The partially averaged Navier–Stokes (PANS) approach has emerged as a viable scale-resolving bridging method over the last decade. Conventional PANS method, based on the linear eddy viscosity closure, overcomes the scale-resolving inadequacies of Reynolds-averaging but still suffers from limitations arising from linear constitutive modeling of turbulent stresses. Linear PANS has been evaluated in a variety of complex flow fields, including the benchmark case of flow around a sphere. In this work, the authors assess the potential of nonlinear eddy viscosity closure and further extend the evaluation of nonlinear closure in predicting thermal characteristics (besides hydrodynamics) of flow past a sphere. The presented evaluation has been performed on the basis of various surface-related and wake-related quantities. Our results are compared against available experimental and direct numerical simulation (DNS)/large eddy simulation studies. Our study shows that for the same value of the filter-control parameters, nonlinear PANS performs significantly better than linear PANS.

In recent past partially averaged Navier-Stokes equation (PANS) has been proposed as a scale-resolving bridging method for turbulence computations. Despite the geometric simplicity of the involved boundary conditions, the flow past a sphere is ripe with various complex flow phenomena, which make it an excellent test bed to evaluate various computational fluid dynamics modelling methodologies − both in terms of numerical schemes as well as turbulence models. Specifically, in this work we evaluate PANS in conjugation with the standard k-ε model in terms of (i) influence of filter parameters, (ii) sensitivity to free stream viscosity ratio and (iii) choice of numerical schemes at supercritical Reynolds number of 1.14x10 6 . Careful evaluations are made by comparing PANS results against available experimental data as well available detached eddy simulation (DES) and large eddy simulation (LES) results. Our study finds that indeed − as purported by the PANS theory − a reduction in the value of the first filter parameter (fk) successfully captures the complex vortical structures that exist past a sphere, shows far superior performance than unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and somewhat improved performance even over some of the LES studies reported in literature. Our study shows that in terms of most of the quantities of interest, PANS performance is almost at par with that of DES.

Purpose In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM). Design/methodology/approach The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM). Findings The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (fk) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in fk, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS. Research limitations/implications Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields. Originality/value Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.

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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.