Research Papers: Two-Phase Flow and Heat Transfer

A Pressure-Base One-Fluid Compressible Formulation for High Speed Two-Phase Flows With Heat and Mass Transfer

[+] Author and Article Information
Yan Luo

Laboratory Technician,
School of Mechanical and Power Engineering,
Nanjing Tech University,
No.6, Puzhu South Road,
Pukou District,
Nanjing 211816, Jiangsu Province, China
e-mail: 3095068802@qq.com

Jianqiu Zhou

School of Mechanical and Power Engineering,
Nanjing Tech University,
No.6, Puzhu South Road,
Pukou District,
Nanjing 211816, Jiangsu Province, China
e-mail: 3110837040@qq.com

Xia Yang

School of Mechanical and Electrical Engineering,
Wuhan institute of Technology,
No.1, Liufang Avenue,
Jiangxia District,
Wuhan 430073, Hubei Province, China
e-mail: 3348489608@qq.com

Zhanxiang Jiang

School of Mechanical and Electrical Engineering,
Wuhan institute of Technology,
No.1, Liufang Avenue,
Jiangxia District,
Wuhan 430073, Hubei Province, China
e-mail: 411841183@qq.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 14, 2017; final manuscript received March 13, 2018; published online April 19, 2018. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 140(8), 082901 (Apr 19, 2018) (17 pages) Paper No: HT-17-1603; doi: 10.1115/1.4039686 History: Received October 14, 2017; Revised March 13, 2018

