Multi-plume sprays interacting with subsonic compressible gas jets

Applied Energy 190 (2017) 623–633

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Multi-plume sprays interacting with subsonic compressible gas jets Abbas Ghasemi a, Aaron Pereira a, Xianguo Li a,⇑, Yi Ren b a b

Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada General Motors Company, Pontiac, MI, USA

h i g h l i g h t s
Multi-plume sprays injected in subsonic compressible cross-flow jets are studied.
Simulated spray topology and the volumetric shadowgraphy images agree well.
Numerically predicted droplet velocities agree well with the PIV measurements.
Presence of the cross-flow jet produces finer droplet sizes in a shorter time.
Velocity and pressure field of the cross-flow jet is altered by multi-plume spray.

a r t i c l e

i n f o

Article history: Received 14 July 2016 Received in revised form 3 January 2017 Accepted 4 January 2017

Keywords: Spray LES Shadowgraphy PIV Jet Cross flow

a b s t r a c t Injection of multi-plume sprays into subsonic compressible cross-flow jets is commonly encountered in practical applications and it is investigated experimentally and computationally in this study for the Mach numbers of 0.35 and 0.58. It is shown that comparing with the volumetric shadowgraphy images, the instantaneous topology of the sprays issued into the cross-flowing jets is well resolved by the present large eddy simulation (LES) with the Eulerian-Lagrangian multiphase formulation. The droplet velocities obtained from the simulations compare well with the particle imaging velocimetry (PIV) measurements. Compared to the multi-plume spray evolution in a stagnant ambient, the presence of the cross-flow jet is found to accelerate the break-up and produce smaller droplets. The individual spray plumes are found to penetrate symmetrically with respect to the central plane of the cross-flow jet. The penetration of the multi-plume sprays into the core of the cross-flows is shown to alter the velocity and pressure field of the compressible jet. Ó 2017 Published by Elsevier Ltd.

1. Introduction In many of the industrial applications atomization of fuel sprays is used to produce droplets with high surface area to volume ratios to promote rapid vaporization. The ability of a fuel nozzle to promote atomization in stagnant air is dependent mostly on the fuel properties and the injection itself, with the disintegration of the liquid column and larger droplets being attributed to instabilities in the fluid. In single plume spray injection into stagnant air, various ambient [1,2] and injection conditions [3] affect the mixture formation. However in a real in-cylinder environment, combustion chamber flow pattern [4,5] plays an important role in mixture formation. In many conditions, interaction of spray with air flow in the combustion chamber is similar to cross flow effect which has

⇑ Corresponding author. E-mail addresses: [email protected] (A. Ghasemi), Xianguo.Li@uwaterloo. ca (X. Li). http://dx.doi.org/10.1016/j.apenergy.2017.01.008 0306-2619/Ó 2017 Published by Elsevier Ltd.

been reported in previous studies [6,7]. Also the tumble flow effects at high temperatures on the spray evolution are numerically investigated near the intake ports of the gasoline direct injection (GDI) engine [8]. Using particle imaging velocimetry (PIV) and Mie scattering of fuel droplets, Stiehl et al. [9] studied the instantaneous features of the combustion chamber flow and the consequent effects on spray evolution. Also, cycle-to-cycle variation of the air flow and the spray interaction with the tumble flow are investigated using PIV measurements [10]. There have been numerous studies on the single plume spray evolution in cross flow. Leong et al. [11] noted that the injection of fuel transversely into a gaseous cross-flow with sufficiently strong momentum is one method of inducing additional instability to promote atomization. Mashayek and Ashgriz [12] further explains that the penetration of the liquid jet into the cross-flow allows for an increased exposure of the jet to the air flow and as a result is one of the main characteristics of a liquid column in a cross-flow. This momentum ratio is typically used to describe the

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Nomenclature dp D Dj F FD Gðr; xÞ kr Po Pinj pm q Sm t t u

droplet diameter nozzle diameter cross flow jet nozzle diameter momentum source drag force filter function residual kinetic energy ambient pressure injection pressure modified resolved pressure momentum ratio mass source time non-dimensional time continuous phase velocity

