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.

Sink flow turbulent boundary layers

1969 ◽  
Vol 38 (4) ◽  
pp. 817-831 ◽  
Author(s):  
B. E. Launder ◽  
W. P. Jones
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Turbulent Shear ◽  
Mixing Length ◽  
Mean Velocity ◽  
Acceleration Parameter ◽  
Turbulent Shear Stress ◽  
Good Agreement

The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows, constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value.The predicted solutions, which are in good agreement with available experimental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased.

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.

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.

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