An OpenFOAM-Based Extension of Low-Re k–ε Model to the Partially Averaged Navier–Stokes Methodology for Simulating Separated Flows With Heat Transfer

The partially averaged Navier–Stokes (PANS) methodology is known to give improved performance over the traditional Reynolds-averaged Navier–Stokes (RANS) formulation at an affordable computational cost. Over the years, PANS has gained popularity in both industry and academia. In this work, we strive to improve the performance of the k–ε-based PANS methodology by formulating a low-Reynolds-number (LRN) k–ε model-based PANS closure. We have compared the PANS closure based on Launder-Sharma k–ε model (LSKE) with PANS closure based on the conventional two-layer k–ε model (TLKE) in the classical case of separated flow past a heated square cylinder at Reynolds number (Re) of 21,400. The PANS methodologies are compared on the basis of flow hydrodynamics, heat transfer rate, and computational time. These methodologies are compared with the benchmark experimental and direct numerical simulation (DNS) results. The PANS + LSKE methodology clearly outperforms the conventional PANS + TLKE methodology in predicting the flow hydrodynamics and is computationally much faster as well. Moreover, the performance of the LSKE model in conjunction with the PANS methodology is found to be comparable to the more recent models like the shear stress transport (SST)–k–ω and the k–ε–ζ–f model. In heat transfer aspects, the performance of LSKE (with Yap correction)-based closure is the best on the stagnation surface, while the LSKE (without Yap correction)-based closure performs comparably better on the lateral and rear surfaces.