Backward Facing Step

Problem Definition:

The problem consists of a flow over a backward facing step with expansion ratio H/h =1.94. As shown in figure below, h is the inlet height, H is the total height, (S + h) where S denotes the step height. All geometrical length scales are dimensionless based on the channel height h. The length of the channel Ld is equal to 20 times the inlet height. In order to simulate a fully developed laminar channel flow upstream of the step, a standard parabolic velocity profile with a maximum velocity Umax=3/2Ub is given where Ub is the bulk (average) velocity of the inlet flow. The only non-dimensional parameter in the governing equation is the Reynolds number. For the considered flow problem, the following definition is used:

where ρ and μ are the density and the dynamic viscosity, respectively. As mentioned before Ub is the bulk (average) velocity of the inlet flow. D is chosen as the hydraulic diameter of the inlet channel, which is equivalent to twice its height, D=2h. For the present test case the inlet velocity is parabolic with Ub=1, ρ=1 and Reynolds no is varied by changing the dynamic viscosity.

Results:

A hexahedral grid with 36000 cells is used for the simulations. The streamlines at Re=50 and 100 are shown in Figs. 3.2 and 3.3 respectively. The variation of length x of the primary recirculation region normalized by the step height S is shown in Fig. 3.4 and results are compared with the published results of Biswas et al. [1].

Figure 3.2: Streamlines at Re= 50


Figure 3.3: Streamlines at Re= 100


Figure 3.4: Comparison of the primary recirculation length

References:

[1] Biswas G., Breuer M., and Durst F. (2004) ‘Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers’, Journal of Fluids Engineering, Vol.126, pp.362-374