Evaluation of Several Turbulence Models for Turbulent Flow in Concentric and Eccentric Annuli

1998 ◽  
Vol 120 (4) ◽  
pp. 268-275 ◽  
Author(s):  
I. Azouz ◽  
S. A. Shirazi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Momentum Equation ◽  
Equation Model ◽  
Numerical Code ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Curvilinear Boundary ◽  
Numerical Predictions ◽  
Eccentric Annuli

Turbulent flow in concentric and eccentric annuli is numerically simulated as part of an investigation aimed at modeling drilled cuttings transport in wellbores. A numerical code is developed to solve the time-averaged momentum equation wherein the Reynolds stresses are modeled using the eddy viscosity approach. A nonorthogonal curvilinear, boundary-fitted coordinate system is used to facilitate the implementation of boundary conditions. Several turbulence models, including a one-layer mixing length model developed as part of this study, a two-layer mixing-length model, and a low Reynolds number, two-equation (k-τ) model are used to simulate turbulent flow in several concentric and eccentric annuli. Performance of these turbulence models is evaluated by comparing numerical predictions to experimental data obtained from several sources. Results show that the proposed one-layer mixing length model performs as well as the two-layer mixing length model and the two-equation model while avoiding some of the difficulties associated with the implementation of these models.

Numerical Prediction of Flow in a Nuclear Fuel Bundle With Various Turbulence Models

2002 ◽  
Author(s):  
Wang Kee In ◽  
Dong Seok Oh ◽  
Tae Hyun Chun
Keyword(s):  
Turbulent Flow ◽  
Nuclear Fuel ◽  
Turbulence Models ◽  
Convective Transport ◽  
Stress Model ◽  
Convergence Criteria ◽  
Mean Flow ◽  
Numerical Predictions ◽  
Viscosity Models ◽  
Fuel Bundle

The numerical predictions using the standard and RNG k–ε eddy viscosity models, differential stress model (DSM) and algebraic stress model (ASM) are examined for the turbulent flow in a nuclear fuel bundle with the mixing vane. The hybrid (first-order) and curvature-compensated convective transport (CCCT) schemes were used to examine the effect of the differencing scheme for the convection term. The CCCT scheme was found to more accurately predict the characteristics of turbulent flow in the fuel bundle. There is a negligible difference in the prediction performance between the standard and RNG k-ε models. The calculation using ASM failed in meeting the convergence criteria. DSM appeared to more accurately predict the mean flow velocities as well as the turbulence parameters.

On Application of Nonlinear k-ε Models for Internal Combustion Engine Flows

2002 ◽  
Vol 124 (3) ◽  
pp. 668-677 ◽  
Author(s):  
G. M. Bianchi ◽  
G. Cantore ◽  
P. Parmeggiani ◽  
V. Michelassi
Keyword(s):  
Internal Combustion Engine ◽  
Eddy Viscosity ◽  
Combustion Engine ◽  
Turbulence Models ◽  
Internal Combustion ◽  
Moment Closure ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Numerical Predictions ◽  
Viscosity Models

The linear k-ε model, in its different formulations, still remains the most widely used turbulence model for the solutions of internal combustion engine (ICE) flows thanks to the use of only two scale-determining transport variables and the simple constitutive relation. This paper discusses the application of nonlinear k-ε turbulence models for internal combustion engine flows. Motivations to nonlinear eddy viscosity models use arise from the consideration that such models combine the simplicity of linear eddy-viscosity models with the predictive properties of second moment closure. In this research the nonlinear k-ε models developed by Speziale in quadratic expansion, and Craft et al. in cubic expansion, have been applied to a practical tumble flow. Comparisons between calculated and measured mean velocity components and turbulence intensity were performed for simple flow structure case. The effects of quadratic and cubic formulations on numerical predictions were investigated too, with particular emphasis on anisotropy and influence of streamline curvature on Reynolds stresses.

