Direct numerical study of speed of sound in dispersed air-water two-phase flow.

*(English)*Zbl 07328369Summary: Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified flow model [C.-H. Chang and M.-S. Liou, J. Comput. Phys. 225, No. 1, 840–873 (2007; Zbl 1192.76030)]. In this method, each face is divided into gas-gas, gas-liquid, and liquid-liquid parts via reconstruction of volume fraction. The numerical fluxes of both liquid and gas flows are calculated by AUSM\(^+\)-up scheme, and the flux due to interactions between different phases is solved by the exact Riemann solver. The effects of frequency (below the natural frequency of bubbles), volume fraction, viscosity and heat transfer are investigated. With frequency \(f=1\) kHz, under viscous and isothermal bubble conditions, the simulation results agree with the experimental results. The simulation results show that the speed of sound in air-water bubbly two-phase flow is larger when the frequency is higher. At lower frequency, the homogeneous condition is better satisfied for the phase velocity. Considering the phasic temperatures, an isothermal bubble behavior is observed during the pressure wave propagation. Finally, the dispersion relation of acoustics in two-phase flow is compared with analytical results below the natural frequency. This work for the first time presents an approach to the direct numerical simulations of speed of sound and other compressibility effects in multiphase flow, which can be applied to study more complex situations, especially when it is hard to do experimental study.

Reviewer: Reviewer (Berlin)

##### Keywords:

speed of sound; two-phase; stratified flow model; compressibility effects; homogeneous flow; bubble thermodynamics##### Software:

AUSM
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\textit{K. Fu} et al., Wave Motion 98, Article ID 102616, 19 p. (2020; Zbl 07328369)

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[1] | Guo, Z.; Wu, X., Compressibility effect on the gas flow and heat transfer in a microtube, Int. J. Heat Mass Transfer, 40, 3251-3254 (1997) |

[2] | Albagli, D.; Gany, A., Compressibility effect on the gas flow and heat transfer in a microtube, Int. J. Heat Mass Transfer, 46, 1993-2003 (2003) · Zbl 1032.76695 |

[3] | Asako, Y.; Pi, T.; Turner, S.; Faghri, M., Effect of compressibility on gaseous flows in micro-channels, Int. J. Heat Mass Transfer, 46, 3041-3050 (2003) · Zbl 1045.76552 |

[4] | Miyamoto, M.; Shi, W.; Katoh, Y.; Kurima, J., Choked flow and heat transfer of low density gas in a narrow parallel-plate channel with uniformly heating walls, Int. J. Heat Mass Transfer, 46, 2685-2693 (2003) |

[5] | Chizhov, A.; Takayama, K., The impact of compressible liquid droplet on hot rigid surface, Int. J. Heat Mass Transfer, 47, 1391-1401 (2004) · Zbl 1045.76544 |

[6] | Yoon, H.; Ishii, M.; Revankar, S., Choking flow modeling with mechanical and thermal non-equilibrium, Int. J. Heat Mass Transfer, 49, 171-186 (2006) · Zbl 1189.76666 |

[7] | Lijo, V.; Kim, H.; Setoguchi, T., Effects of choking on flow and heat transfer in micro-channels, Int. J. Heat Mass Transfer, 55, 701-709 (2012) · Zbl 1262.80036 |

[8] | Kim, S.; Mudawar, I., Review of two-phase critical flow models and investigation of the relationship between choking, premature CHF, and CHF in micro-channel heat sinks, Int. J. Heat Mass Transfer, 87, 497-511 (2015) |

[9] | Chen, N.; Wang, F.; Hu, R.; Hossain, M., Compressibility effect on natural convection flow along a vertical plate with isotherm and streamwise sinusoidal surface temperature, Int. J. Heat Mass Transfer, 99, 738-749 (2016) |

[10] | Corradini, M. L.; Zhu, C.; Fan, L.; Jean, R., Multiphase flow, (Johnson, R. W., Handbook of Fluid Dynamics (2016), CRC Press: CRC Press Boca Raton) |

