Challenges in Modelling and Simulation of Turbulent Flows with Spatially-Developing Coherent Structures

Abstract

The objective of this work is to investigate the fundamental challenges encountered in modelling and simulation of turbulent flows driven by spatially-developing coherent structures. Scale-Resolving Simulations (SRS's) of practical interest are expressly intended for efficiently computing such flows by resolving only the most important features of the coherent structures and modelling the remainder as stochastic field. With reference to a typical Large-Eddy Simulation (LES), practical SRS methods seek to resolve a considerably narrower range of scales (physical resolution) to achieve an adequate degree of accuracy at reasonable computational effort. The success of SRS methods depends upon three important factors: i) ability to identify key flow mechanisms responsible for the generation of coherent structures; ii) determine the optimum range of resolution required to adequately capture key elements of coherent structures; and iii) ensure that the modelled part is comprised nearly exclusively of fully-developed stochastic turbulence. This study considers the canonical case of the flow around a circular cylinder to address the aforementioned three key issues. It is first demonstrated using experimental evidence that the vortex-shedding instability and flow-structure development involves four important stages. The inherent limitations of the Reynolds-Averaged Navier-Stokes (RANS) approach in addressing the flow physics in these four stages of development are explained. A series of SRS computations of progressively increasing resolution (decreasing cut-off length) are performed. An a priori basis for locating the origin of the coherent structures development is proposed and examined. The criterion is based on the fact that the coherent structures are generated by the Kelvin-Helmholtz (KH) instability. The most important finding is that the key aspects of coherent structures can be resolved only if the effective computational Reynolds number (based on total viscosity) exceeds the critical value of the KH instability in laminar flows. Finally, a quantitative criterion assessing the nature of the unresolved field based on the strain-rate ratio of mean and unresolved fields is examined. Based on the findings, quantitative guidelines for determining the optimal degree of physical resolution in flows of practical interest are proposed.