ability of the cross-flow to deflect or change the spray trajectory [12]. Increasing momentum ratio means higher fuel spray momentum which leads to a greater penetration into the air flow and less deflection, while the opposite holds true for lower values. The aerodynamic forces, which impact the liquid jet as it penetrates the cross-flow, also serve to change the cross-sectional shape of the liquid jet. Due to the aerodynamic forces, liquid jet with an initially circular cross-section, begins to flatten until eventually the cross-section resembles a fish-head structure [12]. During the deformation of the liquid column, surface waves and internal waves lead the column to break up into ligaments and large droplets. Desantes et al. [13] also studied the deflection angle and entrainment of gaseous jets and sprays in cross-flow. The effect of the Reynolds number on the spray axis is also considered in the work of Amighi et al. [14] who considered the effects of elevated pressures and temperatures of the cross-flow on the centerline trajectory and the windward boundary trajectory. Unlike above mentioned studies in which cross-flow acts normal upon the liquid column, there have been studies on the injection of the spray in cross flow with an angle [15,16]. In multi-plume sprays, an important parameter is whether the plumes are interacting [17] or develop independently. At the presence of a cross flow, there is a high level of interaction between the plumes due to the deflection of the spray axes. Due to the shaping of the injector multi-plume sprays experience interaction between jets under ambient conditions. Abraham noted that there exists an optimum angle between adjacent jets, and decreasing this angle resulted in increased jet to jet interaction with decreased mixing. Furthermore, Yu et al. [18] studied the behavior of multiple jets aligned in tandem when exposed to a cross-flow. In this study the initial cross-flow velocity varied from 0.04 to 0.28 m/s with the jet velocity ranging between 59.8 to 89 m/s. The results suggest that the leading jet has a sheltering effect on the downstream jets and that there exists a reduced effective cross-flow velocity which acts on the subsequent downstream jets. This velocity was found to depend on the velocity ratio between the cross-flow and the liquid jet as well as the spacing between the spray plumes. Spray plume trajectories were predicted until the point where the multiple spray plumes merge. Survey through the literature reveals that an investigation into multi-plume injections into high velocity cross-flows in the order of Ma = 0.58 and injection pressures in the range of practical operating conditions of internal combustion engines is necessary, and it is the subject and focus of the present study. Present work is a continuation of our recent experimental and LES study of multi-plume

up particle velocity U inj injection velocity xi ðx1 ¼ X; x2 ¼ Y; x3 ¼ ZÞ Cartesian coordinate DP injection pressures difference D minimum grid size dij Kronecker delta function la air viscosity m kinematic viscosity qa air density ql liquid density r surface tension sRij residual stress tensor srij anisotropic residual stress tensor
ðxi ; tÞ filtered (resolved) field u u0 ðxi ; tÞ residual (sub-grid) field

sprays in stagnant ambient air [19]. Also, we have studied the characteristics of the compressible starting jets [20] and their impact on multi-plume sprays [21]. Therefore, the present study aims at integrated computational and experimental investigation of the multi-plume spray interaction with a steady compressible subsonic air jet. The liquid fuel is pressurized in fuel injection system through a commercial multi-hole fuel injector up to Pinj/Po = 150. Using a volumetric imaging technique, the multi-plume spray development into the shear layer of the air jet is visualized. In addition, PIV is used to characterize the droplet velocity field. Finally, Eulerian-Lagrangian multiphase methodology is conducted along with large eddy simulation (LES) of the gas field to obtained detailed flow structures present in multi-plume sprays in crossflow.

2. Computational setup 2.1. Numerical approach Liquid spray development and interaction with its ambient gas field is solved using Lagrangian-Eulerian (LE) multiphase method [22]. Discrete liquid particles injected into the domain are represented by Lagrangian description. Eulerian concept is adopted in terms of mass, momentum and energy conservation equations in order to account for the gas field dynamics. Proper differential equations are solved using a control volume approach in a space xi ðx1 ¼ X; x2 ¼ Y; x3 ¼ ZÞ time (t) framework. The temporal variations of the desired parameters in Navier-Stokes equations are needed to be properly subjected to turbulence effect. In Reynolds-Averaged Navier-Stokes (RANS) equations eddyviscosity [23] based turbulence models are implemented. The averaging process involved in the derivation of RANS equations as well as the isotropic presumption does not allow for obtaining information associated with the instantaneous flow dynamics. Alternatively, large eddy simulation (LES) [23] can be carried out which allows for the direct resolving of the large scale flow quantities. The finer unresolved structures are filtered out [23] and need to be modeled. In order to filter a flow quantity uðxi ; tÞ, it can be decomposed into resolved (filtered) element uðxi ; tÞ and sub-grid scale (residual) u0 ðxi ; tÞ element. The filtered (resolved) field, is obtained through the convolution integration uðxi ; tÞ ¼ R Gðr; xÞuðx  r; tÞdr over the flow field. To simplify the integration, the filtering function Gðr; xÞ can be considered homogeneous and independent of x [23]. In such a case, a typical Gaussian filtering

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 2   2 in which D is function takes the form of GðrÞ ¼ p6D2 exp  6r D2 the specified filter width. Validity of the statement R Gðr; xÞdr ¼ 1, guarantees normalization of the filter function. In large eddy simulation of compressible flows, Favre-averaging (dene ¼ qu sity based weighting) is conducted using u q in which q is density. Therefore, the Navier-Stokes equations governing conservation of the mass, momentum and energy of the filtered variables in a unsteady compressible viscous flow are as follows:

@ q @ðq~xi Þ ¼ Sm þ @xi @t

ð1Þ


@ rij @ qsrij ~ i @ qu ~i u ~j @ qu @p ¼ þ  þF þ @xi @xj @t @xj @xj

ð2Þ

~ j q~e ~ ~ @ q~e @ u @u @u @ @ Te
j þ rij i þ ¼ p K þ @xj @t @xj @xj @xj @xj ! X @ yf @ þ qDa hm m þ S @xj @xj m

!

