1. Introduction 2. Experimental setup

Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998

FIRST RESULTS FROM THE CYRÈNE EXPERIMENT: FLOW MAP AND CONVECTIVE BOILING HEAT TRANSFER OF AMMONIA IN MICROGRAVITY Olivier Lebaigue, Jean-Marc Delhaye,

Catherine Colin,

Nathalie Bouzou, Thierry Maciaszek

Commissariat à l’Energie Atomique/Grenoble Centre National d'Etudes Spatiales/Toulouse Direction des Réacteurs Nucléaires Institut de Mécanique des Fluides CNES / DGA/T/AE/MTE/TH Département de Thermohydraulique UMR CNRS/INPT/UPS 5502 Division Mécanique/Thermique/Energétique et de Physique Département de Thermique

__________________________________________________________________________________

1. Introduction The experimental setup Cyrène has been designed, constructed and is now operated by CEA in partnership with CNES and IMFT in order to provide future designers of two-phase ammonia environmental control systems with adequate knowledge and data. Two-phase gas-liquid flow and phase change heat transfer are of great interest for satellites and other in-orbit systems thermal control. The basic advantage of two-phase heat extraction and transportation lies in its narrower temperature range for a lower pumping power (compared, for instance, to single-phase loops). The objective of the experiment is not to demonstrate the capability of a specific technology, but rather to provide accurate data on the most simple configuration, i.e., a circular tube, and to develop the corresponding experimental correlations. The experimental setup was designed to work in a microgravity environment and to measure the heat transfer and pressure drop coefficients for ammonia in a 4.8 mm aluminum circular pipe. The mass flow rate and quality values range up to 0.24 g/s and 0.8, respectively. High speed video visualizations on earth and in parabolic flights provide information on the flow configuration. Detailed temporal signals also will be used to validate existing thermalhydraulic codes. Experiments were conducted on earth in horizontal configuration and during two campaigns of parabolic flights in an aircraft. A test in a sounding rocket will complete this set of experiments. - The first campaign of parabolic flights with the Cyrène ammonia experiment took place in June 1995 on the CNES Caravelle. The pump of the secondary, cooling loop broke down during this campaign. Consequently, the obtained data were restricted to the boiling heat transfer coefficient at low quality and saturation pressure of 1.0 MPa. - A second campaign of parabolic flights was performed in May 1997 on the CNES Airbus A300. All loops of the Cyrène experiment worked perfectly during this second campaign. Data were acquired on boiling and condensing heat transfer coefficients as well as on pressure drops. Information on flow regime also was obtained and will be compared to existing flow maps. Three different pressures, 0.9, 1.3, and 1.8 MPa, were investigated. - A sounding rocket flight is needed to achieve a long period of microgravity time and confirm the trends observed at high quality for the condensing heat transfer coefficients. Such a long duration is necessary to achieve a proper thermal equilibrium in condensation. A first attempt was performed in January 1998 on a MASER rocket provided by the Swedish Space Corporation with the support of the European Space Agency (ESA). Due to malfunctioning of the telemetry service module no data are available for the moment. This paper presents a first analysis of the data acquired during the plane campaigns and focuses on results obtained from flow visualization and heated wall temperature measurements. Flow visualizations in microgravity lead to flow pattern map and mean vapor velocity. Evaporator data analysis leads to a correlation of local saturated boiling heat transfer coefficient valid for micro-, normal and 1.8 g gravity.

2. Experimental setup The experimental setup Cyrène has been described in detail in a previous paper (Lebaigue and Maciaszek, 1995) with a schematic and initial results. We will only give a short description of the experimental setup in this section. The equipment is made of two loops exchanging heat through a series of five exchangers. The primary working fluid is anhydrous ammonia. The secondary working fluid is water. Electric power is used to heat in the evaporator. This power is convected by latent heat, extracted in the condensers and driven to the heat sink, a phase change material (ice). 1

Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998 The ammonia loop is mainly constituted by a mechanical, variable speed pump, a special capillary (Picoflow®) used both for the loop stability and flow rate measurement, an evaporator consisting in a straight aluminum pipe with heating wire and insulation, a two-phase adiabatic pipe equipped with two flow visualization boxes, four cocurrent condensers, a subcooler and a pressurizer. The water loop primarily consists of a tank for the phase change material, a single mechanical variable speed pump flowing in five branches each composed of an adjustment valve, a flow metering device and a heat exchanger. Along with these two loops, the electronics provides instrumentation adapted to rocket telemetry (temperatures, absolute and differential pressures, flow rate measurements) and control (heaters, pump speeds, burnout detectors, ...). The setup also includes a strong envelope for ground and plane staff safety.

