 ## General

#### How is the dissipation rate calculated in the initialization panel from the turbulent intensity and viscosity ratio specified at the boundary?

• FAQ
Participant

Let’s say you have specified the following conditions at a pressure-inlet boundary: (Operating Pressure = 0 Pa) Total Pressure, Pt = 51056 Pa Supersonic/Initial Pressure, Ps = 27364 Pa Total Temperature, Tt = 793.2 K Turbulent Intensity, I = 0.05 (5%) Turbulent Viscosity Ratio, Mut/Mu, Rv = 10 The material used is Air, with Density specified as ‘Ideal Gas’ and Viscosity specified using ‘Sutherland’ method. Standard k-epsilon turbulence model is being used. When you go to the initialization panels and use that boundary as the source (Compute From), the following values are given by Fluent: Temperature, T = 663.9422 K X Velocity, Vx = 510.0763 m/s Turbulent Kinetic Energy, k = 975.6668 (m/s)^2 Turbulent Dissipation Rate, e = 6.874611e+07 m2/s3 From display contour, the density and viscosity are as follows: Density, rho = 0.1435854 kg/m3 Molecular Viscosity, mu = 3.22212e-05 kg/(ms) Using ideal gas, isentropic relations, and the above equations, we can confirm that all the initialization values given by Fluent are correct, except for the value of Turbulent Dissipation Rate, e. The Turbulent Kinetic Energy, k, and Turbulent Dissipation Rate, e, are given by the following equations: k = 1.5*(Uavg*I)^2 e = rho*Cmu*(k*k/Mu)*(1/Rv) For Standard k-epsilon turbulence model the model constant, Cmu = 0.09 The value of e computed using the above equation is 3.817808E+07 m2/s3. Why is the value of e in the initialization panel different? Explanation For initialization only, the value of mu used in the calculation of epsilon above is the constant value of mu for standard air and NOT the value computed using the Sutherland formula above. It is true that for consistencies, the value of mu computed by the Sutherland formula should be used instead, but most likely the flow is insensitive to the initial value of e, hence the procedure used by Fluent is acceptable. As verification, using mu=1.7894e-5 kg/(ms), the value of Turbulent Dissipation Rate is given as e = 6.874616E+07 m2/s3 (which is very close to the value given by the initialization panel). Once the iteration is started, the correct value of mu computed using the Sutherland formula is used. 