Turbulence Modeling for Secondary Flow Prediction in a Turbine Cascade

1992 ◽  
Vol 114 (3) ◽  
pp. 590-598 ◽  
Author(s):  
J. G. E. Cleak ◽  
D. G. Gregory-Smith
Keyword(s):  
Secondary Flow ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Equation Model ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Mixing Length ◽  
Turbine Cascade ◽  
Mean Flow ◽  
Complex Flow

Predictions of secondary flow in an axial turbine cascade have been made using three different turbulence models: mixing length, a one-equation model and a k–ε mixing length hybrid model. The results are compared with results from detailed measurements, not only by looking at mean flow velocities and total pressure loss, but also by assessing how well turbulence quantities are predicted. It is found that the turbulence model can have a big influence on the mean flow results, with the mixing length model giving generally the best mean flow. None of the models give good predictions of the turbulent shear stresses in the vortex region, although the k–ε model gives quite good turbulent kinetic energy values. The one-equation model is the only one to contain a transition criterion. The importance of such a criterion is illustrated, but the present one needs development to give reliable predictions in the complex flow within a blade passage.

An Expression of Reynolds Stresses in Turbulent Lubrication Theory

1992 ◽  
Vol 114 (1) ◽  
pp. 57-60 ◽  
Author(s):  
A. K. Tieu ◽  
P. B. Kosasih
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Flow ◽  
Low Reynolds Number ◽  
Stress Gradient ◽  
Lubrication Theory ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Shear Stress Gradient ◽  
Low Reynolds

This paper proposes an alternative model of Reynolds stresses for turbulent lubrication theory. The approach relies on Prandtl’s mixing length theory which is based on a modified Van Driest mixing formula [1]. However, unlike the previous theories [2, 3] the proposed equation is capable of accounting for the effect of shear stress gradient on the mixing length. Thus it is well suited to turbulent flow analysis in bearings where the presence of shear stress gradient due to the effect of pressure gradient should be considered. A series of velocity measurements in thin channels in the low Reynolds number turbulent flow range are analysed using the theory. The data analysis shows a strong effect of shear stress gradient on the viscous sublayer in the low Reynolds number regime. As a result, a new model of mixing length applicable to the turbulent lubrication analysis in thin film at low or high Reynolds numbers or under low or high shear stress gradient is presented.

scholarly journals Turbulence Modelling for Secondary Flow Prediction in a Turbine Cascade

1991 ◽  
Author(s):  
J. G. E. Cleak ◽  
D. G. Gregory-Smith
Keyword(s):  
Secondary Flow ◽  
Turbulence Models ◽  
Equation Model ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Mixing Length ◽  
Turbine Cascade ◽  
Mean Flow ◽  
Complex Flow ◽  
The One

Predictions of secondary flow in an axial turbine cascade have been made using three different turbulence models; mixing length, a one equation model and a k-epsilon/mixing length hybrid model. The results are compared with results from detailed measurements, not only by looking at mean flow velocities and total pressure loss, but also by assessing how well turbulence quantities are predicted. It is found that the turbulence model can have a big influence on the mean flow results, with the mixing length model giving generally the best mean flow. None of the models give good predictions of the turbulent shear stresses in the vortex region, although the k-epsilon model gives quite good turbulent kinetic energy values. The one equation model is the only one to contain a transition criterion. The importance of such a criterion is illustrated, but the present one needs development to give reliable predictions in the complex flow within a blade passage.

