Abstract
AbstractThe quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.
Highlights
Despite the availability of high-fidelity computational approaches, such as large-eddy simulations (LES) and direct numerical simulations (DNS), the prohibitive cost of these approaches means that, for design purposes, Reynolds-averaged Navier–Stokes (RANS) methods remain ubiquitous in the aerospace industry
The aim of the analysis is to investigate the capabilities of three eddy-viscosity models: an Linear eddy-viscosity models (LEVMs), conventional quadratic constitutive relation (QCR) and the proposed extension to QCR
The analysis in this paper shows that the conventional form of QCR provides a definite improvement but does not, in general, compute the turbulent stresses very accurately, which may help to explain why its success in mean flow prediction for many flow fields has been limited
Summary
Despite the availability of high-fidelity computational approaches, such as large-eddy simulations (LES) and direct numerical simulations (DNS), the prohibitive cost of these approaches means that, for design purposes, Reynolds-averaged Navier–Stokes (RANS) methods remain ubiquitous in the aerospace industry Practical applications in this industry often feature complex geometries, such as wing–body junctions and turbine blade–hub junctions, where anisotropies in the turbulent stress distributions are known to influence the mean flow(1). These flow fields include canonical cases — channel flow(10,11), boundary layers(12–14) and pipe flow(15) — as well as more complex flows, such as the separated boundary layers(16) and square duct flow(17). The DNS-based analysis has the significant advantage that it is independent of any turbulence model and so provides a direct test of the eddy-viscosity models themselves
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