DNS Study on Eddy Viscosity Turbulence Model

The Boussinesq eddy viscosity assumption (1872) is still widely used in turbulence modeling although Reynolds stress transport model is considered. In this paper, we use DNS to study the Boussinesq assumption and found the Boussinesq eddy viscosity assumption is lack of scientific foundation. It may be viable in the second quarter (ejection as u’<0 and w’>0) and fourth quarter (sweep as u’>0 and w’<0) but fails even in sign which is not adjustable in the first quarter and third quarter. A counterexample is given for the case of high speed flow passing a micro vortex generator (MVG), where the flow separation appears. Both computation and experiment show there is no direct relation between Reynolds stress and the mean velocity gradients. We will try to use the DNS data to develop model for Reynolds stress. I