zbMATH — the first resource for mathematics

A comparative validation of concepts for collision algorithms for stochastic particle tracking. (English) Zbl 1390.76754
Summary: Long-standing concerns about the accuracy of stochastic particle collision algorithms in Monte Carlo simulations have given rise to hybrid collision algorithms, which incorporate ideas from deterministic collision calculations in order to improve the realism of the collision calculation. Some hybrid collision algorithms have spread across commercial and research computational fluid dynamics codes without prior validation. The current work focuses on the predicted incidence of collision, using mathematical analyses and computational tests to validate the stochastic and hybrid concepts. Employing simplified cases permits direct mathematical evaluation of the accuracy of the candidate algorithms. Results indicate that hybrid collision algorithms fail if the predicted collision probability does not scale proportionally to the collision cross-section, relative velocity, number of computational particles and computational time-step. Based on these findings, a general guideline for proper hybridization of deterministic collision algorithms is given. Following these guidelines, hybrid collision algorithms are as accurate as stochastic collision algorithms, with some specific benefits and disadvantages.

76M28 Particle methods and lattice-gas methods
65C35 Stochastic particle methods
65C05 Monte Carlo methods
76T20 Suspensions
PDF BibTeX Cite
Full Text: DOI
[1] Abani, N.; Munnannur, A.; Reitz, R. D., Reduction of numerical parameter dependencies in diesel spray models, J Eng Gas Turbines Power, 130, 032809, (2008)
[2] Ashgriz, N.; Poo, J. Y., Coalescence and separation in binary collisions of liquid drops, J Fluid Mech, 221, 1, 183-204, (1990)
[3] AVL. AVL FIRE® Lagrangian multiphase. Tech. Rep. Doc.No: 04-01-05010, Advanced Simulation Technologies AVL List GmbH; 2013.
[4] Brenn, G.; Valkovska, D.; Danov, K. D., The formation of satellite droplets by unstable binary drop collisions, Phys Fluids, 13, 2463, (2001) · Zbl 1184.76071
[5] Chen, M.; Kontomaris, K.; McLaughlin, J. B., Direct numerical simulation of droplet collisions in a turbulent channel flow. part I: collision algorithm, Int J Multiphase Flow, 24, 7, 1079-1103, (1999) · Zbl 1121.76434
[6] Estrade, J.-P.; Carentz, H.; Lavergne, G.; Biscos, Y., Experimental investigation of dynamic binary collision of ethanol droplets - a model for droplet coalescence and bouncing, Int J Heat Fluid Flow, 20, 5, 486-491, (1999)
[7] Gustavsson J, Golovitchev V. 3D simulation of multiple injections in DI diesel engines. In: International symposium on diagnostics and modeling of combustion in internal combustion engines; 2004.
[8] Gwon, H. K.; Ryou, H. S., Droplet collision processes in an inter-spray impingement system, J Aerosol Sci, 36, 11, 1300-1321, (2005)
[9] Hou S, Are S, Schmidt DP. A generalized adaptive collision mesh for multiple injector orifices. In: SAE world congress 2003; 2003.
[10] Hou, S.; Schmidt, D. P., Adaptive collision meshing and satellite droplet formation in spray simulations, Int J Multiphase Flow, 32, 935-956, (2006) · Zbl 1136.76531
[11] Kollár, L. E.; Farzaneh, M.; Karev, A. R., Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution, Int J Multiphase Flow, 31, 1, 69-92, (2005) · Zbl 1135.76463
[12] MacInness, J. M.; Bracco, F. V., Comparisons of deterministic and stochastic computations of drop collisions in dense sprays, Prog Astronaut Aeronaut, 135, 615-642, (1991)
[13] Munnannur, A.; Reitz, R. D., Comprehensive collision model for multidimensional engine spray computations, Atomization Sprays, 19, 597-619, (2008)
[14] Nobari, M. R.H.; Tryggvason, G., Numerical simulations of three-dimensional drop collisions, AIAA J, 34, 4, 750-755, (1996)
[15] Nordin N. Complex chemistry modeling of diesel spray combustion. Ph.D. Thesis, Chalmers University of Technology; 2001.
[16] Orme, M., Experiments on droplet collisions, bounce, coalescence and disruption, Prog Energy Comb Sci, 23, 65-79, (1997)
[17] O’Rourke PJ. Collective drop effects on vaporizing sprays. Ph.D. Thesis, Department of Mechanical and Aerospace Engineering, Princeton University; 1981.
[18] Pan, Y.; Suga, K., Numerical simulation of binary liquid droplet collision, Phys Fluids, 17, 1-14, (2005), 082105 · Zbl 1187.76398
[19] Pawar, S. K.; Padding, J. T.; Deen, N. G.; Kuipers, J. A.M.; Jongsma, A.; Innings, F., Eulerian-Lagrangian modelling with stochastic approach for droplet-droplet collisions, (Ninth international conference on CFD in the minerals and process industries, (2012), CSIRO)
[20] Pischke, P.; Cordes, D.; Kneer, R., A collision algorithm for anisotropic disperse flows based on ellipsoidal parcel representations, Int J Multiphase Flow, 38, 1-16, (2012)
[21] Pischke, P.; Cordes, D.; Kneer, R., The velocity decomposition method for second-order accuracy in stochastic parcel simulations, Int J Multiphase Flow, 47, 160-170, (2012)
[22] Post, S. L.; Abraham, J., Modeling the outcome of drop-drop collisions in diesel sprays, Int J Multiphase Flow, 28, 6, 997-1019, (2002) · Zbl 1136.76612
[23] Qian, J.; Law, C. K., Regimes of coalescence and separation in droplet collision, J Fluid Mech, 331, 59-80, (1997)
[24] Schmidt, D. P.; Rutland, C. J., A new droplet collision algorithm, J Comp Phys, 164, 62-80, (2000) · Zbl 0988.76079
[25] Schmidt, D. P.; Rutland, C. J., Reducing grid dependency in droplet collision modeling, J Eng Gas Turbines Power, 126, 227-233, (2004)
[26] Sommerfeld, M., Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence, Int J Multiphase Flow, 27, 10, 1829-1858, (2001) · Zbl 1137.76744
[27] Subramaniam, S., Lagrangian-Eulerian methods for multiphase flows, Prog Energy Comb Sci, 39, 215-245, (2012)
[28] Taskirana, O. O.; Ergeneman, M., Trajectory based droplet collision model for spray modeling, Fuel, 152, 896-900, (2014)
[29] Wang, L. P.; Wexler, A. S.; Zhou, Y., Statistical mechanical description and modeling of turbulent collision of inertial particles, J Fluid Mech, 415, 117-153, (2000) · Zbl 0964.76086
[30] Wang, L.-P.; Ayala, O.; Kasprzak, S. E.; Grabowski, W. W., Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere, J Atmosph Sci, 62, 7, 2433-2450, (2005)
[31] Weller; Henry, G.; Tabor, G.; Hrvoje, Jasak; Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput Phys, 12, 6, 620-631, (1998)
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.