scholarly journals Calculation of Turbulent Shear Stress in Supersonic Boundary-Layer Flows

AIAA Journal ◽  
1975 ◽  
Vol 13 (2) ◽  
pp. 224-227 ◽  
Author(s):  
CHEN-CHIH SUN ◽  
MORRIS E. CHILDS
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Supersonic Boundary Layer ◽  
Turbulent Shear ◽  
Boundary Layer Flows ◽  
Turbulent Shear Stress

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.

Conditional Sampling in a Transitional Boundary Layer Under High Freestream Turbulence Conditions

2003 ◽  
Vol 125 (1) ◽  
pp. 28-37 ◽  
Author(s):  
Ralph J. Volino ◽  
Michael P. Schultz ◽  
Christopher M. Pratt
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Streamwise Velocity ◽  
Turbulent Shear ◽  
Conditional Sampling ◽  
Freestream Turbulence ◽  
Mean Velocity ◽  
Transitional Boundary Layer ◽  
Turbulent Shear Stress ◽  
Order Of Magnitude

Conditional sampling has been performed on data from a transitional boundary layer subject to high (initially 9%) freestream turbulence and strong (K=ν/U∞2dU∞/dx as high as 9×10−6) acceleration. Methods for separating the turbulent and nonturbulent zone data based on the instantaneous streamwise velocity and the turbulent shear stress were tested and found to agree. Mean velocity profiles were clearly different in the turbulent and nonturbulent zones, and skin friction coefficients were as much as 70% higher in the turbulent zone. The streamwise fluctuating velocity, in contrast, was only about 10% higher in the turbulent zone. Turbulent shear stress differed by an order of magnitude, and eddy viscosity was three to four times higher in the turbulent zone. Eddy transport in the nonturbulent zone was still significant, however, and the nonturbulent zone did not behave like a laminar boundary layer. Within each of the two zones there was considerable self-similarity from the beginning to the end of transition. This may prove useful for future modeling efforts.

The Mixing Length Derived from Kármán’s Similarity Hypothesis

1973 ◽  
Vol 24 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Michio Nishioka ◽  
Shūsuke Iida
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reasonable Agreement ◽  
Diffusion Constant ◽  
Turbulent Shear ◽  
Appreciable Effect ◽  
Mixing Length ◽  
Similarity Hypothesis ◽  
Turbulent Shear Stress ◽  
Good Agreement

SummaryFrom Kármán’s similarity hypothesis, we derive the equation which describes the mixing length in terms of the turbulent shear stress. For a boundary layer with linear stress distribution, the equation is in reasonable agreement with Bradshaw’s measurements. For a boundary layer with injection, it is shown that injection has an appreciable effect upon the mixing length when (vw/2) /(τ/ρ)1/2becomes comparable to the Kármán constant. Close similarity is also pointed out between the hypotheses due to Kármán and Townsend. Moreover, the diffusion constant in Townsend’s hypothesis is determined to be 0.25, which is in good agreement with the value 0.2 obtained by Townsend from one experiment.

scholarly journals Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory

1975 ◽  
Vol 70 (1) ◽  
pp. 127-148 ◽  
Author(s):  
B. Van Den Berg ◽  
A. Elsenaar ◽  
J. P. F. Lindhout ◽  
P. Wesseling
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Swept Wing ◽  
Test Plate ◽  
Turbulent Shear Stress

First a three-dimensional turbulent boundary-layer experiment is described. This has been carried out with the specific aim of providing a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept-wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate was subjected to an adverse pressure gradient, which led to three-dimensional separation near the trailing edge of the plate. Next, a calculation method for three-dimensional turbulent boundary layers is discussed. This solves the boundary-layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. Agreement is good over a considerable distance; but large discrepancies are apparent near the separation line.

On the Shear-Stress Integral of Turbulent Boundary Layers

1986 ◽  
Author(s):  
H. Pfeil ◽  
M. Göing
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Integral Method ◽  
Turbulent Boundary Layers ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Basic Assumptions ◽  
Turbulent Shear Stress ◽  
The Moment ◽  
Momentum Integral

The paper presents an integral method to predict turbulent boundary layer behaviour in two-dimensional, incompressible flow. The method is based on the momentum and moment-of-momentum integral equations and a friction law. By means of the compiled data of the 1968-Stanford-Conference, the results show that the integral of the turbulent shear-stress across the boundary layer, which appears in the moment-of-momentum integral equation, can be described by only two basic assumptions for all cases of flow.

