On the laminar separation of the flow over a backward facing step : the effect of the step ratio on the recirculation zone length

In most of the available work, the Reynolds number based on the step height (step Reynolds number R_<eh>) was used as a single parameter that defined the reattachment length (recirculation zone length) in the laminar backward facing step flow. However, B. F. Armaly et al. (1983) suggested that the reattachment length in the laminar backward facing step flow was not a function of a single variable but was more likely to be a function of three or more variables such as the expansion ratio or step ratio, the velocity profile at the step or inlet-section and the step Reynolds number. A basic data concerning this suggestion has already been reported in our previous paper (1988). In this paper, the variation of the reattachment length was examined as a function of the step Reynolds number and the step ratio. For the flow over a backward facing step mounted in a two-dimensional channel, the Navier-Stokes equations and the continuity equation were solved numerically by the finite difference method. The calcuation was performed for the range of step Reynolds number 1≦R_<eh>≦250,and for the range of step ratio 0.1≦h_s≦1.0. The calculation results clearly indicated that the reattachment length increased with increasing the step Reynolds number and decreasing the step ratio. In addition, the reattachment length for a constant step Reynolds number in channel with different step ratios was presented and was discussed in order to search for the step ratio on the reattachment length.