Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Accepted Manuscript Experimental Investigation of a Developing Two-Phase Bubbly Flow in Horizontal Pipe M. Bottin, J.P. Berlandis, E. Hervieu, M. Lance, M. Marchand, O.C. Öztürk, G. Serre PII: DOI: Reference:

S0301-9322(14)00005-6 http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.12.010 IJMF 1991

To appear in:

International Journal of Multiphase Flow

Received Date: Revised Date: Accepted Date:

13 May 2013 17 October 2013 27 December 2013

Please cite this article as: Bottin, M., Berlandis, J.P., Hervieu, E., Lance, M., Marchand, M., Öztürk, O.C., Serre, G., Experimental Investigation of a Developing Two-Phase Bubbly Flow in Horizontal Pipe, International Journal of Multiphase Flow (2014), doi: http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.12.010

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Experimental Investigation of a Developing Two-Phase Bubbly Flow in Horizontal Pipe

M. Bottin*, J. P. Berlandis*, E. Hervieu
, M. Lance, M. Marchand**, O. C. Öztürk* and G. Serre

* CEA/DEN/DM2S/STMF/LIEFT, 17 rue des Martyrs, 38054, Grenoble, France ** CEA/DRT/LITEN/DTBH/LTB, 17 rue des Martyrs, 38054, Grenoble, France  CEA/DEN/DM2S/STMF/LMES, 17 rue des Martyrs, 38054, Grenoble, France


CEA/DEN/CAD/DTN/STPA, 13108, St Paul lez Durance, France LMFA, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully, France Corresponding author: [email protected] Tel: +33 4 38 78 33 02

Keywords: Horizontal pipe, bubbly two-phase flow, experiment, physical modeling

Abstract

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water-gas coordinated regimes corresponds to a new transition criterion CT=2, derived from a generalized representation with the dimensionless coordinates of Taitel, Y. & Dukler, A. E., 1976, American Institute of Chemical Engineers (AIChE) Journal, Vol. 22. Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for JL=4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond JG=0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the

1

single phase case. The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.

1.

Introduction

Horizontal two-phase flows in pipes have extensively been studied since they are encountered in many industrial plants. Most of the available data and physical models found in the literature have been obtained in pipe regions where the flow is fully developed, although the notion of established regime is somewhat misleading in two-phase flow. Horizontal pipe flows are also relevant in nuclear power plant safety studies due to the risk of breaks in primary circuits. However, the pipe lengths in nuclear power plants are about ten times the pipe hydraulic diameter. Thus, nuclear two-phase flow regimes are never fully developed. Literature data and models have therefore to be completed by studies on short pipes in order to take into account entry and developing effects. This is the aim of the METERO experiment, designed to study developing horizontal pipe two-phase flows. This experiment has been developed in the frame of the NEPTUNE project, jointly developed by CEA, EDF, AREVA and IRSN. It aims at improving accuracy of the numerical tools used for safety studies, including physical models and data for validation. More precisely, the two-phase model developed for the MCFD scale module of NEPTUNE (Morel et al. (2004), Morel et al. (2005)), devoted to the calculation of two-phase flows in reactor components, needs further experimental validation in adiabatic conditions. Another goal of METERO is the validation of the 1D turbulence model developed by Chandesris et al. (2006), Chandesris & Serre (2005) and Serre & Bestion (2005).

From a physical point of view, the evolution of a horizontal pipe bubbly flow results from a balance between competing hydrodynamic mechanisms. On one hand, turbulence of the main liquid flow is responsible for bubble dispersion and has also an influence on bubble break up and coalescence. On the other hand, gravity tends to separate the two phases: when rising up, the bubbles can coalesce. Consequently, depending on the influence of these two phenomena, an initial bubbly flow will remain in this regime or evolve toward a stratified configuration. The features of vertical bubbly flows have been extensively documented (see for instance Wang et al. (1987), Lance & Bataille (1991), Liu & Bankoff (1993), Suzanne et al. (1998)). But less literature can be found on horizontal pipes, especially concerning turbulence data. Even though numerous studies were devoted to the characterization of horizontal flow patterns (see for example Govier & Aziz (1972), Andreussi et al. (1999), Barnea (1987)…) there is, up to now, no theoretical model

2

predicting the local distribution of gas fraction or turbulence field in a horizontal pipe. The need for data collection to improve physical modeling still remains. The bibliographical references we relied on for this study are the experimental works of Kocamustafaogullari & Wang (1991), Kocamustafaogullari et al. (1994), Kocamustafaogullari & Hang (1994), Iskandrani & Kojasoy (2001) and the numerical simulation of Ekambara et al. (2008).

The paper is organized as follows. After a brief presentation of the experimental apparatus and measurement techniques, the flow pattern is described using a complete video database. As a complement to this video database, local measurements performed at the maximum axial distance, 40 diameters (40D) downstream of the inlet, are provided. These results are presented in a chapter divided into two sections: -the first one is depicting the structure and dynamics of the liquid: first without any gas supply to compare with literature on pipe flows and then in interaction with the gas; -the second one is devoted to the study of the gaseous phase: structure, dynamics and interface behavior. Then the two-phase flow axial evolution, from 5D to 40D is studied and an attempt is made to describe its mechanisms. Conclusions and prospects end the paper.

2.

Experimental set-up

2-1

Facility

A description of the facility is presented in Fig 1. The device is made of stainless steel pipes linked to a Plexiglas test section. Two independent air and water supply circuits merge upstream of the test section through an injection/settling system. This system provides a horizontal bubbly flow at the inlet of the test section. At the outlet, water and air are separated in a 1500 liters storage tank. The water temperature is kept constant (around 18° C) by means of a heat exchanger located inside the tank. The main characteristics of the experimental apparatus are summarized in Table 1. Concerning water supply, the circuit is composed by a FinderTM pump, of driving pressure 2.8 bar, maximum flowrate 150 m3/h (which corresponds to a maximum water velocity of 5.3 m/s) linked to the test section by means of two lines including flow meters: a line of 25 mm in inner diameter for the scale 0 to 15 m3/h and a 100 mm inner diameter line for the scale 15 to 150 m3/h. For the small flowrates (0-15 m3/h), a YokogawaTM Coriolis mass flow meter is used (accuracy about 0.2 % of the measurement point). For the higher flowrates (15 to 150 m3/h), a KrohneTM electromagnetic volumetric flow meter is used. It offers a lower accuracy than the Coriolis flow meter but introduces a smaller pressure drop into the circuit. The inlet water temperature is measured by a K-type thermocouple with a +/-0.5°C measurement accuracy. This accuracy was not sufficient for hot film

3

measurements that are very sensitive to flow temperature variations. For that reason, the thermocouple was calibrated using a calibration bath and a platinum PT100 sensor. The resulting accuracy was then +/- 0.1°C. The water surface tension has been measured by a KRUSS® K8 interfacial tensiometer and compared with several samples of water as illustrated in Table 2. METERO water surface tension is close to the tap water one. Moreover, pipe cleaning operations are made only with dry cloth to ensure that no additional surfactant -that may alter the properties of bubble coalescence or break-up- is present in the water flow. Concerning the air supply, it is composed of a 6 bar pressure supply line involving a depressurization/filtration system and two lines for regulation and measurement of the flowrate: one line for the range 0 to 50 l/mn and a second one for the range 50 to 350 l/mn, corresponding to a maximum gas velocity of 0.7 m/s. The air circuit is open: after separation from the water in the tank, the air is vented to the atmosphere. The two flow meters are Brooks Emerson TM thermal mass flow meters (accuracy is 0.7 % of the measurement point). They include a PID regulation system that provides steady inlet conditions. The air temperature is measured by a K-type thermocouple, with a measurement accuracy of +/-0.5°C. The inlet and outlet pressures are measured by means of two Keller TM high precision membrane sensors. They measure the pressure relative to the atmosphere in the range 0-3 bar with an accuracy of +/- 0.015 % of the full scale, i.e. +/- 0.45 mbar. The test section, 5.40 m long, has an inner diameter D = 0.1 m. It is composed of interchangeable and rotating sections including instrumentation modules. The inlet injection/settling system (Fig. 2) is made of 320 tubes for the water and 37 for the air. The number and diameter of the air injection tubes have been set by iterative tests to ensure in the same time uniform bubble injection in the inlet section and low pressure drop for the required gas flowrates. The void fraction, directly depending on the number and sizes of the bubbles injected, is modified by varying the air mass flowrate. The system also includes a series of grids designed to break remaining vortices generated by upstream elbows and then ensure a low turbulence level - the so-called grid turbulence- at the inlet of the test section. Moreover, a grid, located 3 diameters away from the injectors, mixes the liquid and gas phases to avoid the signature of injector wakes on the velocity profiles and then ensure uniform bubble distribution. As mentioned previously, the originality of this experiment lies in the fact that developing flows, both in single and two-phase conditions, are studied. All the flow parameters can be controlled and/or acquired directly from the control/command room, via a personal computer and use of LabviewTM programs. These programs also pilot the instrumentation data acquisition. Several experimental techniques are implemented to measure the relevant parameters of the flow at 3 axial locations: 5D, 20D and 40D (see Fig. 3). The three measurement instruments used on the installation and presented hereafter are hot films, optical probes and high speed video camera.

