area of the droplet (Eq. (14)). This post-processing
routine is inspired by the algorithm presented by Grosshans and Fuchs (2011) and Herbert et al. (2008). Ad =
n X
αi ∆yi ∆zi
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i=1
Pn i=1 αi Ui Ud = P n i=1 αi
(13)
(14)
The analysis of the accumulated liquid at the trailing edge is challenging. An analysis at a fixed position, similar to the droplets, is not suitable as the
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liquid film oscillates and changes its shape and position from time step to time step. To determine characteristic sizes, like the breakup length and the streamwise deformation velocity, the position of the phase interface needs to be known.
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Therefore an post-processing algorithm has been developed, facilitating an automated analysis of the continuous liquid film.
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The procedure is illustrated in Fig. 13. Based on a predefined α-threshold the phase (liquid or gas) in a grid cell is determined. Corresponding to the identified phase each cell receives the label 1 (liquid) or 0 (gas). A view from
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the top, analogous to the shadowgraphy images, is generated by summing up the labels in x-direction. A sum exceeding 1 signifies that at this position a liquid phase would be observed from the top. A CCL algorithm is applied,
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identifying all liquid structures. A connectivity of 8 is utilized, checking for liquid in each neighboring cell. As only the accumulated liquid at the trailing edge is of interest, any other liquid structure, detected by the CCL, is deleted. Finally, the interface of the accumulated liquid is identified. The result is a one-dimensional plot of the phase interface, that enables an easy and efficient
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Figure 13: Reducing three-dimensional DNS data to a plot of the interface
analysis compared to the original three-dimensional DNS data. The described processing is applied for every time step. The subsequent procedure is reduced
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to the analysis of the recognized phase interface, similar to the experimental data processing. This way an identical definition of the breakup length and the deformation velocity for the experimental and numerical investigations is
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possible.
Reducing the huge amount of DNS data to single plots of the phase-interface
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enables a fast and efficient analysis. But in contrast, two disadvantages have to be mentioned: first, superimposed structures as seen from the top can not be distinguished and thus an overestimation of the liquid sheet expansion into the atomization region is possible. Secondly, the velocity data calculated by the DNS is not used. Both aspects could be avoided by identifying the accumulated liquid in the original DNS domain and extracting the velocity data in each cell 27
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belonging to the liquid sheet or its interface. However, due to the focus of this paper, the DNS data is here reduced, facilitating a more reliable comparison
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against the experimental results. 4. Operating Conditions
Real aircraft engine conditions are characterized by high Reynolds and Weber numbers providing highly turbulent flow conditions and finely atomized droplets. A detailed investigation requires a high resolution in time and space,
challenging for both simulations and experiments. For the present study a mod-
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erate operating point with a comparatively low Reynolds- and Weber number
has been selected. It corresponds to altitude relight conditions and enables an adequate resolution of the breakup events in both investigations. It is therefore suitable for a reliable comparison of the numerical and experimental results. The operating conditions are summarized in Tab. 3. The gas Reynolds num-
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ber Reg is formulated with the half height of the channel δ as Reg = ug δ/νg . Here, ug and νg describe the velocity and the kinematic viscosity of the gas 2
phase. The film weber number, W er,ht = ρg (ug − ul ) ht /σ, considers the in-
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fluence of the density of the gas phase ρg , the velocity difference between gas and liquid as well as the surface tension σ. As characteristic length the prefilmer trailing edge thickness is utilized due to its impact on the breakup length
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identified by Gepperth et al. (2012). To classify the atomization process the momentum flux ratio between gas and liquid phase (M = ρg u2g /ρl u2l ) is also
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specified.
