An Examination of Eddy Viscosity Models for Turbulent Free Shear Flows

1971 ◽  
Vol 93 (4) ◽  
pp. 624-630
Author(s):  
R. J. Elassar ◽  
P. P. Pandolfini
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Difference Scheme ◽  
Eddy Viscosity ◽  
Shear Flows ◽  
Coordinate Plane ◽  
Boundary Layer Equations ◽  
Viscosity Models ◽  
Calculated Velocity ◽  
Empirical Constants

The boundary layer equations based on an eddy viscosity concept are solved numerically in the Crocco coordinate plane. A multilevel linear difference scheme is employed. Four different viscosity models are examined and the resulting solutions are compared. The empirical constants in the viscosity models are evaluated by comparing the calculated velocity profiles with experimental data in the similarity region.

A Transformation for the Numerical Solution of Two-Dimensional Free Mixing Flow Problems

1973 ◽  
Vol 95 (1) ◽  
pp. 103-107
Author(s):  
R. J. Elassar
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Difference Scheme ◽  
Mixing Layer ◽  
Two Dimensional ◽  
Coordinate Plane ◽  
Free Shear Layer ◽  
Layer Width ◽  
Boundary Layer Equations ◽  
Flow Problems

A coordinate transformation which removes the variation of the mixing layer width is introduced. The boundary layer equations are then solved in the new coordinate plane using a multilevel difference scheme. The calculated results for two-dimensional symmetric mixing and free shear layer flows for turbulent flow are compared with experimental data and with other solutions.

The Improvement of k-ε Model in the Turbulent Wave Boundary Layer

2009 ◽  
Author(s):  
Yuliang Zhu ◽  
Jing Ma ◽  
Peipei Dong
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Wave Boundary Layer ◽  
Viscosity Models ◽  
Velocity Equation ◽  
Layer Flow ◽  
Wave Boundary ◽  
Advanced Model ◽  
Turbulent Wave ◽  
Empirical Constants

Numerical model is one of the means for investigating turbulent wave boundary layer. Many scholars have used various eddy-viscosity models to simulate wave turbulent boundary layer flow. On the basis of analyzing existing models, the article uses more reasonable boundary condition to establish an advanced model of turbulent wave boundary layer by k-ε model. Past models have two problems. Firstly, the calculation area is not united since one of the calculation areas is all-water depth and another is boundary layer thickness. Aimed at this problem, this model makes a sensitivity analysis of velocity and eddy-viscosity for various calculation area, which turns out that velocity inside the boundary layer is low-sensitive while the eddy-viscosity is high-sensitive to the change of calculation area. Secondly, a new integration adjust coefficient p is presented to solve the five empirical constants which are difficult to adjust in k-ε model. Although these five empirical constants have recommended value, the universality is not good. In order to obtain better eddy-viscosity value, many methods were suggested to get these five empirical constants, however, most are very complicated. In this article, adjust coefficient p is put before the diffusion item in the velocity equation, and p is a little bit smaller than 1. The result indicates that a reasonable eddy-viscosity can be easily adjusted using this method. The modified model has overcome some shortcomings of the previous models, and gets a better simulation effect.

scholarly journals Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

2012 ◽  
Author(s):  
B. G. Vinod Kumar ◽  
John W. Chew ◽  
Nicholas J. Hills
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Stress ◽  
Integral Method ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Rotating Disc ◽  
Flow And Heat Transfer ◽  
Viscosity Models

Design and optimization of an efficient internal air system of a gas turbine requires thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to numerical modelling of flow and heat transfer in a cylindrical cavity with radial inflow and comparison with the available experimental data. The simulations are carried out with axi-symmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers upto 2.1×106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart-Allmaras and the k-ε, and a Reynolds stress model have been used. For cases with particularly strong vortex behaviour the eddy viscosity models show some shortcomings with the Spalart-Allmaras model giving slightly better results than the k-ε model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

