Dynamic versions of PANS capable of mimicking DES and IDDES
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Hybrid RANS/LES methods (HRLM) seek a compromise between the low computational cost of RANS and the predictive capabilities of LES. Many HRLM’s have been developed over the past three decades. Some of them have theoretical fundaments, while some others are rather empirical. Partially Averaged Navier-Stokes (PANS) belongs to the former category, while Detached Eddy Simulation (DES) and all its derived HRLMs belong to the latter category. As shown by [1], an equivalence criterion can be established between HRLMs, following the simple idea that two computations using the same numerical settings and same closure model for the unresolved scales (i.e. “parent RANS”) but with two differents HRLMs, should lead to similar low order statistics of the flow. This theory, called “H-equivalence”, was reused later to elaborate dynamic versions of PANS capable of mimicking DES [2] and IDDES [3]. The former is called D-PANS, and the latter is called IDD-PANS. The key idea is to express the energy ratio f k as a function of the (ID)DES parameter f_DES . The results, not shown here for the sake of brevity, show that D-PANS is able to reproduce results very similar to DES, while IDD-PANS strongly resembles IDDES. The full paper will discuss D-PANS and IDD-PANS in further details. Computations were performed over (i) periodic channel flow at various friction Reynolds numbers, (ii) periodic hill at a bulk Renolds number of 10595 and (iii) flow over a hump at chord-based Reynolds number of 936000. Moreover, it is theoretically shown that these new versions PANS inherit the robustness of DES-derived HRLMs. REFERENCES [1] Friess, C., Manceau, R., & Gatski, T. B. (2015). Toward an equivalence criterion for hybrid RANS/LES methods. Computers & Fluids, 122, 233-246. [2] Davidson, L., & Friess, C. (2019). A new formulation of fk for the PANS model. Journal of Turbulence, 20(5), 322-336. [3] Friess, C., & Davidson, L. (2020). A formulation of PANS capable of mimicking IDDES. International Journal of Heat and Fluid Flow, 86, 108666.