ð3Þ


denote Cartesian coordinates, the here xi ðx1 ¼ X; x2 ¼ Y; x3 ¼ ZÞ, ui , p local fluid velocity vector and the filtered pressure, respectively. The source terms Sm and F in the above equations account for the exchange of mass and momentum between the gas and liquid phases, respectively. In Eq. (3), e, Da , K, hm , ym are the specific internal energy, diffusion coefficient, gas thermal conductivity, specific enthalpy and species mass fraction, respectively. Using   ~ rij ¼ l @@xu~ji þ @@xuij  23 dij @@xuek , the viscous stress tensor can be evaluated k

in which dij denotes the Kronecker delta function. In the residual ~i u ~ j ), the two terms subgrid-scale (SGS) stress tensor sRij ¼ qð ug i uj  u ~i u ~ j should be distinguished. The anisotropic part of the ug i uj and u

srij ¼ sRij  23 kr dij is evaluated using the dynamic Smagorinsky-Lilly SGS model [24]. Here, kr ¼ 12 sRii gives residual-stress tensor

the residual kinetic energy. At each time step, the resolved quantities of the filter field are adopted in the dynamic updating of the Smagorinsky model constant [24] according to Germano et al. [25] and Lilly [26]. To benefit simultaneously from the central differencing and upwinding schemes, the convective terms in the momentum and energy equations are spatially discretized by a blended scheme. A blending factor of 0.55 is considered where 0.5 and 1 are associated with the second order central differencing and first order upwinding, respectively. Pressure and velocity are coupled employing a modified pressure implicit with splitting of operators (PISO) [27] scheme based on a predictor-corrector technique. Temporal discretization is fulfilled by second order accurate Crank-Nicolson time marching algorithm. The time step dt ¼ 1  107 s was selected to reflect an accurate and stable solution based on the Courant–Friedrichs–Lewy (CFL) criterion. A CFL criterion less than unity limits the time step so that the solution does not spatially evolve more than a certain cell size (D). Dependpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ing on the liquid injection velocity ðU inj ¼ 2ðPinj  Po Þ=ql Þ, the conU

dt

vection CFL number CFLu ¼ injD was evaluated to be 0.17 and 0.14 for Pinj/Po = 150 and Pinj/Po = 100 injection pressure ratios, respectively. Similarly for the cross jet convection, the stability criterion U dt

CFLu ¼ Dj yields values of 0.18 and 0.1 for Ma ¼ 0:58 and Ma ¼ 0:35, respectively. Unlike Eulerian description of the gas phase using fixed control volumes, each liquid droplet travels as a singular control mass through the continuous medium. These discrete liquid particles, continuously exchange mass, momentum and energy with the corresponding local environment. Droplet velocity is reduced as a

625

result of the drag force induced by the gas field [28]. Droplet mass may diffuse into the gas field due to the concentration gradient at the liquid/gas interface. Droplet vaporization is also affected by temperature through the variation of the liquid vapor pressure and mass diffusion coefficient. Diffused fraction of the vaporized liquid mass is transferred to the local environment as a source term in the mass conservation equation. As mentioned earlier the liquid particles influence the gas field through the source terms added to the conservation equations. On the other hand, the boundary conditions for the liquid particles are influenced by the local gas field variables [29]. Another important aspect of the Lagrangian treatment of the droplets is the implementation of Newton’s second law for tracking the droplet path as shown below:

dup 3 qa jurel j CD urel þ g i þ F x ¼ 4 ql dp dt

ð4Þ

where u denotes the local gas velocity, up is the velocity of the droplet and qa is the instantaneous local density of air. Also, g i is the gravitational acceleration, and any other forces acting on the droplet may be accounted for by the acceleration term F x . The drag coefficient of the droplet is given