4

2-2

Instrumentation

2-2-1 Hot film velocimetry

Hot wire and hot film anemometry have been extensively used in single phase flows for the past 50 years and adapted for two-phase flows. We use DantecTM 55R61 two components fibers and 55R41 single component conical hot film probes composed of nickel sensors electrically insulated from the water by quartz coating. The probes are electrically connected to a constant temperature anemometer (DantecTM CTA Streamline). A by-pass filtration system located downstream of the pump is also used before the tests to retain the particles of size greater than 5 µm and ensure that the probes may not be damaged by impacts. However, this filtration system cannot be used during the tests for it generates a high pressure drop. The overall frequency response of the anemometry system, from the sensor to the bridge, is about 7 kHz. Due to the reduced choice of low pass filtering frequencies in the CTA signal conditioner setup (1 kHz, 3 kHz, 10 kHz), the signal is filtered in low pass mode at a 10 kHz frequency. It is sampled at 20 kHz to respect Shannon’s Theorem. For single phase flow configurations, 200,000 points are acquired, corresponding to a 10 second duration. This acquisition time has been defined by analyzing the statistical convergence of the axial and vertical velocity variance. In two phase flow configurations, this duration may be increased to 5 minutes. The data acquisition is performed using a LabviewTM Virtual Instrument. The probe can be moved by a MicrocontrôleTM traversing system to measure velocity profiles on test section diametric (or vertical) intercept (Fig. 3) with a step ranging from 1 to 5 mm. Due to the size of the probe, the profiles are acquired in the range [-0.9< r/R< 0.9], where r is the radial (or vertical) location and R the pipe radius. As well known, the water temperature has a dominant influence on the bridge voltage output. This is partly linked to the low values of the probe heating coefficient: a value of 0.08 is used both to avoid boiling on the films and to increase the life time of the sensors. For that reason, a heat exchanger installed in the water tank contributes to keep the flow temperature around a constant value (18°C). A variation of +/- 0.5°C is allowed around the set point and before applying calibration, the voltages are corrected from the temperature influence, using a mathematical formula proposed by Bearman (1971). The relation between voltage and velocity is then derived from the classical King’s law. The probe calibration is done in single phase flow conditions for various water flowrates: the probe is placed at the center of the pipe where the flow velocity is maximal. The maximum axial velocity is obtained from previously made Pitot tube measurements.

After calibration, the effective cooling velocities on the wires are decomposed into velocities expressed in the laboratory coordinate system. The dual probe velocity decomposition gives access to the axial and radial components of the water instantaneous velocity. A statistical calculation then provides mean and r.m.s velocities, from which turbulent kinetic energy

5

profiles are obtained. The hypothesis is made that the radial and transverse components are of the same order of magnitude. All these operations are performed by home made programs. Thanks to the extreme care taken to water quality, flow temperature control and calibration procedure, a very satisfactory measurement accuracy and reproducibility is achieved. Thus, a discrepancy of less than 0.5 % is obtained between the flowrate reconstructed by integration of mean velocity profiles and the one measured by the flowmeter. For the velocity integration, two different methods are used. In the first one, the velocity profile is directly connected to the wall using the no-slip condition (Uwall = 0) before integration. In the second one, no connection is done and the velocity profile is integrated only on the range [-0.9< r/R< 0.9]. As the mean velocity profile exhibits a 1/n power law, the first method calculation under-estimates the true value of the flowrate whereas the second one over-estimates it. The two results are then averaged and compared to the value obtained from the flowmeter measurement. This gives the estimation of the global error generated by the integration of the velocity measurements. In two-phase flow, a complementary program, dedicated to this application, is used to discriminate the liquid and gas phases. In practice, the occurrence of bubbles generates large negative peaks on the voltage signal, as the heat transfer between the probe and the fluid falls when the sensor is in a gas medium. The principle of the program is to cut out the peaks and keep the signal corresponding to the water velocity. Thresholding principle is used in the discrimination process. This principle is based on the studies of Bel Fdhila et al. (1993) and Suzanne et al. (1998). The phase discrimination program identifies the bubbles one by one by using threshold voltages. The points defined as bubbles are removed from the raw voltage signals. After a discrimination process, the signal portions corresponding to the presence of the gas phase are removed completely and the remaining of the signal is representing only the liquid phase. The influence of the signal connection procedure on the spectral content of the flow is discussed in section 4-1. Finally, an uncertainty around +/-1 % has been obtained on the liquid mean velocities and less than +/- 5 % on the r.m.s. velocity (+/- 10 % on the variance). As the errors are added when performing the evaluation of the turbulent kinetic energy, the error on this quantity is about +/- 15 %.

2-2-2 Optical probes

Home made optical probes are used to measure the temporal phase indicator function (PIF) in two-phase flows. The principle is to emit a laser signal at the tip of an optical fiber by means of an emission/reception box. The air refraction index leads to a total reflection of the signal in bubbles whereas the water refraction index induces a refraction of the signal outside the optical fiber. A photodetector converts this phenomenon into an electrical signal composed by a succession of high levels (fiber tip in air, corresponding to the transit of bubbles when the sensor is placed into a two-phase flow) and low levels (fiber tip in water).

6

This electrical signal is then amplified and a double-thresholding is applied. The resulting binary signal is the PIF (phase indicator function), acquired by the PC card at a 2 MHz sampling frequency. The temporal resolution of the measurement is then high (0.5 µs). The local void fraction α is directly obtained by dividing the residence time of the gaseous phase by the total time of acquisition. This quantity results from a temporal average, relying on the fact that the flow conditions remain constant during all the acquisition. In this configuration, a second fiber is placed downstream of the main one, at a known distance. The interface mean velocity is derived from the cross-correlation between the two fibers PIFs. From this velocity and the phase times, the bubble intercept lengths l are derived. The intercept length histogram provides the distribution function hc of the intercept length l. A statistical processing then gives access to the bubble diameter distribution function hD(l). This function is obtained from the intercept length histogram hC(l), using the following differential relation established by Gundersen (1983):

hD ( l ) =

d ( hC ( l ))  1 hC ( l ) − l   2 dl 

(1)

From the diameter distribution function, it is possible to statistically calculate bubble average diameters. The statistical moment Sp of order p is obtained by integrating the histogram of bubble diameters with the following formula: ∞

∞

S p = ∫ d p .hD ( d ).dd = N b ∫ d p . p ( d ).dd 0

(2)

0

with p( d ) = hD ( d ) and Nb the number of bubbles. Nb The size of a bubble is characterized by calculating an average diameter dpq with the following formula: 1

d pq

Sp = S  q

 p−q   

(3)

The Sauter mean diameter (Kamp et al., 2001) which is frequently used to represent the mean bubble sizes for small and spherical bubbles, is then obtained by: ∞

d 32

S  =  3   S2 

∫d

1 3− 2

=

3

. f (d ).dd (4)

0 ∞

∫d

2

. f (d ).dd

0

The interfacial area concentration (Ai, in m-1) is then derived from the following theoretical expression assuming that bubbles are spherical and monodisperse in size: Ai = 6α d 32

(5)

Visualizations have shown that the bubbles are small and spherical for large water flowrates in the lower and central regions of the pipe. However, for flow regimes close to stratification and in the upper region of the pipe, the assumption of sphericity

7

and monodispersity is questionable. As 4-tip optical probe measurements do not require such assumptions, a detailed study using 4-tip optical probes made in the laboratory has been conducted to compare with 2-tip optical probe measurements and estimate the uncertainty generated in this region on the different quantities by the use of a 2-tip optical probe. The error is 8 % on the interfacial area concentration, 13% on the bubble velocity, 8% on the Sauter mean diameter and 3% on the void fraction. The acquisition of the PIFs and the calculations of void fraction and all other quantities are made via a program developed in the laboratory. Concerning the spatial resolution, the typical size of our probes is 250 µm for the fiber diameter and several microns for its tip. The two fibers radial spacing can be reduced to about 150 µm and the axial distance between the front fiber and the rear one is about 500 microns. The probe is mounted in a probe support that is moved by a traverse system in the same way as for the hot film probes (see Fig. 3). The acquisitions are realized on 200 000 bubbles or 15 minutes for each fiber in order to ensure a good statistical convergence. The measurement error on the quantities measured by an optical probe is not easy to determine. This evaluation was carefully studied by Cubizolles (1996). The error on the void fraction can be estimated to be around +/- 2 % and the one on the quantities derived from the PIF measurement (Sauter mean diameter, bubble mean velocity) is of the order +/- 5 %. From Eq. 5, the error on the interfacial area concentration is estimated to be +/- 7%. In addition, errors linked to the use of 2-tip optical probes, as discussed previously, have to be added to these values. The total error in the upper region may reach 5% for the void fraction, 13% for the SMD, 18% for the bubble velocity and 15% for the interfacial area concentration.