3. Flow pattern Two visualizing test sections are located 323 mm and 1323 mm downstream of the outlet of the evaporator. Flow pictures have been taken with 2 synchronized high-speed video cameras connected to a Kodak Ektapro EM Processor. From these pictures the flow patterns have been identified and the bubble velocities have been measured in bubbly and slug flows. The measurements of the bubble velocity are used to determined the quality when its value is too small to be determined, with accuracy, from a thermal balance of the evaporator.

& ranging between 0.04 g/s and 0.5 g/s and quality, x, up to 0.9, four different flow For mass flow rates m patterns have been found (figure 1). The quality is the ratio of the vapor mass flow rate over the total mass flow & . The flow patterns only have been identified at the first visualization test section corresponding to a rate m distance L from the outlet of the evaporator equal to 67 D, D being the tube diameter. At the second visualization test section (L = 1323 mm), due to the short microgravity periods limited to 20 seconds, at the lowest flow velocities, the flow does not become steady during the microgravity period. Furthermore, flow patterns observed at a distance L = 67 D can be compared with other experiments of the literature for L/D ratio between 60 and 80. Since the microgravity flows do not seem to be spatially established, it is important to compare data of different authors, for the same value of the L/D ratio.

Bubbly flow Slug flow Slug-annular flow Annular Flow Figure 1: Flow pattern of boiling ammonia in a 4.8 mm diameter tube. For very low values of the quality, smaller than 0.002, bubbly flow is observed, with bubbles of diameter close to the pipe diameter. Small bubbles are not present in this flow due to pipe diameter. As soon as nucleation takes place in microgravity, a strong coalescence mechanism leads to a rapid increase in bubble size. Only 2 runs corresponding to bubbly flow have been obtained. As the quality x is increased, slug flow appears. It consists of a succession of long cylindrical bubbles, separated by liquid slugs. The bubbles have a smooth interface. The slugs do not carry small bubbles as usually observed for two-phase flows at higher Reynolds numbers. 2

Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998 For the highest quality values (x > 0.7) an annular flow configuration is observed. It consists of liquid flowing in the form of a film at the pipe wall and gas flowing in the center. The transition between slug and annular flow takes place in a range of quality values between 0.6 and 0.7. A fourth pattern called slug-annular flow is an intermediate configuration between slug and annular flows. The cylindrical bubbles become very long, recover each other and coalesce (figure 1). This flow pattern appears for qualities between 0.4 and 0.7. The flow configurations are plotted on a flow pattern map versus the superficial velocities of the liquid phase jL and the vapor or gas phase jG in order to compare with other results obtained for adiabatic flows & , the quality x and the densities (figure 2). The superficial velocity may be calculated versus the mass flow rate m of the liquid ρ L and gas phase ρG : & x & (1 − x) m m jG = jL = [1] ρG ρL 3.1 Bubbly to slug flow transition The basic mechanism which controls the transition from bubbly to slug flow is the coalescence between bubbles. The rate of coalescence is promoted by an increase in the void fraction α (α is the part of the pipe cross section occupied by the gas phase). The void fraction also may be expressed versus the mean gas velocity U G and the superficial velocity of gas: α = jG / U G . For several studies with two-phase adiabatic and boiling flows, the transition has been found to occur at a critical value of the void fraction α crit. . By using a drift-flux model Colin et al. (1991) have found that the mean gas velocity can be calculated versus the mixture velocity j: j U G = G = C0 j = C0 ( jL + jG ) [2] α A value of C0 between 1.1 and 1.4 has been found for bubbly and slug flow. The mean gas velocity has been determined from image processing or calculated from the mean void fraction measured by conductive probes (Colin et al., 1991, Bousman & Dukler, 1994). Then, the transition between bubble and slug flow may be expressed as: 1 − C0 α crit. jL = jG [3] C0 α crit. The transition has been observed for different values of α crit. . The transition has occurred for a critical void fraction α crit. of 0.45 for air-water flows in tubes of 6, 10, 19 mm diameter (Dukler et al., 1988, Colin & Fabre, 1995), whereas it has been observed for a lower void fraction value of 0.2 for air-water flows in a 40 mm diameter tube, or for R12 boiling flows in a 10 mm diameter tube (Reinarts, 1993). Two regimes of coalescence have been identified: a promoting-coalescence regime for which transition happens for α crit. = 0.2 and an inhibiting-coalescence regime with transition at α crit. = 0.45. A literature survey of the different experimental data has shown that these two regimes are independent of the gas and liquid flow rates and that they only depend on the tube diameter and the fluid properties. These two regimes seem to be well predicted for air-water flow with glycerin or for R114, R12 boiling flows by a dimensionless number N D = σ D / ρ L ν 2L (Colin et al., 1996), where σ is the surface tension, ρ L the liquid density and ν L the kinematic viscosity. For N D smaller than 1.5x106 the coalescence is inhibited partially and the transition between bubbly and slug flows takes place for α crit. = 0.45. For N D greater than 1.5x106, slug flow appears as the void fraction reaches 0.2. For ammonia boiling flow in a 4.8 mm diameter tube, the value of N D is close to 3x106, which suggests that the coalescence will lead to a rapid transition to slug flow. For an experimental value of C0 equal to 1.38 (see section 4), equation [3] is plotted in figure 2 for a value of α crit equal to 0.1. The transition curve corresponding to other results of the literature with adiabatic and boiling flow are also plotted in this figure for C0 = 1.2 and α crit. = 0.2 and 0.45. For ammonia, it seems that the transition from bubbly to slug flow appears at than the value usually found for N number greater than 1.5x106. This strong a lower value of α D

crit.

coalescence rate may be explained by very low gas and liquid superficial velocities compared to other studies, for 3

Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998 which the superficial velocities range between 0.1 and 10 m/s. A smaller value of the superficial velocities in the tube leads to an increase in the residence time and in the coalescence rate. The value of α crit. equal to 0.1 corresponds to a value of the quality equal to 0.002 calculated using [1] and [3]: 1 x= [4] ρ 1 − C 0 α crit. 1+ L ρ V C0 α crit.

1

0.1

0.01

0.001

0.0001 0.0001

0.001

0.01 j G(m/s)

0.1

1

Figure 2: Flow pattern map : bubble, slug, slug-annular, annular flows ____ α crit. = 0.10, __ __ α crit. = 0.20,- - - - α crit. = 0.45, Bubbly-slug transition eq. [3] with: = 0.7. Slug to annular flows transition: __ - __ α crit.

3.2 Slug to annular flow transition For superficial liquid velocity greater than 1 cm/s, no annular flow has been observed in the runs with ammonia, for the investigated mass flow rates and qualities. The transition from slug to slug-annular flows seems to happen at a constant value of the void fraction equal to 0.7, which is a little smaller than the value of 0.755 found by Dukler et al. (1988). These authors have assumed that the void fraction at the transition calculated from both slug flow model and annular flow model must be equal. The value of α has been found by equating the values of the void fraction calculated on one side in slug flow [2] and on the other side from a momentum balance in annular flow. For values of jL smaller than 1 cm/s, the transition from slug to annular flow has not occurred for a critical value of the void fraction but rather for a constant value of the superficial gas velocity jG ranging between 0.3 and 0.5 m/s. These values correspond to Weber number of the gas phase We GS = ρG j2G D / σ between 0.1 and 0.3. Zhao and Rezkallah (1993) have observed for higher flow rates that the transition between slug and frothy-slug annular flows occurred when We GS = 1 and the transition from frothy slug-annular flow and annular flow occurred when We GS = 20. The experiments with ammonia at low flow rates seem to show that the different transitions appear for lower values of α or jG in comparison with other experiments carried out with air-water or R12 flows, for higher gas and liquid velocities.

