# Steady state RANS - change of equation type

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 June 29, 2015, 05:45 Steady state RANS - change of equation type #1 New Member   Lucas Join Date: Jun 2015 Posts: 20 Rep Power: 10 Hello, I do have a question regarding RANS-modelling. My problem is a very simple steady state flow of a gas through a certain device. The device has constant temperatures at the boundaries and the flow itself is not compressible (The mach number is supposed to be below 0.1). I do assume constant gas properties. Out of these statements the Navier Stokes equations (as well as the continuity and energy equation) for a laminar flow problem have to be of an elliptic type (as there is not transient term, only the boundary conditions affect the solution). - Is this assumption correct? I also do expect turbulence phenomena in the flow, therefore RANS is the only option for a steady state flow (as LES and DNS demand a transient flow). I now do assume that the equation does not change from an elliptic type due to RANS modelling. Can anybody tell me under which circumstances this assumption is correct? Thank you very much in advance!

June 29, 2015, 06:47
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,781
Rep Power: 71
Quote:
 Originally Posted by Edeluc Hello, I do have a question regarding RANS-modelling. My problem is a very simple steady state flow of a gas through a certain device. The device has constant temperatures at the boundaries and the flow itself is not compressible (The mach number is supposed to be below 0.1). I do assume constant gas properties. Out of these statements the Navier Stokes equations (as well as the continuity and energy equation) for a laminar flow problem have to be of an elliptic type (as there is not transient term, only the boundary conditions affect the solution). - Is this assumption correct? I also do expect turbulence phenomena in the flow, therefore RANS is the only option for a steady state flow (as LES and DNS demand a transient flow). I now do assume that the equation does not change from an elliptic type due to RANS modelling. Can anybody tell me under which circumstances this assumption is correct? Thank you very much in advance!

The steady state RANS equations are actually elliptic...
just to highlight the fact that many turbulence models use the non-linerar unresolved terms that are part of the hyperbolic equation and transform in modelled terms that are diffusion-like, therefore classified in the parabolic/elliptic equations.

 June 29, 2015, 06:54 #3 New Member   Lucas Join Date: Jun 2015 Posts: 20 Rep Power: 10 Dear Mr. Denaro, Thank you very much for the fast answer to my question.

 Tags elliptic pde, pde type, rans modelling, steady state rans