2-2-1 High speed video cameras

Two numerical PhotronTM Fastcam SA1 and SA3 cameras have been used for the flow visualizations. Their detection matrix size is 1024*1024 pixels2. The sampling frequency is 5400 images per second in full size for the SA1 camera and 2000 images/sec for the SA3. The shutter speed can be set up to 1/10 000 s. Different photographic lenses have been used (focal lengths ranging from 28 to 105 mm). The scene lightning was obtained by use of two DEDOLIGHTTM 575 W spotlights. The software PFVTM ensures the adjustment of the camera parameters and the acquisition of the videos. The camera is placed so as to acquire a side view of the pipe and a 45° mirror which is clamped above the test section provides a top view of the flow in the same time.

3.

Flow pattern

Horizontal pipe two-phase flow patterns have been described by several authors (Govier & Aziz (1972), Andreussi et al. (1999), Barnea (1987), Taitel & Dukler (1976), Dukler & Taitel (1986)) and classified with respect to the values of the

8

superficial liquid and gas velocities, JL and JG. The same classification was made for the present experiment, in an attempt to provide a flow pattern map. The high speed videos realized on the METERO experiment illustrate the various flow regimes classified for instance by Govier & Aziz (1972). Figs. 4 to 8 show photos extracted from the high speed videos corresponding to several specific couples of liquid and gas flowrates/velocities. The correspondences between flowrates and phase velocities are summarized in Table 3. The flowrates (liquid and gas) are summarized in the left column and the right column gives the corresponding phase velocities. In each photo, the fluid is flowing from the right to the left. The bottom part of the photo shows a side view of the test section and the top one gives a view from above thanks to the 45° mirror clamped above the test section. For this experiment, the bubbly regime is more likely related to the so-called buoyant bubbly regime than to the true dispersed regime: due to buoyancy effects, the bubbles are observed to move from the bottom to the top of the pipe leading to an asymmetrical flow. This buoyancy driven type of flow has been investigated by several researchers (for example Holmes & Russel (1975), Kocamustafaogullari & Hang (1994), Beattie (1996), Andreussi et al. (1999) and Iskandrani & Kojasoy (2001). Fig. 4 highlights this bubbly regime generated by high liquid and low gas superficial velocities. When the water flowrate is decreased, the two phase flow enters an intermittent regime: the top bubbles coalesce to form plugs as can be seen in Fig. 5 for JL=2.4 m/s and JG=0.03 m/s. For smaller values of JL, the flow regime completely changes: a free surface is created but as a result of gas injection, Kelvin-Helmoltz instabilities lead the liquid to reach periodically the upper wall, generating a high velocity slug (Fig. 6). Then, for very low values of the liquid flowrate, the waves cannot reach the upper wall and the flow becomes completely stratified whatever the gas flowrate. The gas flowrates are not sufficient to generate wavy stratified or annular flow in this experiment. A precise classification of over 150 videos for various values of JL and JG allowed the building of the METERO flow pattern map for two axial locations: X=20 and 40 diameters downstream of the injectors. These flow pattern maps only slightly depend on the length of the pipe as no important discrepancies were observed between the 20D and the 40D maps. On the other side, they may depend on the gas injection system. This effect has been minimized as much as possible by use of a homogeneous injection system to restrict entry effects. Fig. 7 shows this result for X=40D. Each cross in this figure corresponds to an acquisition for a couple of gas and liquid superficial velocities. The solid lines materialize the transition lines between one regime and another. They were first determined by visual inspection of the videos. It has to be noted that the uncertainty on the transitions is increased by the method used to identify them, however, the thickness of each transition line is not zero as the transition occurs over a range of superficial velocities and not for a precise value. Concerning the high liquid velocity flows, the results show that the intermittent regime corresponding to the evolution from

9

bubbles to plugs, may be described in a more precise way. The observation of the videos shows that for each value of the gas flow rate, there is a liquid flowrate range for which the bubbles form a uniform layer at the top of the test section. This flow regime is characterized by a bubble layer behaving independently of the liquid phase. Therefore, the velocity of the bubble belonging to this layer is significantly lower than the one of the bubbles located in the lowest part of the test section. Despite the high concentration of bubbles in the upper layer in this regime, no coalescence can be pointed out and no plugs are formed. This is illustrated by Fig. 8 where it is possible to see a “mattress” of bubbles in the upper region but no plug is formed. The values of JL and JG for which the flow exhibit significantly different velocities between the upper bubbles (bubble layer) and the lower bubbles (free bubbles) have been used to build a supplementary transition line. This one could be called “transition between buoyant bubbly regime and stratified bubbles regime” (TBBSB). This transition materializes the boundary between a liquid dominant condition (buoyant bubbly flow) and a gas-liquid coordinated condition (stratified bubbles). A more general representation of the flow map can be plotted in the dimensionless coordinates suggested by Taitel & Dukler (1976) and Dukler & Taitel (1986). These authors proposed a generalized flow map for horizontal two-phase flow (see Fig. 9). The dimensionless coordinates X and T are used for dispersed bubbly to intermittent flow transition, as presented by line D in Fig. 9. X is the so-called Lockhart-Martinelli parameter and T can be considered as the ratio of turbulent forces to gravity forces acting on the gas. They are calculated by the following formulas: 2 −n  4C L  u LS D  ρ u LS     L D  υL   2 X2 = −m 2  4C G  u GS D  ρ u GS    G D υ   G  2

(6)

−n 2  4C L  u LS D  ρ u LS     L υL  D  2 T2 =  (ρ L − ρ G )cos β g

(7)

with the constants C G = C L = 0.046 and the exponents n = m = 0.2 for turbulent flows. D is the pipe diameter, uS is the superficial velocity, β is the angle of inclination, ρ is the density, g is the acceleration of gravity and ν is the kinematic viscosity. The subscripts are L for liquid and G for gas. According to the authors, the transition from intermittent to dispersed bubbly flow occurs when turbulent forces are greater than buoyant forces which tend to keep the gas at the top of the pipe. This phenomenon can be expressed by the inequality in Eq. 8.

~ 8A T 2 ≥ ~ ~ ~G~ S iU L2 U L D L

(

)

−n

(8)

The right hand side term of Eq. 8 (hereafter noted κ) depends only on the ratio of the liquid level to the pipe diameter, hL D . The terms of κ are calculated by the following formulas:

~ h = hL D

(9)

10

~ ~ ~ ~  A G = 0.25arccos 2 h − 1 − 2h − 1 1 − 2 h − 1  

(

) (

) (

)

2

 

0. 5

  

(10)

~ ~ ~ ~ A = 0.25π ⇒ AL = A − AG

(11)

2 0.5 ~ ~ S i = 1 − 2 h − 1   

(12)

(

)

~ ~ S L = π − arccos 2 h − 1

(13)

~ ~ ~ U L = A AL

(14)

~ ~ ~ DL = 4 AL S L

(15)

AG AG + AL

(16)

(

α =

)

Additional local void fraction measurements, for all the experimental points in Fig. 7 have been acquired by optical fiber probe and integrated to calculate <α>. Eq. 11 and 16 then give the value of AL. The equivalent liquid level for each test is inferred from AL by a trigonometric relation. The flow pattern map in (X, T) coordinates is represented in Fig. 10. In this new flow pattern map, the transitions between the flow regimes are represented with three lines: -transition from buoyant bubbly to stratified bubbly flow (TBBSB): purple line -transition from stratified bubbly to plug flow (TSBP): green line -transition from plug flow to slug flow (TPS): red line Eq. 8 can be rewritten in Eq. 17. If we define a new transition criterion CT as:

CT =

T

(17)

κ

we can then obtain from Fig.10 the following relations (Eq. 18 to 21) which link each phase transition to a numerical value of CT :

CT ≥ 2 → Buoyant Bubbly Flow

(18)

2 > CT ≥ 1 → Stratified

(19)

1 > CT ≥ 0.55 → Plug 0.55 > CT

→ Slug

Bubbly Flow Flow

Flow

(20) (21)

It is worth noticing that in this representation, the transitions values for CT rank between 1/2 and 2. This means that the phenomena involved in the transitions are well captured by the two parameters T and

4.

