Reynolds Stress Tensors in an End-Wall Three-Dimensional Channel Boundary Layer

1975 ◽  
Vol 97 (4) ◽  
pp. 618-620 ◽  
Author(s):  
F. J. Pierce ◽  
S. H. Duerson
Keyword(s):  
Boundary Layer ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Stress Tensors ◽  
Channel Boundary ◽  
End Wall

Measured Reynolds Stress Tensors in a Three-Dimensional Turbulent Boundary Layer

AIAA Journal ◽  
1978 ◽  
Vol 16 (7) ◽  
pp. 645-646 ◽  
Author(s):  
C. I. Ezekwe ◽  
F. J. Pierce ◽  
J. E. McAllister
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Stress Tensors

Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
J. G. Moore ◽  
S. A. Schorn ◽  
J. Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Surface Model ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

Moore et al. measured the six Reynolds stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence stress tensors. Principal directions and principal normal stresses are found. A solid surface model, or three-dimensional glyph, for the Reynolds stress tensor is proposed and used to view the stresses throughout the tip leakage vortex. Modeled Reynolds stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the three-dimensional graphic representations of the strain and Reynolds stress tensors aids in the understanding of the turbulence and what is required to model it.

An Axial Compressor End-Wall Boundary Layer Calculation Method

1979 ◽  
Vol 101 (2) ◽  
pp. 233-245 ◽  
Author(s):  
J. De Ruyck ◽  
C. Hirsch ◽  
P. Kool
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Velocity Profile ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Tip Clearance ◽  
Wall Region ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
End Wall

An axial compressor end-wall boundary layer theory which requires the introduction of three-dimensional velocity profile models is described. The method is based on pitch-averaged boundary layer equations and contains blade force-defect terms for which a new expression in function of transverse momentum thickness is introduced. In presence of tip clearance a component of the defect force proportional to the clearance over blade height ratio is also introduced. In this way two constants enter the model. It is also shown that all three-dimensional velocity profile models present inherent limitations with regard to the range of boundary layer momentum thicknesses they are able to represent. Therefore a new heuristic velocity profile model is introduced, giving higher flexibility. The end-wall boundary layer calculation allows a correction of the efficiency due to end-wall losses as well as calculation of blockage. The two constants entering the model are calibrated and compared with experimental data allowing a good prediction of overall efficiency including clearance effects and aspect ratio. Besides, the method allows a prediction of radial distribution of velocities and flow angles including the end-wall region and examples are shown compared to experimental data.

Turbulent Boundary Layer Flow on the End Wall of a Cylindrical Vortex Chamber

1975 ◽  
Vol 189 (1) ◽  
pp. 305-315 ◽  
Author(s):  
T. J. Kotas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Vortex Chamber ◽  
Cylindrical Vortex ◽  
Layer Flow ◽  
Momentum Integral ◽  
End Wall

A presentation of some measurements of velocities in the turbulent boundary layer on the end wall of a vortex chamber. These show that the boundary layer flow is three-dimensional with large inward radial velocities. Consequently, most of the fluid entering the vortex chamber passes into the central region through the boundary layers on the end walls rather than the main space of the vortex chamber. A momentum integral solution is used to obtain an estimate of the radial flow through the end-wall boundary layers. A comparison of the theoretical curves with the experimental results gives support to the main assumptions used in the solutions.

Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

1989 ◽  
Vol 202 ◽  
pp. 263-294 ◽  
Author(s):  
Shawn D. Anderson ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Free Stream ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Stress Vector ◽  
Dimensional Boundary ◽  
Cross Wire

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

Modelling of spanwise mixing in compressor through-flow computations

1997 ◽  
Vol 211 (3) ◽  
pp. 243-251 ◽  
Author(s):  
J Dunham
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Navier Stokes ◽  
Streamline Curvature ◽  
Wall Boundary Layer ◽  
Through Flow ◽  
Compressor Design ◽  
Multistage Compressors ◽  
End Wall

Although three-dimensional Navier-Stokes computations are coming into use more and more, streamline curvature through-flow computations are still needed, especially for multistage compressors, and where codes which run in minutes rather than hours are preferred. These methods have been made more realistic by taking account of end-wall effects and spanwise mixing by four aerodynamic mechanisms: turbulent diffusion, turbulent convection by secondary flow, spanwise migration of aerofoil boundary layer fluid and spanwise convection of fluid in blade wakes. This paper describes the models adopted in the DRA streamline curvature method for axial compressor design and analysis. Previous papers are summarized briefly before describing the new part of the model—that accounting for aerofoil boundary layers and wakes. Other changes to the previously published annulus wall boundary layer model have been made to enable it to cater for separations and end bends. The resulting code is evaluated against a range of experimental and computational results.

scholarly journals Vortex/inflectional-wave interactions with weakly three-dimensional input

1997 ◽  
Vol 348 ◽  
pp. 247-294 ◽  
Author(s):  
S. N. TIMOSHIN ◽  
F. T. SMITH
Keyword(s):  
Boundary Layer ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Longitudinal Vortex ◽  
Momentum Balance ◽  
Wave Interactions ◽  
Wave Modulation ◽  
The Cross ◽  
Low Amplitude

