Numerical simulation of droplet coalescence in turbulent stream using level set method

Full Text (PDF, 484KB), PP.13-27

Views: 0 Downloads: 0

Author(s)

Ashraf Balabel 1,2,*

1. Taif University, Taif City, Alhawya, 21974, Kingdom of Saudi Arabia

2. Menoufiya University, Shebin El-Kom, Egypt

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2013.01.02

Received: 5 Mar. 2013 / Revised: 16 Apr. 2013 / Accepted: 23 May 2013 / Published: 29 Jun. 2013

Index Terms

Colliding droplets, Level set method, Numerical simulation, Turbulence modelling, two-phase flow

Abstract

In the present paper a novel numerical method for solving the problem of two-phase flow with moving interfaces in both laminar and turbulent flow regimes is developed. The developed numerical method is based on the solution of the Reynolds-Averaged Navier Stokes equations in both phases separately with appropriate boundary conditions located at the interface separating the two fluids. The solution algorithm is performed on a regular and structured two-dimensional computational grid using the control volume approach. The complex shapes as well as the geometrical quantities of the interface are determined via the level set method. The numerical method is firstly validated against the prediction of the well known flow dynamics over a circular cylinder. Further, the numerical simulation of two colliding droplets in gas flow is numerically predicted showing the important dynamics associated with the different flow regimes considered. The remarkable capability of the developed numerical method in predicting turbulent two-phase flow dynamics enables us to predict further a wide range of two-phase flow industrial and engineering applications.

Cite This Paper

Ashraf Balabel,"Numerical simulation of droplet coalescence in turbulent stream using level set method", IJEM, vol.3, no.1, pp.13-27, 2013.DOI: 10.5815/ijem.2013.01.02

Reference

[1] Fuster, D., Agbaglah, G., Josserand, C., Popinet, S. and Zaleski, S., Numerical simulation of droplets, bubbles and waves: state of the art, Fluid Dyn. Res. 41:1-24, 2009.

[2] Lefebvre, A. H., Atomization and sprays, Hemisphere Publishing Corporation, 1989.

[3] Kolev N.I., Multiphase flow dynamics: Thermal and Mechanical Interaction", Springer, 2007.

[4] Yang V., Habiballah M., Hulka J. and Popp M., Liquid Rocket Thrust Chambers: Aspects of Modeling, Analysis, and Design", American Institute of Aeronautics and Astronautics, Inc., 2004.

[5] Linne M., Paciaroni M., Hall T., and Parker T., Ballistic imaging of the near field in a dense spray", Exp. Fluids., 49(4): 911-923, 2006

[6] Menard T., Tanguy S. and Berlemont A., Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet, Int. J.Multiphase Flow, 33:510-524, 2007.

[7] Desjardins, O., Moureau, V. and Pitsch, H., An accurate conservative level set/ghost fluid method for simulating turbulent atomization, Journal of Computational Physics, 227: 8395–8416, 2008.

[8] Hinze JO., Turbulence, New York, McGraw-Hill, 1959.

[9] Eggers, J., Nonlinear Dynamics and Breakup of Free-Surface Flow, Rews. Modern Phys., 69(3): 865–929, 1997.

[10] Crowe C. T., Troutt T. R. and Chung J. N., Numerical models for two-phase turbulent flows", Annu. Rev. Fluid Mech., 28:11-43, 1996.

[11] Shinjo J. and Umemura A., Simulation of liquid primary breakup: Dynamics of ligament and droplet formation", Int. J. Multiphase Flow, 36(7): 513-532, 2010.

[12] Rgea S., Bini M., Fairweather M. and Jones W. P., RANS modelling and LES of a single-phase, impinging plane jet, Computer and Chemical engineering, 33: 1344.1533, 2009.

[13] Launder, B. E., Spalding, D. B., The numerical computation of turbulent flow, Computer Methods in Applied Mechanics and Engineering, 3(2): 269-289, 1974.

[14] Nichols B. D. and Hirt C. W., Methods for calculating multi-dimensional, transient free surface flows past bodies, Proc. First Int. Conf. Num. Ship Hydrodynamics Gaithersburg, 20–23, 1975.

[15] Osher S. and Sethian J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations, Journal of Computational Physics, 79: 12–49, 1988.

[16] Li, Z., Jaberi, F. A. and Shih, T., A hybrid Lagrangian–Eulerian particle-level set method for numerical simulations of two-fluid turbulent flows, Int. J. Num. Methods in Fluids, 56: 2271-2300, 2008.

[17] Scardovelli, R. and Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., 31: 567–603, 1999.

[18] Peters N., Turbulent combustion", Cambridge University Press, Cambridge, UK, 2000.

[19] Balabel, A., Binninger,B., Herrmann, M., and Peters, N., Calculation of Droplet Deformation by Surface Tension Effects using the Level Set Method, Combust. Sci. Technology , 174(11-12):257–278, 2002.

[20] Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flows, J. Comp. Physics, 114: 146-159, 1994.

[21] Sethian, J. A. and Smereka, P., Level Set Methods for Fluid Interfaces, Annu. Rev. Fluid. Mech., 35: 341-372, 2003.

[22] Brackbill, J. U., Kothe, D. B. and Zemach. A., A Continuum Method for Modeling Surface Tension, J. Comp. Physics, 100: 335-354, 1992.

[23] Balabel A., Numerical simulation of Gas-Liquid interface dynamics using the level set method, Dissertation, RWTH Aachen, Germany, 2002.

[24] Griffin O. M. and Hall M. S., Review: vortex shedding lock-inand flow control in bluff body wakes, ASME J. Fluids Eng., 113: 526-537, 1991.

[25] Balabel A., Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface, Int. J. Heat Fluid Flow, 32:1226–1239, 2011.

[26] Balabel A., Numerical Modelling of Turbulence-Induced Interfacial Instability in Two-Phase Flow with moving Interface, Applied Mathematical Modelling, 36:3593-3611, 2012.

[27] Narsimhan, G., Model for drop coalescence in a locally isotropic turbulent flow field, J. of Colloid and Interface Science, 272:197–209, 2004.

[28] Ronnie, A. and Bengt, A., On the breakup of fluid particles in turbulent flow, AIChE, 52 (6):2020-2030, 2006.

[29] Balabel A., Numerical prediction of droplet dynamics in turbulent flow, using the level set method, International Journal of Computational Fluid Dynamics, 25(5): 239-235, 2011.

[30] Bayvel, L. and Orzechowski, Z., Liquid Atomization", Taylor and Francis, London, 1993.