Effects of an Upstream Circular Manipulator on the Flow Past a Cylinder-Flat Plate Junction

2003 ◽  
Author(s):  
Alan Dow ◽  
George Elizarraras ◽  
Hamid R. Rahai ◽  
Hamid Hefazi
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flat Plate ◽  
Horseshoe Vortex ◽  
Turbulent Shear ◽  
Plate Surface ◽  
Mean Velocity ◽  
Time Resolved ◽  
Turbulent Shear Stress ◽  
Flow Past A Cylinder

Measurements of three components of mean velocity and simultaneous time-resolved measurements of axial and vertical turbulent velocities and their cross moment were made at three perpendicular planes slightly upstream of the corner and in the downstream interaction region of a cylinder-flat plate junction with and without an upstream circular manipulator. The circular manipulator was a smooth circular cylinder of 1.25 mm diameter, which was placed upstream of the cylinder at X/D = 1.2, within the boundary layer above the flat plate surface. Results show that when the manipulator is in place, there is a decrease in the axial mean velocity and increases in the axial mean squared turbulent velocity and turbulent shear stress at the first plane. There is an expanded region of secondary flow with reduced circulation, indicating that the manipulator has reduced the strength of the horseshoe vortex in this region.

Mechanisms of Turbulence Transport in a Turbine Blade Coolant Passage With a Rib Turbulator

1999 ◽  
Vol 121 (1) ◽  
pp. 152-159 ◽  
Author(s):  
P. K. Panigrahi ◽  
S. Acharya
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Shear Layer ◽  
Large Scale ◽  
Turbulence Models ◽  
Turbulent Shear ◽  
Large Scale Structures ◽  
Turbulent Shear Stress ◽  
Scale Structures

This paper provides detailed measurements of the flow in a ribbed coolant passage, and attempts to delineate the important mechanisms that contribute to the production of turbulent shear stress and the normal stresses. It is shown that the separated flow behind the rib is dictated by large-scale structures, and that the dynamics of the large-scale structures, associated with sweep, ejection, and inward and outward interactions, all play an important role in the production of the turbulent shear stress. Unlike the turbulent boundary layer, in a separated shear flow past the rib, the inward and outward interaction terms are both important, accounting for a negative stress production that is nearly half of the positive stress produced by the ejection and sweep mechanisms. It is further shown that the shear layer wake persists well past the re-attachment location of the shear layer, implying that the flow between ribbed passages never recovers to that of a turbulent boundary layer. Therefore, even past re-attachment, the use of statistical turbulence models that ignore coherent structure dynamics is inappropriate.

Conditional Sampling in a Transitional Boundary Layer Under High Free-Stream Turbulence Conditions

2001 ◽  
Author(s):  
Ralph J. Volino ◽  
Michael P. Schultz ◽  
Christopher M. Pratt
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Turbulent Shear ◽  
Conditional Sampling ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Transitional Boundary Layer ◽  
Turbulent Shear Stress

Conditional sampling has been performed on data from a transitional boundary layer subject to high (initially 9%) free-stream turbulence and strong K=ν/U∞2dU∞/dxas high as9×10-6 acceleration. Methods for separating the turbulent and non-turbulent zone data based on the instantaneous streamwise velocity and the turbulent shear stress were tested and found to agree. Mean velocity profiles were clearly different in the turbulent and non-turbulent zones, and skin friction coefficients were as much as 70% higher in the turbulent zone. The streamwise fluctuating velocity, in contrast, was only about 10% higher in the turbulent zone. Turbulent shear stress differed by an order of magnitude, and eddy viscosity was three to four times higher in the turbulent zone. Eddy transport in the non-turbulent zone was still significant, however, and the non-turbulent zone did not behave like a laminar boundary layer. Within each of the two zones there was considerable self-similarity from the beginning to the end of transition. This may prove useful for future modeling efforts.

The effects of successive distortions on a turbulent boundary layer in a supersonic flow

1997 ◽  
Vol 351 ◽  
pp. 253-288 ◽  
Author(s):  
DOUGLAS R. SMITH ◽  
ALEXANDER J. SMITS
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Turbulent Boundary Layer ◽  
Flow Direction ◽  
Initial Boundary ◽  
Turbulent Shear ◽  
Boundary Layer Flows ◽  
Turbulent Shear Stress ◽  
Small Change ◽  
High Reynolds

Experiments were conducted to investigate the response of a high-Reynolds-number turbulent boundary layer in a supersonic flow to the perturbation presented by a forward-facing ramp. Two ramps were used: one with sharp corners, the other with rounded corners having radii of curvature equal to 15 initial boundary layer thicknesses. The flow was turned through 20° in each of the compressions and expansions. Hence, there was no net change in the flow direction over the ramps and only a small change in free-stream conditions due to the entropy increase across relatively weak shocks. The two experiments gave similar results. In the middle of the relaxing boundary layer, the streamwise Reynolds stress undershot the undisturbed levels and exhibited a response similar to that observed in subsonic boundary layer flows recovering from an impulse of streamline curvature (Smits, Young & Bradshaw 1979b). The turbulent shear stress vanished throughout most of the boundary layer, and an overall destruction of the turbulence production mechanisms was apparent as the boundary layer exhibited a slow recovery.

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