This paper presents a numerical method for high-speed compressible cavitating flows. The method is derived from one-fluid formulation in a sense that the two phases are well mixed and the mixture is considered as a locally homogeneous media. Energy equation is solved to predict the temperature evolution which is then used together with pressure to update the density field. A volume of fluid (VOF) phase-fraction based interface capturing approach is used to capture the phase front between the two immiscible fluids. The derived formulations have been implemented into a pressure-based, segregated algebraic semi-implicit compressible solver in Openfoam, which can be used to solve for high-speed compressible two-phase flows involving phase changing. Numerical examples include the cavitating flows induced by an ultrasonic oscillating horn with and without a counter sample. The numerical results by the proposed method are validated against the published experimental data as well as numerical results and good agreements have been obtained. Our calculation demonstrates that the proposed numerical method is applicable to the study of high-speed two phase flows with phase transition and wave propagation, such as shock waves induced by the collapse of the cavitation bubbles.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Choo, K. S. , and Kim, S. J. , 2010, “ Heat Transfer and Fluid Flow Characteristics of Two-Phase Impinging Jets,” Int. J. Heat Mass Transfer, 53(25–26), pp. 5692–5699. [CrossRef]
Parker, R. R. , Klausner, J. F. , and Mei, R. W. , 2012, “ Supersonic Two-Phase Impinging Jet Heat Transfer,” ASME J. Heat Transfer, 135(2), p. 022201. [CrossRef]
Lu, X. , John Chandar, D. D. , Chen, Y. , and Lou, J. , 2017, “ An Overlapping Domain Decomposition Based Near-Far Field Coupling Method for Wave Structure Interaction Simulations,” Coastal Eng., 126, pp. 37–50. [CrossRef]
Martinez Ferrer, P. J. , Causon, D. M. , Qian, L. , Mingham, C. G. , and Ma, Z. H. , 2016, “ A Multi-Region Coupling Scheme for Compressible and Incompressible Flow Solvers for Two-Phase Flow in a Numerical Wave Tank,” Comput. Fluids, 125, pp. 116–129. [CrossRef]
Lugni, C. , Brocchini, M. , and Faltinsen, O. M. , 2006, “ Wave Impact Loads: The Role of the Flip-Through,” Phys. Fluids, 18(12), p. 122101. [CrossRef]
Bullock, G. N. , Obhrai, C. , Peregrine, D. H. , and Bredmose, H. , 2007, “ Violent Breaking Wave Impacts—Part1: Results From Large Regular Wave Tests on Vertical and Sloping Walls,” Coastal Eng., 54(8), pp. 602–617. [CrossRef]
Wu, J. Y. , Utturkar, Y. , and Shyy, W. , 2003, “ Assessment of Modeling Strategies for Cavitating Flow around a Hydrofoil,” Fifth International Symposium on Cavitation, Osaka, Japan, Nov. 1–5.
Lindau, J. W. , Boger, D. A. , Medvitz, R. B. , and Kunz, R. F. , 2005, “ Propeller Cavitation Breakdown Analysis,” ASME J. Fluids Eng., 127(5), pp. 995–1002. [CrossRef]
Luo, X. W. , Ji, B. , Peng, X. X. , Xu, H. , and Nishi, M. , 2012, “ Numerical Simulation of Cavity Shedding From a Three-Dimensional Twisted Hydrofoil and Induced Pressure Fluctuation by Large-Eddy Simulation,” ASME J. Fluids Eng., 134(4), p. 041202. [CrossRef]
Miller, S. T. , Jasak, H. , Boger, D. A. , Paterson, E. G. , and Nedungadi, A. , 2013, “ A Pressure-Based, Compressible, Two-Phase Flow Finite Volume Method for Underwater Explosions,” Comput. Fluids, 87, pp. 132–143. [CrossRef]
Saito, Y. , Takami, R. , Nakamori, I. , and Ikohagi, I. , 2007, “ Numerical Analysis of Unsteady Behavior of Cloud Cavitation Around a NACA0015 Foil,” Comput. Mech., 40(1), pp. 85–96. [CrossRef]
Zhang, L. X. , and Khoo, B. C. , 2014, “ Dynamics of Unsteady Cavitating Flow in Compressible Two-Phase Fluid,” Ocean Eng., 87, pp. 174–184. [CrossRef]
Tseng, C. C. , and Shyy, W. , 2010, “ Modeling for Isothermal and Cryogenic Cavitation,” Int. J. Heat Mass Transfer, 53(1–3), pp. 513–525. [CrossRef]
Arndt, R. E. A. , 2012, “ Some Remarks on Hydrofoil Cavitation,” J. Hydrodyn., 24(3), pp. 305–314. [CrossRef]
Arndt, R. E. A. , 2012, “ Cavitation Research From an International Perspective,” IOP Conf. Ser.: Earth Environ. Sci., 15, p. 012002.
