Simple test case for k-epilon model

mathletic · September 27, 2012, 19:05

Hi,
I wrote a CFD code using the k-epsilon turbulence model, currently only with Dirichlet and outflow boundary conditions. I tested it with the lid-driven cavity flow but I get false solution with k and epsilon dropping to zero everywhere except for the Dirichlet boundary.

So I am looking for a simple test case that helps me to find my mistake. Preferably it would be 1D, so I can examine the complete stiffness matrix. And the example gets extra points, if an analytic solution exists. Does anyone know such a test case or a paper / a book describing it?

I scanned many CFD books and found only the "Grid turbulance" example in [1]. It is 1D, steady state and give analytic solutions for k and epsilon. But still the informations given seems incomplete. Left are Dirichlet boundary conditions, what do I use on the right? What are the solutions for velocity and pressure? What is the turbulent viscosity nu_t and how large is the production term? Where is the example from, why is no source given? How is the analytic solution obtained? Has someone done the calculation for this example?

The lack of good test cases for the k-epsilon model with reference data is discouraging. Everybody seems happy with the back-ward facing step...

[1] Mohammadi, Pironneau: "Analysis of the K-Epsilon Turbulence Model", §V.5.1, page 74

ogloth · September 28, 2012, 03:12

Good morning,

Dirichlet boundary conditions alone will not enable you to compute wall bounded flows, because for the standard k-epsilon model you need to implement a wall function. You could, however, test your code with free shear flows (e.g. jets). I believe Wilcox's famous book on "Turbulence Modelling for CFD" should have a few suitable test cases.

Once you have a decent wall boundary condition you can solve a flat plate boundary layer.

Since I am not at all a turbulence expert -- maybe someone else has some better proposals.

Regards,
Oliver

mathletic · September 28, 2012, 04:04

Godd morning Oliver,
thanks for your quick reply. I hesitate to implement wall functions and add complexity to my program because I want to fix my bug-ridden k-espilon code first.

Wolcox's book has three 2d examples but they are described only vague and I'd like to have a complete description - idiot proof :-)

I am still hoping to get a 1D example or more details about the example from Mohammadi and Pironneau.

September 27, 2012, 19:05	Simple test case for k-epilon model	#1
mathletic New Member Join Date: Sep 2011 Location: Germany Posts: 7 Rep Power: 15	Hi, I wrote a CFD code using the k-epsilon turbulence model, currently only with Dirichlet and outflow boundary conditions. I tested it with the lid-driven cavity flow but I get false solution with k and epsilon dropping to zero everywhere except for the Dirichlet boundary. So I am looking for a simple test case that helps me to find my mistake. Preferably it would be 1D, so I can examine the complete stiffness matrix. And the example gets extra points, if an analytic solution exists. Does anyone know such a test case or a paper / a book describing it? I scanned many CFD books and found only the "Grid turbulance" example in [1]. It is 1D, steady state and give analytic solutions for k and epsilon. But still the informations given seems incomplete. Left are Dirichlet boundary conditions, what do I use on the right? What are the solutions for velocity and pressure? What is the turbulent viscosity nu_t and how large is the production term? Where is the example from, why is no source given? How is the analytic solution obtained? Has someone done the calculation for this example? The lack of good test cases for the k-epsilon model with reference data is discouraging. Everybody seems happy with the back-ward facing step... [1] Mohammadi, Pironneau: "Analysis of the K-Epsilon Turbulence Model", §V.5.1, page 74

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September 28, 2012, 03:12		#2
ogloth Senior Member Oliver Gloth Join Date: Mar 2009 Location: Todtnau, Germany Posts: 121 Rep Power: 17	Good morning, Dirichlet boundary conditions alone will not enable you to compute wall bounded flows, because for the standard k-epsilon model you need to implement a wall function. You could, however, test your code with free shear flows (e.g. jets). I believe Wilcox's famous book on "Turbulence Modelling for CFD" should have a few suitable test cases. Once you have a decent wall boundary condition you can solve a flat plate boundary layer. Since I am not at all a turbulence expert -- maybe someone else has some better proposals. Regards, Oliver

September 28, 2012, 04:04		#3
mathletic New Member Join Date: Sep 2011 Location: Germany Posts: 7 Rep Power: 15	Godd morning Oliver, thanks for your quick reply. I hesitate to implement wall functions and add complexity to my program because I want to fix my bug-ridden k-espilon code first. Wolcox's book has three 2d examples but they are described only vague and I'd like to have a complete description - idiot proof :-) I am still hoping to get a 1D example or more details about the example from Mohammadi and Pironneau.