Local study

11

κ which balance by a factor 2.

4-1 Liquid phase structure and dynamics

This chapter is devoted to the study of the liquid phase behavior. As mentioned previously, the velocity measurements have been carried out for 3 axial locations (5, 20 and 40D) but in this chapter, only the location 40 D is presented, first in single phase flow conditions, then in interaction with the gas. The measurements made for 5D and 20D will be presented in chapter 5 devoted to the study of the flow axial evolution.

4-1-1 Single phase

Preliminarily, series of instantaneous velocity measurements have been carried out for various water flowrates and different locations inside the test section. They confirmed that the behavior of the single phase liquid flow is in rather good agreement with literature on pipe flows. Fig. 11 shows a comparison at 40 diameters downstream of the pipe inlet (40D) between the non dimension axial mean velocity profiles U measured on METERO and the classical profiles of Laufer (1953) collected in a pipe for a small and a high value of the Reynolds number. The measurement uncertainty (1 %) is also plotted. As mentioned in section 2-2-1, due to the probe size, measurements cannot be made in the near wall region. The agreement is good with the high Reynolds number case of the Laufer experiment, close to the one of METERO experiment. It is interesting to stress that the Laufer experiment corresponds to fully developed conditions. This shows that for X values around 40D, the flow on METERO is close to fully developed for the single phase case. As already mentioned, the spatial integration of the mean velocity profiles provides an experimental value of the liquid flowrate. The difference with the flowrate measured by the test section flowmeter is about 0.5 %, as mentioned previously. Fig. 12 shows a 40D profile of the liquid axial velocity root mean square u’ divided by the local mean velocity Uave, local. It is compared with data collected from literature (Laufer (1953), Ljus et al. (2002), Lewis et al. (2002)) for various values of the Reynolds number based on the pipe diameter. The experiment METERO (Re=410 000) is in rather good agreement with the Laufer data (+/- 16 %). The turbulence level is nonetheless about 20% higher at the center of the test section. The same remarks can be made for the turbulent kinetic energy profiles K presented in Fig. 13 and compared to the Laufer experiment profiles. The profiles are dimensionless, thanks to the use of the friction velocity Uτ . Uτ is calculated from the Colebrook formula valid for Reynolds numbers greater than 105 in rough pipes. The error on Uτ is negligible compared to the one on K (+/- 15 %). The merging of the two curves (METERO, Re=410 000 and Laufer Re=430 000) is within the uncertainty, even when approaching the near wall region.

12

4-1-2 Two-phase

4-1-2-1 Velocities and energy

Two-phase flow velocity measurements have been carried out at 40D for one value of the liquid superficial velocity (JL=4.42 m/s) and various values of the air superficial velocities ranging from 0 (single phase) to 0.127 m/s. In a first attempt, 2 components of the liquid instantaneous velocity were measured but for liquid superficial velocities greater than 3.5 m/s, air pockets were trapped in the wake of the hot films and then spoiled the voltage signal. The solution was to replace the 2 component probe by a conical one, not sensitive to this phenomenon. As a result, only the axial velocity component was measured. Therefore, the turbulent kinetic energy is calculated from the axial component of the r.m.s. velocity assuming isotropy. The lack of validity of this assumption when approaching the wall of the pipe induces a bias on the results. In two-phase flow configuration, liquid velocity and turbulent kinetic energy profiles exhibit a strong dependence on the bubbles for gas superficial velocities greater than JG=0.063 m/s (see Figs. 14, 15 and 17). The effect of gas injection on the mean liquid velocity can be seen in Fig. 14 presenting 40D profiles of the axial mean velocity versus r/R for the liquid superficial velocity JL= 4.42 m/s and various values of the gas superficial velocities, ranging from 0 to 0.127 m/s. r is the radial coordinate and R is the pipe radius. For small values of the gas superficial velocities (0 to 0.025 m/s) the profiles overlap fairly well, but for JG > 0.063 m/s, the velocity profile falls in the upper part of the test section (r/R  1) and consequently rises in the lower region (r/R  -1), due to the reduction of the liquid flow area induced by the presence of the bubbles in the upper pipe region. It has to be noticed that the value of r/R for which the velocity is maximal, is shifted from 0 to -0.2 for the highest value of the gas flowrate. Fig. 15 shows radial profiles of the local turbulence intensity for the same values of JL and JG. The gas influence is characterized by an increase of the fluctuating velocities and energy in the upper region (r/R  1) associated with a decrease in the lowest region of the pipe (r/R  -1). This main feature of horizontal two-phase flow turbulence has been observed by authors such as Iskandrani & Kojasoy (2001) as illustrated in Fig. 16. The same turbulent behavior is observed on the fluctuating velocity profiles plotted in Fig. 15 and Fig. 16, corresponding to high values of the gas superficial velocities. Especially, if we compare the case JG=0.127 m/s in Fig.15 and =0.25 m/s in Fig. 16, we observe a good qualitative agreement between the two curves, namely a sharp increase in the upper region (r/R  1). For all the curves, the increase is less obvious for the METERO experiment, probably because the gas superficial velocities are lower (the maximum gas superficial velocity investigated in METERO is 0.127 m/s whereas it reaches 0.8 m/s in the Iskandrani & Kojasoy (2001) experiment). In METERO, like in this other study, it can be pointed out the expansion of the bubble layer in the upper wall region and a slight inflexion in the curve for JG=0.127 m/s and r/R 1. Anyway, the sharp decrease of u’/Umoy, local when r/R 1 highlighted in Fig. 16 for =0.5 and 0.8 m/s, is not clearly observed in the METERO results. This is probably due to the large size of the thermal sensor that prevents measurements closer than 2.5 mm

13

from the wall. Another reason, as mentioned previously, is that the METERO phase velocities are lower than that of Iskandrani & Kojasoy (2001). Another feature related to gas injection is that the minimum of r.m.s fluctuation is shifted towards the lower part of the pipe when the gas velocity increases. This behavior is in agreement with Fig. 16: the u’/Umoy, local curve minimum is shifted from 0 to -0.1 for =0.8 m/s. A physical explanation has been given by Kocamustafaogullari & Wang (1991) for this behavior: the effect of the bubble layer is to slow down the main flow in the upper region. As a consequence, the flow speed is increased in the lower region to ensure the continuity condition. This behavior is entirely consistent with the visualizations presented before and with the flow pattern maps derived from them. The thickness of the bubble layer exhibited by the videos is the same as the one highlighted by the velocity profiles for each experimental condition of JL and JG. More surprisingly, Fig. 15 exhibits a slight increase in u’/Umoy, local for the highest values of the gas flowrate in the lower region of the pipe (-0.8 < r/R < -0.2). This accounts for turbulent kinetic energy production related to the increase of the gradient ∂U in this region, as the liquid flow area is reduced by the increasing gas fraction. This phenomenon can be seen ∂r

also in Fig. 17, as will be discussed below. Another consequence of gas injection is the enhancement of the turbulent kinetic energy in the upper region by the additional effect of bubble induced velocity fluctuations. This is highlighted in Fig. 17 by the radial profile of u’2 for X/D=40, JL=4.42 m/s and JG=0 to 0.127 m/s. Indeed, if the flow is assumed isotropic, u’2 gives a good estimation of the turbulent kinetic energy (K is then equal to 3/2 u’2).

4-1-2-2 Spectral analysis

A spectral analysis program has been used to calculate the one-dimensional spectral energy density (denoted "1D spectrum") from the axial component velocity fluctuations of the liquid phase. This program, developed at the Laboratory of Fluid Mechanics and Acoustics of the Ecole Centrale de Lyon calculates the Fourier transform of the axial component autocorrelation. Various block sizes can be selected to enhance the spectrum convergence. Some tests have shown that a 10 000 samples block size provides well converged spectra and minimizes the gap between the variance calculated by spectrum integration and the one obtained from statistical calculation. The program provides the frequencies f and related amplitudes E11(f) corresponding to the 1D spectrum (the 3D amplitude spectrum is denoted E(f)). The frequencies are necessarily limited to 10 kHz due to the cutoff frequency of the electronic filter used for the acquisition.

