I have a question about the backward facing step problem. At low Reynolds numbers (based on velocity upstream of step and step height), the reattachment length increases linearly with the Reynolds number. As the Re number gets larger, does the reattachment length stop increasing with further increases in Re? Does it approach a constant value for that particular geometry?

(1). A good question, but I am not sure. (2). Within laminar assumption, I guess, this self similar behavior will continue. (3). For turbulent flow , it is around six step height.

With laminar assumption, I guess the length would increase with Re in a typical case.

However, I am not too sure if the Re (as defined based on velocity and step height) is a relevant quantity at very high Re. The vortex shedding at the bend may be depend a lot on the step height. I do not think any self-similar behavior exists in this problems due to the singular behavior at the bend and the reattatchment point.

pete,

It is true that at low reynolds no. if you increase Re reattachment length increases.At higher Re this reattachment length decreases ... interseting fact indeed.

Have a look at landmark paper in Journal of Fluid mechanics. Vol 117. n1. Page 17-23.

I forgot the author.

good luck

jitendra

The following paper will probably answer most of your questions:

B.F. Armaly, F. Durst, J.C.F. Pereira: "Experimental and theoretical investigation of backward-facing step flow", J.Fluid.Mech Vol.127,pp.473-496,1983

As you said for low Reynolds number the reattachement length will increase approximately linearly. For a Re number based on the maximum inlet velocity and the hydraulic diameter of the inlet section (in case the inlet section has a channel like configuration) that is between 1200 and 6600 the flow is in a transition region and the average reattachement length will decrease gradually to a constant average reattachement length of about 6 for turbulent flows. For other inlet sections (say a boundary layer) these numbers will probably differ a bit.

(1). Yes, I was thinking about the steady state solution of the shear layer. (2). The structure of the recirculation region will be somewhat different. (3). For the transient flow solution, it is a completely different issue.