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.

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.

An Integral Method for Turbulent Boundary Layers on Rotating Disks

1993 ◽  
Vol 115 (4) ◽  
pp. 614-619 ◽  
Author(s):  
S. Abrahamson ◽  
S. Lonnes
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Integral Method ◽  
Radial Profile ◽  
Tangential Velocity ◽  
Turbulent Boundary Layers ◽  
Similarity Solutions ◽  
Layer Growth ◽  
Rotating Disks ◽  
Boundary Layer Growth

An integral method for computing turbulent boundary layers on rotating disks has been developed using a power law profile for the tangential velocity and a new model for the radial profile. A similarity solution results from the formulation. Radial transport, boundary layer growth, and drag on the disk were computed for the case of a forced vortex frees tream flow. The results were compared to previous similarity solutions. The method was extended to a Rankine vortex freestream flow. Differential equations for boundary layer parameters were developed and solved for different Reynolds numbers to look at the net entrainment, boundary layer growth, and drag on the disk.

The boundary layer due to a three-dimensional vortex loop

1987 ◽  
Vol 185 ◽  
pp. 569-598 ◽  
Author(s):  
S. Ersoy ◽  
J. D. A. Walker
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Layer Growth ◽  
Plane Wall ◽  
Vortex Loop ◽  
Loop Shape ◽  
Layer Flow ◽  
Boundary Layer Growth ◽  
Moving Vortex

The nature of the boundary layer induced by the motion of a three-dimensional vortex loop towards a plane wall is considered. Initially the vortex is taken to be a ring approaching a plane wall at an angle of attack in an otherwise stagnant fluid; the ring rapidly distorts into a loop shape due to the influence of the wall and the trajectory is computed from a numerical solution of the Biot-Savart integral. As the vortex loop moves, an unsteady boundary-layer flow develops on the wall. A method is described which allows the computation of the flow velocities on and near the symmetry plane of the vortex loop within the boundary layer. The computed results show the development of a variety of complex three-dimensional separation phenomena. Some of the solutions ultimately show strong localized boundary-layer growth and are suggestive that a boundary-layer eruption and a strong viscous-inviscid interaction will be induced by the moving vortex.

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.

Characterization and Impact of Secondary Flows in a Discrete Passage Centrifugal Compressor Diffuser

2018 ◽  
Author(s):  
David W. Erickson ◽  
Choon S. Tan ◽  
Michael Macrorie
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Centrifugal Compressor ◽  
Incidence Angle ◽  
Pressure Rise ◽  
Leading Edge ◽  
Layer Growth ◽  
Secondary Flows ◽  
The Impact ◽  
Boundary Layer Growth

Truncating the exit of a discrete passage centrifugal compressor diffuser is observed to enhance a research compressor’s stall line. By interrogating the experimental data along with a set of well-designed Reynolds-Averaged Navier Stokes computations, this improvement is traced to reduced impact of secondary flows on the truncated diffuser’s boundary layer growth. The secondary flow system is characterized by counter-rotating streamwise vortex pairs that persist throughout the diffuser passage. The vortices are traced to two sources: background vortices resulting from impeller exit flow non-uniformity, and incidence vortices resulting from flow separation off the leading edge cusps unique to a discrete passage diffuser. The incidence vortices detrimentally impact the diffuser pressure rise capability by accumulating high loss flow along the diffuser wall near the plane of symmetry between the vortices. This contributes to a large passage separation in the baseline diffuser. Using reduced order flow modeling, the impact of the vortices on the boundary layer growth is shown to scale inversely with diffuser aspect ratio, and thus the separation extent is reduced for the higher aspect ratio truncated diffuser. Because the diffuser incidence angle influences the strength and location of the vortices, this mechanism can affect the slope of the compressor’s pressure rise characteristic and impact its stall line. Stall onset for the baseline diffuser configuration is initiated by the transition of the vortex location and corresponding passage separation between diffuser pressure and suction sides with increased cusp incidence. Conversely, because the extent of the passage separation in the truncated diffuser is diminished, the switch in separation from pressure to suction side does not immediately initiate instability.

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.

