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1

Chang, I.-Shih. "Three-dimensional, two-phase, transonic, canted nozzle flows." AIAA Journal 28, no. 5 (1990): 790–97. http://dx.doi.org/10.2514/3.25121.

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2

CAI, LI, JUN ZHOU, FENG-QI ZHOU, and WEN-XIAN XIE. "A HYBRID SCHEME FOR THREE-DIMENSIONAL INCOMPRESSIBLE TWO-PHASE FLOWS." International Journal of Applied Mechanics 02, no. 04 (2010): 889–905. http://dx.doi.org/10.1142/s1758825110000810.

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We present a hybrid scheme for computations of three-dimensional incompressible two-phase flows. A Poisson-like pressure equation is deduced from the incompressible constraint, i.e., the divergence-free condition of the velocity field, via an extended marker and cell method, and the moment equations in the 3D incompressible Navier–Stokes equations are solved by our 3D semi-discrete Hermite central-upwind scheme. The interface between the two fluids is considered to be the 0.5 level set of a smooth function being a smeared out Heaviside function. Numerical results are offered to verify the desired efficiency and accuracy of our 3D hybrid scheme.
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3

Zhao, Chun-Xia, and Anton P. J. Middelberg. "Two-phase microfluidic flows." Chemical Engineering Science 66, no. 7 (2011): 1394–411. http://dx.doi.org/10.1016/j.ces.2010.08.038.

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4

Sassi, Paolo, Youssef Stiriba, Julia Lobera, Virginia Palero, and Jordi Pallarès. "Experimental Analysis of Gas–Liquid–Solid Three-Phase Flows in Horizontal Pipelines." Flow, Turbulence and Combustion 105, no. 4 (2020): 1035–54. http://dx.doi.org/10.1007/s10494-020-00141-1.

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AbstractThe dynamics of three-phase flows involves phenomena of high complexity whose characterization is of great interest for different sectors of the worldwide industry. In order to move forward in the fundamental knowledge of the behavior of three-phase flows, new experimental data has been obtained in a facility specially designed for flow visualization and for measuring key parameters. These are (1) the flow regime, (2) the superficial velocities or rates of the individual phases; and (3) the frictional pressure loss. Flow visualization and pressure measurements are performed for two and three-phase flows in horizontal 30 mm inner diameter and 4.5 m long transparent acrylic pipes. A total of 134 flow conditions are analyzed and presented, including plug and slug flows in air–water two-phase flows and air–water-polypropylene (pellets) three-phase flows. For two-phase flows the transition from plug to slug flow agrees with the flow regime maps available in the literature. However, for three phase flows, a progressive displacement towards higher gas superficial velocities is found as the solid concentration is increased. The performance of a modified Lockhart–Martinelli correlation is tested for predicting frictional pressure gradient of three-phase flows with solid particles less dense than the liquid.
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5

Pereira, Francisco, and Morteza Gharib. "A method for three-dimensional particle sizing in two-phase flows." Measurement Science and Technology 15, no. 10 (2004): 2029–38. http://dx.doi.org/10.1088/0957-0233/15/10/012.

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6

OUYANG, C. J. P., and G. B. TATTERSON. "THE EFFECT OF DISTRIBUTORS ON TWO-PHASE AND THREE-PHASE FLOWS IN VERTICAL COLUMNS." Chemical Engineering Communications 49, no. 4-6 (1987): 197–215. http://dx.doi.org/10.1080/00986448708911803.

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7

Kaban'kov, O. N., and A. P. Sevast'yanov. "TWO-PHASE FLOWS: A REVIEW." Heat Transfer Research 31, no. 1-2 (2000): 103–22. http://dx.doi.org/10.1615/heattransres.v31.i1-2.200.

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8

Hwang, S. T., H. M. Soliman, and R. T. Lahey. "Phase separation in dividing two-phase flows." International Journal of Multiphase Flow 14, no. 4 (1988): 439–58. http://dx.doi.org/10.1016/0301-9322(88)90021-3.

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9

Koobus, B., S. Camarri, M. V. Salvetti, S. Wornom, and A. Dervieux. "Parallel simulation of three-dimensional complex flows: Application to two-phase compressible flows and turbulent wakes." Advances in Engineering Software 38, no. 5 (2007): 328–37. http://dx.doi.org/10.1016/j.advengsoft.2006.08.009.

