Numerical Investigation of the Three-Dimensional Flow around a Surface-Mounted Rib and the Onset of Unsteadiness

Abstract

The incompressible laminar isothermal flow of a Newtonian fluid at steady state around a surface-mounted rib is studied in a three-dimensional (3D) numerical experiment. The dimensionless Navier–Stokes equations are solved numerically using the Galerkin finite element method for Reynolds numbers 1 to 800. The expansion ratio of the problem is 1:9.6, while the aspect ratio is 1:20. The transition from the steady to the unsteady state and the identification of the critical Reynolds number are investigated in this paper. Numerical results of the skin-friction lines at the bottom and streamlines throughout the computational field are presented. A comparison between the 2D and 3D flow is made to show the effect of the walls on the flow, which reaches the plane of symmetry and affects the flow there; hence, also affecting the stability of the flow. It is concluded that the flow is three-dimensional even for a Reynolds number equal to 10. The critical Reynolds number is 600, and the steady-state equations can be used for any calculations up to this value.

Nonlinear Phenomena of Fluid Flow in a Bioinspired Two-Dimensional Geometric Symmetric Channel with Sudden Expansion and Contraction

“…Researchers from different engineering backgrounds have explored the nonlinear phenomena of fluid flow within various geometrical structures and the bifurcation of their solutions [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Except in the study of Erturk and Allahviranloo [7], the physical models studied in this literature [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] share one common feature: some kind of symmetry in geometrical structure. However, the flow in these models may be asymmetric and steadystate (i.e., static bifurcation has occurred).…”

“…The bifurcation of blood flow behavior, nonlinear behavior and bifurcation of solutions within the planar contraction-expansion channel are analyzed at different Re and contraction ratios. Laskos et al [18] simulated the nonlinear behavior of flow in a three-dimensional rectangular cross-sectional channel with a surface-mounted rib. Wang et al [19] investigated the nonlinear behavior of flow and heat transfer in a protruding channel with a circular obstacle.…”