Morgut, M. , Nobile, E. , and Bilus, I. , 2011, “ Comparison of Mass Transfer Models for the Numerical Prediction of Sheet Cavitation Around a Hydrofoil,” Int. J. Multiphase Flow, 37(6), pp. 620–626. [CrossRef]
Kubota, A. , Kato, H. , and Yamaguchi, H. , 1992, “ A New Modelling of Cavitating Flows: A Numerical Study of Unsteady Cavitation on a Hydrofoil Section,” J. Fluid Mech., 240(1), pp. 59–96. [CrossRef]
Gopalan, S. , and Katz, J. , 2000, “ Flow Structure and Modeling Issues in the Closure Region of Attached Cavitation,” Phys. Fluids, 12(4), pp. 895–911. [CrossRef]
Senocak, I. , and Shyy, W. , 2002, “ Evaluations of Cavitation Models for Navier-Stokes Computations,” ASME Paper No. FEDSM2002-31011.
Kunz, R. F. , Boger, D. A. , Stinebring, D. R. , Chyczewski, T. S. , Lindau, J. W. , Gibeling, H. J. , Venkateswaran, S. , and Govindan, T. R. , 2000, “ A Preconditioned Navier-Stokes Method for Two-Phase Flows With Application to Cavitation Prediction,” Comput. Fluids, 29(8), pp. 849–875. [CrossRef]
Singhal, A. K. , Athavale, M. M. , Huiying, L. , and Yu, J. , 2002, “ Mathematical Basis and Validation of the Full Cavitation Model,” ASME J. Fluids Eng., 124(3), pp. 617–624. [CrossRef]
Merkle, C. L. , Feng, J. Z. , and Buelow, P. E. O. , 1992, “ Computational Modeling of the Dynamics of Sheet Cavitation,” Third International Symposium on Cavitation, Grenoble, France, Apr. 7–10.
Senocak, I. , and Shyy, W. , 2002, “ A Pressure-Based Method for Turbulent Cavitating Flow Computations,” J. Comput. Phys., 176(2), pp. 363–383. [CrossRef]
Baer, M. R. , and Nunziato, J. W. , 1986, “ A Two-Phase Mixture Theory for the Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials,” Int. J. Multiphase Flows, 12(6), pp. 861–889. [CrossRef]
Saurel, R. , and Abgrall, R. , 1999, “ A Multiphase Godunov Method for Compressible Multi-Fluid and Multiphase Flows,” J. Comput. Phys., 150(2), pp. 425–467. [CrossRef]
Zein, A. , Hantke, M. , and Warnecke, G. , 2010, “ Modeling Phase Transition for Compressible Two-Phase Flows Applied to Metastable Liquids,” J. Comput. Phys., 229(8), pp. 2964–2998. [CrossRef]
Murrone, A. , and Guillard, H. , 2005, “ A Five-Equation Reduced Model for Compressible Two-Phase Flow Problems,” J. Comput. Phys., 202(2), pp. 664–698. [CrossRef]
Petitpas, F. , Franquet, E. , Saurel, R. , and Le Metayer, O. , 2007, “ A Relaxation–Projection Method for Compressible Flows—Part II: Artificial Heat Exchanges for Multiphase Shocks,” J. Comput. Phys. Arch., 225(2), pp. 2214–2248. [CrossRef]
Venkateswaran, S. , Lindau, J. W. , Kunz, R. F. , and Merkle, C. L. , 2002, “ Computation of Multiphase Mixture Flows With Compressiblility Effects,” J. Comput. Phys, 180(1), pp. 54–77. [CrossRef]
Keshtiban, I. J. , Belblidia, F. , and Webster, M. F. , 2004, “ Compressible Flow Solvers for Low Mach Number Flows—A Review,” Int. J. Numer. Methods Fluids, 23, pp. 77–103.
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemishpere, New York.
Chorin, A. J. , 1967, “ A Numerical Method for Solving Incompressible Viscous Flow Problems,” J. Comput. Phys., 2(1), pp. 12–26. [CrossRef]
Karki, K. , and Patankar, S. , 1989, “ Pressure Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations,” AIAA J., 27(9), pp. 1167–1178. [CrossRef]
Issa, R. I. , 1986, “ Solution of the Implicitly Discretized Fluid Flow Equations by Operator Splitting,” J. Comput. Phys., 62(1), pp. 40–65. [CrossRef]
Lu, X. , Kumar, P. , Bahuguni, A. , and Wu, Y. L. , 2014, “ A CFD Study of Focused Extreme Wave Impact on Decks of Offshore Structures,” ASME Paper No. OMAE2014-23804.
Mostafa Ghiaasiaan, S. , 2011, Convective Heat and Mass Transfer, Cambridge University Press, Cambridge, UK, pp. 24–26. [CrossRef]
Haider, J. , 2013, “ Numerical Modelling of Evaporation and Condensation Phenomena,” Ph.D. thesis, Universität Stuttgart, Stuttgart, Germany.
Richter, O. , Turnow, J. , Kornev, N. , and Hassel, E. , 2017, “ Numerical Simulation of Casting Processes: Coupled Mould Filling and Solidification Using VOF and Enthalpy-Porosity Method,” Heat Mass Transfer, 53(6), pp. 1957–1969. [CrossRef]
Utturkar, Y. , 2005, “ Computational Modeling of Thermodynamic Effects in Cryogenic Cavitation,” Ph.D. dissertation, University of Florida, Gainesville, FL.