(

C D;sphere ¼

0:424 Red > 1000   2=3 24 1 1 þ 6 Red Red < 1000 Re

ð5Þ

d

Red ¼

qa dp jurel j la

C D ¼ C D;sphere ð1 þ 2:632nÞ

ð6Þ ð7Þ

In Eqs. (5) and (6), Re, la , ql , and dp denote the relative Reynolds number, molecular viscosity of the air, liquid density and droplet diameter, respectively. Eq. (7) modifies the drag coefficient due to the droplet distortion from spherical shape. Distortion parameter varies between n ¼ 0 and n ¼ 1, and is according to the Taylor analogy break-up (TAB) model [29]. Spherical droplets are characterized with n ¼ 0 and n ¼ 1 for completely flattened drops. 2.2. Grid generation and CFD solver CONVERGE CFD solver is implemented to simulate the multiphase phenomena taking place in the interaction of multi-plume fuel sprays injected into a cross-flow air jet. Computational domain used for the present study is shown in Fig. 1. The domain dimensions are expressed based on the spray nozzle diameter (D) and cross flow jet nozzle diameter (Dj). The computational domain diverges with the downstream distance of the cross flow jet. This expansion of the domain is presumed based on the expected evolution of the cross flow jet in the downstream. The multi-plume spray is injected into the shear layer of the cross flow jet at a location of X/Dj = 1.36 downstream of the air nozzle exit, at the injection pressure ratios of Pinj/Po = 100 and Pinj/Po = 150, respectively. Adaptive mesh refinement (AMR) is launched during the runtime to locally refine the base Cartesian grid in the high curvature and large gradient zones in which sub-grid scale of flow quantities [30,31] becomes higher than a desired threshold. Implementation of AMR is practically a very efficient approach for large eddy simulation in which local filtering can be controlled by the adapted grid size. As an illustration, Fig. 2 displays how the grid can be locally refined. Generation of a proper grid for large eddy simulation is achieved based on the speculated intention of LES that is to directly resolve the large scale quantities and sub-grid scale modeling of fine scales. Accordingly, definition of fine and large scales is established through the context of turbulence energy cascade. As stated in [23], greater part of dissipation comes about by length scales ranging 8–60 times the Kolmogorov length scale. It

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was also proposed that a remarkable resolving of the large scales would be achieved in filter resolutions down to 12 times Komogorov length scale. Despite the above mentioned criteria, it is not always feasible to reach that fine level of resolution due to several reasons such as domain extent and complexity of the flow as well as the computational resources. For instance, in the present study there are several issues that can be pointed out. Firstly, we are dealing with a complex multiphase flow field generated by multi-plume sprays and a turbulent compressible jet. Secondly, the ratio of the turbulence length scales (even in the integral range) produced by the cross jet and individual liquid sprays are significantly large (in the order of Dj =D  122). Thirdly, as shown in Fig. 1, the extent of the computational domain is in the order of thousands of spray nozzle diameters while it allows only for 16 air nozzle diameters which can only cover developing region of the air jet. For the case of Lagrangian/Eulerian spray modeling, the study by Senecal et al. [32] proposes a favorable range of minimum grid size (filter width). For the spray nozzle diameter D and filter width of D, they studied a range of DD ¼ 0:07  4:48. The optimum range they proposed to produce relatively reasonable flow structure was DD ¼ 0:72  1:44. It should be noted that this grid size was recommended for the LES of a single spray in quiescent conditions. Simulation of the present study is much more demanding and very fine mesh can result into enormous number of cells. Therefore, for the present study a minimum grid size of DD ¼ 1:32 was found to provide reasonable accuracy considering the available computational resources. 2.3. Modeling spray processes Fig. 1. (a) Computational domain (dimensions in spray nozzle diameter D and gas jet diameter Dj) in the truncated cone shape along the gas jet or X direction; (b) side-view (XZ) of the domain with spray, injector and gas jet illustrations with spray injected in the downward or Z direction.

Interactive liquid/gas dynamics induce the occurrence of various events and demand appropriate models in order to predict these events. A turbulent dispersion model [33] accounts for the effect of gas phase fluctuations on the liquid phase. Prediction for collision and coalescence events are obtained using No Time Counter (NTC) model of Schmidt and Rutland [34]. NTC provides higher accuracy in comparison with O’Rourke [35] model and is computationally more affordable. Heat absorption from the ambient gas by the liquid increases the liquid temperature and eventually contributes to the droplet vaporization [36]. Chiang et al. [37] model predicts the rate of change in droplet diameter because of liquid mass diffusion to the ambient. Occurrence of liquid break-up is known to be induced by Kelvin-Helmholtz and Rayleigh-Taylor instabilities. Information associated with the propagation of instability wave augmented at the liquid surface, can be obtained by the instability analysis of a cylindrical viscous liquid jet as shown by Reitz and Bracco [38]. Consequently, time scales intrinsic in the break-up process as well as the produced droplet diameters obtainable can be determined in line with the characteristics of the unstable interface [38]. An enhanced version of Kelvin-Helmholtz/Rayleigh-Taylor KH-RT model, implements a competing effect of the two principal instabilities to evaluate the corresponding time and length scales of the break-up [39]. 2.4. Liquid injection setup

Fig. 2. Typical adapted grid at the edge of a jet.