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10

Mitra-Majumdar, D., B. Farouk, Y. T. Shah, N. Macken, and Y. K. Oh. "Two- and Three-Phase Flows in Bubble Columns: Numerical Predictions and Measurements." Industrial & Engineering Chemistry Research 37, no. 6 (1998): 2284–92. http://dx.doi.org/10.1021/ie980022i.

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11

Li, Yibao, Ana Yun, Dongsun Lee, Jaemin Shin, Darae Jeong, and Junseok Kim. "Three-dimensional volume-conserving immersed boundary model for two-phase fluid flows." Computer Methods in Applied Mechanics and Engineering 257 (April 2013): 36–46. http://dx.doi.org/10.1016/j.cma.2013.01.009.

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12

Celata, G. P., M. Cumo, F. D'Annibale, and G. E. Farello. "Two-phase flow models in unbounded two-phase critical flows." Nuclear Engineering and Design 97, no. 2 (1986): 211–22. http://dx.doi.org/10.1016/0029-5493(86)90109-3.

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13

Deng, Bin, Chang Bo Jiang, Zhi Xin Guan, and Chao Shen. "Verification of STACS-VOF Based Two-Phase Flow Model for Interfacial Flows." Applied Mechanics and Materials 212-213 (October 2012): 1098–102. http://dx.doi.org/10.4028/www.scientific.net/amm.212-213.1098.

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The numerical calculation and simulation of gas-liquid two-phase flows with interfacial deformations have nowadays become more and more popular issues in various scientific and industrial fields. In this study, a three-dimensional gas-liquid two-phase flow numerical model is presented for investigating interfacial flows. The finite volume method was used to discretize the governing equations. A High-resolution scheme of VOF method (STACS) is applied to capture the free surface. The paper outlines the methodology of STACS and its validation against three typical test cases used to verify its accuracy. The results show the STACS-VOF gives very satisfactory results for three-dimensional two-phase interfacial flows problem, and this scheme performs more accurate and less diffusive preserving interface sharpness and boundedness.
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14

Yang, Sheng Qiang, Wen Hui Li, and Shi Chun Yang. "Flows Field Simulation of Two-Phase Swirling Flows Finishing." Advanced Materials Research 24-25 (September 2007): 17–22. http://dx.doi.org/10.4028/www.scientific.net/amr.24-25.17.

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Two-phase swirling flows finishing is put forward mainly for hole surface. By theoretic analysis and experimental research, the characteristics of flows field will directly affect finishing quality and efficiency. On the basic premise of defining Renault stress model on swirling flows field, numerical simulation of velocity vector graph, turbulent kinetic energy graph, turbulent dissipation ratio graph, pressure distribution graph, vorticity magnitude distribution graph etc. are made, and vorticity magnitude and tangential velocity in different mediums are contrasted, which provide theoretic basis for thorough research.
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15

Cordier, Floraine, Pierre Degond, and Anela Kumbaro. "Phase Appearance or Disappearance in Two-Phase Flows." Journal of Scientific Computing 58, no. 1 (2013): 115–48. http://dx.doi.org/10.1007/s10915-013-9725-9.

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16

Abbas, H. A. M. Hasan. "Measurement of a Void Fraction in Bubbly Gas-Water Two Phase Flows Using Differential Pressure Technique." Applied Mechanics and Materials 152-154 (January 2012): 1221–26. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.1221.

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Multiphase flows, where two or even three fluids flow simultaneously in a pipe are becoming increasingly important in industry. In order to measure the flow rate of gas-water two phase flows accurately, the void fraction (gas volume fraction) in two phase flows must be precisely measured. The differential pressure technique has proven attractive in the measurement of volume fraction. This paper presents the theoretical and experimental study of the void fraction measurement in bubbly gas water two phase flows using differential pressure technique (the flow density meter).
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17

WATANABE, Keizo. "Drag Reduction in Two-Phase Flows." JAPANESE JOURNAL OF MULTIPHASE FLOW 6, no. 4 (1992): 371–78. http://dx.doi.org/10.3811/jjmf.6.371.

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18

Hahn, Andreas, Kristin Held, and Lutz Tobiska. "ALE-FEM for Two-Phase Flows." PAMM 13, no. 1 (2013): 319–20. http://dx.doi.org/10.1002/pamm.201310155.

