Journal ArticleDOI
On nonlinear K-l and K-ε models of turbulence
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In this paper, a nonlinear K-l and K-e model is proposed to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model, and the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts.Abstract:
The commonly used linear K-l and K-e models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-e models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.read more
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Journal Article
Closure of "Velocity Distribution in Compound Channel Flows by Numerical Modeling"
TL;DR: In this paper, the authors examined the problem of predicting uniform turbulent flow in a compound channel with the nonlinear k-e model, which is capable of predicting the secondary currents caused by the anisotropy of normal turbulent stresses, as they determine the transverse momentum transfer.
Journal Article
On Predicting The Turbulence-induced Secondary Flows Using Nonlinear K-∈ Models
TL;DR: In this article, low turbulent Reynolds number direct simulation data are used to calculate the invariants of the Reynolds stress and the turbulent dissipation rate in a square duct, and numerical simulation using Reynolds averaged Navier-Stokes equations with these models was performed.
Journal ArticleDOI
Turbulence modelling and turbulent-flow computation in aeronautics
TL;DR: The intuitive nature of turbulence modelling, its strong reliance on calibration and validation and the extreme sensitivity of model performance to seemingly minor variations in modelling details and flow conditions all conspire to make turbulence modelling an especially challenging component of CFD, but one that is crucially important for the correct prediction of complex flows.
Introductory Turbulence Modeling
Abstract: NOMENCLATURE English B k production of turbulent kinetic energy by buoyancy B ε production of turbulent dissipation by buoyancy C f friction coefficient D k destruction of turbulent kinetic energy D ε destruction of turbulent dissipation k specific turbulent kinetic energy l mfp mean-free path length l mix mixing length p pressure p* modified pressure P k production of turbulent kinetic energy P ε production of turbulent dissipation q i Reynolds flux S source term S ij mean strain rate tensor t time u velocity u + dimensionless velocity (wall variables) u * friction velocity x horizontal displacement (displacement in the streamwise direction) y + dimensionless vertical distance (wall variables) Greek Symbols δ boundary layer thickness δ v * displacement thickness δ ij Kroenecker delta function ε dissipation rate of turbulent kinetic energy φ generic scalar variable φ' fluctuating component of time-averaged variable φ Φ mean component of time-averaged variable φ φ Reynolds time averaged variable φ Γ diffusion coefficient Γ t turbulent diffusivity κ von-Karman constant µ molecular viscosity v ν t eddy viscosity Π ij pressure-strain correlation tensor ρ density σ turbulent Prandtl-Schmidt number σ k Prandtl-Schmidt number for k τ ij Reynolds stress tensor τ w wall shear stress ω dissipation per unit turbulent kinetic energy (specific dissipation) Ω ij mean rotation tensor 1 1.0 INTRODUCTION Theoretical analysis and prediction of turbulence has been, and to this date still is, the fundamental problem of fluid dynamics, particularly of computational fluid dynamics (CFD). The major difficulty arises from the random or chaotic nature of turbulence phenomena. Because of this unpredictability, it has been customary to work with the time averaged forms of the governing equations, which inevitably results in terms involving higher order correlations of fluctuating quantities of flow variables. The semi-empirical mathematical models introduced for calculation of these unknown correlations form the basis for turbulence modeling. It is the focus of the present study to investigate the main principles of turbulence modeling, including examination of the physics of turbulence, closure models, and application to specific flow conditions. Since turbulent flow calculations usually involve CFD, special emphasis is given to this topic throughout this study. There are three key elements involved in CFD: (1) grid generation (2) algorithm development (3) turbulence modeling While for the first two elements precise mathematical theories exist, the concept of turbulence modeling is far less precise due to the complex nature of turbulent …
Journal ArticleDOI
Reynolds stress closure for nonequilibrium effects in turbulent flows
TL;DR: In this paper, a new Reynolds stress closure for nonequilibrium effects in turbulent flows has been developed, formally derived from the Reynolds stress anisotropy transport equation, which results in an effective strain rate tensor that accounts for the strain rate history to which the turbulence has been subjected.
References
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Journal ArticleDOI
Progress in the development of a Reynolds-stress turbulence closure
TL;DR: In this article, the authors developed a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.
Journal ArticleDOI
A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers
TL;DR: In this article, the three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers.
Journal ArticleDOI
Numerical investigation of turbulent channel flow
Parviz Moin,John Kim +1 more
TL;DR: In this article, a large-scale flow field was obtained by directly integrating the filtered, three-dimensional, time dependent, Navier-Stokes equations, and small-scale field motions were simulated through an eddy viscosity model.
Book ChapterDOI
Computational Modeling of Turbulent Flows
TL;DR: In this article, it is shown that direct simulation is not an alternative for practical computation and that the various sophisticated closures suffer from essentially the same problems as the direct simulations and therefore, are limited to homogeneous situations.
Journal ArticleDOI
A Reynolds stress model of turbulence and its application to thin shear flows
Kemal Hanjalic,Brian Launder +1 more
TL;DR: In this paper, the authors provided a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor the turbulence energy κ and e.g., the turbulent shear stress does not vanish where the mean rate of strain goes to zero.