Turbulence modelling and turbulent-flow computation in aeronautics

Leschziner, M. A.; Drikakis, Dimitris

doi:10.1017/s0001924000092137

Cited by 55 publications

(7 citation statements)

References 191 publications

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“…Unfortunately, the numerical convergence of Reynolds stress models is notoriously difficult, which has given rise to nonlinear eddyviscosity models. 21 These models exhibit similar numerical convergence as linear eddy-viscosity models and overcome their limitations regarding non-inertial reference frame turbulence by extending the Boussinesq approximation with additional terms that account for system rotation or streamline curvature.…”

Section: Introductionmentioning

confidence: 96%

Symmetries and turbulence modeling

2020

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This work applies new insights into turbulent statistics gained by Lie symmetry analysis to the closure problem of turbulence. Founded in the mathematics of partial differential equations, Lie symmetries have helped advances in many fields of modern physics. The main reason for this is their ability to encode important physical principles that are implicitly expressed by governing equations. Newly discovered symmetries of the multi-point correlation equations describing turbulent motion have been shown to encode two central effects of turbulent statistics: intermittency and non-Gaussianity. Moreover, these symmetries play a pivotal role in obtaining turbulent scaling laws such as the logarithmic law of the wall. Evidently, correctly preserving these symmetry properties in a turbulence model would render it capable of accurately predicting important effects of turbulent statistics and turbulent scaling. As these symmetry constraints have so far not been taken into account when devising turbulence models, we present a completely new modeling framework that can yield models fulfilling these conditions. In order to accomplish this, it turns out to be helpful, if not necessary, to introduce an entirely new symmetry-based modeling strategy that allows systematically constructing equations based on symmetry constraints imposed on them. From these considerations, it can be shown that in order to create meaningful turbulence models that fulfill these constraints, it is necessary to introduce a new velocity and pressure field. A possible skeleton of model equations for second moment closure is presented.

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Section: Introductionmentioning

confidence: 96%

Symmetries and turbulence modeling

2020

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“…A comparison of numerical results with experimental data and their analysis for supersonic flows [40,81] showed that these implicit effects are insignificant for flows with Mach numbers smaller than 5.…”

Section: Allowance For Compressibility Effects In High-order Closure ...mentioning

confidence: 99%

“…Such models are called the secondorder closure models. Various variants of these models take into account the effect of flow rotation (swirling), external forces, and significant curvature of streamlines, which results in anisotropy of turbulence in three-dimensional flows [8,[78][79][80][81].…”

Section: Models Based On Equations For the Reynolds Stressmentioning

confidence: 99%

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Chapter 15: Modeling of Turbulent Compressible Near-Wall Flows

2013

Hypersonic Aerodynamics and Heat Transfer

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Semiempirical turbulence models for numerical calculation of near-wall flows of a compressible gas are presented. Various issues of modification of both algebraic and differential models, which were originally developed for low-velocity flows, to studying supersonic and hypersonic near-wall flows with intense heat exchange with the surface and the applicability limits of these models determined by the free-stream parameters and the temperature factor of the surface are considered.Semiempirical turbulence models are introduced in numerical investigations of external high-velocity flows of a compressible gas with turbulent regimes to close systems of Reynolds-averaged or boundary layer equations. The models are classified in accordance with known criteria. Two major classes (algebraic and differential models) are usually distinguished. These classes, in turn, are divided on the basis of accepted hypotheses; in addition, the second class is divided in terms of the number of differential equations.Differential models can be conventionally divided into one-equation, two-equation, and multiequation models. Two simple subclasses consist of one-equation and two-equation models based on equations derived by Kolmogorov [1] and Prandtl [2], which were further developed, for instance, in Refs. 3-5. These models are widely used not only for solving boundary layer problems, but also for analyzing more general formulations of fluid flows with allowance for viscosity.The most effective models of these classes discussed in this chapter were developed for calculating low-velocity flows with allowance for the properties of the near-wall region of the boundary layer. Later on, the range of problems solved with the use of these models was extended to regions with low Reynolds numbers, laminar-turbulent transition, and separation. It is also possible to take into account the three-dimensional character of the flow with anisotropic properties. The range of these problems also includes the calculation of high-velocity flows with heat transfer and with gas/surface interaction. For near-wall supersonic flows, the use of these model is justified by Morkovin's hypothesis with allowance for variability of the mean density of the flow only. Extension of the area of applicability of semiempirical models to hypersonic nonequilibrium flows with shock

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“…There are various values for constants in equation ( 11) depending on the proposed models. Leschziner and Drikakis (2002) pointed out that the predictive quality with which any nonlinear eddy-viscosity model resolves anisotropy depends on the calibration of the model's coefficients. The following assumption can be applied to get the constants next to quadratic terms.…”

Section: Mathematical Modelmentioning

confidence: 99%

A nonlinear eddy-viscosity model based on an elliptic relaxation approach

Basara

2009

Fluid Dyn. Res.

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The present paper proposes a nonlinear eddy-viscosity model, which combines an elliptic relaxation concept with the nonlinear stress-strain modelling. The basis model used here is the variant of v 2 -f model, namely ζf model. This recently proposed model essentially improves the numerical robustness over the original v 2 -f model; it is even used as the default turbulence model instead of the standard industrial k-ε model in the in-house commercial computational fluid dynamics (CFD) code, which was applied for all computational work presented here. This paper aims to extend the capability of the ζf model by employing the nonlinear stress-strain relationship including both quadratic and cubic nonlinear terms, and with that, to eliminate deficiencies arising from the linear Boussinesq assumption. The ζf model is applied in conjunction with universal wall treatment, which combines the integration up to the wall with wall functions. Computational results are compared with available experimental data for four different applications: a backward-facing step, a 180 • turn-around duct, a swirling combustor and a three-dimensional (3D) incylinder engine flow. The results obtained clearly show where the main benefits from a more general eddy-viscosity model could be expected.

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Turbulence modelling and turbulent-flow computation in aeronautics

Cited by 55 publications

References 191 publications

Symmetries and turbulence modeling

Symmetries and turbulence modeling

Chapter 15: Modeling of Turbulent Compressible Near-Wall Flows

A nonlinear eddy-viscosity model based on an elliptic relaxation approach

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