In the afore mentioned study by Gepperth et al. (2012) the influence of dif-
ferent properties of several liquids has been investigated besides the influence of
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geometrical parameters like prefilmer length and trailing edge thickness. From the investigated liquids Shellsoll D70 with a low surface tension at ambient conditions has been selected. The surface tension plays a decisive role as it antagonizes the disintegration. When the surface tension force is low, the interface behaves less stable and breakup events occur faster. Therefore the size of the
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Table 3: Operating conditions
Unit
Value
Reg
13,333
W er,hl
21.4
ρl /ρg
636.4
M
16.0
Gas properties m/s
ug
kg/m
1.2
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ρg
50 3
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Parameter
m /s
1.50e-05
m/s2
0.5
kg/m3
770
m2 /s
2.03e-06
2
νg
Liquid properties ul ρl νl
kg/s
0.0275
mm2 /s
50
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V˙ /b
M
σ
2
numerical domain can be kept small in the present investigation. In addition
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the physical properties of Shellsoll D70 are close to those of aviation fuels. The liquid volume flow rate per unit length V˙ /b is kept constant at 50 mm2 /s
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during both the experiment and the simulation. At the liquid inlet slit of the DNS domain the velocity is set to 0.5 m/s. In contrast, the bulk air velocity of
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the air is 50 m/s. 5. Qualitative Results In Fig. 14 a snapshot of the disintegrating liquid film obtained by the shad-
owgraphy is shown. A red rectangle illustrates the cross section of the DNS domain in comparison to the experimental field of view. Due to the numerical 29
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effort, the DNS domain is smaller and actually reduced to the primary breakup region. The domain covers 1 mm upstream and 5 mm downstream of the prefilmer trailing edge in normal direction. In parallel to the trailing edge the
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domain measures 4 mm. In both investigations the following breakup process is observed: waves are formed on top of the prefilmer, transporting the liquid to the prefilmer trailing edge, where a reservoir is formed. Out of this reser-
voir elongated structures (ligaments) as well as bag like structures are formed, grow in size and finally break up into droplets. The droplets differ in their size,
small as well as big bulgy droplets are generated. During the atomization no
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dewetting of the prefilmer is observed.
Figure 14: Experimental field of view and the used image section of the size of the DNS
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domain for the comparison of the breakup phenomena
To visualize the breakup process, two different snapshot sequences are shown
in Fig. 15 and Fig. 16. The side- and topview of the experiment and the sim-
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ulation are shown. All image sections correspond to the dimensions of the numerical domain. The time lag between two numerical snapshots is 0.3 ms, which corresponds to every second high speed shadowgraphy image (frame rate 7 kHz). The time stamp of the first snapshot in Fig. 15 is set to 0 ms and serves as reference time.
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In the first sequence the formation of ligaments, arising from the liquid reservoir at the trailing edge, is visualized. The surface tension force can not counteract against the disintegration of the accumulated liquid so that the liquid
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starts to break up. Initial holes are formed and grow in time. Separated ligaments are left over, that are elongated deeper into the atomization region until parts of the ligaments are separated. In the experiment as well as in the simula-
tion varying ligament dimensions have been observed. Especially the maximum
length of single ligaments differs, a stable breakup length could not be identified. From the sideview of the numerical snapshots weak oscillations around
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the prefilmer (on the x-axis) are noticed. Thereby, a synchronous flapping of all ligaments along the prefilmer is not observed. This becomes apparent in the experimental sideview images, that capture a higher number of breakup events related to the increased experimental prefilmer width. The large variation in the ligament flapping leads to a strong overlapping and at least to a reduced sharpness of the sideview images.
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In the second sequence, starting at 2.9 ms, the ligaments have already been torn away. Out of the liquid reservoir a bag is formed by the gaseous flow,
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that increases particularly fast and finally bursts. The rim of the bubble-like structure is more stable and remains attached to the reservoir for a short time, before it disintegrates into ligaments or bigger droplets. The generation of
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bubbles occurs fast compared to the ligament formation in Fig. 15. From 2.9 ms to 3.1 ms the bag observed in the numerical snapshots has already been bursted
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and a second bag has started to develop close to the trailing edge. The same dynamic is noticed in the experiment: at 2.86 ms only the rim of the bag is
visual, at 3.43 ms a new bag is generated, that has already been bursted at
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3.72 ms. The disintegration of the bags or bubble-like structures results in the generation of multiple droplets and is more intensive compared to the ligament breakup. In conjunction with the formation of bags, strong oscillations around the prefilmer are visible. The investigations showed that the bags are formed alternating up- and downwards, according to an oscillation to the right and to the left in the sideview snapshots. However, similar to the ligaments this 31
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appears to be a stochastic process and flapping of all generated bags to the same side of the prefilmer with the same frequency is not observed. It should be noted that no continuous liquid sheet is developed behind the
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prefilmer. The bags and ligaments arise directly from the accumulated liquid at the trailing edge, flapping not in phase. As a consequence it is hard to identify
a global oscillation frequency as it is typical specified for flat sheet atomizer
designs. In addition, the bags and ligaments along the prefilmer do not start to
develop at the same time, whereby the spanwise spacing between ligaments or bags is changing permanently. The inter-ligament distance is strongly affected
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by separating or new arising ligaments and bags at varying positions.