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4. Mean gas velocity and phase fraction In these experiments, the cross-sectional averaged void fractions have not been measured. The mean gas velocities U G have been directly measured for bubbly and slug flows, from flow visualization after image processing. The mean gas velocity is plotted versus the mixture velocity j = jG + jL in figure 3. The values of the mean gas velocity calculated by a drift-flux model [2] are in good agreement with the experimental data for a value of C0 equal to 1.38. The experiments with ammonia are compared with experiments carried out with airwater flows in 6 and 19 mm diameter tubes (figure 4). The value of C0 found for flows in the 10 and 19 mm diameter tube is close to 1.2, whereas it seems to be slightly greater for experiments in the 6 mm diameter tube. In the experiments with boiling ammonia no significant difference with air-water flow experiments have been observed on the mean gas velocity.

0.8

3 2.5

0.6

2 0.4

1.5 U (m/s) 1 G

0.2

0.5 0

0 0

0.1

0.2 0.3 j (m/s)

0.4

0.5

0

1 1.5 j (m/s) Figure 4: Mean gas velocity ammonia boiling flow D=4.8mm

Figure 3: Mean gas velocity ammonia boiling flow ____ Eq. [2] with C0=1.38.

0.5

2

air-water flow D=19mm, D=10mm, D=6 mm Eq. [2] with ____ C0=1.38, - - - - C0=1.2.

5. Saturated boiling heat transfer coefficients 5.1. Origin of the database Heat transfer data obtained during the parabolic flights concern one-phase, subcooled boiling, saturated boiling and post-CHF regimes. However, only saturated boiling data are analyzed in this section. This regime is the most important for the two-phase thermal control loop design and most of the data points were acquired in this regime. To select the data used in this analysis, we chose points with positive equilibrium quality. A further analysis of the other data points will give information on subcooled nucleate boiling of CHF and post-dryout regimes. Data points used in this section were obtained from 54 parabolas distributed in 3 flights, each dedicated to a different global pressure (0.9, 1.3 and 1.8 MPa) corresponding to 3 saturation temperatures (ca. 20, 30 and 45 °C). For each pressure (each flight), the test matrix was performed twice. It consists in 3 outlet qualities (ca. -2 0.3, 0.6 and 0.8) crossed with 3 heat flux (ca. 0.17, 0.33 and 0.50 kW.m ). Mass flow rates were imposed with respect to latent heat, quality and heat flux values. Four local wall temperature measurements provide an estimate of saturated heat transfer coefficient he i

(

)

through the classical equation hei = q / Tw ,i − Tsat , where q is the heat flux, Tw , i the wall temperature at the i location and Tsat the saturation temperature at the global pressure of the loop. These thermocouples are located respectively at ca. 17, 118, 152 and 186 mm from inlet of the 202.5 mm evaporator. The thermal time constant due to the thickness of the wall is estimated to be 6-7 seconds and suggests that a fair thermal equilibrium can be reach in a 22 second parabola. th

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Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998 Equilibrium quality is estimated by using a thermal balance with the inlet subcooled temperature and integrated heat flux. Temperature records are processed with a 0.6 s time constant filtering to improve signal to noise ratio. The 4 local heat transfer coefficients are collected in the 54 selected parabolas for normal, hyper- and microgravity. Figure 5 gives an example of heat transfer coefficients. In the case of figure 5, a clear increase of heat transfer is observed in microgravity close to the outlet (he6) whereas a slight is observed at low quality close to inlet (he1). The reverse situation is observed in the 1.8 g periods close to the microgravity.

