Evaluation of PANS Methodology With Nonlinear Eddy Viscosity Closure: Flow Past a Heated Sphere

Abstract

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.

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

“…To have a comprehensive evaluation of the cubic PANS methodology, in Table 3, we have included results of the linear and quadratic PANS methodologies as well. 19 Evidently, the performance of the cubic PANS methodology is substantially superior to its linear and quadratic counterparts over the entire range of f k considered in this study.…”

“…In Figure 8 we present the variations in the mean Nusselt number (19) on the sphere surface. In this figure, we include results from the linear, quadratic, and cubic PANS simulations.…”

“…These latter results are sourced from our recently published work. 19 Each PANS simulations begins with a uniformly initialized flow field, which is then allowed to evolve over the duration of three flow-through times, where a flow through time is defined as 30D/V 0 , where 30D is the stream-wise extent of the computational domain, and the symbol V 0 represents the free stream velocity. Subsequently, various statistics are calculated using time-averaging of flow variables (over six flow through cycles).…”

“…The authors demonstrated that, indeed, the quadratic version of the PANS keeps the desired sensitivity to its filter parameters both in terms of (1) the unresolved kinetic energy and (2) a weakening alignment tendency between the resolved strain rate tensor and the unclosed turbulent stresses. Saroha, et al 19,20 have further demonstrated the superior performance of a quadratic-eddy viscosity closure of PANS in unsteady three-dimensional flows past a sphere and a cylinder. The authors further extended the modelling philosophy of a higher order eddy viscosity closure for the unclosed turbulent stress to the unclosed heat flux term in the energy equation.…”

“…[22][23][24][25] To clearly identify the advantages of the cubic PANS methodology, comparisons are also made with the corresponding results employing the PANS methodologies using linear and quadratic eddy viscosity closures. 19 The remaining part of the paper is organized into four sections. Next, we present the governing equation of PANS and provide details about the cubic version of the PANS closure equations.…”