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19

Han, Daozhi, Dong Sun, and Xiaoming Wang. "Two-phase flows in karstic geometry." Mathematical Methods in the Applied Sciences 37, no. 18 (2013): 3048–63. http://dx.doi.org/10.1002/mma.3043.

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20

Lun, I., R. K. Calay, and A. E. Holdo. "Modelling two-phase flows using CFD." Applied Energy 53, no. 3 (1996): 299–314. http://dx.doi.org/10.1016/0306-2619(95)00024-0.

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21

Vinberg, A. A., L. I. Zaichik, and V. A. Pershukov. "Calculation of two-phase swirling flows." Fluid Dynamics 29, no. 1 (1994): 55–60. http://dx.doi.org/10.1007/bf02330622.

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22

Chen, Yongliang, and Stephen D. Heister. "Two-phase modeling of cavitated flows." Computers & Fluids 24, no. 7 (1995): 799–809. http://dx.doi.org/10.1016/0045-7930(95)00017-7.

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23

Oddie, G., H. Shi, L. J. Durlofsky, K. Aziz, B. Pfeffer, and J. A. Holmes. "Experimental study of two and three phase flows in large diameter inclined pipes." International Journal of Multiphase Flow 29, no. 4 (2003): 527–58. http://dx.doi.org/10.1016/s0301-9322(03)00015-6.

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24

Takahira, Hiroyuki, Tomonori Horiuchi, and Sanjoy Banerjee. "An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows." Journal of Fluids Engineering 126, no. 4 (2004): 578–85. http://dx.doi.org/10.1115/1.1777232.

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For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.
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25

Kawano, Akio. "A simple volume-of-fluid reconstruction method for three-dimensional two-phase flows." Computers & Fluids 134-135 (August 2016): 130–45. http://dx.doi.org/10.1016/j.compfluid.2016.05.014.

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26

Nguyen, Van-Tu, Van-Dat Thang, and Warn-Gyu Park. "A novel sharp interface capturing method for two- and three-phase incompressible flows." Computers & Fluids 172 (August 2018): 147–61. http://dx.doi.org/10.1016/j.compfluid.2018.06.020.

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27

van der Pijl, S. P., A. Segal, C. Vuik, and P. Wesseling. "Computing three-dimensional two-phase flows with a mass-conserving level set method." Computing and Visualization in Science 11, no. 4-6 (2008): 221–35. http://dx.doi.org/10.1007/s00791-008-0106-0.

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28

De Rosis, Alessandro, and Enatri Enan. "A three-dimensional phase-field lattice Boltzmann method for incompressible two-components flows." Physics of Fluids 33, no. 4 (2021): 043315. http://dx.doi.org/10.1063/5.0046875.

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29

Krawczyk, John. "Two Phases, Three Runs." Mechanical Engineering 123, no. 10 (2001): 74–75. http://dx.doi.org/10.1115/1.2001-oct-7.

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Premcor Port Arthur Refinery, part of the Premcor Refining Group has been expanding the capacity of a vacuum tower processing almost one million pounds per hour of heavy hydrocarbon feed. The feed is deficient in lighter, more volatile components and is extremely viscous at room temperature. The process is intended to squeeze as much useful fuel as practical out of the oil feed. During the past 5 years, CFD has become noticeably more widespread in solving single-phase flow problems, but progress in solving multiphase flows has been much slower. There are at least three primary solution methods currently available to solve a dispersed multiphase flow problem. The contract with Premcor called for the use of a Eulerian method. Later, as an in-house test, Flow Simulations studied the model of the tower using two other methods.
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30

Morel, Christophe. "On the surface equations in two-phase flows and reacting single-phase flows." International Journal of Multiphase Flow 33, no. 10 (2007): 1045–73. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2007.02.008.

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31

Liu, Shuhong, Yulin Wu, Yu Xu, and Hua-Shu Dou. "Analysis of Two-Phase Cavitating Flow with Two-Fluid Model Using Integrated Boltzmann Equations." Advances in Applied Mathematics and Mechanics 5, no. 05 (2013): 607–38. http://dx.doi.org/10.4208/aamm.12-m1256.