With a momentum flux ratio of 16 the primary breakup of the analyzed operating point is located inside the torn sheet breakup regime according to the breakup regime classification by Fernandez (2010). The classification is oriented to the morphological aspects of the breakup instead of instability mechanisms. Fernandez specified a momentum flux ratio between 5 and 22 for the torn-sheet
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breakup. Typically, the liquid sheet is eventually torn away due to the shear effect by the gaseous flow. The generation of longitudinal streamwise ligaments,
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irregular shaped, and the formation of big bulgy droplets is also significant for the torn-sheet regime. Referring to the images in Fig. 15 and Fig. 16 a wide
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range of droplet sizes, including big bulgy droplets are generated.
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x
y
z
y
z
x
z
0.0 ms
0.3 ms
M
0.29 ms
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0.0 ms
z
0.6 ms
0.86 ms
0.9 ms
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0.57 ms
33 Figure 15: Disintegration sequence at the atomizing edge with ligament formation. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation
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x
y
z
y
z
z
2.9 ms
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2.86 ms
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3.1 ms
M
3.14 ms
x
z
3.4 ms
3.72 ms
3.7 ms
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3.43 ms
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Figure 16: Disintegration sequence at the atomizing edge with the formation of bag like structures. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation
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6. Quantitative Results Quantitative data are obtained in order to compare the numerical and experimental results. The accumulated liquid film at the trailing edge is characterized
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by its breakup length and its streamwise deformation velocity. The analysis pro-
cedure to extract those quantities is presented, providing a consistent definition for the numerical and experimental results. As the numerical results are linked
to a predefined threshold for the liquid volume fraction α (see section 3), the influence of this parameter on the numerical results is additionally discussed. Finally the droplet sizes and droplet velocities are compared. In addition to
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their mean values the distributions of all compared quantities are presented. 6.1. Characterization of the accumulated liquid
The analysis of the accumulated liquid is based on the phase interface. For the experimental investigation the analysis procedure is included in the software by Müller (2015), utilized for the post-processing of the shadowgraphy
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images. The analysis of the numerical results has been implemented in the post-processing routine introduced in section 3.3. Both algorithms follow the
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same procedure to determine the breakup length and the streamwise deformation velocity as described in the following section. The expansion of the liquid film into the atomization region is quantified by
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the length of ligaments, arising from the accumulated liquid. A single ligament length Lstr is defined as the distance between the ligament peak and the trailing
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edge of the prefilmer. The mean value of all ligament lengths is defined as the breakup length Lbu . Ligaments are identified as maxima of the phase interface plot. A central
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aspect is a well-defined choice of the detected maxima to suppress repeated counting of ligaments with a wrinkled contour. As a criterium a minimum distance between adjacent minima and maxima of 50 µm is predefined to obtain a more global behaviour, as illustrated in Fig. 17. The choice of the minimum distance is always a trade-off, as also small ligaments close to the trailing edge should be detected. 35
1
1
2
2
3
3
4
4
5
5
6 −2
−1
0 [mm]
1
2
6 −2
−1
0 [mm]
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0
[mm]
0
1
2
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[mm]
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(a)
(b)
Figure 17: Peak detection for the phase interface (a) and the effect of a minimum distance of 50 µm (b) for the analysed operating point
The breakup length is obtained as a mean value of several snapshots, using
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the current length of each ligament. This means a significant modification for the analysis of the numerical results in relation to previous studies by Sauer
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(2014), where the breakup length was defined as the maximum ligament length taken from a series of time steps. The analysis procedure has been started after the first breakup event occured.
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In case of the simulation ligaments attached to the sides of the numerical domain are not included in the analysis. Due to the slip condition, mentioned in section 3.2, these ligaments are prevented from breaking through the sides.
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In the simulation no significant deviation in the ligament development has been observed for ligaments in the vicinity of the sides or in the center of the domain,
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as the dominating expansion is in the streamwise direction. However, to avoid any errors, these ligaments are neglected. To determine the streamwise velocity of the continous liquid film in the
experiment the displacement of the phase interface between two timesteps is used. This approach is also adapted for the numerical results, providing an identical definition of the deformation velocity. The unique assignement of a 36
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specific interface point at two consecutive timesteps t1 and t2 is difficult due to variations in the wrikled contour or the seperation of liquid structures. In order to simplify the calculation, the determination of the displacement of each
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interface point is replaced by utilizing only the most remote interface point zmax per y-position at t1 and t2 . The streamwise deformation velocity at position yi is then calculated as udef,i = zmax,yi (t2 ) − zmax,yi (t1 )/(t2 − t1 ).