The spectral analysis is first aimed at determining the slope of the spectra represented as E11 = f (k), where k=

2πf UL

(22)

14

is the wave number (m-1), f is the frequency and UL the liquid average axial velocity at the point where measurements are performed. Indeed, even if the one-dimensional spectrum does not correctly represent the energy of a three-dimensional turbulent flow, the power laws valid for a 3-D turbulent spectrum remain valid for a 1-D spectrum (Tennekes & Lumley, 1972). Integral scale Lg, Taylor micro-scale λg, Kolmogorov scale η, turbulence Reynolds number Rλ and local energy dissipation rate ε are then estimated by a spectrum integration method. The classical laws of isotropy are considered valid at small-scale for two-phase flows in pipe (ibid.). The one- and three-dimensional spectral densities of energy for a homogeneous isotropic turbulent flow follow the relationships below (ibid.): ∞

2

u ' = ∫ E11 ( f ) df

(23)

0

∞

(24)

ε = 2ν ∫ k 2 E( k )dk 0

where u'2 is the variance of the axial component velocity fluctuations. The two sides of Eq. 23 correspond to one-dimensional variables and the integration of the 1D spectrum provides a correct estimate of u’2. However, in Eq. 24, the 3D spectrum E(k) is not known. The formulation of this equation is then replaced by the relationship shown by Bailly and Comte-Bellot (2003): ∞

(25)

ε = 30ν ∫ k 2 E11 (k )dk 0

In the same manner, the Taylor microscale λg is derived from: 1

λg

2

=

2 u

'

2

∞

∫k

2

(26)

E11 ( k )dk

0

The Reynolds number Rλ based on the Taylor scale, the Kolmogorov scale η corresponding to smaller eddies and the integral scale Lg can be calculated by classical isotropy relationships (Tennekes and Lumley 1972). The Kolmogorov scale is associated with the frequency fk that corresponds to the highest frequency of the flow and with the Kolmogorov wave number kη which is written: kη =

2πf k UL

where fk is derived from

η=

U 1 = L kη 2πf k

(27)

η

by the following relationship:

(28)

Remarks:

15

1) Relations (23) and (24) are valid for isotropic turbulence, which is in our case assumed at small scale. These relationships are not appropriate to take into account correctly the contribution of all scales of the flow.

2) Due to the frequency response of the measurement system, the maximum measured frequencies are well below those of some vortices present in the flow. This prevents the integration of the whole spectrum and may induce errors. Fortunately, the error on the integral of E11 (k)dk and E11(f)df is small since the maximum of energy is located at larger scales, i.e. at small wave numbers and the missing part of the spectrum contains only a small amount of energy (corresponding to the smallest eddies in the dissipative zone). Yet, the integral of k².E11(k) is probably much more distorted, as the result of multiplying E11(k) by k2 gives more weight to large wave numbers. To quantify the error induced by the lack of measurement for very large frequencies, a study was conducted by varying arbitrarily the shape of a spectrum (corresponding to a measurement point at the top of the pipe in a two-phase flow case for JL = 4.42 m/s and JG = 0.0637 m/s). The spectrum has been truncated and artificially extended linearly to 25 kHz (which corresponds roughly to the Kolmogorov frequency). Different extrapolation functions have been tested for the extension of the spectrum (k-2, k-3, k-10/3 and k-11/3). The turbulent quantities calculated from the integration of the reconstructed spectra have then been compared to those obtained from the raw spectrum and the dispersion in the results has been quantified. This gives an estimate of the uncertainty caused by the lack of measurements at high frequency. To estimate the maximum discrepancy, the k-3 and k-11/3 spectra have been used, as the power law of the true spectrum is likely in the range [k-3- k-11/3]. The maximum uncertainties on the turbulent quantities are then: +/- 4 % on Kolmogorov scale and frequency, +/- 7 % on Taylor scale λg and Reynolds number Rλ, +/- 14 % on the integral scale Lg, +/- 17 % on the dissipation rate ε. As mentioned above, the dissipation rate ε is the quantity the most affected by the choice of the spectrum extrapolation at high frequencies.

3) The raw instantaneous liquid velocity signal contains unusable parts corresponding to the passing bubbles on the hot film. These "bubbly parts" must be removed in order to calculate the spectrum. Finally the remaining "liquid parts" of the signal are connected together. This discrimination procedure on the signal is questionable: does it have an influence on the spectrum calculation or not? In order to answer this question, a LabviewTM program has been used to test the influence of the signal connection during the process of discrimination. Starting from a file of single phase case velocity measurements (1 minute of acquisition, 1.2 106 points), the program randomly removes different parts of the file corresponding to METERO typical

16

bubble sizes (0.5 to 3 mm). Then, the remaining parts of the file are pasted sharply. Finally, the file is used to build a spectrum that is compared to the original one. Several cases have been tested: removal of 600, 1800, 3000 bubbles etc ... up to 18 000 bubbles, which is much higher than the number of bubbles counted by an optical probe during 1 minute in the upper region of the flow. The measurement location has also been tested (areas near the upper part and in the central region of the flow). The spectra obtained from these truncated files do not show large differences with respect to that calculated for the single-phase, as shown in Fig. 18. In addition, the quantities calculated from the integration of the spectra are only slightly different (the maximum difference is 0.4 %). This suggests that the sharp connection made after the bubble removal has little influence on the spectrum. Fig. 19 shows the one-dimensional spectral densities of energy E11(k) versus the wave number k, at 40 diameters for the single-phase flow (JL=4.42 m/s) and different measurement points along the vertical axis (r/R=1 represents the top and r/R=0 the center of the pipe). Fig. 20 shows the same results for the two-phase flow (case JL=4.42 m/s, JG=0.0637 m/s). Concerning Fig. 19, it can be noticed first that the spectra extend over nearly 6 decades in energy and 3 in wave number. The inertial range is characterized by a k-5/3 slope over a decade and a half. For larger wave numbers, the dissipative range is drawn but a slope common to all points cannot be clearly established. For the highest wave numbers, due to physical limitations of the measurement system (frequency response, filter), the spectra slopes are biased and the analysis becomes questionable. The plot of the spectra radial evolution shows that the flow energy level increases gradually when approaching the top of the pipe. Indeed, the turbulence level increases due to wall induced shear. Concerning the two-phase flow (Fig. 20) the same remarks can be made, namely an increase in the energy spectra in the upper region with amplified trends. The energy level for a given wave number k, is about 20 times higher in the near wall region than in the central region of the pipe. In single-phase, this ratio is only about 10. In other words, while the spectra energy levels in the central region are nearly the same for two-phase and single-phase cases, they differ widely when reaching the upper region. This is consistent with previous observations: the small bubbles in the center of the pipe have a negligible effect on the turbulence of the liquid phase while large bubbles accumulated in the upper region influence significantly the dynamics of the liquid phase. Furthermore, we can note the appearance of a bump at the end of the inertial range, more pronounced when approaching the top of the pipe. The wave number corresponding to the appearance of the bump is about 1000 m-1. This would correspond to turbulent structures sizes in the millimeter range, roughly equaling the mean bubble size (see Fig. 25). It has been checked that this bump is not related to discrimination artefacts and indeed accounts for liquid-gas interactions. It could be explained by a main streamwise bubble wake. Indeed, if in the pipe central region the axial slip velocity is probably almost zero (see §4-2-2) this may not be true in the upper wall region. It may also be related to the bubble random vertical motion. The bubble mean vertical velocity has been estimated from videos to be several cm/s. The bubble vertical

17

instantaneous velocity measurements have also shown that vertical velocity fluctuations are important. Fig. 20 also exhibits a different behavior of the spectra in the dissipation range (k> 5000). Whereas for the single phase flow (Fig.19) the spectra collapse in this region, the two phase spectra (Fig. 20) seem to exhibit a k-3 slope. This could be related to turbulence production in the dissipative range due to the bubbles. In the literature, several authors describe the influence of bubbles on turbulence. Among them are Lance (1985) which describes the turbulent flow in a vertical channel of square section with the presence of grid, Liu (1989) and Wang (1985) who analyze the turbulence of a flow in vertical pipe. These authors point out several trends in two-phase case such as a decrease in turbulence scales and an enrichment of the spectrum at high frequencies. The k-3 slope has been observed in vertical flows by Lance & Bataille (1991) and Riboux et al. (2009) but for larger scales. These observations seem to be confirmed on METERO for the upper region. In the rest of the pipe, the influence of the bubbles is slight. However, the flow in METERO is quite more complex with a vertical increasing concentration of bubbles that move in both horizontal streamwise direction and vertical direction where they cross a high shear flow responsible for lift. The radial evolution of the liquid phase dissipation rate derived from spectrum integration can be seen in Figs. 35 (single phase) and 36 (two-phase) for X=40D. Whereas the

ε profile is symmetric in single phase flow at 40D (Fig. 35), it becomes

asymmetric in two-phase flow (Fig. 36). Concerning εmax, the maximum value of

ε for r/R  1, it is more than 4 times

higher for the two-phase case than for the single phase case. The ratio εmax / ε0 (where ε0 is the dissipation rate at the center of the pipe) is also increased by a factor 4.4 : it increases from 13 in single phase flow to 57 in two phase flow, confirming the influence of the bubbles in the upper wall region and only in this region. In single-phase flows, the dissipation rate varies with the ratio u’3/Lg where u' is the standard deviation of the turbulent velocity and Lg the turbulent integral length scale. Assuming that this behavior remains in bubbly flows, as we have noted in METERO, the increase of the dissipation rate can then be explained by three mechanisms: -The integral length scale Lg decreases in the presence of bubbles as already mentioned by Lance and Bataille (1991). -In the presence of bubbles the flow agitation increases from the center to the top of the test section. Therefore, the turbulent velocity increases and so does the dissipation rate. -The mean velocity gradients responsible for part of the turbulent production are stronger near the wall at the top of the test section. Thus, turbulent velocity and dissipation increase from the center to the top.

