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

Abstract

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.

Improved scale-resolved predictions of flow and heat transfer past a bluff body using partially averaged Navier–Stokes and a high-order eddy viscosity closure

“…Liu et al 11 implemented the RNG k - ϵ model (instead of the simple linear Boussinesq eddy viscosity model) and demonstrated improved predictions over an aerofoil and in a flow through a centrifugal pump. Recently, Chakraborty et al 12 performed a detailed comparative study of three prominent wall-resolving models within the k − ϵ framework (the Launder Sharma k − ϵ model, 13 the two-layer k − ϵ (TLKE) model of Chen and Patel 14 and the Lam–Bremhorst model 15 ) and demonstrated that despite the more frequent use of the TLKE model in conjugation with PANS in the previous studies, it is the Launder–Sharma k − ϵ model which shows significantly improved predictions of hydrodynamics as well as the heat transfer coefficients in flows past bluff bodies.…”