Numerical Investigation of a Steady Flow of an Incompressible Fluid in a Lid Driven Cavity

Abstract

In this paper, numerical investigation for 2-D steady-state, incompressible pseudoplastic viscous flow is presented. Pseudo time derivative is used to solve the continuity and momentum equations with suitable boundary conditions. Depending on high Reynolds number, wall motions of flow are investigated with respect to nonlinear viscosity by using Cross model. This study has been undertaken as a first step toward understanding in heat and mass transport in solvent and polymer processing equipment. Solution to the vorticity equation for moving top wall is obtained numerically and found to be stable and convergent for high value of Reynolds numbers. In fact some new results, which are governed by inertia and variable shear-rate, are obtained and then this has been documented first time.

Keywords

• 2-D steady-state, Incompressible pseudoplastic viscous flow, Pseudo-time derivative, High Reynolds number.

References

1. E. Barragy, G.F. Carey. Stream function-vorticity driven cavity solutions using p finite elements. Computers and Fluids, 26, 453-468,(1997).
2. R.M.Beam, R.F.Warming. An implicit factored scheme for the compressible N-S equations. AIAA J., 16, 393-420,(1978).
3. A.S.Benjamin, V.E.Denny. On the convergence of numerical solutions for 2-D flows in a cavity at large Re. J. Comp. Physics, 33, 340-358,(1979).
4. O.Botella,R. Peyret. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids, 27, 421-433,(1998).
5. H.Demir. The Stability Properties of Some RheologicalFlows. Ph. D. Thesis, The University of Glamorgan, School of Accounting and Mathematics, Division of Maths and Computing, Glamorgan, 264p,1996.
6. E.Ert¨urk, T.C.Corke, C.G¨ok¸c¨ol. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. J. Numer. Meth. Fluids, 48, 747-774,(2005).
7. U.Ghia, K.N.Ghia, C.T.Shin. High-Re solutions for incompressible flow using the N-S equations and a multigrid method. J. Comp. Physics, 48, 387-411,(1982).
8. O.Goyon. High-Re number solutions of N-S equations using incremental unknowns. Computer Methods in Applied Mechanics and Engineering , 130, 319-335,(1996).

9. M.M.Gupta, M.M. High accuracy solutions of incompressible N-S equations. J. Comp. Physics, 93, 343-359,(1991).
10. S.Hou, Q.Zou, S.Chen, G.Doolen, A.C.Cogley. Simulation of cavity flow by the lattice boltzmann method. J. Comp. Physics, 118, 329-347,(1995).
11. M.Li, T.Tang, B.Fornberg. A compact forth-order finite difference scheme for the steady incompressible N-S equations. Int. J. Numer. Methods Fluids, 20, 1137-1151,(1995).
12. S.J.Liao,J.M. Zhu. A short note on higher-order stream function-vorticity formulation of 2-D steady state N-S equations. Int. J. Numer. Methods Fluids, 22, 1-9,(1996).
13. S.G.Rubin,P.K. Khosla. N-S calculations with a coupled strongly implicit method. Computers and Fluids, 9, 163-180,(1981).
14. R.Schreiber, H.B.Keller. Driven cavity flows by efficient numerical techniques. J. Comp. Physics, 49, 310-333,(1983).
15. J.C. Tennehill,D.A. Anderson,R.H.Pletcher. Computational Fluid Mechanics and Heat Transfer. Taylor and Francis, 792p,1997.