At first a relative simple simulation will be done of a one-directional incompressible turbulent flow. It will show how different turbulencemodels performat a Reynolds number of 15,000 inside a conical diffuser with an angle of 2θ=8°, no separation is expected in this geometry. The turbulence models investigated are the k-ε, the k- ω and the RSM model. The mesh refinement is tested on produced accuracy of the results. The final results of the simulations are compared with both DNS (direct numerical simulation) and experimental results. All models produce different behavior, due to transport equations, algebraic models and empirical constants used. The deviations are dependent on geometry and flow conditions, where certain turbulence models are better for specific cases. The simulations showed different representations. The flow behavior of the k- ω model was the most realistic, due to the correct core velocity although it showed flow reversal at the wall. Various parameters are reviewed, such as velocity profile, flow reversal, pressure coefficient, friction coefficient and turbulent statistics.

The oscillating flow will represent a case which is more closely to the flow seen inside a thermoacoustic engine. The geometry is a rectangular diffuser and the flow is compressible. It is a much more complex flow with frequencies ranging from 6-21 Hz during the simulations. Laminar, transitional and turbulent cases are simulated by Reδ numbers of 380, 580 and 740 with varying displacement amplitudes. The transitional k-kl-ω model is used, because of its ability to also simulate laminar and transitional cases besides only turbulent cases. Additional the k- ω SST model is tested. The velocity profiles are not simulated well with the k-kl-ω model, which was caused by the under estimation of simulated turbulence near the wall. It was found that for both models separation will induce early and low in the diffuser and expand downstream as the cycle passes. As a result the Reynolds shear stresses show higher values earlier in the cycle. It was also seen that the reattachment would differ in pattern. The trend is found that separation begins earlier with increasing Reynolds number and increasing displacement amplitude. The minor losses, or irreversibilities, vary in accuracy, the effect of the displacement amplitude is not always seen for variables which are dependent on the magnitude of the pressure. In addition turbulence would not show an increase at the point of transition compared to turbulent cases. Both models seem to deliver deviating results, but the k- ω SST models the cases better.