4-2 Gaseous phase structure and dynamics - Interaction with liquid 4-2-1 Void fraction

Two-phase flow optical probe measurements have been carried out on radial profiles at the same 3 axial locations (5, 20 and

18

40D), for one value of the liquid superficial velocity, JL=4.42 m/s (QL=125 m3/h) and the same various values of the air superficial velocities, ranging from 0.008 to 0.127 m/s. In this section, the results are presented for the X=40D location. Complementary measurements were performed for this axial location for JL=5.3 m/s and the same values of the gas superficial velocities. Local void fraction, interface area concentration and mean Sauter diameter profiles are derived from the PIFs. The time spacing between the front tip and the rear tip PIFs also gives access to the bubble velocity. The results show that the local void fraction α increases with JG whatever the vertical location. Fig. 21, showing the void fraction profiles versus y/D, gives an example of this feature: the JL=4.42 m/s void fraction profiles rise when JG is increased and especially in the region y/D  0 (upper part). This plot has to be put in the perspective of the velocity fluctuations behavior highlighted by Fig. 15. It should be emphasized that the value of r/R (or y/D) for which the curves are strongly inflected is the same for the two figures. This confirms that the bubble layer, responsible for substantial void fraction increase, has a direct effect on the liquid dynamics. It is also consistent with the visualizations of the flow, as mentioned previously. On the contrary, the void fraction decreases in the upper part of the test section (and increases in the lower part) when the liquid superficial velocity is increased from 4.42 to 5.3 m/s. This may illustrates the fact that for high water flowrates, the bubbles are more dispersed by turbulence in the flow and the void fraction profiles tend to flatten. It is also likely that the flow development is different for higher bulk velocity. This could as well explain some of the observed differences. The same profiles acquired for JL=5.3 m/s exhibit a noticeable change of slope near the upper region (see plots for JL=0.025 and 0.063 m/s in Fig. 22, giving the radial α profiles versus y/D for JL=5.3 m/s and JG=0.008, 0.025, 0.063 and 0.127 m/s). This behavior has already been observed by Iskandrani & Kojasoy (2001) and Ekambara et al. (2008) for a value of the liquid superficial velocity equal to 5.1 m/s. It is worth noting with regard to these publications that for lower values of JL (JL=3.8 m/s), this peak is observed also, but only for values of JG greater than 0.5 m/s. As the gas superficial velocities are lower on METERO, this could be the reason why it was not observed for JL=4.42 m/s. Some attempts were made to compare the void fraction measured by optical probes to the one derived from the hot film voltage signal in two-phase configuration. Indeed, the discrimination gives access to the fractions of voltage signal corresponding to bubble occurrence and then the possibility to infer a local void fraction. Anyway, the comparison revealed a very bad agreement between the void fractions calculated from the two methods (the one measured by conical probe was far too high compared to the one acquired by the optical probe). This could be explained by the size of the conical sensor (0.2 mm*1.4 mm) which is very large compared to the one of the optical probe tip and even with the bubble size which is quite small (about 1 mm in diameter). The velocity probe dimensions may be too high to ensure an accurate local measurement of the void fraction.

4-2-2 Bubble velocity

19

First, the bubble velocities have been measured by optical probes as shown in Fig. 23 representing the radial profiles of the bubble axial mean velocities for X/D=40, JL=4.42 m/s and two gas superficial velocities. Although optical probe measurement accuracy (around +/-15 % see 2-2-2) can explain some of the discrepancies, these results account for a bubble velocity systematically lower than the liquid one and thus for a negative slip velocity between the liquid and the gas. As the physical explanation for this phenomenon is not obvious, this specific point had to be cleared by using another experimental technique to increase confidence in the bubble velocity measurement. This is the reason why further tests have been made on the pipe axis by high speed video camera combined with PIV processing. This region is accessible to accurate PIV measurements as it is a flow region where the void fraction is rather low (< 3%, see for instance Fig. 21) and the bubbles are small. The videos were made 40 diameters downstream of the injectors (40D) for conditions of liquid superficial velocity and temperature (4.42 m/s, 18 °C) and gas superficial velocities (ranging from 0.01 to 0.1 m/s) equivalent to the acquisitions made earlier with optical sensors. The camera is a PhotronTM SA1 equipped with a 1024 x 1024 pixels2 detector and operating at 5400 frames per second in full frame. Several actions were made to ensure accurate measurement of the bubble speed: -Using a large camera lens focal distance and a small camera-to-pipe distance to obtain a good spatial resolution (small field) and a shallow depth of field. This ensures that the measurements are made in a plane. -Use of a calibration target located on the pipe central plane. The calibration target contains 80 dots separated by a constant distance in the x and y directions. This target allows focusing the camera on the central plane. Moreover, as the calibration target is centered on the y (vertical) and z (transverse) axes, it then allows knowing precisely the center of the test section both in the vertical and transverse directions. The axial velocity is then measured precisely on the pipe central axis, where it is maximum. The calibration target gives the conversion of bubble displacements from pixels to meters and also permits verification that the image distortion on the axial displacements is negligible along the pipe axis, as the camera is placed normally to the pipe. Once the calibration is made, the target is removed for the measurements. -Using a precise mounting system for the camera so that the plane of focus does not move during testing (especially when the target is removed) and the distance pipe-camera remains constant. - Blocking of certain air injectors to reduce the number of bubbles, affecting the quality of images. Only 4 of the 37 injectors are operating. It has to be noted that even if this configuration is not exactly the same as the one used for optical probe measurements, the main features of the two-phase flow (small bubbles, low void fraction) are conserved. The post-processing method is automatic, using a free PIV software for determining speeds, bubbles being the seeder. The main interest in this method is that it gives access to statistical quantities (mean and standard deviation of velocity fluctuations). Nonetheless, due to the fact that bubbles are used as tracers and the illumination is volumetric (no laser sheet), the measurement accuracy is not simple to estimate for this case. The software implements advanced processing methods

20

developed and published for several years (Keane & Adrian (1990), Westerweel et al. (1997), Scarano & Riethmuller (1999), Nogueira et al. (1999), Prasad et al. (1992)). The PIV is here combined with the shadowgraphy technique. Whereas in single phase flows, PIV techniques, using laser sheets, have significant success to measure the liquid velocity, they have major disadvantages in multiphase flows due to the presence of the gas phase. The gas phase, more specifically the bubbles, brings difficulties in velocity measurements since the bubbles can reflect the laser beams and this phenomenon results in a saturation of the camera sensor. As a result, it is not possible to detect the tracer particles in the flow. For that reason, shadowgraphy has been developed to eliminate the problems caused by the presence of bubbles. The principle of the measurement technique is to acquire shadow images of the bubbles, created by a strong light source coming from the back side of the bubbles and recorded by a high speed video camera. Shadow images of the bubbles are used as tracer particles, like in PIV technique, in order to calculate the bubble velocities (Lindken & Merzkirch (2002), Sathe et al. (2010)). The procedure is first to convert the video images acquired (.PNG format) in binary images (black & white). A median filter is chosen to retain only the clearest bubbles. It retains only the bubbles which are located in the center of the test section. In other words, the filter eliminates the bubbles which are in the foreground and the background of the focused area in the test section. A filter size [7, 7] is chosen, which is lower than the size of the bubbles. A +/- 64 pixels region of interest around the central axis is defined. The definition of processing parameters must obey specific rules (Keane & Adrian (1990), Prasad et al. (1992)) to ensure an accurate measurement of speeds. In particular, as a rule of thumb, the size of the analysis window must be chosen so that a particle (a bubble here) does not travel more than a quarter of the window span during the time between the two images considered. Thus, an analysis window of 128 pixels has been chosen for post-processing. A smaller window (64 pixels) would act as a filter, focusing on short displacements (low speeds), resulting in an underestimation of the velocities. A 50 % overlapping between two analysis windows has been taken to + / - 64 pixels, which is the value most commonly used. Thanks to the care brought to these PIV measurements (acquisition, post-processing) and since they have been made in a region where the bubbles are small and dilute in the liquid phase, the error on the bubble axial mean velocity in this region is confidently reduced with respect to the one made on the optical probe measurement. An example of results is shown in Fig. 24. In this figure are represented the instantaneous velocities calculated on the 1000 images recorded for one gas flowrate case. At the top of the graph is shown the mean velocity and standard deviation of fluctuations derived from the distribution of instantaneous velocities for all the acquisitions. Average axial speeds range from 5.31 to 5.39 m/s and standard deviations from 0.18 to 0.27 m/s according to the gas flowrates. This is in good agreement with the liquid velocities measured by hot film probes in the same conditions and location (see Fig. 14) and calls for a bias (about 10 to 15 %) on the bubble velocity measurement by optical probe. From visualizations of the interaction with optical probe tip, an attempt to explain the reasons for this bias has been proposed.

