Interpretation of turbulent viscosity

vemmonstr · August 11, 2016, 05:54

Hello everyone,

I'm new in the forum and just got in the world of CFD.

I have a question concerning the turbulent viscosity term in the k-epsilon model. What is in general term this term and its real need? Where does it come from?

Thanks in advance.

fluid23 · August 11, 2016, 10:46

By averaging the Navier-Stokes equations (RANS analysis) we introduce non-linear terms called Reynolds stresses which prevent a closed solution of the equations as is. You can think of these as turbulence dependent terms. One way of addressing this is the so called Boussinesq approximation. This sets the Reynolds stresses as a function of the mean flow such that a closed solution can be found but in the process introduces a term called eddy viscosity. Essentially, it is a way in which we can understand and model the dissipation of turbulent energy in the flow. It’s very much analogous to the idea of molecular viscosity (aka fluid viscosity) which dissipates mechanical energy into thermal energy through friction. This is the basis of most of the common turbulence models; k-e, k-w, spalart-allmaras, etc…

August 11, 2016, 05:54	Interpretation of turbulent viscosity	#1
vemmonstr New Member Alex Baptistella Join Date: Aug 2016 Posts: 1 Rep Power: 0	Hello everyone, I'm new in the forum and just got in the world of CFD. I have a question concerning the turbulent viscosity term in the k-epsilon model. What is in general term this term and its real need? Where does it come from? Thanks in advance.

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August 11, 2016, 10:46		#2
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 18	By averaging the Navier-Stokes equations (RANS analysis) we introduce non-linear terms called Reynolds stresses which prevent a closed solution of the equations as is. You can think of these as turbulence dependent terms. One way of addressing this is the so called Boussinesq approximation. This sets the Reynolds stresses as a function of the mean flow such that a closed solution can be found but in the process introduces a term called eddy viscosity. Essentially, it is a way in which we can understand and model the dissipation of turbulent energy in the flow. It’s very much analogous to the idea of molecular viscosity (aka fluid viscosity) which dissipates mechanical energy into thermal energy through friction. This is the basis of most of the common turbulence models; k-e, k-w, spalart-allmaras, etc…