Samkhaniani, N. , and Ansari, M. R. , 2017, “ The Evaluation of the Diffuse Interface Method for Phase Change Simulations Using OpenFOAM,” Heat Transfer—Asian Res., 46(8), pp. 1173–1203.
Kunkelmann, C. , 2011, “ Numerical Modeling and Investigation of Boiling Phenomena,” Ph.D. dissertation, Universitäts Darmstadt, Darmstadt, Germany.
Zwart, P. J. , 2005, “ Numerical Modelling of Free Surface Flows and Cavitating Flows Industrial CFD Applications of Free Surface and Cavitating Flows,” Course, Industrial Two-Phase Flow CFD, Rhode Saint Genese, Belgium, p. 8.
Schnerr, G. H. , and Sauer, J. , 2001, “ Physical and Numerical Modeling of Unsteady Cavitation Dynamics,” Fourth International Conference on Multiphase Flow (ICMF), New Orleans, LA, May 27–June 1.
Vinze, R. , Chandel, S. , Limaye, M. D. , and Prabhu, S. V. , 2016, “ Effect of Compressibility and Nozzle Configuration on Heat Transfer by Impinging Air Jet Over a Smooth Plate,” Appl. Therm. Eng., 101(25), pp. 293–307. [CrossRef]
Mottyll, S. , and Skoda, R. , 2016, “ Numerical 3D Flow Simulation of Ultrasonic Horns With Attached Cavitation Structures and Assessment of Flow Aggressiveness and Cavitation Erosion Sensitive Wall Zones,” Ultrason. Sonochem., 31, pp. 570–589. [CrossRef] [PubMed]
Žnidarčič, A. , Mettin, R. , Cairos, C. , and Dular, M. , 2014, “ Attached Cavitation at a Small Diameter Ultrasonic Horn Tip,” Phys. Fluids, 26(2), p. 023304. [CrossRef]
Mottyll, S. , Muller, S. , Niederhofer, P. , Hussong, J. , Huth, S. , and Skoda, R. , 2014, “ Analysis of the Cavitating Flow Induced by an Ultrasonic Horn—Numerical 3D Simulation for the Analysis of Vapour Structures and the Assessment of Erosion-Sensitive Areas,” EPJ Web Conf., 67, p. 02078. [CrossRef]
Franc, J. P. , and Michel, J. M. , 2004, Fundamentals of Cavitation, Fluid Mechanics and Its Applications, Vol. 76, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Schmidt, S. J. , Thalhamer, M. , and Schnerr, G. H. , 2009, “ Inertia Controlled Instability and Small Scale Structures of Sheet and Cloud Cavitation,” Seventh International Symposium on Cavitation (CAV), Ann Arbor, MI, Aug. 17–22.
Žnidarčič, A. , Metti, R. , and Dular, M. , 2015, “ Modeling Cavitation in a Rapidly Changing Pressure Field—Application to a Small Ultrasonic Horn,” Ultrason. Sonochem., 22, pp. 482–492. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Schematic of ultrasonic horn test: (1) case A is adopted from the work done by Žnidarčič et al. [46]; (2) case B is based on the test conducted by Mottyll et al. [47]. The geometries are only displayed in a half and the complete domains are used in the actual computational fluid dynamics (CFD) simulations. All the lengths are in unit of mm if other declared.

Grahic Jump Location
Fig. 2

A zoom view of the mesh close to the horn tip. The local refinement of grid size is required to predict the time evolution of the attached cavity.

Grahic Jump Location
Fig. 3

Time history of the probed pressure ph, vapor cavity volume αint from the CFD simulation of case A.1. The middle grid is used.

Grahic Jump Location
Fig. 4

Frequency spectrum of the time-dependent pressure data computed with three different grids for case A.1. The DFT function in matlab is used with 10 ms of time window.

Grahic Jump Location
Fig. 5

Time sequence of the attached cavity beneath the horn tip roughly for one complete subharmonic cycle: (a) the shadowed cavity structures are formed via silhouettes of isosurfaces of γ=0.9 for case A.1, where Âpp=164μmand (b) contours of temperature field

Grahic Jump Location
Fig. 6

Snapshot of the pressure wave field beneath the horn tip. Time instant is right after the collapse of a vapor cavity.

Grahic Jump Location
Fig. 7

Time history of the integral vapor volume fraction αint and registered maximum pressure pmax for the simulation of case B. The middle grid size is used.

Grahic Jump Location
Fig. 8

Snapshots from instantaneous contours of water phase volume fraction, velocity magnitude, and temperature, from top to bottom, respectively



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In