Fig. 18 illustrates the phase interface contour at two consecutive timesteps
and a cumulative distribution of the calculated velocities. Negative velocities indicate the separation of liquid structures (E1), whereas very high velocities
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indicate the expansion or movement of a ligament to the side, leading to an overestimation of the displacement at a close-by y-position (E2). The maximum velocity per frame or timestep is well represented by the 90 %-quantile, its mean
value of all timesteps provides the characteristic deformation velocity udef,str of
E2 Udef,i [m/s]
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E2
E1 N/N total
y [mm]
(a)
(b)
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z [mm]
E1
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the investigated operating point.
Figure 18: Time displacement of the phase interface and ambiguities by its determination
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6.2. Breakup length and deformation velocity The breakup length Lbu and the deformation velocity udef,str determined
from the experiment and the DNS are summarized in Tab. 4. For their determination the phase interface position is required, that is found by a predefined liquid volume fraction (α = 0.5) in case of the simulation. In oder to study the 37
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sensitivity of the numerical results against α, additional thresholds have been utilized in the post-processing routine described in section 3.3. In Tab. 4 the numerical results for α = 0.5 and α = 0.01 are shown and compared to the
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experimental results. Table 4: Characteristic values for the accumulated liquid
α = 0.5
α = 0.01
Lbu [mm]
3.2
2.2
2.7
udef,str [m/s]
15.7
8.2
14.4
fbu [1/s]
4906.3
3727.3
5259.3
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Experiment
The breakup lengths of the DNS are a little smaller, albeit all breakup lengths are in the same order. For a better understanding of the determined
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values, the distribution of the ligament lengths is provided in Fig. 19. In the experiment a small amount of ligaments greater than the DNS domain (Lbu > 5 mm) are observed, leading to a greater breakup length. In the simulation the
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accumulated liquid reaches the outlet of the computational domain at no time step, the maximum ligament length measures 4.8 mm. Nevertheless, a reliable prediction of a maximum ligament length is difficult, due to the size of the
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numerical domain in streamwise direction. The long ligaments detected in the experiment are single structures, typically with a very thin connection to the
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liquid film. They appear occasional and can be detected by shadowgraphy due to a greater time period of recording. It is based on 300 frames with a time span of 100 ms between each frame. In contrast to that, the numerical results
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of 190 time steps with a time span of 20 µs are analyzed. Due to the numerical effort, the physical simulation time is kept short and a time span corresponding to the experiment is not feasible. The variation of the numerical threshold for the volume fraction implies
a displacement of the interface and has an effect on the numerical results by
38
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0.3
0.2
0.1
0 0
5 Lstr [mm]
0.2
0.1
0 0
10
Experiment Sim. α=0.01
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Experiment Sim. α=0.5 N/Ntotal
N/Ntotal
0.3
5 Lstr [mm]
10
Figure 19: Distribution of the ligament length 0.2
0.15
N/Ntotal
0.1 0.05
Experiment Sim. α=0.01
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total
0.15 N/N
0.2
Experiment Sim. α=0.5
0.1
0.05
0 0
20 40 Udef,str [m/s]
60
0 0
20 40 Udef,str [m/s]
60
M
Figure 20: Distribution of the deformation velocity
principle. As the grid resolution is small compared to ligament lengths the
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influence by the interface smearing is minor. Critical is the point of separation, when the connection between a ligament and the remaining accumulated liquid
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becomes very thin and is finally below the grid resolution. If α is reduced, the separating ligament is seen attached a few more timesteps, while it is further expanded in the streamwise direction. This effect is seen in the ligament length
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distribution for α = 0.01. The threshold is extremely low and illustrated as a lower bound. However, as illustrated in Fig. 21, the overall impact on the characteristic value for the breakup length is small. The deviation from Lbu (α =
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0.5) is smaller than ±7 % in the range of 0.1 < α < 0.9 and comparable to the experimental measurement uncertainty.
