Smooth Particle Hydrodynamics Scheme for Numerical Simulation of Multiphase Flows With Complex Interface Surfaces

Mahmoodi Mehrizi, Mahdi; Sefid, Mohammad; Salehizadeh, Amir Madood

doi:10.47176/jcme.41.2.8502

Smooth Particle Hydrodynamics Scheme for Numerical Simulation of Multiphase Flows With Complex Interface Surfaces

Document Type : Original Article

Authors

10.47176/jcme.41.2.8502

Abstract

Numerical simulation of multiphase problems with complex interface as well as high density ratios is one of the numerical challenges associated with particle scattering and divergence. Fewer problems have been performed with density-based smooth particle hydrodynamics (WCSPH) to solve complex joint surface currents, and most simulations have been performed using Incompressible Smooth Particle Hydrodynamics (ISPH). Solution of high density flows by the smooth particle hydrodynamics is associated with particle dispersion and divergence. Various methods have been used to eliminate the scattering of particles, such as a repulsive force at the interface or the corrected density re-value, but there is a problem of particle disintegration at the interface at higher times. In the present simulation, to simulate multiphase flows with complex surfaces and high density ratios, a new density-based smooth particle hydrodynamics approach has been utilized. To prevent the scattering of particles, especially at the interface at the end times, a simple method with the removal of incompatible particles is used. In the present study, the particle displacement optimization scheme for regularization at the interface of the phase is created by precisely implementing a two-stage change algorithm, so as to maintain the regular particle distribution continuously and conservatively. To examine the accuracy of the present simulation method, it is firstly compared with two-phase Poiseuille flow with three fluids having different values of viscosity, Reynolds-Taylor instability and single bubble rising in a fully filled container., Then it is compared with analytical and numerical solutions. The accuracy and consistency of the current simulation is higher or equal to other simulations.