10 9 8 7 6 5

he1 he4 he5 he6 µg

4 3 2 1 0 3420

3440

3460

3480

3500

3520

3540 -2

3560

3580

-1

Figure 5: Local heat transfer coefficient he i and gravity level (kW.m .K ) vs. time (s) -2 Parabola 12 from flight 1 (0.9 MPa); Inlet quality: -0.05; outlet quality: 0.29; heat flux: 0.32 kW.m ; mass flow: 0.246 g/s; Gravity sensor was limited to ± 0.1 g but is plotted as 0 to 1 Y-axis unit. All data points with positive quality have been qualified for the database. This includes points in the nucleate boiling regime, the saturated or convective boiling regime and also points where CHF is achieved. However, CHF data are restricted to 190 °C wall overheat due to an electronic burnout detection that limits heat flux and prevents wall temperature from exceeding this value (in measured location). The total number of data points is 189 for each gravity condition, that is a total of 567 points. Negative quality points are not studied in the present paper. 5.2. Data reduction According to the strategy defined in Delhaye and Lebaigue (1991), boiling heat transfer coefficients were first compared to classical earth correlations. The general purpose correlations of Chen (1966), Gungor and Winterton (1986) were first compared to experimental data. They predict heat transfer coefficients from our database in 0g, 1g and 1.8 g with 40-50 % accuracy, except for the data points related to one-phase or critical heat flux (CHF) situations. This is in fact produced by the nucleate boiling part of the correlation and not by the enhancement/suppression adjustment. Chen's correlation relies on Forster and Zuber (1955) expression for nucleate boiling; Gungor and Winterton correlation relies on Cooper expression (Cooper, 1984). The Bowring correlation (1972), adapted from the Thom et al. (1965) expression for nucleate boiling (though dedicated to subcooled boiling) provided us with the best estimate of the existing general correlations. All partial expressions for the nucleate boiling part give results similar to complete correlation, due to the fact that the convective contribution has no effect. This can be justified also by the liquid Péclet value of our data points (100 to 500), far below the Pe = 70,000 limit between thermal and hydrodynamic regimes of the Saha and Zuber analysis (1974). 6

Third International Conference on Multiphase Flows, ICMF’98 Lyon, France, June 8-12, 1998 Clearly, all our heat transfer coefficients are in the thermal regime and the convective contribution of the general correlations is of no use. This also is enforced by the inadequate contribution of the general correlations built from the convective Dittus and Boelter (1930) expression, whereas liquid Reynolds number remains lower than 2,000 in our experiments. Therefore, a data reduction based only on a nucleate boiling heat transfer is given in this section. The different nucleate boiling correlations given in the previous paragraph have been checked against the experimental data. The expression closest to the data is the Thom et al. expression. In addition, attempts made to construct correlations with a given structure on these different bases lead always to the same results: Thom et al. empirical expression [5] has to be preferred: Psat   h T hom = 44.15 q Exp 0.023 [5]   100,000  -2 -1 -2 where h T hom is in W.m .K , q is the imposed heat flux (W.m ), and Psat the saturation pressure. A sensitivity analysis indicates two major dependencies: the quality, x, as in the Steiner and Taborek approach (1992) and the Bond number, Bo, which is the best nondimensional number to take gravity into account. Data reduction through the simple expression [6] gives a description of the experimental data points with a scattering of ± 25.8 % (with c1 = 0.7388, c 2 = -0.4150 and c 3 = -0.0178):

h1 = (c1 + x (c 2 + Bo c 3 )) h T hom

[6]

10 8 6

x0.4 -25%

4

+25%

2 0 0

2

4

6

8

10 -2

-1

Figure 6: Predicted by expression [7] vs. measured local heat transfer coefficient he i (kW.m .K ) a=0.04895 et b=22.01. Expression [6] gives a correct description of saturated nucleate (x < 0.4 in our example) boiling heat exchange coefficients. Discrepancies occur at quality higher than 0.4 due to the possibility of CHF. To try to capture some CHF events, we modify the expression [6] by simple asymptotic correction: 3 h 2−3 = h1−3 + (a + b X tt ) h −Dittus ,V

[7]

where h Dittus, V is the classical Dittus-Boelter correlation calculated with vapor only and X tt the classical Martinelli parameter. Figure 6 indicates that this simple improvement allows to take care of some CHF events -2 -1 (scattering of ± 24.8 %). However, other events remain non predicted (points predicted higher than 2 W.m .K -2 -1 and measured lower than 2 W.m .K ) and further work is needed.

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6. Conclusion This short paper presents some results for flow configuration map, vapor velocity and saturated boiling heat transfer coefficient. Extension of the adiabatic data analysis will provide us with a link between pressure drop and flow regime. More work also is needed to understand subcooled boiling and inset of nucleate boiling, especially in microgravity. A special care also will be given to the CHF limits that is of first importance for the design of high quality thermal control loop. Acknowledgments: We would like to thank CNES for financial support and organization of the parabolic flight campaigns.

