A Note on a Generalized Eddy-Viscosity Hypothesis

1992 ◽  
Vol 114 (3) ◽  
pp. 463-466 ◽  
Author(s):  
P. Andreasson ◽  
U. Svensson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Eddy Viscosity ◽  
Channel Flows ◽  
Length Scale ◽  
Asymmetric Channel ◽  
Boundary Layer Flows ◽  
Turbulent Length Scale ◽  
Model Predictions

The standard eddy-viscosity concept postulates that zero velocity gradient is accompanied by zero shear stress. This is not true for many boundary layer flows: wall jets, asymmetric channel flows, countercurrent flows, for example. The generalized eddy-viscosity hypothesis presented in this paper, relaxes this limitation by recognizing the influence of gradients in the turbulent length scale and the shear. With this new eddy-viscosity concept, implemented into the standard k–ε model, predictions of some boundary layer flows are made. The modelling results agree well with measurements, where predictions with the standard eddy-viscosity concept are known to fail.

Eddy Viscosity Transport Equations and Their Relation to the k-ε Model

1997 ◽  
Vol 119 (4) ◽  
pp. 876-884 ◽  
Author(s):  
F. R. Menter
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Equation Model ◽  
Turbulent Shear ◽  
Boundary Layer Flows ◽  
Turbulent Layer ◽  
Turbulent Shear Stress ◽  
The One

A formalism will be presented which allows transforming two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on Bradshaw’s assumption that the turbulent shear stress is proportional to the turbulent kinetic energy. This assumption is supported by experimental evidence for a large number of boundary layer flows and has led to improved predictions when incorporated into two-equation models of turbulence. Based on it, a new one-equation turbulence model will be derived from the k-ε model. The model will be tested against the one-equation model of Baldwin and Barth, which is also derived from the k-ε model (plus additional assumptions) and against its parent two-equation model. It will be shown that the assumptions involved in the derivation of the Baldwin-Barth model cause significant problems at the edge of a turbulent layer.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

scholarly journals Prediction of Heat Transfer From Laminar Boundary Layers, With Emphasis on Large Free-Stream Velocity Gradients and Highly Cooled Walls

1966 ◽  
Vol 88 (3) ◽  
pp. 249-256 ◽  
Author(s):  
L. H. Back ◽  
A. B. Witte
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Free Stream ◽  
Variable Density ◽  
Similarity Solutions ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Gradient Parameter

Laminar boundary-layer heat transfer and shear-stress predictions from existing similarity solutions are extended in an approximate way to perfect gas flows with a large free-stream velocity gradient parameter β and variable density-viscosity product ρμ across the boundary layer resulting from a highly cooled wall. The dimensionless enthalpy gradient at the wall gw′, to which the heat flux is related, is found not to vary appreciably with β. Thus the application of similarity solutions on a local basis to predict heat transfer from accelerated flows to an arbitrary surface may be a reasonable approximation involving a minimum amount of calculation time. Unlike gw′, the dimensionless velocity gradient at the wall fw″, to which the shear stress is related, is strongly dependent on β.

A Boundary Layer Transition Model

1996 ◽  
Author(s):  
Mark W. Johnson ◽  
Ali H. Ercan
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Transition ◽  
Test Cases ◽  
Length Scale ◽  
Transition Model ◽  
Freestream Turbulence ◽  
Layer Transition ◽  
Frequency Spectra ◽  
Low Frequencies ◽  
Turbulent Length Scale

A new boundary layer transition model is presented which relates the velocity fluctuations near the wall to the formation of turbulent spots. A relationship for the near wall velocity frequency spectra is also established, which indicates an increasing bias towards low frequencies as the skin friction coefficient for the boundary layer decreases. This result suggests that the dependence of transition on the turbulent length scale is greatest at low freestream turbulence levels. This transition model is incorporated in a conventional boundary layer integral technique and is used to predict eight of the ERCOFTAC test cases. Three of these test cases are for nominally zero pressure gradient and the remaining five are for a pressure distribution typical of an aft loaded turbine blade. The model is demonstrated to predict the development of the boundary layer through transition reasonably accurately for all the test cases. The sensitivity of start of transition to the turbulent length scale at low freestream turbulence levels is also demonstrated.

scholarly journals A Theory for Predicting the Turbulent-Spot Production Rate

1998 ◽  
Author(s):  
R. E. Mayle
Keyword(s):  
Boundary Layer ◽  
Production Rate ◽  
Free Stream ◽  
Length Scale ◽  
Bypass Transition ◽  
Turbulence Level ◽  
Turbulent Spot ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
New Correlation

A theory is presented for predicting the production rate of turbulent spots. The theory, based on that by Mayle-Schulz for bypass transition, leads to a new correlation for the spot production rate in boundary layer flows with a zero pressure gradient. The correlation, which agrees reasonably well with data, clearly shows the effects of both free-stream turbulence level and length scale. In addition, the theory provides an estimate for the lowest level of free-stream turbulence causing bypass transition.

A Theory for Predicting the Turbulent-Spot Production Rate

1999 ◽  
Vol 121 (3) ◽  
pp. 588-593 ◽  
Author(s):  
R. E. Mayle
Keyword(s):  
Boundary Layer ◽  
Production Rate ◽  
Free Stream ◽  
Length Scale ◽  
Bypass Transition ◽  
Turbulence Level ◽  
Turbulent Spot ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
New Correlation

A theory is presented for predicting the production rate of turbulent spots. The theory, based on that by Mayle–Schulz for bypass transition, leads to a new correlation for the spot production rate in boundary layer flows with a zero pressure gradient. The correlation, which agrees reasonably well with data, clearly shows the effects of both free-stream turbulence level and length scale. In addition, the theory provides an estimate for the lowest level of free-stream turbulence causing bypass transition.

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