The Turbulent Flow at the Plane of Symmetry of a Collateral Three-Dimensional Boundary Layer

1964 ◽  
Vol 86 (2) ◽  
pp. 227-233 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Integral Equations ◽  
Three Dimensional ◽  
Layer Growth ◽  
Curvilinear Coordinates ◽  
Experimental Program ◽  
Simple Physical Interpretation ◽  
Dimensional Boundary ◽  
Momentum Integral

Momentum integral equations for the turbulent flow at the plane of symmetry of a three-dimensional boundary layer are rigorously derived. The use of orthogonol curvilinear coordinates allows a simple physical interpretation to be given to the terms of the resulting equations. Evaluation and comparison are made between the derived results and earlier works in Cartesian sets and ambiguities are discussed. Results of an experimental program are reported for the case of a plane of symmetry flow in a collateral three-dimensional turbulent boundary layer wherein four different momentum integral equations are examined in predicting boundary-layer growth. As an aside, two common variations of shape parameter equations were also tested to determine their adequacy in application to this case.

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

1983 ◽  
Vol 105 (3) ◽  
pp. 403-411
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 ◽  
Momentum Integral ◽  
Boundary Layer Growth

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 endwall boundary layers. The latter influence is assumed to arise mainly from mainstream distortion due to secondary flows created by the endwall 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.

Three-Dimensional Boundary-Layer Computation on the Stationary End-Walls of Centrifugal Turbomachinery

1976 ◽  
Vol 98 (3) ◽  
pp. 431-441 ◽  
Author(s):  
W. R. Davis
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Layer Growth ◽  
Wall Region ◽  
Boundary Layer Equations ◽  
Computation Technique ◽  
Dimensional Boundary ◽  
Boundary Layer Growth ◽  
Good Agreement

An integral entrainment computation technique is presented for the three-dimensional boundary-layer growth on the stationary end-walls of centrifugal turbomachinery. The analytical model assumes axisymmetric inviscid core flow and viscous flow in the wall region, and the interaction between the two layers is considered. A novel form of the three-dimensional boundary-layer equations is presented. The form is physically appealing for this axisymmetric application and provides distinct advantages in the prediction of boundary-layer growth. It is demonstrated that it is essential to use the meridional boundary-layer profile to compute the Head entrainment function for this type of flow, as opposed to the streamwise velocity profile, as is more commonly done. Comparison with experimental measurements shows good agreement in the integral parameters. In addition, good agreement with experimental velocity profiles was achieved for a separating and reattaching flow.

Turbulent boundary layer on a rotating helical blade

1972 ◽  
Vol 51 (3) ◽  
pp. 545-569 ◽  
Author(s):  
B. Lakshminarayana ◽  
A. Jabbari ◽  
H. Yamaoka
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Outer Region ◽  
Tangential Velocity ◽  
Layer Growth ◽  
Tangential Component ◽  
Blade Surface ◽  
Helical Blade ◽  
Blade Tip ◽  
Momentum Integral

This paper investigates the boundary-layer characteristics on a helical blade of large chord length, enclosed in an annulus and rotating in a fluid otherwise at rest. The three-dimensional form of momentum integral equations is derived, and used to predict the boundary-layer growth and limiting streamline angles on the blade surface. The measurements are in general agreement with the predictions. The wall shear stress correlation, which includes both Reynolds number and rotation parameters, valid for a rotating blade operating at zero pressure gradient, is derived. Radial and tangential velocity profiles, the tangential component of turbulence intensity and blade static pressures are measured at several locations on the blade surface. The nature of flow near the blade tip is discussed. An expression for the radial velocity profile, valid in the outer region of the boundary layer, is derived theoretically.

The Turbulent Boundary Layer at a Plane of Symmetry in a Three-Dimensional Flow

1960 ◽  
Vol 82 (3) ◽  
pp. 622-628 ◽  
Author(s):  
James P. Johnston
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Factor ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Momentum Thickness ◽  
Three Dimensional Flow ◽  
Dimensional Boundary ◽  
Momentum Integral

Methods for treating a turbulent three-dimensional boundary layer at a plane of symmetry are presented. Reasonable agreement with experiment was achieved by the use of momentum integral techniques in the prediction of momentum thickness, shape factor, wall shear stress, and the location of separation.

A Momentum-Integral Analysis of the Three-Dimensional Turbine End-Wall Boundary Layer

1971 ◽  
Vol 93 (4) ◽  
pp. 386-396 ◽  
Author(s):  
R. P. Dring
Keyword(s):  
Boundary Layer ◽  
Integral Equations ◽  
Three Dimensional ◽  
Solution Technique ◽  
Suction Surface ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
The Stability ◽  
Momentum Integral ◽  
End Wall

An analysis is presented which is a combination of existing momentum-integral equations and existing studies of profile shapes for incompressible three-dimensional turbulent boundary layers. These, along with a number of suitable refinements and assumptions, result in a solution technique which is particularly well suited for turbine end-wall boundary layer calculations. The solution gives the distribution of the boundary layer thickness and skewing over the end-wall as well as the amount and flux of total pressure deficit of the flow leaving the end-wall at the suction surface corner. The analysis also disclosed that a shear term which is normally neglected in the boundary layer approximations must in fact be retained, at least in approximate form, in order to insure the stability of the integral equations.

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.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

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