The Numerical Prediction of Developing Turbulent Flow in Rectangular Ducts

1981 ◽  
Vol 103 (3) ◽  
pp. 445-453 ◽  
Author(s):  
F. B. Gessner ◽  
A. F. Emery
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Momentum Equation ◽  
Scale Model ◽  
Length Scale ◽  
Basic Technique ◽  
Numerical Predictions ◽  
Iterative Procedures

Comparisons are made between experimental data and numerical predictions based on a three-dimensional length-scale model applicable to developing turbulent flow in rectangular ducts of arbitrary aspect ratio. The numerical method utilizes an explicit (Dufort-Frankel) differencing scheme for the axial momentum equation and involves no iterative procedures. Although the basic technique has been applied previously to another class of three-dimensional flows, it has not been applied until now to slender shear flows dominated by secondary flow of the second kind. The merits of the length-scale model and the computational procedure are assessed by means of comparisons with results referred to both k–ε and full Reynolds stress closure models which have been applied in recent years.

scholarly journals Adjoint Complement to the Universal Momentum Law of the Wall

2021 ◽  
Author(s):  
Niklas Kühl ◽  
Peter M. Müller ◽  
Thomas Rung
Keyword(s):  
Fluid Dynamic ◽  
Algebraic Closure ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Direct Consequence ◽  
Momentum Equation ◽  
Algebraic Expression ◽  
Mixing Length ◽  
Law Of The Wall ◽  
Logarithmic Layer

AbstractThe paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima at no computational surplus in comparison to the frozen turbulence approach.

Prediction of Developing Turbulent Flow in a 90° Curved Duct Using Linear and Nonlinear Low-Re k-ε Models

Volume 1 ◽  
2004 ◽  
Author(s):  
M. Raisee ◽  
H. Alemi ◽  
H. Iacovides
Keyword(s):  
Turbulent Flow ◽  
Pressure Coefficient ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Main Stream ◽  
Local Pressure ◽  
Flow Measurements ◽  
Numerical Predictions ◽  
Flow Development ◽  
Curved Section

This paper reports the outcome of applying two different low-Re number eddy-viscosity models to resolve the complex three-dimensional motion that arises in turbulent flow in a square cross-section duct passing around a 90° bend. Flow computations have been obtained using a three-dimensional, non-orthogonal flow solver. For modeling of turbulence, the Launder and Sharma low-Re k–ε model and a recently modified version of nonlinear low-Re k–ε model that have been shown to be suitable for flow and thermal predictions in re-circulating and impinging jet flows, have been employed. A bounded version of the QUICK scheme was used for the approximation of convection in all transport equations. The numerical predictions are validated through comparisons with the reported flow measurements and are used to explain how the curvature influences the flow development. The results of the present investigation indicate that the curvature induces a strong secondary flow in the curved section of the duct. The secondary motion also persists downstream of the bend, although it slowly disappears with the main stream development. At the entrance of the curved section, the curvature alters the flow development by displacing the fluid towards the convex (inner) wall. Comparisons of the predicted stream-wise and cross-stream velocity components with the measured data indicate that both turbulence models employed in the present study can produce reasonable predictions, although the non-linear model predictions are generally closer to the measurements. Both turbulence models successfully reproduce the distribution as well as the levels of the local pressure coefficient in the curved section of the duct.

Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow

1982 ◽  
Vol 104 (3) ◽  
pp. 350-359 ◽  
Author(s):  
A. M. K. P. Taylor ◽  
J. H. Whitelaw ◽  
M. Yianneskis
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Hydraulic Diameter ◽  
Radius Ratio ◽  
Reynolds Stresses ◽  
Flow Development ◽  
Secondary Motion ◽  
Laminar And Turbulent Flow ◽  
Orthogonal Components ◽  
Secondary Velocity

Two orthogonal components of velocity and associated Reynolds stresses have been measured in a square-sectioned, 90 degree bend of 2.3 radius ratio using laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. The boundary layers at the bend inlet were 0.25 and 0.15 of the hydraulic diameter and resulted in secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity respectively. Comparison with fully-developed inlet flow shows that the boundary layer thickness is important to the flow development (mainly in the first half of the bend), particularly so when it is reduced to 0.15 of the hydraulic diameter. Turbulent flow in an identical duct with a radius ratio of 7.0 gives rise to smaller secondary velocities than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. The detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models. Partially-parabolic techniques are applicable to the flows studied and their reduced storage requirements seem essential if satisfactory numerical accuracy is to be achieved.

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