The development and application of two-time-scale turbulence models for non-equilibrium flows

Abstract

This study re-visits the largely overlooked, but highly promising, topic of multi-scale RANS modelling for non-equilibrium turbulent flows. The paper presents the development of RANS models which, at an effective-viscosity level, involve two transport equations for the turbulent kinetic energy; one for the energy of the large scale, energy-producing, eddies and one for that of the smaller eddies, which, through continuous break-up, transfer turbulence energy to the dissipative scales. Two transport equations for the transfer-rate of the turbulent kinetic energy are also necessary, one for the rate of energy transfer from the large to the smaller scales and one for the rate of transfer from the smaller to the dissipative scales, the latter being of course the dissipation rate of turbulence. The two-timescale model of Hanjalic et al. (1980) has been the starting point of the current developments. The coefficients of the terms which appear in these models have been determined from asymptotic analyses of decaying grid turbulence, homogeneous shear flows and local-equilibrium boundary-layer flows. The models were subsequently further developed to become more responsive to strong non-equilibrium features, such as those caused by strong shear. It has been identified that in general, models which have been optimised to satisfy equilibrium flows (as is usually done) are unable to capture the strong changes the flows are subjected to due to highly non-equilibrium effects, thus needing further development. Within the two-timescale framework, it has been found possible to overcome this problem, by exploiting the additional information available on the turbulence spectrum. In a further departure from the development of earlier effective-viscosity two-time scale models, here the eddy viscosity expression is made sensitive to the local strain rate, as was also the case in single-scale models developed by Craft et al. (1996). The original contribution of this research is the development of two widely tested two-timescale linear-eddy-viscosity models, referred to here as NT1 and NT2. The difference between these two models is primarily in the eddy viscosity formulation. The two resulting models have been tested over nine test cases and their performance has been compared to those of the standard high-Reynolds number k − ε model, the SSG Reynolds stress transport model and the two-timescale model of Hanjalic et al. (1980). The test cases comprise of homogeneous shear and normally strained flows, adverse-pressure-gradient, favourable-pressure-gradient and oscillatory boundary layer flows, fully developed oscillatory and ramp up pipe flows and steady and pulsated backward-facing step flows. The models proposed here show considerable promise. They perform well in all cases tested and provide clear improvements over a range of single-and multi-scale models tested in an earlier study (Klein et al., 2015), over a set of test cases which cover a wide range of physical flow phenomena. Moreover, these improvements are achieved without any ...

An algebraic non-equilibrium turbulence model of the high Reynolds number transition region

“…Turbulence models with multiple time scales have been treated in (Hanjalić et al, 1980), with more recent further development to be found in (Klein et al, 2018). We base our discussion on homogeneous flow, where equations for the time evolution of 𝑘 and 𝜀 can be written (Hamlington & Ihme, 2014):…”

An Algebraic Non-Equilibrium Turbulence Model of the High Reynolds Number Transition Region

“…Turbulence models with multiple time scales have been treated in [27], with more recent further development to be found in [28]. We base our discussion on homogeneous flow, where equations for the time evolution of k and ε can be written as [29]:…”

A Two-Time-Scale Turbulence Model and Its Application in Free Shear Flows

“…There are quite a number of turbulence models within the eddy-viscosity framework. Recent advances on the numerical modelling of turbulent flows can be found in the papers by Argyropoulos and Markatos [1], Klein et al [2,3], and Nie et al [4]. Despite its many shortcomings, the k-ε model of turbulence is one of the most widely used turbulence models and it is capable of simulating an extensive collection of flows.…”