21

This could be linked to the deformation of the bubble during its interaction with the first tip of the optical probe (from a spherical shape to an elliptical shape) that would create a longer transit time between the two tips and consequently result in a misestimate of the bubble speed. In the upper region of the pipe, it is not possible to correct the bubble velocity measurement by optical probe, as no PIV measurement could be performed. Thus, the way the error evolves with the radius is unknown. As a consequence, it is reasonable to assert that the slip velocity is negligible in the central region of the pipe, due to the low void fraction and small size of the bubbles. Nonetheless, in the upper region of the pipe, the slip velocity could be higher and induce a lift effect, as mentioned in 4-1-2-2.

4-2-3 Bubble size

In Fig. 25 are shown the profiles of Sauter mean diameter (SMD) at 40D for JL=4.42 m/s and two gas flowrates. These profiles have a similar shape: the bubbles are distributed in the pipe according to their size. Due to buoyancy effects -proportional to the volume of a bubble- that promote vertical migration, the average bubble size declines with the vertical distance from the top of the pipe. At the top of the pipe (for r/R ≥ 0.3), there exists a homogeneous layer with average bubble diameters nearly constant (2-3 mm). In the central region (0.3 ≥ r/R ≥ -0.3), the bubbles average diameter decreases almost linearly with their distance to the upper wall. Finally, in the lower part of the pipe, the SMD drops but this decrease is less marked than in the central area. At the bottom of the pipe, the mean diameter is 1-1.5 mm. The flow is constituted by two layers of bubbles almost homogeneous in size, separated by a transition zone. This distribution is the result of several mechanisms. The larger bubbles tend to cluster at the top of the pipe, driven under the influence of buoyancy forces. Coalescence is likely to take place, especially in the upper region of high concentration of bubbles, thereby increasing the average size of bubble. On the contrary, turbulent forces, favored by high liquid flowrates, cause the spreading of the bubbles in the rest of the pipe. Now let us consider the bubble sizes used to calculate the Sauter diameter and the average interfacial area. In what follows, the intercept lengths distributions, which are the raw data measured by optical probes, are plotted instead of Sauter diameters that require more processing steps inducing possible errors. The intercept lengths in bubble frequencies (number of bubbles divided by the duration of acquisition) at 40 D are shown in Fig. 26 as a succession of histograms versus the location along the vertical axis for JL = 4.42 m/s and JG = 0.0637 m/s. The maxima of these histograms follow the same trend as the values of SMD along a profile. The following trends, discussed above, are found: - In the upper part (r/R ≥ 0.34) the intercept length are identical (corresponding to a maximum of 4 mm) and 1.5 mm intercept lengths are most commonly measured. The number of bubbles decreases with r/R. The large width of particle sizes reflects

22

the accumulation of larger bubbles in this area. - Then there is a transition zone (0.34 ≥ r/R ≥ 0.04) where the maximum frequency is translated to the short intercept lengths. Two humps, corresponding to two populations of bubbles are clearly seen: one containing a majority of bubble intercept lengths measuring 1.5 mm, the other with a majority of bubbles of 0.3 mm intercept lengths. With increasing distance to the top, the first population is decreasing gradually to disappear and leave only the second population. The larger bubbles, driven by buoyancy forces, migrate to the top of the pipe, while for smaller bubbles buoyancy force is not strong enough to offset the turbulent one that tends to disperse them. -Finally, in the pipe bottom region, a population of small bubbles is observed, getting scarce while approaching the bottom of the pipe. Interfacial area concentration profiles, not presented here can be directly inferred from void fraction and Sauter mean diameter profiles using Eq. 5.

5.

Flow axial evolution

Figs. 27 to 36 depict the flow axial evolution from the pipe entry to 40 D. Figs. 27 to 30 present the quantities derived from optical probe measurements. The X=5D profiles are rather flat and symmetric. The slight dissymmetry observed in Figs. 27 and 30 in the upper region (r/R  1) can be explained by the non uniformity of bubble injection but this effect disappears from 20D. The void fraction

profiles (Fig. 27) evolve sharply from 5 to 20 D. From 20 to 40D, the changes are less obvious, nonetheless sizable differences can be pointed out, mainly in the regions where the void fraction is low. The void fraction profiles highlight a flow organized in two layers: a lower region with low void fractions and an upper one with sharply increasing void fractions. On the contrary, the profiles of the other quantities (SMD, liquid and gas velocities and dissipation rate) evolve continuously along the pipe. This accounts for the fact that the void fraction alone is a poor indicator to describe the flow axial evolution. Fig. 28 shows the axial evolution of the bubble Sauter mean diameter profiles: it highlights bubble segregation with a mean bubble diameter increasing versus the pipe axis in the upper region. Nevertheless, it doesn’t give more details about the mechanisms responsible for this increase. More information is given in Fig. 29 plotting the axial evolution of the intercept lengths histograms. At 5D, the peak is high and narrow with a median bubble size around 0.5 mm. This corresponds to a great number of small bubbles. At 20D, the histogram is flattened and shifted towards bigger sizes (1.3 mm). This phenomenon is amplified at 40D with increased bubble sizes (median value around 1.5 mm). Moreover, the maximum intercept length evolves from 2.5 to 4.5 mm when going from 5 to 40D. This relates the predominance of coalescence: as the two phases flow inside the pipe, small bubbles merge and rise. This was reported previously by Razzaque et al. (2003). The axial evolution of the gas phase velocity profiles (Fig. 30) can be related to the liquid phase one (Fig. 32). They highlight

23

the hydraulic development of the flow, the dissymmetry from 20D due to the bubble layer friction in the pipe upper region and the shift of the maximum velocity towards the lower side of the test section at 40D. Figs. 31 to 36 show the axial evolution of the liquid phase dynamics for the two-phase case JL=4.42 m/s, JG=0.0637 m/s. Each graph is compared with the single phase case. For the mean velocity (Figs. 31 and 32), the differences in the evolution between the two-phase and single phase cases are not large, probably due to the low gas to liquid ratio. The discrepancies are more noticeable for the velocity fluctuations with a growing dissymmetry of the plots for 20D and 40D in the pipe upper region for the two-phase case (see Figs. 33 and 34 for the variance of the liquid velocity fluctuations). This is even more obvious on the dissipation rate derived from the 1D spectrum integration (Eq. 24, Figs. 35 and 36). The ratio between the two-phase and single phase maximum dissipation rates is equal to 1.4 for 5D, 2.3 for 20D and more than 4 for 40D. Moreover, the ratio εmax/ε0 (where ε0 is the dissipation rate at the center of the pipe) is increased by a factor 4.4 in two-phase flow at 40D whereas it remains constant at 5 and 20D. This accounts, non solely for the local bubble effect, but also for the effects of the bubbles on the axial flow regime development.

6.

Conclusions

By use of complementary measurement methods, this paper brings new information on developing adiabatic two-phase bubbly flow in a horizontal pipe. Concerning the region where the flow is almost fully developed (40 pipe diameters downstream of the pipe inlet), comparisons with literature on pipe flows showed that the METERO single phase flow mean velocity profile is in good agreement with Laufer (1953) and for instance Ljus et al. (2002) or Lewis et al. (2002). For the two-phase flow, comparisons of fluctuating velocities and void fraction profiles show a good qualitative agreement with Iskandrani & Kojasoy (2001) or Ekambara et al. (2008). Given the sensivity of the flow to initial conditions and the tenuous existence of the fully developed state, a good quantitative agreement between these results and data from the literature cannot be expected. The layering organization of the two phase flow, mainly highlighted by optical probe measurements has been confirmed by videos. Especially, the thicknesses of the layers exhibited by the three measurement means used (video, hot films and optical probes) are consistent. Flow pattern maps derived from the videos exhibit the regime transitions described by Govier & Aziz (1972). From these, we propose a supplementary boundary line that details the transition from a water dominant regime (buoyant bubbly flow) to a water-gas coordinated regime (stratified bubbles). This regime has to be distinguished from the slug regime occurring for lower values of the liquid velocity.