Characterization and Impact of Secondary Flows in a Discrete Passage Centrifugal Compressor Diffuser

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
David W. Erickson ◽  
Choon S. Tan ◽  
Michael Macrorie
Keyword(s):  
Boundary Layer ◽  
Centrifugal Compressor ◽  
Incidence Angle ◽  
Pressure Rise ◽  
Leading Edge ◽  
Streamwise Vortex ◽  
Layer Growth ◽  
Secondary Flows ◽  
The Impact ◽  
Boundary Layer Growth

Truncating the exit of a discrete passage centrifugal compressor diffuser is observed to enhance a research compressor's stall line. By interrogating the experimental data along with a set of well-designed Reynolds-Averaged Navier–Stokes computations, this improvement is traced to the reduced impact of secondary flows on the truncated diffuser's boundary layer growth. The secondary flow system is characterized by counter-rotating streamwise vortex pairs that persist throughout the diffuser passage. The vortices originate from two sources: flow nonuniformity at the impeller exit and separation off the leading edge cusps unique to a discrete passage diffuser. The latter detrimentally impacts the diffuser pressure rise capability by accumulating high loss flow along the diffuser wall near the plane of symmetry between the vortices. This contributes to a large passage separation in the baseline diffuser. Using reduced-order modeling, the impact of the vortices on the boundary layer growth is shown to scale inversely with the diffuser aspect ratio, and thus, the separation extent is reduced for the truncated diffuser. Because the diffuser incidence angle influences the strength and location of the vortices, this mechanism can affect the slope of the compressor's pressure rise characteristic and impact its stall line. Stall onset for the baseline diffuser configuration is initiated when the vortex location and the corresponding passage separation transition from pressure to suction side with increased cusp incidence. Conversely, because the extent of the passage separation in the truncated diffuser is diminished, the switch in separation side does not immediately initiate instability.

Features of a developing turbulent boundary layer measured in a bounded flow

1979 ◽  
Vol 57 (3) ◽  
pp. 477-485 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Physical Mechanism ◽  
Interaction Mechanism ◽  
Turbulent Boundary Layers ◽  
Layer Growth ◽  
Developing Flow ◽  
Boundary Layer Growth ◽  
Flatness Factor

Experimental results are presented for turbulence intensities, correlations, skewness of u, ∂u/∂t. boundary layer growth, flatness factor of u, and intermittency for the bounded developing flow in the inlet region of a pipe (Re = 54 900). The results exhibit several unique features which are not observed for unbounded or flat plate turbulent boundary layers. A hypothetical physical mechanism accounting for the findings is offered which suggests that, for bounded flows, an exaggerated interaction occurs at the interface between the constrained core fluid and the surrounding, growing turbulent boundary layer. This hypothetical interaction mechanism could account for the nonasymptotic development of bounded flows and it is suggested that a more detailed study using interface conditioned sampling measurements is warranted.

Boundary-layer growth at a three-dimensional rear stagnation point

1975 ◽  
Vol 67 (2) ◽  
pp. 289-297 ◽  
Author(s):  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Similarity Solutions ◽  
Layer Growth ◽  
Initial Value ◽  
Stagnation Points ◽  
Boundary Layer Growth ◽  
Rear Stagnation Point

The theory of boundary-layer growth at a rear stagnation point, first presented by Proudman & Johnson, is here extended to cover fully three-dimensional rear stagnation points. Supporting numerical solutions of the full initial-value problem establish the relevance of the in viscid similarity solutions obtained.

Calculation of Three-Dimensional Boundary Layers on Rotor Blades Using Integral Methods

1993 ◽  
Vol 115 (2) ◽  
pp. 342-353 ◽  
Author(s):  
M. T. Karimipanah ◽  
E. Olsson
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Rotor Blades ◽  
Rotating Flow ◽  
Momentum Thickness ◽  
Transonic Compressor ◽  
Integral Methods ◽  
Momentum Integral

The important effects of rotation and compressibility on rotor blade boundary layers are theoretically investigated. The calculations are based on the momentum integral method and results from calculations of a transonic compressor rotor are presented. Influence of rotation is shown by comparing the incompressible rotating flow with the stationary one. Influence of compressibility is shown by comparing the compressible rotating flow with the incompressible rotating one. Two computer codes for three-dimensional laminar and turbulent boundary layers, originally developed by SSPA Maritime Consulting AB, have been further developed by introducing rotation and compressibility terms into the boundary layer equations. The effect of rotation and compressibility on the transition have been studied. The Coriolis and centrifugal forces that contribute to the development of the boundary layers and influence its behavior generate crosswise flow inside the blade boundary layers, the magnitude of which depends upon the angular velocity of the rotor and the rotor geometry. The calculations show the influence of rotation and compressibility on the boundary layer parameters. Momentum thickness and shape factor increase with increasing rotation and decrease when compressible flow is taken into account. For skin friction such effects have inverse influences. The different boundary layer parameters behave similarly on the suction and pressure sides with the exception of the crossflow angle, the crosswise momentum thickness, and the skin friction factor. The codes use a nearly orthogonal streamline coordinate system, which is fixed to the blade surface and rotates with the blade.

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