[01] Ashraf Balabel, Mechanical Engineering Dept., Faculty of Engineering, Taif University, Al-Haweiah, Taif, Saudi Arabia.

The aim of this work is to provide a high accuracy computational technique for tracking moving interfaces, which can be found in a wide range of micro- and nano-mechatronic devices, using the level set method. The solution of the time-dependent partial differential equation of the level set is performed by replacing the spatial derivatives with central difference and with a second order Runge-Kutta scheme for the temporal advance. The fulfilment of the Eikonal equation is performed through a modified reinitialization process. By adjusting the values of constants used in the reinitialization process for the considered cases, one should not have to evolve more than a few iterations to achieve the steady state solution. That is found to have a large effect on the error in mass conservation that is associated with level set methods. The total calculation time is reduced, as the reinitialization process becomes a non-iterative one. This computational technique does not require an entropy-satisfying approximation to the gradient terms and it can easily be combined with the Fast Extension Velocity Method. Some numerical test cases have been performed and good results have been obtained.

Level Set Method, Micro/Nano-Devices, Numerical Simulation, Two-Phase Flow

[01] Nie, Z. H., Seo, M. S., Xu, S. Q., Lewis, P. C., Mok, M., Kumacheva, E., Whitesides, G. M., Garstecki, P. and Stone, H. A., Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids, Microfluid. Nanofluid., 5, 585-594, 2008. [02] Yuehao Li, Mranal J. and Krishnaswamy N., Numerical Study of Droplet Formation inside a Microfluidic Flow-Focusing Device, Excerpt from the Proceedings of the COMSOL Conference, Boston, 2012. [03] Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. Journal of Computational, Physics, vol. 79, pp. 12–49, 1988. [04] Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comp. Phys. 114, 146–154, 1994. [05] Garzon, M, Gray, L.J. and Sethian, J.A., Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method, J. of Comp. Physics, 228, 6079–6106, 2009. [06] Balabel, A., Binninger, B., Herrmann, M. and Peters, N., Calculation of droplet deformation by surface tension effects using the level set method, Combustion Science and Technology, 174 (11-12), 257–278, 2002. [07] Balabel, A., Numerical prediction of droplet dynamics in turbulent flow, using the level set method, International J. of Computational Fluid Dynamics, 25 (5), 239–253, 2011. [08] A. Balabel, Numerical simulation of two-dimensional binary droplets collision outcomes using the level set method, International Journal of Computational Fluid Dynamics, vol. 26, no. 1, pp. 1-21, 2012. [09] A. Balabel, Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface Applied Mathematical Modelling, vol. 36, pp. 3593–3611, 2012. [10] A. Balabel, A Generalized Level Set-Navier Stokes Numerical Method for Predicting Thermo-Fluid Dynamics of Turbulent Free Surface. Computer Modeling in Engineering and Sciences (CMES), vol.83, no.6, pp. 599-638, 2012. [11] A. Balabel, Numerical Modelling of Turbulence Effects on Droplet Collision Dynamics using the Level Set Method. Computer Modeling in Engineering and Sciences (CMES), vol. 89, no.4, pp. 283-301, 2012. [12] A. Balabel, Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface, Applied Mathematical Modelling, vol. 36, no. 8, pp. 3593-3611, 2012. [13] A. Balabel, Numerical prediction of droplet dynamics in turbulent flow, using the level set method. International Journal of Computational Fluid Dynamics, vol. 25, no. 5, pp. 239-253, 2012. [14] A. Balabel, Numerical Modelling of Liquid Jet Breakup by Different Liquid Jet/Air Flow Orientations Using the Level Set Method, Computer Modeling in Engineering and Sciences (CMES), vol. 95, no.4, pp. 283-302, 2013. [15] Peters, N, Turbulent combustion. Cambridge University Press, Cambridge, UK, 2000. [16] Chiu, P. and Lin, Y., A conservative phase field method for solving incompressible two-phase flows, J. of Comp. Physics, vol. 230, pp. 185–204, 2011. [17] Hirt, C. W. and Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. of Computational Physics, vol. 39, pp. 201-225, 1981. [18] Adalsteinsson, D. and Sethian, J. A., The Fast Construction of Extension Velocities in Level Set Methods, J. Comp.Phys., vol. 148, pp. 2-22, 1999. [19] Shu, C.-W. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes II. J. Comp. Phys., vol. 83, pp. 32-78, 1989. [20] Sethian J., Level set methods, Cambridge University Press, 1996. [21] Taotao Fu., Yining Wu., Youguang Ma, Huai Z.Li, Droplet formation and breakup dynamics in microfluidic flow-focusing devices: From dripping to jetting, Chem. Eng. Sci., vol. 84, pp. 207-217, 2012. [22] Bayvel, L. and Orzechowski, Z., Liquid Atomization, Taylor and Francis, London., 1993.