Fig. 3 displays the multi-orifice injector utilized for generating the multi-plume sprays. Orifices are properly numbered on the figure to be used in the forthcoming result discussions. The injector is a solenoid type with 6 orifices for fuel injection. Liquid sprays issue from the six nozzle holes distributed symmetrically around the minor and major axes of an ellipse. In Fig. 3, the orientation of

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Fig. 3. Orifice distribution and orientation of the spray injector with respect to the cross flow jet velocity Uj.

the orifices is suitably displayed using the coordinate systems with the origin located at the centroid of the orifices. Fuel is pressurized into the shear layer of the cross flow jets with the liquid injection pressure up to Pinj/Po = 100 and Pinj/Po = 150, respectively. IsoOctane ðiC8 H18 Þ is used as fuel in the present study with properties given in Table 1. It should be noted that the ambient and flow pressures and temperatures are lower than typical in-cylinder environments. This is due to the aim of the present study to investigate the cross-flow effects on the spray evolution in a standard and wellcharacterized ambient and flow conditions. As a validated benchmark, the present numerical solver can be further extended to account for the extreme engine pressure, temperature and flowfields which are difficult to analyze experimentally.

separate traversing systems as shown in Fig. 4b to allow for independent control of the location between the two components. In the present work, two main measurement set-ups were used. The first was for the purpose of planar techniques which include PIV and regular Mie scattered images. The second is for volumetric imaging of the spray plumes. The set-up used for the planar techniques orients the camera orthogonal to the axis of the cross-flow, such that it can capture the vertical plane. The laser sheet which defines the plane of interest and is used to focus the camera, illuminates the vertical plane along the air jet axis, and the spray axis. For the second technique of volumetric imaging, the camera remained in the same location and two stroboscopic lights each with a pulse width of 0.5–3 s were utilized to illuminate the spray plumes from underneath.

3. Results and discussions

3.1. Evolution of the multi-plume spray cloud into the cross flow

Computational results are compared with experimental measurements which is briefly described here. The experimental apparatus consists of two main components: the fuel delivery system and air delivery system. A commercial multi-hole injector is used to produce the multi-plume sprays. The injector holes oriented with different angles and six orifices are distributed in an elliptic pattern. A specially designed smooth contraction air nozzle considering the principles of wind tunnel test section design to provide a uniform and low turbulence jet [40,41] is used to provide a high velocity air jet. The air nozzle and fuel injector are placed inside the tunnel shown in Fig. 4a, with the front end remaining open to the ambient. The air nozzle and fuel injector were mounted onto

Before investigating the multi-plume spray development into the cross flow, it is worthwhile to have a brief description of the spray evolution in quiescent air as shown in Fig. 5 where t⁄ = tUinj/D is a non-dimensional time. Further details on the evolution of the multi-plume sprays in quiescent air can be found in [19]. Also liquid to air momentum ratio is defined as

Table 1 Fuel properties. Fuel type Density (kg/m3) Viscosity (Pa s) Surface tension (mN/m) Injection temperature

Iso-Octane (iC8H18) 697 0.0005 18.6 25 °C

q ¼ ql U 2inj =qa U 2j . In Fig. 5, one instance of the spray droplet cloud is shown at t⁄ = 303 after the start of liquid injection (ASOI) for the injection pressure of Pinj/Po = 150. In the absence of the cross flow jet, spray plumes evolve individually. The interaction between the spray plumes is not very significant and each plume expands due to the air entrainment in a manner similar to a single-plume spray injected into a quiescent ambient. In Figs. 6 and 7, the particle clouds obtained from the present numerical simulations are compared with the experimental shadowgraph images of the multi-plume sprays in cross flow jets for different non-dimensional times at the liquid injection pressure of Pinj/Po = 100 and 150, respectively. A very good qualitative agreement is observed between the computations and experiments as the multi-plume sprays evolve into the cross flow jet. It

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Fig. 4. (a) Experiment enclosure setup; (b) traversing system.

Fig. 5. Multi-plume spray at the injection pressure Pinj/Po = 150 in quiescent air (Uj = 0 m/s) at t* = 303 (after the start of liquid injection, or ASOI).

can be observed that the initial sprays relatively retain the multihole injection characteristics similar to the injections into a quiescent ambient. However, beyond this initial development the cores of the individual plumes tend to merge into a single cloud of droplets. For both Pinj/Po = 100 and 150 injection pressure ratios, the spray plumes are stretched more towards the downstream direction of the cross flow jets for the Mach number Ma = 0.58. Dispersion of the spray plume into a larger volume as well as finer droplet

formation can enhance air/fuel mixing distributed more uniformly in the domain. Near the edges of the plumes formation of the finer droplets can be noticed by lighter image intensity. On the other hand, near the spray deflected axis, higher image intensities are associated with a stronger liquid core at the presence of larger droplets and/or higher number density of droplets. In Fig. 8, mutual influence of the spray plume and the cross flow jet on one another is shown for the injection pressure of

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Fig. 6. Evolution of the multi-plume spray (liquid injection pressure Pinj/Po = 100) into a cross-flow air jet of Ma = 0.35 and 0.58, respectively, at the non-dimensional time of t* = 82.5, 330, and 577.5 (ASOI).