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AbstractIn the present work, both computational and experimental methods are employed to study the two-phase flow occurring in a model pump sump. The two-fluid model of the two-phase flow has been applied to the simulation of the three-dimensional cavitating flow. The governing equations of the two-phase cavitating flow are derived from the kinetic theory based on the Boltzmann equation. The isotropic RNGk — ε — kcaturbulence model of two-phase flows in the form of cavity number instead of the form of cavity phase volume fraction is developed. The RNGk—ε—kcaturbulence model, that is the RNGk — eturbulence model for the liquid phase combined with thekcamodel for the cavity phase, is employed to close the governing turbulent equations of the two-phase flow. The computation of the cavitating flow through a model pump sump has been carried out with this model in three-dimensional spaces. The calculated results have been compared with the data of the PIV experiment. Good qualitative agreement has been achieved which exhibits the reliability of the numerical simulation model.
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32

Gao, Zhong-Ke, Ning-De Jin, Wen-Xu Wang, and Ying-Cheng Lai. "Phase characterization of experimental gas–liquid two-phase flows." Physics Letters A 374, no. 39 (2010): 4014–17. http://dx.doi.org/10.1016/j.physleta.2010.08.005.

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33

Ageev, S. E., V. T. Movchan, A. M. Mkhitaryan, and E. A. Shkvar. "Modeling two-phase flows with a phase interfacial surface." Journal of Applied Mechanics and Technical Physics 31, no. 6 (1991): 827–30. http://dx.doi.org/10.1007/bf00854193.

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34

Bakhtar, F., S. R. Otto, M. Y. Zamri, and J. M. Sarkies. "Instability in two-phase flows of steam." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2091 (2007): 537–54. http://dx.doi.org/10.1098/rspa.2007.0087.

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In two-phase flows of steam, when the velocity is between the equilibrium and frozen speeds of sound, the system is fundamentally unstable. Because any disturbance of the system, e.g. imposition of a small supercooling on the fluid, will cause condensation, the resulting heat release will accelerate the flow and increase the supercooling and thus move the system further from thermodynamic equilibrium. But in high-speed flows of a two-phase mixture, dynamic changes affect the thermodynamic equilibrium within the fluid, leading to phase change, and the heat release resulting from condensation disturbs the flow further and can also cause the disturbances to be amplified at other Mach numbers. To investigate the existence of instabilities in such flows, the behaviour of small perturbations of the system has been examined using stability theory. It is found that, although the amplification rate is highest between the equilibrium and frozen speeds of sound, such flows are temporally unstable at all Mach numbers.
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35

Nowakowski, Jacek, Piotr Ostalczyk, and Dominik Sankowski. "APPLICATION OF FRACTIONAL CALCULUS FOR MODELLING OF TWO-PHASE GAS/LIQUID FLOW SYSTEM." Informatics Control Measurement in Economy and Environment Protection 7, no. 1 (2017): 42–45. http://dx.doi.org/10.5604/01.3001.0010.4580.

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In recent years the use of fractional calculus in control system identification is becoming popular and it has found new applications. The paper presents application of fractional calculus for modelling of two-phase gas/liquid flows in a test rig. The installation consists of three horizontal and vertical measuring segments with different diameters, which allow to investigate flows in a wide range of parameters. Flow components supply is measured/controlled by NI PXI system and a set of flow meters/controllers. The paper presents model of the two-phase flow in the above described installation, which leads to precise and accurate flow mathematical model. The main goal of the flow model is to describe steady flow parameters, especially the flow fractions, or type of the flow. The model describes flows more accurately, that classical second order system model.
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36

TAKADA, Naoki, Junichi MATSUMOTO, and Sohei MATSUMOTO. "916 Interface-tracking Simulations of Two- and Three-phase Fluid Flows Using a Phase-field Model Approach." Proceedings of The Computational Mechanics Conference 2011.24 (2011): 315–16. http://dx.doi.org/10.1299/jsmecmd.2011.24.315.

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37

He, Ping, Nai Chao Chen, and Dan Mei Hu. "Study of Wake Characteristics of a Horizontal-Axis Wind Turbine within Two-Phase Flow." Key Engineering Materials 474-476 (April 2011): 811–15. http://dx.doi.org/10.4028/www.scientific.net/kem.474-476.811.

