Analysis of the k-epsilon turbulence model for simulation of compressible flows

The k–ε turbulence model is widely used to simulate compressible flows. The model has been evaluated extensively in incompressible flows. However, the extension of the model to compressible flows needs more testing. This dissertation presents a detailed analysis and a comprehensive evaluation of the k–ε model for compressible flows using direct numerical simulation (DNS) of a Mach 4 boundary layer. Specifically, the modeling of the Reynolds stress, the turbulent kinetic energy equation and the solenoidal dissipation rate equation are tested. The incompressible model for the Reynolds stress and for the unclosed terms in the turbulent kinetic energy, k, equation are found to work well in the compressible case. Further, it is shown that the solenoidal dissipation, ε _s, follows almost the same dynamics as the dissipation rate in an incompressible flow. As a result, the modeled ε-equation for incompressible flows can be used to compute ε_s in the compressible case. In addition, the explicit effects of compressibility on k and ε_s are found to be very small. Turbulence-chemistry interactions are also studied and two models are evaluated against DNS of homogeneous turbulence. Overall, the k–ε model and the associated turbulence-chemistry models are found to reproduce the characteristics of the compressible test flows reasonably well. Thus, these models can be used simulate compressible flows of practical interest.; A numerical method is developed to compute compressible turbulent flows using the k–ε model. The method is based on an implicit finite-volume approach, and it solves the turbulence model equations fully coupled to the mean flow equations. The numerical method is then used to solve two real life flow problems, namely, shock interaction flow on a double cone geometry and the flow in Atlas II rocket plumes. Laminar simulations of these flows are far from reality and some of the discrepancy is believed to be due to turbulence. The effect of turbulence on these flows is studied using the k–ε model and the results from the DNS testing of the model are used to improve the accuracy of the flow solutions. It is found that the turbulent solutions compare better with the experimental data.