The subtle impact of the spanwise scaling in nonlinear interactions between oblique instability waves and the induced longitudinal vortex field is considered theoretically for the case of a Rayleigh-unstable boundary-layer flow, at large Reynolds numbers. A classification is given of various flow regimes on the basis of Reynolds-stress mechanisms of mean vorticity generation, and a connection between low-amplitude non-parallel vortex/wave interactions and less-low-amplitude non-equilibrium critical-layer flows is discussed in more detail than in previous studies. Two new regimes of vortex/wave interaction for increased spanwise lengthscales are identified and studied. In the first, with the cross-scale just slightly larger than the boundary-layer thickness, the wave modulation is governed by an amplitude equation with a convolution and an ordinary integral term present due to nonlinear contributions from all three Reynolds-stress components in the cross-momentum balance. In the second regime the cross-scale is larger, and the wave modulation is found to be governed by an integral/partial differential equation. In both cases the main-flow non-parallelism contributes significantly to the coupled wave/vortex development.

A Theory for Boundary Layer Growth on the Blades of a Radial Impeller Including End Wall Influence

1982 ◽  
Author(s):  
H. Ekerol ◽  
J. W. Railly
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Prediction Method ◽  
Suction Side ◽  
Layer Growth ◽  
Secondary Flows ◽  
Curvature Effects ◽  
Wall Boundary ◽  
End Wall

Experimental data on the wall shear stress of a turbulent boundary layer on the suction side of a blade in a two-dimensional radial impeller is compared with the predictions of a theory which takes account of rotation and curvature effects as well as the three-dimensional influence of the end-wall boundary layers. The latter influence is assumed to arise mainly from mainstream distortion due to secondary flows created by the end-wall boundary layers and it appears as an extra term in the momentum integral equation of the blade boundary layer which has allowance, also for the Coriolis effect; an appropriate form of the Head entrainment equation is derived to obtain a solution and a comparison made. A comparison of the above theory with the Patankar-Spalding prediction method, modified to include the effects of Coriolis (including mixing length modification, MLM) is also made.

Simultaneous flow visualization and Reynolds-stress measurement in a turbulent boundary layer

1986 ◽  
Vol 163 ◽  
pp. 459-478 ◽  
Author(s):  
A. M. Talmon ◽  
J. M. G. Kunen ◽  
G. Ooms
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flow Visualization ◽  
Reynolds Stress ◽  
Stress Measurement ◽  
Three Dimensional ◽  
Time Dependent ◽  
Flow Structures ◽  
Wall Region ◽  
Measured Velocity

Flow visualization and Reynolds-stress measurement were combined in an investigation of a turbulent boundary layer in a water channel. Hydrogen bubbles were used to visualize the flow; a laser-Doppler anemometer capable of measuring two velocity components was applied to measure the instantaneous value of the Reynolds stress. Owing to the three-dimensional, time-dependent character of the flow it was rather difficult to identify flow structures from measured velocity signals, especially at larger distances from the wall. Despite this difficulty a method based on the instantaneous value of the Reynolds stress could be developed for detecting bursts in the wall region of the boundary layer. By this method the three-dimensional, time-dependent character of the flow is taken into account by attributing to the same burst ejections occurring successively with very short time intervals. This identification procedure is based on a comparison on a one-to-one basis between visualized flow structures and measured values of the Reynolds stress. The detected bursts were found to make a considerable contribution to the momentum transport in the boundary layer.

A Model for Describing the Influences of SUC-EW Dihedral Angle on Corner Separation

2007 ◽  
Author(s):  
LuCheng Ji ◽  
WeiWei Shao ◽  
WeiLin Yi ◽  
Jiang Chen
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Dihedral Angle ◽  
Present Model ◽  
Three Dimensional ◽  
Cross Flow ◽  
Corner Separation ◽  
Wall Boundary ◽  
Intersection Line ◽  
End Wall

This paper presents a model for describing the influences of SUC-EW dihedral angle on corner separation in turbomachinery, in which SUC-EW dihedral angle refers to the dihedral angle at the intersection line between blade ‘SUCtion’ and End-Wall surfaces. Based on the physical intuition of that the three-dimensional (3D) corner boundary layer is the conflux of both blade and end wall boundary layers, an equivalent two-dimensional(2D) corner boundary layer is put forward to predict the behavior of corner boundary layer. In this procedure, the cross flow effect in corner boundary layer and the three-dimensionality of the nearby main flow are ignored. The influence of the SUC-EW dihedral angle is included by another assumption. That is, the aero blockage and momentum loss of both blade and end wall boundary layers are conserved during the procedure of superimposing the two (both blade and end wall) 2D boundary layers to form the equivalent corner one. Then the corner separation is judged by combining the behaviors of the three boundary layers, i.e. the blade, the end wall and the equivalent 2D corner boundary layers. The present model reveals the influence of the SUC-EW dihedral angle and its streamwise gradient on the corner separation. Carefully monitoring and controlling this dihedral angle and its streamwise gradient are important ways to alleviate or even eliminate the corner separation. Simple numerical investigations show that the model is qualitatively correct.

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