Velocity Profiles of Turbulent Boundary Layers

1969 ◽  
Vol 73 (698) ◽  
pp. 143-147 ◽  
Author(s):  
M. K. Bull
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Experimental Work ◽  
Constant Pressure ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Equations

Although a numerical solution of the turbulent boundary-layer equations has been achieved by Mellor and Gibson for equilibrium layers, there are many occasions on which it is desirable to have closed-form expressions representing the velocity profile. Probably the best known and most widely used representation of both equilibrium and non-equilibrium layers is that of Coles. However, when velocity profiles are examined in detail it becomes apparent that considerable care is necessary in applying Coles's formulation, and it seems to be worthwhile to draw attention to some of the errors and inconsistencies which may arise if care is not exercised. This will be done mainly by the consideration of experimental data. In the work on constant pressure layers, emphasis tends to fall heavily on the author's own data previously reported in ref. 1, because the details of the measurements are readily available; other experimental work is introduced where the required values can be obtained easily from the published papers.

High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

2005 ◽  
Vol 127 (4) ◽  
pp. 666-673 ◽  
Author(s):  
Steffen Stolz
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Correct Prediction ◽  
Smagorinsky Model ◽  
Eddy Simulation ◽  
Viscosity Models ◽  
Large Eddy ◽  
High Pass

In this contribution we consider large-eddy simulation (LES) using the high-pass filtered (HPF) Smagorinsky model of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of ∼4500. The HPF eddy-viscosity models employ high-pass filtered quantities instead of the full velocity field for the computation of the subgrid-scale (SGS) model terms. This approach has been proposed independently by Vreman (Vreman, A. W., 2003, Phys. Fluids, 15, pp. L61–L64) and Stolz et al. (Stolz, S., Schlatter, P., Meyer, D., and Kleiser, L., 2003, in Direct and Large Eddy Simulation V, Kluwer, Dordrecht, pp. 81–88). Different from classical eddy-viscosity models, such as the Smagorinsky model (Smagorinsky, J., 1963, Mon. Weath. Rev, 93, pp. 99–164) or the structure-function model (Métais, O. and Lesieur, M., 1992, J. Fluid Mech., 239, pp. 157–194) which are among the most often employed SGS models for LES, the HPF eddy-viscosity models do need neither van Driest wall damping functions for a correct prediction of the viscous sublayer of wall-bounded turbulent flows nor a dynamic determination of the coefficient. Furthermore, the HPF eddy-viscosity models are formulated locally and three-dimensionally in space. For compressible flows the model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique in which the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at the inflow position (Stolz, S. and Adams, N. A., 2003, Phys. Fluids, 15, pp. 2389–2412).

Numerical Investigation of Low-Reynolds Number Airfoil Flows Using Transition-Sensitive and Fully Turbulent RANS Models

2014 ◽  
Author(s):  
Varun Chitta ◽  
Tausif Jamal ◽  
D. Keith Walters
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Boundary Layer Transition ◽  
Transition Flow ◽  
Layer Transition ◽  
Laminar Separation ◽  
Viscosity Models ◽  
Separation Bubbles ◽  
Laminar Separation Bubbles

A numerical analysis is performed to study the pre-stall and post-stall aerodynamic characteristics over a group of six airfoils using commercially available transition-sensitive and fully turbulent eddy-viscosity models. The study is focused on a range of Reynolds numbers from 6 × 104 to 2 × 106, wherein the flow around the airfoil is characterized by complex phenomena such as boundary layer transition, flow separation and reattachment, and formation of laminar separation bubbles on either the suction, pressure or both surfaces of airfoil. The predictive capability of the transition-sensitive k-kL-ω model versus the fully turbulent SST k-ω model is investigated for all airfoils. The transition-sensitive k-kL-ω model used in this study is capable of predicting both attached and separated turbulent flows over the surface of an airfoil without the need for an external linear stability solver to predict transition. The comparison between experimental data and results obtained from the numerical simulations is presented, which shows that the boundary layer transition and laminar separation bubbles that appear on the suction and pressure surfaces of the airfoil can be captured accurately by the use of a transition-sensitive model. The fully turbulent SST k-ω model predicts a turbulent boundary layer on both surfaces of the airfoil for all angles of attack and fails to predict boundary layer transition or separation bubbles. Discrepancies are observed in the predictions of airfoil stall by both the models. Reasons for the discrepancies between computational and experimental results, and also possible improvements in eddy-viscosity models, are discussed.