Fig. 7. Evolution of the multi-plume spray (liquid injection pressure Pinj/Po = 150) into a cross-flow air jet of Ma = 0.35 and 0.58, respectively, at the non-dimensional time of t* = 101, 404, and 707 (ASOI).

Fig. 8. Effect of multi-plume spray (injection pressure Pinj/Po = 100) on the cross flow velocity field for the Mach number of Ma = 0.35 at the non-dimensional time of t* = 825 (ASOI).

Pinj/Po = 100 and cross-flow air jet of Ma = 0.35 at the nondimensional time of t⁄ = 825 (ASOI). In a typical single phase jet, the velocity field is characterized by a potential core in the nearfield [42]. In the potential core higher velocity occurs near the centerline and lower velocity is observed near the edges of the jet as a result of interaction with the low velocity ambient. As a result of the jet entrainment [43], jet region tends to expand downstream. Boundaries of the jet, which can be defined based on the turbulent/non-turbulent interface [44], are subjected to contractions and expansions as well as a meandering (wavy) behavior. In the present study, the presence of the multi-plume spray alters the evolution of the air jet. As shown by the proper arrows in Fig. 8, edge of the jet is deflected inward and then outward by the spray plume, and a low velocity zone is observed near the centerline

from X/Dj = 2.2 to X/Dj = 3.8. It can also be seen that the jet potential core is broken down at X/Dj = 2.2. In a classical jet flow, the potential core break-down usually occurs between X/Dj = 4–6. Another important parameter in the study of any fluid flow is the pressure field which is shown in Fig. 9. Here the intermediate pressure field is filtered out since we are more interested in the high pressure and low pressure regions. The highest pressure occurs in region (A) as shown in the figure. Interestingly, the spray plume is acting similarly to a bluff body in front of the cross jet stream. Accordingly, the high pressure region (A) is serving as a stagnation point. There are also some localized low pressure zones appearing in the flow domain which belong to two categories. First category, which is illustrated as regions (B) and (C), is the low pressure formed inside the spray plumes. These regions are the cause

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Fig. 9. Effect of multi-plume spray (injection Pinj/Po = 100) on the pressure field for the cross flow jet velocity of Ma = 0.35 at t* = 825 (ASOI).

for the air entrainment into the spray plumes. This air suction into low pressure regions can enhance the air/fuel mixing. Second category of low pressure zones are observed in (D), (E) and (F). These low pressure regions (D, E and F), characterize the vortex cores formed in the shear layer of the cross flow jet. These vortex cores expand as moving downstream and eventually coalesce in the centerline due to the shear layer merging beyond the jet potential core. 3.2. Quantitative evolution of the multi-plume spray into the cross flow Fig. 10 displays a quantitative distribution of the droplet velocity (up) throughout the multi-plume spray cloud for the cross air flow with the Mach number of 0.35 at the air nozzle exit. PIV technique was adopted experimentally to obtain the droplet velocity distribution. Comparison is made against the PIV results for the corresponding velocity distribution achieved in the large eddy simulations for Pinj/Po = 100 and Pinj/Po = 150 at t⁄ = 825 and 1010 ASOI, respectively. It is observed that the maximum velocity occurs near the nozzle exit where the droplets still bear a large momentum and are not decelerated yet. It should be noted that this region is not well displayed in the experimental velocity field. This is because, in the particle image velocimetry, laser reflection from the injector tip results in poor imaging and generates spurious displacement vectors. In addition, the dense liquid core in the spray near field does not allow for a perfect tracking of individual droplets. Furthermore, care must be taken when comparing the LES against the PIV droplet velocity distribution. The PIV results present a rather 2D velocity field mainly similar to a planar averaging normal to the image plane. Another high velocity zone is observed

at the tip of the merged plume in the downstream of the cross flow jet. It should be noted that, spray plumes 2 and 5 are injected in the Y = 0 plane (see Fig. 3) and therefore are located into the cross flow jet central plane. This is particularly more evident for spray plume 2 which is the leading plume. Spray plume 2 gains more momentum from the cross flow jet and forms a high velocity region in the tip of the merged plume. On the other hand, for both Pinj/ Po = 100 and 150 injection pressures, a low velocity region is observed in the mid bottom region of the plumes. Attention must be paid that this low velocity region is formed due to the orientation of the injection associated with spray plumes 1, 3, 4 and 6. Sprays plumes 1, 3, 4 and 6 are injected outwards from the Y = 0 plane and travel towards the edges of cross flow jet rather than towards its potential core. Accordingly, either sides of the merged spray plume are decelerated due to the interaction with the low velocity gas field there. Another important parameter in the study of sprays is the temporal evolution of the tip of the spray. The complexity of the flowfield in a multi-plume spray injected into a high speed cross flow jet does not allow the experiments to produce detailed spatial and temporal information on the individual plumes. However, for the computations, the development of individual spray plumes pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðL ¼ X 2 þ Y 2 þ Z 2 Þ can be tracked independently. In Fig. 11, the penetrations of the individual plumes are presented for different injection and cross flow jet scenarios. For comparison purpose, the injection of the multi-plume sprays in a stagnant air at Pinj/ Po = 100 and 150 are shown in Fig. 11a and b, respectively. It can be seen that for both injection pressures all the plumes behave fairly similarly in penetration at the absence of a cross flow jet. On the other hand, at the presence of the cross flow jets different plumes penetrate differently. In spite of different penetrations,