As specified in Tab. 4, a twice as high deformation velocity is measured
in the experiment in comparison to the DNS, if α = 0.5 is predefined for the phase interface. In contrast to the breakup length, a significant impact of the α39
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16
L [mm] bu
U
[m/s]
def
8
4
0
0.2
0.4
α
0.6
0.8
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12
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Figure 21: Sensitivity of breakup length and deformation velocity dependent on the liquid
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fraction α
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(a)
(b)
(c)
Figure 22: Representation of bubbles in the experiment (a) and the simulation with α=0.5
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(b) or α=0.05 (c)
threshold on the deformation velocity has been noticed, analyzing the numerical
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data. Reducing this threshold, the velocity distribution expands to greater velocities, assimilating the experimental distribution as shown in Fig. 20. The deformation velocity at several α-values is shown in Fig. 21. A moderate change
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for the deformation velocity is observed down to α = 0.2. Below this value, the velocity rises steeply, reaching a value of nearly 15 m/s at a liquid volume fraction of 1 %. It is presumed that the influence on the velocity can be attributed to an insuf-
ficient resolution of bubbles, arising from the accumulated liquid (see section 5).
40
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A typical bubble, observed during the experiment, is shown in Fig. 22(a). It is characterized by a thicker rim and a bag formed by a very thin liquid film. Typically, these bags rise faster than the rim into the atomization region and reach
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high velocities when they burst. In the simulation bag-like structures are also observed, but as the bags grow and the liquid sheet becomes thinner, a suitable resolution is hard to achieve. This is visualized in Fig. 22(b) and Fig. 22(c).
Considering a low threshold of α, the liquid film of a bubble is visible and higher velocities are observed.
As discussed in section 5 a global oscillation frequency is hard to determine
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as no continuous flapping sheet exists behind the trailing edge. As an alternative
the mean breakup frequency is calculated as a measure for the time distance between consecutive atomization events. It is directly obtained from the deformation velocity and the breakup length as fbu = udef /Lbu . For the analyzed operating point the frequency is in the range of 5000 1/s as specified in Tab. 4. Due to the variation of the deformation velocity for the DNS data only a range
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for the breakup frequency can be determined.
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6.3. Droplets
For the design of a combustion chamber the properties of the droplets generated by the airblast nozzle are a valuable information. The droplet size distribu-
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tions from the experiment and the simulation are shown in Fig. 23. The droplet diameters are obtained 5 mm downstream of the trailing edge, corresponding to the outlet position of the numerical domain. This analysis position differs
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from preliminary experimental studies by Gepperth et al. (2012), in which the entire field of view has been taken as a basis. The adaption improves the com-
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parability of the experimental and numerical results. Similar to the liquid film analysis two sets of numerical droplet data are compared to the experimental results: droplet data regarding a predefined α-threshold of 0.5 and a minor one (α = 0.03). In all three cases droplets with a diamteter up to 300 µm are observed (Fig. 23). For the numerical results a high number of small droplets in the 41
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range of a few micrometers is noticeable. For α = 0.03 the shape of the distribution differs strongly from the experimental results. Sauer et al. (2016) defined the liquid detected by this low threshold as the atomized mass that is not re-
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solved by the grid. This definition promotes the localization of small subgrid droplets, that are also not detectable by the experimental resolution. Experiment Sim. α=0.5 Sim. α=0.03
0.03 0.02 0.01 0 0
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PDF [1/µm]
0.04
100
200 dd [µm]
300
Figure 23: Droplet size distribution: Comparison between experiment and simulation
The knowledge of the smallest droplets generated by primary breakup is
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a fundamental problem caused by the resolution limit of numerical as well as experimental investigations. From the numerical simulation a determination of the liquid mass, that is not resolved by the numerical grid, is possible. As the
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VOF approach is mass conservative, the choice of the α-criterion defines how many mass is lost in the process. Each cell containing at least a volume fraction of α is taken into account for the droplet analysis. Droplets determined by
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α = 0.5 are defined as resolved droplets in this paper. For the quantification of the resolved liquid mass the droplet mass md at the outflow of the DNS
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domain is studied for varying α-values. In addition, the corresponding number of droplets Nd , passing through the outflow plane, is determined. The results
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are visualized in Fig. 24, normalized by their respective value taken at α = 0.01. The evaluation of the liquid mass depending on α shows that 80 % of the
total liquid mass are represented for α = 0.5. This mass is carried by 20 % of the liquid structures. It becomes evident that the large and mass carrying structures are resolved by the numerical grid, but that a resolution of the total liquid mass due to the huge amount of fine droplets is hard to achieve. Fig. 23,
42
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m /m d
d,total
N /N d
d,theo
1
0
0.2
0.4
α
0.6
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0.5
0.8
Figure 24: Small structure properties extracted at the eDNS outflow: droplet mass and number of droplets
which depicts the droplet distribution for α = 0.03, includes these fine droplets,
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not resolved, but estimated as atomized mass.
