Back
 JAMP  Vol.2 No.12 , November 2014
Bifurcation of Bingham Streamline Topologies in Rectangular Double-Lid-Driven Cavities
Jianying Zhang*
Show more
Abstract: Numerical simulation of the bifurcation of Bingham fluid streamline topologies in rectangular double-lid-driven cavity, with varying aspect (height to width) ratio A, is presented. The lids on the top and bottom move at the same speed but in opposite directions so that symmetric flow patterns are generated. Similar to the Newtonian case, bifurcations occur as the aspect ratio decreases. Special to Bingham fluids, the non-Newtonian indicator, Bingham number B, also governs the bifurcation besides the bifurcation parameter A.
Keywords: Bingham Fluids, Double-Lid-Driven Cavity Flow, Bifurcation, Non-Newtonian Fluids
Cite this paper: Zhang, J. (2014) Bifurcation of Bingham Streamline Topologies in Rectangular Double-Lid-Driven Cavities. Journal of Applied Mathematics and Physics, 2, 1069-1072. doi: 10.4236/jamp.2014.212122.
References

[1]   Joseph, D.D. and Sturges, L. (1978) The Convergence of Biorthogonal Series for Biharmonic and Stokes Flow Edge Problems: Part II. SIAM Journal on Applied Mathematics, 34, 7-27. http://dx.doi.org/10.1137/0134002

[2]   Sturges, L. (1986) Stokes Flow in a Two-Dimensional Cavity with Moving End Walls. Physics of Fluids, 29, 1731- 1734. http://dx.doi.org/10.1063/1.866008

[3]   Zhang, J. (2013) Streamline Topologies and Yield Surfaces in Bingham Fluid Flow within Lid-Driven Cavities. Proceedings of the International Conference on Advances in Physics and Engineering Mathematics (ICAPEM), Shanghai.

[4]   Gürcan, F. (2003) Streamline Topologies in Stokes Flow within Lid-Driven Cavities. Theoretical and Computational Fluid Dynamics, 17, 19-30. http://dx.doi.org/10.1007/s00162-003-0095-z

[5]   Zhang, J. (2012) An Augmented Lagrangian Approach to Simulating Yield Stress Fluid Flows around a Spherical Gas Bubble. International Journal for Numerical Methods in Fluids, 69, 731-746. http://dx.doi.org/10.1002/fld.2611

[6]   Fortin, M. and Glowinski, R. (1983) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems. North-Holland, Amsterdam.

[7]   Glowinski, R. (1984) Numerical Methods for Nonlinear Variational Problem. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-3-662-12613-4

[8]   Duvaut, G. and Lions, J.L. (1976) Inequalities in Mechanics and Physics. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-642-66165-5

[9]   Latché, J.-C. and Vola, D. (2004) Analysis of the Brezzi-Pitk?ranta Stabilized Galerkin Scheme for Creeping Flows of Bingham Fluids. SIAM Journal on Numerical Analysis, 42, 1208-1225. http://dx.doi.org/10.1137/S0036142903424386

 
 
Top