scholarly journals Reinvestigating the Parabolic-Shaped Eddy Viscosity Profile for Free Surface Flows

Hydrology ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 126
Author(s):  
Rafik Absi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Velocity Profile ◽  
Eddy Viscosity ◽  
Velocity Profiles ◽  
Free Surface Flows ◽  
Analytical Models ◽  
Surface Flows ◽  
Viscosity Models ◽  
Viscosity Profile

The flow in rivers is turbulent. The main parameter related to turbulence in rivers is the eddy viscosity, which is used to model a turbulent flow and is involved in the determination of both velocities and sediment concentrations. A well-known and largely used vertical distribution of eddy viscosity in free surface flows (open channels and rivers) is given by the parabolic profile that is based on the logarithmic velocity profile assumption and is valid therefore only in the log-law layer. It was improved thanks to the log-wake law velocity profile. These two eddy viscosities are obtained from velocity profiles, and the main shortcoming of the log-wake profile is the empirical Coles’ parameter. A more rigorous and reliable analytical eddy viscosity model is needed. In this study, we present two analytical eddy viscosity models based on the concepts of velocity and length scales, which are related to the exponentially decreasing turbulent kinetic energy (TKE) function and mixing length, namely, (1) the exponential-type profile of eddy viscosity and (2) an eddy viscosity based on an extension of von Karman’s similarity hypothesis. The eddy viscosity from the second model is -independent, while the eddy viscosity from the first model is -dependent (where is the friction Reynolds number). The proposed analytical models were validated through computation of velocity profiles, obtained from the resolution of the momentum equation and comparisons to experimental data. With an additional correction function related to the damping effect of turbulence near the free surface, both models are similar to the log-wake-modified eddy viscosity profile but with different values of the Coles’ parameter, i.e., for the first model and for the second model. These values are similar to those found in open-channel flow experiments. This provides an explanation about the accuracy of these two analytical models in the outer part of free surface flows. For large values of ( > 2000), the first model becomes independent, and the two coefficients reach asymptotic values. Finally, the two proposed eddy viscosity models are validated by experimental data of eddy viscosity.

scholarly journals Comparison of k-ε Models in Predicting Heat Transfer and Skin Friction Under High Free Stream Turbulence

1996 ◽  
Author(s):  
Ganesh R. Iyer ◽  
Savash Yavuzkurt
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Skin Friction Coefficient ◽  
Empirical Correlations ◽  
Free Stream Turbulence ◽  
Boundary Layer Equations

Calculations of the effects of high free stream turbulence (FST) on heat transfer and skin friction in a flat plate turbulent boundary layer using different k-ε models (Launder-Sharma, K-Y Chien, Lam-Bremhorsi and Jones-Launder) are presented. This study was carried out in order to investigate the prediction capabilities of these models under high FST conditions. In doing so, TEXSTAN, a partial differential equation solver which is based on the ideas of Patankar and Spalding and solves steady-flow boundary layer equations, was used. Firstly, these models were compared as to how they predicted very low FST (≤ 1% turbulence intensity) cases. These baseline cases were tested by comparing predictions with both experimental data and empirical correlations. Then, these models were used in order to determine the effect of high FST (>5% turbulence intensity) on heat transfer and skin friction and compared with experimental data. Predictions for heat transfer and skin friction coefficient for all the turbulence intensities tested by all the models agreed well (within 1–8%) with experimental data. However, all these models predicted poorly the dissipation of turbulent kinetic energy (TKE) in the free stream and TKE profiles. Physical reasoning as to why the aforementioned models differ in their predictions and the probable cause of poor prediction of free-stream TKE and TKE profiles are given.

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