Comparing the numerical and experimental droplet data the definition of a minimum droplet size, detectable in both investigations, is useful. In the experiment the lower limit of a droplet diameter is 20 µm, assuming a resolution of a single droplet by two pixels. Neglecting all droplets with a diameter smaller
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than 20 µm for the numerical data, the droplet distributions in Fig 25(a) are obtained. A good agreement of numerical and experimental results is observed. As a resolution of 10 µm is already realized by the numerical grid, the choice of
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α has no specific influence.
0.03 0.02
0 0
Experiment Sim. α=0.5
0.15
0.01
CE AC
0.2
PDF [s/m]
Experiment Sim. α=0.5 Sim. α=0.03
PT
PDF [1/µm]
0.04
0.1 0.05
100
200 d [µm]
0 0
300
d
20
u [m/s]
40
60
x
(a)
(b)
Figure 25: Droplet distribution for diameter and streamwise velocity: Comparison between experiment and simulation
The droplet velocity distributions in the streamwise direction are shown in Fig. 25(b). The mean values of both investigations are of the same order, mea43
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suring 14.5 m/s for the experiment and 10.4 m/s for the simulation. Nevertheless a significant amount of droplets with a velocity above 15 m/s is observed in the experiment, leading to a wider distribution and a higher mean velocity as in
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the simulation. It is presumed that the insufficient numerical resolution of the bubbles leads to an underestimation of the droplet velocity in the vicinity of the atomizing edge. As the fast development of a bubble is not predicted completely (see section 6.2), a correct prediction of the droplet acceleration, induced by the bursting of bubbles, is also prevented.
80
40
150
300 dd [µm]
450
M
0 0
Experiment Simulation
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uz [m/s]
120
Figure 26: Scatter plot for the droplet diameter dd and the streamwise droplet velocity uz .
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A deeper insight into the droplet properties is obtained by the scatter plot of the droplet diameter and velocity in Fig. 26. Raw data is shown, including the small droplets (dd < 20 µm) in case of the simulation. In addition, high droplet
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velocities in the experimental data (50 - 115 m/s) that are found due to errors in the droplet detection algorithm, are not filtered. These high values correspond
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to a false detection of the same droplet in two consecutive images, leading to an overestimation in the droplet velocity. In the scatter plot a wider spread of the experimental droplet properties can be observed. This is due to a greater time
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period for the sampling, and therefore, a higher amount of samples compared to the simulation. Single droplets with a velocity up to 50 m/s are recorded as well as droplet diameters up to 500 µm. These droplets occur occasionally and
have no significant influence on the number based distributions. In contrast, the Sauter mean diameter (as a volume based quantity) is affected even by a small number of larger droplets. In the present study it measures 154.8 µm for the 44
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experiment and 128.1 µm for the simulation. To improve the statistics regarding very large droplets in the simulation, a greater simulation time is required. Nevertheless, comparing the number based distributions, a good agreement has
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been identified. 7. Conclusions
In this paper a detailed comparison of numerical and experimental results of the primary breakup of a prefilming airblast atomizer was presented. Particle and ligament tracking velocimetry based on back light illumination was applied
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in the experiment, whereas the embedded DNS methodology was utilized in the simulation. An operating point in the range of altitude relight conditions
has been studied. A detailed discussion of the observed breakup phenomena and quantitative results of the breakup length, the deformation velocity of the liquid accumulation, droplet sizes and droplet velocities demonstrated the com-
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parability of the results. To ensure a consistent definition of the characteristic dimensions in case of the liquid accumulation, the three-dimensional DNS data was reduced to the topview corresponding to the shadowgraphy images. There-
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fore, the same analysis procedure could be applied to the experimental and the numerical data. Both investigation methods provided a similar prediction of the primary breakup, but an underestimation of large ligaments and very large
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droplets could be identified for the simulation. As observed in the experiment, these liquid structures appear occasionally and have a minor effect regarding
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the total number of droplets or ligaments. The comparison clearly illustrates the challenges for the spatial resolution of a thin liquid film in the numerical investigation. Bubbles arising from the liquid reservoir at the trailing edge were
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insufficently resolved as they grow and the liquid film becomes thinner. A further grid refinement down to 5 µm is in the focus of a current study. For the comparison of the droplet data a minimum size of 20 µm was specified, cor-
responding to the resolution of the experiment. Based on this value a good agreement between numerical and experimental droplet data was found. The
45
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results confirm the applicability of both methods, offering a detailed insight in the phenomena of primary breakup during airblast atomization.
