Hi Friends !!

i need some Compressible-Viscous-Laminar test cases to validate my code. Plz suggest some papers regarding that...

Thanks Mohammad

Dear Mohammed,

The paper by Jawahar and Kamath(JCP 2001) contain test cases for viscous flows, pertaining more to flow past airfoils. You could try a few internal viscous flow cases, specifically two of them. The first one is the laminar flow past a compression ramp (Hung and Maccormack, Delanye and Essers). This is a supersonic laminar flow case and possibly (I am not sure, but you should get it) can also be found in Chung's text book on CFD. The only problem possibly you would face if you referred to the papers of Hung and Maccormack, Delanye and Essers is that the geometry is a little vague.

Ref:

1. Delanye M and Essers J, AIAA Paper 95-1710,"An accurate finite volume scheme for Euler and N/S eqns. on unstructured adaptive grids".

2. Hung C M and MacCormack R W, AIAA Jl. (around 1968), "Numerical simulation of supersonic and hypersonic laminar compression flows"

The second case you could try is the supersonic laminar flow past a circular arc bump.( Kallinderis etal.). Unfortunately, the first paper of his where I saw the case, had some inaccuracies and printing mistakes. However, in this case the configuration has no ambiguity and I am giving the geometry and test conditions below.

The height of channel = 1.0 The length of channel = 3.0

[ The length is split in three equal parts of 1.0 each, the first and third are plane walls, the second contains the bump. A 4% circular arc bump means the max. height of the bump is 0.04*(the distance over which the arc is spread) ie. here 0.04*1.0 = 0.04. The arc therefore is circular and the max. height is 0.04.].This completes the geometrydefinition.

The test conditions : M = 1.4, Re=16000.

You could look into the following reference of Kallinderis for the second problem, but do not adopt it completely, just use it to understand how the geometry looks like. It is important that the geometry is proper so that the solution converges.

Also, as far as the boundary condition is concerned, in both the cases above a small portion on the lower wall is given an inviscid or slip bc. This would be the first 20% in the first test case and the first segment of 1.0 in the second test case.

Ref:

Kallinderis and Baron, AIAA Jl. 14(4),1976, " Adaptation methods for a new Navier-Srokes algorithm".

The third case you could try is a very common case, the laminar flow past a circular cylinder at Re<40. This is just like the airfoil case replaced by airfoil. The Mach of ariund 0.3 is fine. You could use Re of 40, 30 and 20. You could try out google for some of the standard results.

Hope this helps.

Regards,

Ganesh