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The two-phase flow is addressed for the more accurate estimation of the wake characteristic for the horizontal-axis wind turbine operating in the complexly unsteady environmental states. The computational fluid dynamics (CFD) method is implemented for performing the three-dimensional wind turbine using the simulating software tool of FLUNT. Three types of environmental states, single-phase flow, liquid-gas flow and solid-gas flow, are performed for the comparison of velocity and pressure distribution to derive the specify feature for wind turbine within two-phase flow environmental state. The calculated results shows that there has the similar evolutional tendency of velocity distribution for both single- and two-phase flows and the velocity decrement at the distance of 20 meter away from wind turbine still reach to 80% of inflow speed. But the turbine blade within two-phase flow is subject to the unsteady flow with the larger velocity gradient compared with that within single-phase flow. For the static pressure, large difference occurred in these three types of environmental state reveals that the second material in addition to atmospheres causes the prominent influence of aerodynamic force and its power coefficient. The results exhibit that wind turbine within solid-gas flow has the largest power coefficient that those within the gas and liquid-gas flows.
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38

Pereira, Francisco, and Morteza Gharib. "Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows." Measurement Science and Technology 13, no. 5 (2002): 683–94. http://dx.doi.org/10.1088/0957-0233/13/5/305.

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39

Minko, V. A., T. N. Ilyina, A. V. Minko, and D. A. Emelyanov. "Calculation of Ducts for Two-Phase Flows." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 22, no. 4 (2016): 648–56. http://dx.doi.org/10.17277/vestnik.2016.04.pp.648-656.

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40

Valizadeh, A., M. Shafieefar, J. J. Monaghan, and S. A. A. Salehi Ney. "Modeling Two-Phase Flows Using SPH Method." Journal of Applied Sciences 8, no. 21 (2008): 3817–26. http://dx.doi.org/10.3923/jas.2008.3817.3826.

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41

Bousfield, Douglas W., and Mikael Rigdahl. "Two phase flows under the coating blade." Nordic Pulp & Paper Research Journal 15, no. 5 (2000): 376–81. http://dx.doi.org/10.3183/npprj-2000-15-05-p376-381.

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42

Cunningham, R. "Liquid jet pumps for two-phase flows." International Journal of Multiphase Flow 22 (December 1996): 147. http://dx.doi.org/10.1016/s0301-9322(97)88574-6.

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43

Radvogin, Yu B., V. S. Posvyanskii, and S. M. Frolov. "Stability of 2D two-phase reactive flows." Journal de Physique IV (Proceedings) 12, no. 7 (2002): 437–44. http://dx.doi.org/10.1051/jp4:20020313.

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44

Brandner, Markus, and Gert Holler. "Optical velocimetry in cryogenic two-phase flows." Procedia Engineering 5 (2010): 1474–77. http://dx.doi.org/10.1016/j.proeng.2010.09.395.

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45

Ng, T. S., C. J. Lawrence, and G. F. Hewitt. "Friction Factors in Stratified Two-Phase Flows." Chemical Engineering Research and Design 82, no. 3 (2004): 309–20. http://dx.doi.org/10.1205/026387604322870426.

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46

Rudman, Murray. "One-field equations for two-phase flows." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 2 (1997): 149–70. http://dx.doi.org/10.1017/s033427000000878x.

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AbstractA new derivation of the averaged heat and mass transport equations for two-phase flows is presented. A volume averaging technique is used in which averaging is perform over both phases simultaneously in order to derive equations that describe transport the mixture, rather than transport in each phase. The derivation is particularly applicable to incompressible liquid/solid systems in which the two phases are tightly coupled. An example of the numerical solution of the equations is then presented in which a thermally convecting suspension is modelled. It is seen that large-scale instability can result from the interaction of thermal and compositional density gradients.
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47

Filippov, Yu P. "Characteristics of horizontal two-phase helium flows." Cryogenics 39, no. 1 (1999): 59–68. http://dx.doi.org/10.1016/s0011-2275(98)00114-3.

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48

Filippov, Yu P. "Characteristics of horizontal two-phase helium flows." Cryogenics 39, no. 1 (1999): 69–75. http://dx.doi.org/10.1016/s0011-2275(98)00115-5.

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49

Daniel, E., R. Saurel, M. Larini, and J. C. Loraud. "A multiphase formulation for two phase flows." International Journal of Numerical Methods for Heat & Fluid Flow 4, no. 3 (1994): 269–80. http://dx.doi.org/10.1108/eum0000000004107.

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50

Jaberi, F. A., and F. Mashayek. "Temperature decay in two-phase turbulent flows." International Journal of Heat and Mass Transfer 43, no. 6 (2000): 993–1005. http://dx.doi.org/10.1016/s0017-9310(99)00185-4.

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