Fig. 10. Droplet velocity distribution for Ma = 0.35: (a, b) q = 665 and Pinj/Po = 100 at t* = 825 (ASOI); (c, d) q = 991 and Pinj/Po = 150 at t* = 1010 (ASOI).

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Fig. 11. Temporal development of individual plumes (L) under different injection and cross flow scenarios (LES).

an interesting pattern is recognizable for all the cases. In all the cross flow cases, spray plume 2 obtains maximum penetration. This is due to the fact that spray plume 2 is injected as leading plume in the downstream direction of the cross flow jet. Consequently, with relatively little resistance from the other plumes, spray plume 2 travels farther downstream with the assistance of higher momentum available at the central plane of the cross flow jet as well as its original orientation. Conversely, spray plume 5 which is initially oriented towards the upstream and is also opposed by the cross flow central plane momentum has the lowest penetration. In addition, a similar penetration is observed for spray plume pair 1 and 3 as well as spray plume pair 4 and 6. However, spray plume pair 1 and 3 show a larger penetration compared to the pair 4 and 6. In general, individual tracking of the spray plumes as they penetrate suggests a symmetry with respect to Y = 0 plane. Variation of a representative droplet diameter with time can be helpful in monitoring the global break-up event. Among many representative droplet sizes, Sauter mean diameter (SMD) provides useful information about general fineness of a spray. SMD which

is an overall measure of droplet volume to surface ratio can be P 3 P 2 defined as ðSMD ¼ ni¼1 dp = ni¼1 dp Þ. In Fig. 12, the temporal variations of the SMD predicted by the simulations for Pinj/Po = 100 and 150 multi-plume sprays are shown under the effect of cross flow jets of Ma = 0.35 and 0.58. For a single plume spray injected into a stagnant air, break-up rate and droplet size distribution are related to liquid and ambient properties [45] such as liquid kinematic viscosity m [m2/s], surface tension r [N/m], liquid density ql [kg/m3], gas density qa [kg/m3] as well as injection pressure DP½bar. According to the above mentioned factors, Elkotb [46] proposed a correlation to predict SMD [micron]:

SMD ¼ 6156m0:385 r0:737 q0:737 q0:06 DP0:54 l a

ð8Þ

Since the spray plumes of the present study are not highly interacting while injected in the ambient air, this correlation is used for the validation of the final SMD values for the case Uj = 0 m/s. As it can be seen, in all of the cases droplets start to be issued relatively as large as nozzle size. This fact is substantially resulted from the

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Fig. 12. Effect of cross flow jet on the temporal SMD variation for Ma = 0.35 and 0.58: Simulation (Sim); analytical correlation (AN) [46].

droplet initialization method using the blob injection based on the nozzle diameter [29]. For all the cases, there is a sharp transition from the initially large droplet size to small droplet size as long as the aerodynamic inertia overcomes droplet surface tension. With reduced droplet size surface tension forces become dominant and it is hard to break-up droplets by the inertial forces. During this time instabilities generated at the liquid/gas interface are easily dampened by viscosity and no further break-up results in the asymptotic behavior of the SMD graph. In the absence of a cross flow jet (Uj = 0 m/s), this asymptotic trend approaches values predicted by the correlation of Eq. (8). However at the presence of the cross flow jets, it can be clearly seen that smaller droplet sizes are achievable. The finer spray droplets have an enhanced interfacial area resulting in improved fuel/air mixing. In addition, at higher cross flow velocities break-up occurs at a faster rate. This factor is important to be aware of since it is directly related to mixing timing and physical ignition delay. Rate of mixture preparation highly influences the ensuing processes such as ignition, combustion and pollutant formation in a spray combustion system. 4. Conclusions Interaction of multi-plume sprays with turbulent compressible subsonic cross flow jets is investigated experimentally and computationally. Shadowgraphy imaging as well as particle imaging velocimetry (PIV) is adopted to study the evolution of the multiplume sprays into the cross flow jets qualitatively and quantitatively. Large eddy simulation (LES) of the flow is carried out using Eulerian/Lagrangian multiphase approach. Instantaneous evolution of the shape of the spray in cross flow simulated by LES and imaged by volumetric shadowgraphy show good agreement. Furthermore, it is shown that the spray injection alters the instantaneous velocity and pressure fields of the cross flow jet. Comparing the droplet velocity distribution obtained from the present LES and PIV revealed the presence of the faster droplets near the core of the cross flow jet and slower droplets near the edges. In addition, individual spray plumes are found to penetrate symmetrically with respect to the central plane of the cross flow jet. Finally, in comparison with the evolution of the multi-plume spray in a quiescent ambient, the cross flow jet is found to enhance the droplet break-up by producing smaller droplet sizes in a shorter time. Acknowledgement This research is supported by Ontario Research Fund-Research Excellence Program under contract # ORF-RE-02-019, Natural