24

Moreover, the generalized representation in the (X, T) coordinates suggested by Taitel & Dukler (1976), gives a numerical criterion for the parameter CT for this transition. In this representation, each phase transition is linked to a numerical value of CT. The transition from buoyant bubbly to stratified bubbly flow corresponds to the value CT = 2. A local study has been performed 40 pipe diameters downstream of the pipe inlet, to analyze the influence of the bubble layer generated at the top of the test section when JG rises for a fixed value of JL. This influence can be seen as follows: an increase in u’ and u’2 at the top and, on the contrary, a decrease near the bottom of the test section. As a consequence of the bubbles distribution, the mean liquid velocity decreases at the top and increases in the lower region. Moreover, an attempt of spectral analysis derived from the liquid velocity measurements confirms the effects of the bubbles on the liquid dynamics: injection of energy at high wave numbers, corresponding to the mean bubble size and increasing of the dissipation rate in the upper region of the flow, whereas in the lower part of the test section, turbulence does not differ much from the single phase case. The ratio between the dissipation rate in the upper region and in the pipe center reaches more than 50 for the two phase case whereas it is only about 13 for the single phase flow. The Sauter mean diameter radial profiles exhibit the same trends. An analysis of the bubble sizes, based on the bubble intercept lengths histograms, has revealed that the flow is organized in two layers of bubbles separated by a sharp transition zone. Concerning the flow axial evolution, the results show that both optical probes and hot film measurements have to be looked at together in order to fully describe the two-phase flow behavior along the pipe. First, the analysis of the void fraction axial evolution shows that from 20D the flow tends to separate into two zones: the lower region of the pipe with low void fractions and the upper region exhibiting high void fractions. But it is the analysis of bubble sizes and mainly bubble intercept lengths histograms that reveals the axial increase of bubble coalescence as well as the migration of the larger bubbles to the top of the pipe under the action of buoyancy. The impact of this upper bubble layer on the liquid flow is highlighted by the axial evolution of the turbulent quantities, mostly the dissipation rate. The ratio between the two-phase and single phase maximum dissipation rate grows with the axial distance, reaching more than 4 at 40D. This accounts for the bubble impact on the liquid flow development inside a horizontal pipe in two-phase flow. Finally, results of the optical probes measurements also raise questions about the bubble velocity, appearing about 10% lower than the liquid phase axial velocity. This feature is in agreement with some results of Iskandrani & Kojasoy (2001) and may be explained by 3 dimensional effects. Nonetheless, further PIV measurements made on the pipe axis, using bubbles as a tracer tend to show that the axial slip velocity between liquid and gas is almost zero in the central region of the pipe.

25

Acknowledgements

This work has been achieved in the framework of the NEPTUNE project granted by CEA, EDF, IRSN (Institute for Radioprotection and Nuclear Safety) and AREVA-NP.

References

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Ekambara, K., Sanders, R.S., Nandakumar, K. & Masliyah, J.H. CFD simulation of bubbly two-phase flow in horizontal pipes, Chemical Engineering Journal, Vol. 144, 277–288 (2008). Govier, G.W. & Aziz, K., The flow of complex mixtures in pipes, Van Nostrand Reihold Company, New York (1972). Holmes, T. L. & Russel, T. W. F. Horizontal bubble flow, Int. J. Multiphase Flow Vol. 2, 51-66 (1975). Iskandrani A. & Kojasoy, G. Local void fraction and velocity field description in horizontal bubbly flow, Nucl. Eng. Des. Vol. 204, 117-128 (2001). Keane, R. D. and Adrian, R. J. Optimization of particle image velocimeters. Part 1 : Double pulsed systems Measurement Science and Technology 1, 1990.

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Tables

Inlet temperature air-water

18°C

Maximum outlet temperature

20°C

Maximum driving pressure

2.8 bar

Water flow rate

0 to 150 m3/h

Water velocity

0 to 5 m/s

Air mass flow rate

0 to 350 l/mn

Air superficial velocity

0 to 0.7 m/s

Table 1: METERO main working parameters

Sample

Surface tension (mN/m)

Sample Metero n°1

58

Sample Metero n°2

59

Non mineralized water

66

Tap water

61.5

Doubly distillated water

72.6

Table 2: METERO water surface tension

QL (m3/h)=

125

JL (m/s)=

4.42

QL (m3/h)=

150

JL (m/s)=

5.30

QG (l/min) = 4

JG (m/s)=

0.008

QG (l/min) = 12

JG (m/s)=

0.025

QG (l/min) = 30

JG (m/s)=

0.063

QG (l/min) = 60

JG (m/s)=

0.127

Table 3: Correspondences between flowrates and phase velocities

29

Figure Caption: Fig. 1: Schematic diagram of the test setup Fig. 2: Bubble injection and water tranquilization system Fig. 3: Test section and measurement location Fig. 4: Buoyant bubbly flow regime (JL=5.30 m/s; JG=0.025 m/s) Fig. 5: Plug flow regime (JL=2.4 m/s; JG=0.03 m/s) Fig. 6: Slug flow regime (JL=0.53 m/s; JG=0.062 m/s) Fig. 7: METERO flow pattern for X/D=40. Transition from slug to stratified flow (TSS): pink line; transition from plug to

slug flow (TPS): orange line; transition from buoyant bubble flow to stratified bubble flow (TBBSB): green line; transition from stratified bubbles regime to plug (TSBP): purple line. Crosses correspond to video acquisitions for couples of JL and JG. Fig. 8: Stratified bubbles flow regime (JL=4.55 m/s; JG=0.094 m/s) Fig. 9: Generalized flow regime map for horizontal two-phase flow (Taitel & Dukler 1976) Fig. 10: METERO flow pattern for X=40D with dimensionless coordinates Fig. 11: Single-phase radial mean velocity profiles Fig. 12: Single-phase radial r.m.s velocity profiles Fig. 13: Single-phase radial kinetic energy profiles Fig. 14: Two-phase radial mean velocity profiles Fig. 15: Two-phase radial r.m.s velocity profiles Fig. 16: Two-phase radial u’ profiles from Iskandrani & Kojasoy (2001) Fig. 17: Two-phase radial u’2 profiles Fig. 18: Influence of the discrimination procedure on spectra Fig. 19: Radial evolution of turbulence spectra in single-phase flow (JL=4.42 m/s) Fig. 20: Radial evolution of turbulence spectra in two-phase flow (JL=4.42 m/s, JG=0.0637 m/s) Fig. 21: Radial void fraction profiles for X/D=40 and various JL and JG Fig. 22: Radial void fraction profiles for X/D=40 and JL=5.3 m/s Fig. 23: Radial profiles of the bubble mean velocity for X/D=40 and JL=4.42 m/s Fig. 24: Instantaneous bubble axial velocities on pipe axis measured by PIV for JL=4.42 m/s and JG=0.01 m/s Fig. 25: Radial mean Sauter diameter profiles for X/D=40 and JL=4.42 m/s Fig. 26: Intercept length histogram JL=4.42 m/s, JG=0.0637 m/s Fig. 27: Void fraction axial evolution from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s Fig. 28: Sauter mean diameter axial evolution from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s Fig. 29: Axial evolution of the intercept length histograms from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s

30

Fig. 30: Bubble velocity axial evolution from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s Fig. 31: Liquid mean velocity axial evolution from 5 to 40 D for JL=4.42 m/s Fig. 32: Liquid mean velocity axial evolution from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s Fig. 33: Liquid u’2 axial evolution from 5 to 40 D for JL=4.42 m/s Fig. 34: Liquid u’2 axial evolution from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s Fig. 35: Axial evolution of the liquid dissipation rate from 5 to 40 D for JL=4.42 m/s Fig. 36: Axial evolution of the liquid dissipation rate from 5 to 40 D JL=4.42 m/s, JG=0.0637 m/s

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

Highlights :  We propose a new boundary line for transition from water dominant to water-gas coordinated regimes  We introduce a new transition criterion derived from the representation of Taitel & Dukler (1976)  The local study shows that the gas influence increases beyond a gas superficial velocity threshold  The maximum two phase dissipation rate is increased by a factor 5 compared to the single phase case  The axial evolution of the bubble intercept length histograms exhibit bubble coalescence

52