Keywords

20.1001.1.22287698.1401.41.2.7.1

References

Unverdi, S. , and Tryggvason, G., “A Front-Tracking Method for Viscous, Incompressible, Multi-Fluid Flows”, Journal of Computational Physics, Vol. 100, pp. 25-37, 1992.
Sussman, M., and Smereka, P., and Osher, S., “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow”, Journal of Computational Physics, Vol. 114, pp. 146-159,
Hirt, C. W, Nichols, B. D., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries”, Journal of Computational Physics, Vol. 39, pp. 201-225, 1981.
Yoon, H. Y., and Koshizuka, S., and Oka, Y., “Direct Calculation of Bubble Growth, Departure, and Rise in Nucleate Pool Boiling”, International Journal of Multiphase Flow, Vol. 27, pp. 277-298, 2001.
Khayyer, A., and Gotoh, H., “Enhancement of Performance and Stability of MPS Mesh-Free Particle Method for Multiphase Flows Characterized by High Density Ratios”, Journal of Computational Physics, Vol. 242, pp. 211-233, 2013.
Gingold, R. A., and Monaghan, J. J., “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars”, Monthly Notices of the Royal Astronomical Society, Vol. 181, pp. 375-389,
SPHERA v.9.0.0: “A Computational Fluid Dynamics Research Code Based on the Smoothed Particle Hydrodynamics Mesh-Less Method”, Computer Physics Communications, Vol 250, pp. 107-157, 2020.
Colagrossi, A., and Landrini, M., “Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics”, Journal of Computational Physics, Vol. 191, pp. 448-475, 2003.
Grenier, N., Antuono, M., Colagrossi, A., Le Touzé, D., and Alessandrini, B., “An Hamiltonian Interface SPH Formulation for Multi-Fluid and Free Surface Flows”, Journal of Computational Physics, Vol. 228, pp. 8380-8393, 2009
Monaghan, J., and Kocharyan, A., “SPH Simulation of Multi-Phase Flow”, Computer Physics Communications, Vol. 87, pp. 225-235, 1995.
Cummins, S. J., and Rudman, M., “An SPH Projection Method”, Journal of Computational Physics, Vol. 152, pp. 584-607, 1999.
Hu, X., and Adams, N. A., “An Incompressible Multi-Phase SPH Method”, Journal of Computational Physics, Vol. 227, pp. 264-278, 2007.
Shao, S., “Incompressible Smoothed Particle Hydrodynamics Simulation of Multifluid Flows”, International Journal for Numerical Methods in Fluids, Vol. 69, pp. 1715-1735, 2012.
Monaghan, J. J., and Rafiee, A., “A Simple SPH Algorithm for Multi-Fluid Flow with High Density Ratios”, International Journal for Numerical Methods in Fluids, Vol. 71, pp. 537-561,
Tartakovsky, A. M., and Panchenko, A., “Pairwise Force Smoothed Particle Hydrodynamics Model for Multiphase Flow: Surface Tension and Contact Line Dynamics”, Journal of Computational Physics, Vol. 305, pp. 1119-1146,
Krimi, A., Rezoug, M., Khelladi, S., Nogueira, X., Deligant, M., and Ramírez, L., “Smoothed Particle Hydrodynamics: A Consistent Model for Interfacial Multiphase Fluid Flow Simulations”, Journal of Computational Physics, Vol. 358, pp. 53-87,
Chen, Z., Zong, Z., Liu, M., Zou, L., Li, H., and Shu, C., “An SPH Model for Multi-Phase Flows with Complex Interfaces and Large Density Differences”, Journal of Computational Physics, Vol. 283, pp. 169-188, 2015.
Zheng, B., and Chen, Z., “A Multiphase Smoothed Particle Hydrodynamics Model with Lower Numerical Diffusion”, Journal of Computational Physics, Vol. 382, pp. 177-201, 2019.
Lee, E. S., Moulinec, C., Xu, R., Violeau, D., Laurence, D., and Stansby, P., “Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method”, Journal of computational Physics, Vol. 227, pp. 8417-8436,
Antuono, M., Colagrossi, A., and Marrone, S,. “Numerical Diffusive Terms in Weakly-Compressible SPH Schemes”, Computer Physics Communications, Vol. 183, pp. 2570-2580, 2012.
Fatehi, R., and Rahmat, A., Tofighi, N., Yildiz, M., and Shadloo, M. S., “Density-Based Smoothed Particle Hydrodynamics Methods for Incompressible Flows”, Computers & Fluids , Vol. 185, pp. 22-33,
Khayyer, A., Gotoh, H., and Shimizu, Y., “Comparative Study on Accuracy and Conservation Properties of Two Particle Regularization Schemes and Proposal of an Optimized Particle Shifting Scheme in ISPH Context”, Journal of Computational Physics , Vol. 332, pp. 236-256, 2017.
Morris, J. P., “Simulating Surface Tension with Smoothed Particle Hydrodynamics”, International Journal for Numerical Methods in Fluids, Vol. 33, pp. 333-353,
Morris, J. P., Analysis of Smoothed Particle Hydrodynamics with Applications, Monash University Australia, 1996.
Chen, J., Beraun, J., and Carney, T., “A Corrective Smoothed Particle Method for Boundary Value Problems in Heat Conduction”, International Journal for Numerical Methods in Engineering, Vol. 46, pp. 231-252,
Bonet, J., and Lok, T. S., “Variational and Momentum Preservation Aspects of Smooth Particle Hydrodynamic Formulations”, Computer Methods in Applied Mechanics and Engineering, Vol. 180, pp. 97-115,
Fatehi, R., and Manzari, M. T., “Error Estimation in Smoothed Particle Hydrodynamics and a New Scheme for Second Derivatives”, Computers & Mathematics with Applications, Vol. 61, pp. 482-498, 2011.
Sefid, M., Fatehi, R., and Shamsoddini, R., “A Modified Smoothed Particle Hydrodynamics Scheme to Model the Stationary and Moving Boundary Problems for Newtonian Fluid Flows”, Journal of Fluids Engineering, Vol. 137, 2015.
Adami, S., Hu, X., and Adams, N. A., “A new Surface-Tension Formulation for Multi-Phase SPH Using A Reproducing Divergence Approximation”, Journal of Computational Physics, Vol. 229, pp. 5011-5021,
Brackbill, J. U., and Kothe, D. B., and Zemach, C., “A Continuum Method for Modeling Surface Tension”, Journal of Computational Physics, Vol. 100, pp. 335-354.
Xu, R., and Stansby, P., and Laurence, D., “Accuracy and Stability in Incompressible SPH (ISPH) Based on the Projection Method and A New Approach”, Journal of Computational Physics, 228 , pp. 6703-6725, 2009.
Lind, S., Xu, R., Stansby, P., and Rogers, B. D., “Incompressible Smoothed Particle Hydrodynamics for Free-Surface Flows: A Generalised Diffusion-Based Algorithm for Stability and Validations for Impulsive Flows and Propagating Waves”, Journal of Computational Physics, Vol. 231, pp. 1499-1523,
Salehizadeh, A., and Shafiei, A., “Modeling of Granular Column Collapses with U(I) Rheology Using Smoothed Particle Hydrodynamic Method”, Granular Matter, Vol. 21, pp. 32-39, 2019.
Hysing, S. R., Turek, S., Kuzmin, D., Parolini, N., Burman, E., and Ganesan, S., “Quantitative Benchmark Computations of Two-Dimensional Bubble Dynamics”, International Journal for Numerical Methods in Fluids, 60, pp.1259-1288, 2009
Grenier, N., Le Touzé, D., Colagrossi, A., Antuono, M., and Colicchio, G., “Viscous Bubbly Flows Simulation with an Interface SPH Model”, Ocean Engineering, Vol. 69, pp. 88-102,
Bird, R. B., Stewart, W. E., and Lightfoot, E. N,. Transport Phenomena, John Wiley & Sons, Inc, New York, 2002.
, A. M., ad Lind, S. J., Stansby, P. K., and Rogers, B. D., “An ISPH Scheme with Shifting for Newtonian and Non-Newtonian Multi-Phase Flows”, Proceedings of the 10^th International SPHERIC Workshop, Vol. 75, pp. 84-91, 2015.
Shadloo, M. S., Zainali, A., and, Yildiz, M., “Simulation of Single Mode Rayleigh–Taylor Instability By SPH Method”, Computational Mechanics, Vol. 51 pp. 699-715, 2013.
Szewc, K., Pozorski, J., and Minier, J. P., “Spurious Interface Fragmentation in Multiphase SPH”, International Journal for Numerical Methods in Engineering, Vol. 103, pp. 625-649, 2015.