Sciences and Engineering Research Council of Canada (NSERC) via a Discovery Grant, and Ontario Centres of Excellence (OCE) TalentEdge Internship Program (TIP) under Project Number 25398. The authors would also like to thank Drs. Daniel Lee and Yunliang Wang of Convergent Science for their assistance in the numerical implementation. References [1] Roisman IV, Araneo L, Tropea C. Effect of ambient pressure on penetration of a diesel spray. Int J Multiphase Flow 2007;33:904–20. [2] Park SH, Kim HJ, Lee CS. Comparison of experimental and predicted atomization characteristics of high-pressure diesel spray under various fuel and ambient temperature. J Mech Sci Tech 2010;24:1491–9. [3] Djavareshkian MH, Ghasemi A. Investigation of jet break-up process in diesel engine spray modelling. J Appl Sci 2009;9:2078–87. [4] Ghasemi A, Djavareshkian MH. Investigation of the effects of natural gas equivalence ratio and piston bowl flow field on combustion and pollutant formation of a DI dual fuel engine. J Appl Sci 2010;10:1369–79. [5] Fukuda K, Ghasemi A, Barron R, Balachandar R. An open cycle simulation of DI diesel engine flow field effect on spray processes. SAE technical paper. No. 2012-01-0696; 2012. [6] Stanglmaier RH, Hall MJ, Matthews RD. Fuel-spray/charge-motion interaction within the cylinder of a direct-injected, 4-valve, SI engine. SAE Technical papers. 980155; 1998. p. 1-12. [7] Alger T, Hall M, Matthews R. Fuel spray dynamics and fuel vapor concentration near the spark plug in a direct-injected 4-valve SI engine. SAE technical papers 1999-01-0497; 1999. p. 1–18. [8] Liu Y, Shen Y, You Y, Zhao F. Numerical Simulation on spray atomization and fuel-air Mixing process in a gasoline direct injection engine. SAE technical papers 2012-01-0395; 2012. p. 1–18. [9] Stiehl R, Schorr J, Krüger C, Dreizler A, Böhm B. In-cylinder flow and fuel spray interactions in a stratified spray-guided gasoline engine investigated by highspeed laser imaging techniques. Flow Turbul Combust 2013;91:431–50. [10] Zhang X, Wang T, Jia M, Li W, Cui L, Zhang X. The interactions of in-cylinder flow and fuel spray in a gasoline direct injection engine with variable tumble. Flow Turbul Combust 2015;137:1–11. [11] Leong MY, McDonell VG, Samuelsen SG. Mixing of an airblast-atomized fuel spray injected into a crossflow of air Technical report CR2000-210467. NASA; 2000. [12] Mashayek A, Ashgriz N. Handbook of atomization and sprays, chapter atomization of a liquid jet in a crossflow. New York: Springer; 2011. p. 657–84. [13] Desantes JM, Arregle JJL, Garcia JM. Turbulent gas jets and diesel-like sprays in a crossflow: a study on axis deflection and air entrainment. Fuel 2006;85:2120–32. [14] Amighi A, Eslamian M, Ashgriz N. Trajectory of a liquid jet in high pressure and high temperature subsonic air crossflow. In: Proceedings of 11th international conference on liquid atomization and spray systems, Vail, Colorado, USA, July 2009. Paper no. 225. [15] Kim MK, Song J, Hwang J, Yoon Y. Effects of canted injection angles on the spray characteristics of liquid jets in subsonic crossflows. Atom Sprays 2010;20:749–62. [16] Costa M, Melo MJ, Sousa JMM. Spray characteristics of angled liquid injection into subsonic crossflows. Am Inst Aeronaut Astronaut 2006;44:646–53. [17] Ghasemi A, Barron R, Balachandar R. Spray-induced air motion in single and twin ultra-high injection diesel sprays. Fuel 2014;121:284–329. [18] Yu D, Ali MS, Lee JHW. Multiple tandem jets in cross-flow. J Hydraul Eng 2006;132:971–82. [19] Ghasemi A, Pereira A, Xianguo Li. Evolution of liquid and gas phases in multiplume spray injection. Int J Energy Res 2016.

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