[11] | T.G. Beuthe, Review of two-phase water hammer, in: Proceedings of the 18th Canadian Nuclear Society Conference, Toronto, Canada, 1997. |

[12] | Drysdale, C.; Ferguson, A.; Geddes, A.; Gibson, A.; Hunt, F.; Lamb, H.; Michell, A.; Taylor, G., The mechanical properties of fluids, (Applied Physics Series (1923), Blackie), URL: https://books.google.com/books?id=X8nPAAAAMAAJ · JFM 49.0614.01 |

[13] | Karplus, H. B., The Velocity of Sound in a Liquid Containing Gas BubblesTechnical Report (1958), U.S. Atomic Energy Commission |

[14] | Mecredy, R. C.; Hamilton, L. J., The effects of nonequilibrium heat, mass and momentum transfer on two-phase sound speed, Int. J. Heat Mass Transfer, 15, 61-72 (1972) · Zbl 0224.76095 |

[15] | Kieffer, S. W., Sound speed in liquid-gas mixtures: Water-air and water-steam, J. Geophys. Res., 82, 2895-3118 (1977) |

[16] | Ardron, K. H.; Duffey, R. B., Acoustic wave propagation in a flowing liquid-vapour mixture, Int. J. Multiph. Flow., 4, 303-322 (1978) · Zbl 0381.76071 |

[17] | Cheng, L. Y.; Drew, D. A.; Lahey, R. T., An Analysis of Wave Dispersion, Sonic Velocity, and Critical Flow in Two-Phase MixturesTechnical Report NUREG/CR-3372 (1983), Rensselaer Polytechnic Institute, URL: https://ntrl.ntis.gov/NTRL/ |

[18] | Ruggles, A. E.; Lahey, R. T.; Drew, D. A.; Scarton, H. A., An investigation of the propagation of pressure perturbations in bubbly air/water flows, J. Heat Transfer, 110, 494-499 (1988) |

[19] | Costigan, G.; Whalley, P. B., Measurements of the speed of sound in air-water flows, Chem. Eng. J., 66, 131-135 (1997) · Zbl 1135.76390 |

[20] | Drew, D. A.; Passman, S. L., Theory of Multicomponent Fluids (1999), Springer |

[21] | Brennen, C. E., Fundamentals of Multiphase Flows, 78 (2005), Cambridge University Press |

[22] | Simon, A.; Martinez-Molina, J.; Fortes-Patella, R., A new process to estimate the speed of sound using three-sensor method, Exp. Fluids, 57, 10 (2016) |

[23] | Drui, F.; Larat, A.; Kokh, S.; Massot, M., A hierarchy of simple hyperbolic two-fluid models for bubbly flows (2016), arXiv e-prints, arXiv:1607.08233 |

[24] | Gregor, W.; Rumpf, H., Velocity of sound in two-phase media, Int. J. Multiph. Flow., 1, 753-769 (1975) |

[25] | Schumann, U., Virtual density and speed of sound in a fluid-solid mixture wlth periodic structure, Int. J. Multiph. Flow., 7, 619-633 (1981) · Zbl 0471.76101 |

[26] | Atkinson, C. M.; Kytömaa, H. K., Acoustic wave speed and attenuation in suspensions, Int. J. Multiph. Flow., 18, 577-592 (1992) · Zbl 1144.76341 |

[27] | Lee, S.; Chang, K.; Kim, K., Pressure wave speeds from the characteristics of two fluids, two-phase hyperbolic equation system, Int. J. Multiph. Flow., 24, 855-866 (1998) |

[28] | Gnanaskandan, A.; Mahesh, K., A numerical method to simulate turbulent cavitating flows, Int. J. Multiph. Flow., 70, 22-34 (2015) |

[29] | Li, J.; Carrica, M., An approach to couple velocity/pressure/void fraction in two-phase flows with incompressible liquid and compressible bubbles, Int. J. Multiph. Flow., 102, 77-94 (2018) |