7. References BOUSMAN W. S. & DUKLER A. E., 1994, Studies of gas-liquid flow in microgravity: Void fraction, pressure drop and flow patterns, Proceedings of Symposium on Fluid Mechanics Phenomena in Microgravity, AMD-Vol. 174/FED-Vol.175, ASME Winter Annual Meeting, New Orleans, LA, November 28-December 3, 1993, pp. 23-36 BOWRING W. R., Round tube, uniform heat flux; Dryout correlation for water, U.K. Report, AEEW-R 5005, Harwell, 1972 (Ch. 7.5).CHEN J. C., 1966, Correlation for boiling heat transfer to saturated fluids in convective flow, I&EC Process Design and Development, Vol. 5, No. 3, pp. 322-329. CHEN J. C., 1966, Correlation for boiling heat transfer to saturated liquids in convective flow, Ind. Eng. Chem. Process Des. Dev., Vol. 5, pp. 322-329. COLIN C., FABRE J. & DUKLER A. E., 1991, Gas-Liquid flow at microgravity conditions-I: Dispersed bubble and slug flow, Int. J. Multiphase Flow, Vol. 17, pp. 533-544. COLIN C. & FABRE J., 1995, Gas-liquid pipe flow under microgravity conditions: influence of tube diameter on flow patterns and pressure drops, Adv. Space Res., Vol. 16, pp. 7137-7142. COLIN C., FABRE J. & MCQUILLEN J. B., 1996, Bubble and slug flow at microgravity conditions: state of knowledge and open questions, Chem. Eng. Comm., Vol. 141-142, pp. 155-173. COOPER M. G., 1984, Saturation nucleate pool boiling - A simple correlation, Proc. 1st UK Nat. Conf. on Heat Transfer, Leeds, 3-5 July, 1984, in AIChE Symp. Ser., No. 86, pp. 785-793. DELHAYE J. M. & LEBAIGUE O., 1991, Forced convection boiling and condensation in microgravity: A critical appraisal of the literature, First European Symposium on Fluids in Space, Ajaccio, France, 18-22 Nov. 1991, ESA SP-353, pp. 311-327. DITTUS F. W. & BOELTER L. M. K., 1930, Heat transfer in automobile radiators of tubular type, Publications in Engineering, Univ. of California, Berkeley, Vol. 2, p. 433-461. DUKLER A. E., FABRE J. A., MCQUILLEN J. B. & VERNON, R., 1988, Gas-liquid flow at microgravity conditions: flow pattern and their transitions, Int. J. Multiphase Flow, Vol. 14, pp. 389-400. FORSTER H. K. & ZUBER N., 1955, Dynamics of vapor bubbles and boiling heat transfer, AIChE Journal, Vol. 1, No. 4, pp. 531-535. GUNGOR K. E. & WINTERTON R. H. S., 1986, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer, Vol. 29, No. 3, pp. 351-358. LEBAIGUE O. & MACIASZEK T., 1995, Cyrène: an ammonia loop to study convective boiling and condensation in microgravity, AIAA Paper 95-3512, Proc. 1995 ASME/AIAA National Heat Transfer Conf., Portland, OR, USA, August 6-9, 1995. REINARTS T. R., 1993, Adiabatic two phase flow regime data and modeling for zero and reduced (horizontal flow) acceleration fields, PhD dissertation, Univ. of Texas A&M. SAHA P. & ZUBER N., 1974, Point of net vapor generation and vapor void fraction in subcooled boiling, Heat Transfer 1974, Proc. of the 5th Int. Heat Transfer Conf., Tokyo, Vol. 4, paper B4.7, pp. 175-179. STEINER D. & TABOREK J., 1992, Flow boiling heat transfer in vertical tubes correlated by an asymptotic model, Heat Transfer Engng., Vol. 13, No. 2, pp. 43-69. THOM J. R. S., WALKER W. W., FALLON T. A. & REISING G. F. S., 1965, Boiling in subcooled water during flow up heated tubes or annuli, Proc. Symp. on Boiling Heat Transfer in Steam Generating Units and Exchangers, Manchester, 15-16 September, IMechE, London. ZHAO L. & REZKALLAH K. S., 1993, Gas liquid flow patterns at microgravity conditions, Int. J. Multiphase Flow, Vol. 19, pp. 751-763.

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