Explicit algebraic Reynolds stress model for compressible flow turbulenceJournal of Turbulence

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Authors
Geon-Hong Kim, Seung O. Park
Year
2013
DOI
10.1080/14685248.2013.823199
Subject
Condensed Matter Physics / Mechanics of Materials / Physics and Astronomy (all) / Computational Mechanics

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Journal of Turbulence

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Explicit algebraic Reynolds stress model for compressible flow turbulence

Geon-Hong Kim a & Seung O. Park a a Aerospace Engineering Department , Korea Advanced Institute of

Science and Technology , Daejeon , Republic of Korea

Published online: 02 Aug 2013.

To cite this article: Geon-Hong Kim & Seung O. Park (2013) Explicit algebraic Reynolds stress model for compressible flow turbulence, Journal of Turbulence, 14:5, 35-59, DOI: 10.1080/14685248.2013.823199

To link to this article: http://dx.doi.org/10.1080/14685248.2013.823199

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Journal of Turbulence, 2013

Vol. 14, No. 5, 35–59, http://dx.doi.org/10.1080/14685248.2013.823199

Explicit algebraic Reynolds stress model for compressible flow turbulence

Geon-Hong Kim and Seung O. Park∗

Aerospace Engineering Department, Korea Advanced Institute of Science and Technology,

Daejeon, Republic of Korea (Received 17 January 2013; final version received 2 June 2013)

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a newARSMmodel is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for

ARSM for compressible flow can hardly be obtained due to dilatation terms.We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.

Keywords: compressible turbulence; algebraic Reynolds stress model; compressible mixing layer; supersonic boundary layer

Introduction

As is well known, the Reynolds-averaged Navier–Stokes (RANS) simulation is most widely used in practical engineering flow simulations. Among various turbulence models for RANS, the two-equation models are the most popular and widely used. For complex flows, however, the two-equation models often result in inaccurate predictions. This can be handled by adopting the Reynolds stress model (RSM), sometimes called as a second-order closure model originated from the work by Launder et al. [1]. However, the RSM is expensive since it involves six transport equations for the Reynolds stresses. This makes the RSM less popular in simulating practical flows.

As a practical alternative, algebraic Reynolds Stress Model (ARSM) was proposed based on two-equation model and algebraic expressions for the Reynolds stresses. Thus, it can predict the Reynolds stresses more accurately than the two-equation models with less computational cost than the RSM. Since its first proposal by Rodi [2], there have been many significant contributions to improve themodel. Pope [3] suggested an effective-viscosity approach and introduced a finite tensor polynomial to formulate the effective-viscosity according to the Cayley–Hamilton theorem. To develop a fully explicit ARSM (EARSM), Gatski and Speziale [4] proposed an EARSMby linearising the production-to-dissipation-rate term to be its equilibrium value. Later, Jongen and Gatski [5] extended the EARSMof Gatski and

Speziale by considering the production-to-dissipation-rate equilibrium.Girimaji [6] pointed ∗Corresponding author. Email: sopark@kaist.ac.kr

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D ec em be r 2 01 4 36 G.-H. Kim and S.O. Park out that previousARSMswere not fully explicit or explicit and not always self-consistent and derived an analytically exact solution of the non-linear weak-equilibrium equation for incompressible two-dimensional mean flows.Wallin and Johansson [7] developed an EARSM which is similar to the work of Girimaji. They simplified the algebraic equation for the

Reynolds stress anisotropy tensor by setting the model coefficients to be of specific values.

Most of the previous ARSMs have been proposed based on incompressible turbulent flows. Wallin and Johansson proposed an EARSM for compressible flows but they only considered the dilatation of the mean flow. Early studies on compressible turbulence models were largely associated with the dilatational effects of velocity fluctuation to result in several models with dilatational terms [8–12]. Recently, however, DNS results [13–17] showed that the dilatation terms were not as significant as they had been reflected. These