Accounting for Shocks in the KEKW Turbulence Model

Although modern turbulence models have been greatly improved in recent years by advances in sub-scale techniques, little has been done to address the interaction be- tween turbulence modeling and aerodynamic shocks. Consequently, modern turbulence models are hampered by inadequate source terms and eddy viscosities that work well on a case by case basis. The objective of this study is to demonstrate straightforward modifications to the blended kkω turbulence model that result in vastly improved com- putations for aerodynamic shocks. A flapped nozzle is chosen as the primary test case due to the complexities of the three dimensional flow field over a wide range of flow conditions. I. Background Judging from current literature, the blended kkω turbulence model 1 is one of the most popular turbulence models in use today. It has been successfully applied to a wide range of problems 2-5 with the SST variant gaining a particularly enviable reputation as a robust and accurate model for complex flows. 6,7 Due to its success on attached and slightly separated flows, the kkω model has been successfully modified for detached eddy simulation (DES) 8,9 and scale-adaptive simulation (SAS) 10 to greatly improve the model's performance for highly separated flows. 3 With all of the achievements presented in literature and also experienced first hand with the SimCenter's Tenasi unstructured flow solver across a vast array of cases with the kkω model, the absolute inablility of this model to predict the flow field in a two dimensional flapped nozzle 11 at any of the nozzle pressure ratios (NPR) was quite surprising and prompted a detailed simulation matrix to identify the cause of this problem as being with the overall algorithm, as being with turbulence modeling in general, or as being specific to the kkω model. As a first step to narrow down the list of potential causes, simulations were conducted at NPR = 1.255, NPR =2 .008, and NPR = 3.014 on the three dimensional grid described in Section VI using the k−� 12 and the one-equation SAS 9,13 turbulence models in Tenasi. These NPR were chosen because they characterize the overall behavior of Hunter's computational results 11 with prematurely separated flow for NPR≤ 1.8, with an "in-between" region for 1.8 < NPR < 2.4 in which the computational and experimental results begin to converge, and with accurate computations for NPR≥ 2.4. Both models accurately predicted the shock location and pressure recovery for NPR = 3.014 and prematurely separated at the geometric throat for NPR = 1.255. Further, both models accurately predicted the centerline location of the shock at NPR = 2.008 with prematurely separated flow at the sideline locations. Additionally, the planar nature of the shocks for NPR = 3.014 was also predicted with the k− � model reproducing the shock stretching displayed by Hunter's computational results 11 while the one-equation SAS model showed some shock contraction. Overall, the behavior of these models was consistent with each other and with Hunter's computational results. The kkω model reproduced similar results for NPR≤ 1.8 but predicted severely delayed shock locations for the remainder of the cases. Thus, there appeared to be a discrepancy with turbulence modeling in general for the flows with lower NPR and a problem specific to the kkω model for the higher NPR. To reduce the scope of this investigation, efforts were focused on correcting the discrepancy of the kkω model and elevating its performance to the level of the k− � and the SAS turbulence models for this case. Identifying and correcting the poor performance of these models at the lower NPR is saved for a later date. Although the results of the k− � and the SAS turbulence models indicated that the problem was with the kkω model and not with the Tenasi unstructured flow solver, a broad simulation matrix was used to examine the overall algorithm for any kind of excessive interaction between the algorithm and