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Review of the shear-stress transport turbulence model experience from anindustrial perspectiveFlorian R. Menter aa ANSYS Germany GMBH, Otterfing, Germany

Online Publication Date: 01 April 2009

To cite this Article Menter, Florian R.(2009)'Review of the shear-stress transport turbulence model experience from an industrialperspective',International Journal of Computational Fluid Dynamics,23:4,305 316To link to this Article: DOI: 10.1080/10618560902773387URL: http://dx.doi.org/10.1080/10618560902773387

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Review of the shear-stress transport turbulence model experience from an industrial perspective

Florian R. Menter*

ANSYS Germany GMBH, Staudenfeldweg 12, Otterng, 83624, Germany

(Received 7 January 2009; nal version received 22 January 2009)

The present author was asked to provide an update on the status and the more recent developments around theshear-stress transport (SST) turbulence model for this special issue of the journal. The article is therefore notintended as a comprehensive overview of the status of engineering turbulence modelling in general, nor on theoverall turbulence modelling strategy for ANSYS computational uid dynamics (CFD) in particular. It is clear frommany decades of turbulence modelling that no single model nor even a single modelling approach can solve allengineering ows. Any successful CFD code will therefore have to oer a wide range of models from simple Eddy-viscosity models through second moment closures all the way to the variety of unsteady modelling conceptscurrently under development. This article is solely intended to outline the role of the concepts behind the SST modelin current and future CFD simulations of engineering ows.

Keywords: SST turbulence model; engineering ows; SAS; unsteady ows; scale-adaptive simulation; laminar-turbulent transition

Introduction

Some 15 years ago, the author proposed a newturbulence model for aerodynamic simulations, termedthe shear stress transport (SST) model (Menter 1994).The need for this model arose from the situation ofCFD in external aerodynamics in the early 1990s. Atthat time, the increase in computing power allowed forthe rst time the systematic application of CFD tothree-dimensional aerodynamic congurations. Thestandard turbulence model used in aeronautics codeswas the Baldwin-Lomax (BL) algebraic model (seeWilcox 1998). The BL model had already beengeneralised from the CebeciSmith model (see Wilcox1998) for easier use outside boundary layer codes, butwas clearly imposing severe limitations on the geo-metric complexity as well as on the mesh topologiesthat could be handled. In attention, it required non-local search algorithms which turned out to be codespecic, making a consistent implementation betweendierent CFD codes problematic. Lastly, new technol-ogies like CFD on unstructured grids and parallelprocessing, based on domain decomposition, requiredmodels which avoided non-local operations.

This need could only be served by models based ontransport equations. Although such models had beendeveloped for many decades, the aeronautics commu-nity was reluctant in adopting them for variousreasons. The rst was that the community had earlyon followed the philosophy of integrating the

equations through the viscous sublayer, while mostother industries using CFD adopted less accurate wallfunctions. This was a stumbling stone mainly for thek-e model, which had and has proven notoriouslydicult to integrate to the wall, despite the many low-Re number extensions proposed. The second issue wasthe inability of standard models to accurately predictow separation and stall characteristics. Signicantprogress in this aspect had been made by Johnson andKing (JK) (Wilcox 1998), in the framework ofalgebraic models, and the community was reluctantin accepting transport models falling behind the highaccuracy that the JK model already provided.

The most widely used alternative to the k-e modelwas the k-o model in the formulation developed byWilcox (1998). This model oered a much more robustand accurate viscous sublayer formulation and alsoproved more accurate for boundary layers in adversepressure gradients. However, the Wilcox model alsohad its weaknesses. The rst was a severe sensitivity ofthe results to the freestream values specied for ooutside boundary and shear layers (Menter 1992,Wilcox 1998). This freestream sensitivity introduced astrong dependency of the solution on relativelyarbitrary values specied for k and o at the inlet, aswell as on their decay upstream of the aerodynamicdevice. Furthermore, the model lacked (like allstandard two-equation models) the eect of SST,which had been demonstrated in its importance for

*Email: orian.menter@ansys.com

International Journal of Computational Fluid Dynamics

Vol. 23, No. 4, AprilMay 2009, 305316

ISSN 1061-8562 print/ISSN 1029-0257 online

2009 Taylor & FrancisDOI: 10.1080/10618560902773387

http://www.informaworld.com

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separation predictions by Johnson and King (JK) (seeWilcox 1998). The eects of freestream dependencyhave also not been eliminated by the new version of thek-o model (Wilcox 2007), see Appendix.

The principle idea behind the SST models was tocombine the best elements of the k-e, the k-o and theJK models. This was achieved by introducing functionswhich gradually blended the dierent elements of thesemodels into a single formulation. Obviously, this is apragmatic engineering approach, justied only by animproved model performance. It is to be explicitlystressed that the SST model owes much of its success tothe robust and accurate near wall formulation of the1988 Wilcox k-o model.

The SST model is implemented into most aero-nautics, as well as into most general-purpose commer-cial CFD codes. In other words, the models applicationrange has expanded signicantly beyond the originalaerodynamic target. It has proven successful, at least incomparison with other models, for a wide range of owsdominated by boundary layer behaviour, includingapplications where wall heat transfer is of relevance(Esch and Menter 2003). Furthermore, the concept ofblending the o- and the e-equations has found its wayinto more complex closures, like Explicit AlgebraicReynolds Stress Models (EARSM) (Hellsten and Laine2000) or full Dierential Reynolds Stress Models(DRSM) (Eisfeld 2006).

On the RANS side, a relatively recent extension wasthe introduction of a formulation for the prediction oflaminar-turbulent boundary layer transition (Langrtyet al. 2006, Menter et al. 2006b,c). Although thetransition phenomena themselves are handled by twoseparate transport equations, this extension still benetsfrom some of the characteristics of the underlying SSTmodel. For reliable transition predictions, it is essentialthat the viscous sublayer formulation of the model doesnot mimic transitional behaviour itself. The k-o andtherefore the SST model avoid low-Re extensions andcan therefore be combined with specic transitionmodels in a robust and reliable way.

Also in recent years, the blending concept hasproven useful in the development of scale-resolvingturbulence models. The SST model (together with theSpalartAllmaras (SA) model (Spalart and Allmaras1994) has served as one of the main platforms forDetached Eddy Simulation (DES) models as proposedby Spalart (2000) and Strelets (2001). It is also one ofthe options for the concept of Scale-Adaptive Simula-tion (SAS) developed by the authors group (Menteret al. 2003, Menter and Egorov 2004, 2005, 2006,Menter et al. 2006a). It is interesting to note that theblending functions have become an essential element ofthe DES approach to prevent undesired eects of theLarge Eddy Simulation (LES) limiter on boundary

layers (Menter and Kuntz 2003), resulting in theDelayed Detached Eddy Simulation (DDES) metho-dology (Menter and Kuntz 2003, Spalart et al. 2006).

The current article will review the SST modelformulation and discuss some of its specics. Exten-sions will cover transition prediction and modelenhancements for unsteady ows. Results obtainedwith the model for a limited number of applicationswill be presented. Finally, model limitations andpotential advancements will be discussed briey.

The SST model

In this section, the complete formulation of the SSTmodel is given, with the limited number of modicationsfrom the original version highlighted (Menter 1994).

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