[30] | Chang, C.; Liou, M., A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM \({}^+\)-up scheme, J. Comput. Phys., 225, 840-873 (2007) · Zbl 1192.76030 |

[31] | Dijk, P.v., Acoustics of Two-Phase Pipe Flows (2005), University of Twente: University of Twente Enschede, Netherlands, (Ph.D. thesis) |

[32] | Flåtten, T.; Morin, A.; Munkejord, S. T., Wave propagation in multicomponent flow models, SIAM J. Appl. Math., 70, 2861-2882 (2010) · Zbl 1429.76112 |

[33] | Baer, M. R.; Nunziato, J. W., A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, Int. J. Multiph. Flow., 12, 861-889 (1986) · Zbl 0609.76114 |

[34] | Zein, A.; Hantke, M.; Warnecke, G., Modeling phase transition for compressible two-phase flows applied to metastable liquids, J. Comput. Phys., 229, 2964-2998 (2010) · Zbl 1307.76079 |

[35] | Saurel, R.; Petitpas, F.; Berry, R. A., Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys., 228, 1678-1712 (2009) · Zbl 1409.76105 |

[36] | Shyue, K., An efficient shock-capturing algorithm for compressible multicomponent problems, J. Comput. Phys., 142, 208-242 (1998) · Zbl 0934.76062 |

[37] | Murrone, A.; Guillard, H., A five equation reduced model for compressible two phase flow problems, J. Comput. Phys., 202, 664-698 (2005) · Zbl 1061.76083 |

[38] | Pelanti, M.; Shyue, K., A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, J. Comput. Phys., 259, 331-357 (2014) · Zbl 1349.76851 |

[39] | Jiang, L.-J.; Deng, X.-L.; Tao, L., DNS study of initial-stage shock-particle curtain interaction, Commun. Comput. Phys., 23, 1202-1222 (2018) |

[40] | X.-L. Deng, L.-J. Jiang, Y. Ding, Direct numerical simulation of long-term shock-particle curtain interaction, in: 2018 AIAA SciTech Forum, Kissimmee, Florida, 2018, pp. 2018-2081. |

[41] | Ishii, M.; Hibiki, T., Thermo-Fluid Dynamics of Two-Phase Flow, 187 (2011), Springer |

[42] | Fu, K.; Anglart, H., Implementation and validation of two-phase boiling flow models in openfoam (2017), arXiv e-prints, arXiv:1709.01783 |

[43] | Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics (2009), Springer · Zbl 1227.76006 |

[44] | Ranjan, D.; Oakley, J.; Bonazza, R., Shock-bubble interactions, Annu. Rev. Fluid Mech., 43, 117-140 (2011) · Zbl 1299.76125 |

[45] | Bai, X.; Deng, X., A sharp interface method for compressible multi-phase flows based on the cut cell and ghost fluid methods, Adv. Appl. Math. Mech., 9, 1052-1075 (2017) |

[46] | Cheng, L. Y.; Drew, D. A.; Lahey, R. T., An analysis of wave propagation in bubbly two-component, two-phase flow, J. Heat Transfer, 107, 402-408 (1985) |

[47] | Ruggles, A. E.; Lahey, R. T.; Drew, D. A.; Scarton, H. A., The relationship between standing waves, pressure pulse propagation, and critical flow rate in two-phase mixtures, J. Heat Transfer, 111, 467-473 (1989) |

[48] | Fox, F. E.; Curley, S. R.; Larson, G. S., Phase velocity and absorption measurements in water containing air bubbles, J. Acoust. Soc. Am., 27, 534-539 (1995) |

[49] | L. Wijngaarden, Some problems in the formulation of the equations for gas/liquid flows, in: 14th IUTAM Congress on Theoretical and Applied Mechanics, Delft, the Netherlands, 1976, pp. 249-260. |

[50] | Hdaneshyar, H., One-Dimensional Compressible Flow (1976), Pergamon press |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.