Compressible Navier-Stokes code was developed to investigate the performance of some turbulence models in predicting compressible turbulent shear flows. Implicit LU-SGS algorithm with second-order TVD scheme was adopted in the code to solve the Favre-averaged Navier-Stokes equations.
In the first part, the performance of turbulence models in computing an axisymmetric supersonic base flow were investigated. Computations were carried out for Herrin and Dutton's base flow having a freestream Mach number of 2.46. The k-ε model and the k-ω model and the Reynolds stress models of Launder, Reece, and Rodi (LRR), of Speziale, Sarkar, and Gastski (SSG), and of Fu, Launder, and Tselepidakis (FLT) were tested. The three Reynolds stress models essentially differ in pressure-strain correlation term modeling. The computational results showed that the k-ε model performed better in mean flow prediction than the k-ω model. The k-ε model yielded greater eddy viscosity around the reattachment point and therefore enhanced the mixing of the outer and the recirculating flow. Although an approximate trend of generation and relaxation of turbulence was predicted by the Reynolds stress models, the high anisotropy of the Reynolds stresses before the flow reattachment and a rapid relaxation to equilibrium state after the reattachment were not reproduced properly by these models. Of the three Reynolds stress models, the FLT model was found to predict best the mean and the turbulent flow data. The effect of the compressibility correction model was also examined in the base flow. It was floud, however, that the compressibility correction deteriorated the performance of the trubulence model. We conjecture that the compressibility correction brings forth an excessive contribution of compressibility effects in and around the subsonic flow region.
In the second part, a modified dilatation term for the k-ω model was suggested by introducing instantaneous Mach number into the current dilatation models. The instantaneous Mach number was defined by the sum of the mean and the turbulent Mach number. Using the instantaneous Mach number, we switched on or off the compressibility effect represented by the dilatation terms in the trubulent kinetic energy equation. The modified dilatation model was applied to a compressible mixing layer and a 20 degree supersonic compression ramp flow. Results indicated that the introduction of an ad hoc function of instantaneous Mach number to alleviate excessive contribution of compressibility effects in the existion models was useful for practical purpose.
Finally, the concern of this thesis was turned into one-equation turbulence models which are commonly used in computation of aerodynamic flows. The Baldwin-Barth and the Spalart-Allmaras model were studied. Modification of the Baldwin-Barth model for non-equlibrium trubulent flow was suggested. The flow configurations chosen for the study of the one-equation models were the 20 degree compression ramp flow and the axisymmetric bump flow. Computational results indicated that the model modification yielded substantially improved solution in the pressure prediction in the recirculation region though it brought out slow recovery after the flow reattachment and large separation bubble.