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Acknowledgment The authors would like to thank the German Research Foundation (DFG) for the financial support under the contract no. JA 544/39-1 and GRK 1344.
The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GSC Super-
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List of Figures Experimental setup (all units are represented in mm) . . . . . . .
8
2
Liquid accumulation at the atomizing edge . . . . . . . . . . . .
9
3
Detected liquid accumulation and droplets after data processing .
10
4
Calibrated droplet diameter as a function of the out-of-focus po-
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1
sition and reference diameter . . . . . . . . . . . . . . . . . . . . 5
12
Calibrated normalised intensity gradients as a function of the
out-of-focus position and reference diameter . . . . . . . . . . . . 6
15
Calculation of the real droplet diameter based on the normalized
16
7
The embedded DNS domain for an annular airblast atomizer . .
17
8
Geometry simplification of the airblast atomizer . . . . . . . . . .
18
9
Application of the eDNS concept to a planar airblast atomizer .
18
10
Impact of the inlet boundary condition variation on the pri-
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intensity gradient and the measured droplet diameter . . . . . . .
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mary breakup. Gas phase: u = 50 m/s, ρ = 3.9 kg/m3 , ν = 4.7 × 10−6 m2 /s. Liquid phase: u = 0.5 m/s, ρ = 650 kg/m3 ,
19
Geometry and grid of the turbulent channel . . . . . . . . . . . .
21
12
Computational domain of the planar prefilmer . . . . . . . . . . .
24
13
Reducing three-dimensional DNS data to a plot of the interface .
27
14
Experimental field of view and the used image section of the size
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.
11
ν = 2.9 × 10−6 m2 /s, σ = 0.0085 kg/s2 . Prefilmer: h = 50 µm.
of the DNS domain for the comparison of the breakup phenomena 30 Disintegration sequence at the atomizing edge with ligament for-
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15
mation. From left to right: Sideview experiment, topview exper-
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iment, topview simulation, sideview simulation . . . . . . . . . .
16
33
Disintegration sequence at the atomizing edge with the formation
of bag like structures. From left to right: Sideview experiment, topview experiment, topview simulation, sideview simulation . . 17
34
Peak detection for the phase interface (a) and the effect of a minimum distance of 50 µm (b) for the analysed operating point
53
36
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18
Time displacement of the phase interface and ambiguities by its 37
19
Distribution of the ligament length . . . . . . . . . . . . . . . . .
39
20
Distribution of the deformation velocity . . . . . . . . . . . . . .
39
21
Sensitivity of breakup length and deformation velocity dependent
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determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
on the liquid fraction α . . . . . . . . . . . . . . . . . . . . . . . 22
Representation of bubbles in the experiment (a) and the simula-
tion with α=0.5 (b) or α=0.05 (c) . . . . . . . . . . . . . . . . . 23
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43
Droplet distribution for diameter and streamwise velocity: Comparison between experiment and simulation . . . . . . . . . . . .
26
42
Small structure properties extracted at the eDNS outflow: droplet mass and number of droplets . . . . . . . . . . . . . . . . . . . .
25
40
Droplet size distribution: Comparison between experiment and
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
40
43
Scatter plot for the droplet diameter dd and the streamwise droplet
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velocity uz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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List of Tables 1
Characteristic parameters of the optical configuration . . . . . .
2
Non-dimensional grid spacings for the turbulent channel. Reg =
13 22
3
Operating conditions . . . . . . . . . . . . . . . . . . . . . . . . .
29
4
Characteristic values for the accumulated liquid . . . . . . . . . .
38
AC
CE
PT
ED
M
AN US
CR IP T
13, 333, Reτ = 777. . . . . . . . . . . . . . . . . . . . . . . . . . .
55