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.

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

1992 ◽  
Author(s):  
M. T. Karimipanah ◽  
E. Olsson
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Rotating Flow ◽  
Flow Angle ◽  
Transonic Compressor ◽  
Integral Methods ◽  
The Cross

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 respectively turbulent boundary layers, originally developed by SSPA Maritime Consulting AB, have been further developed by introducing rotation and compressibility terms in the boundary layer equations. The effect of rotation and compressibility on the transition have been studied. The Coriolis and Centrifugal forces which contribute to the development of the boundary layers and influence its behaviour, 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 has inverse influences. The different boundary layer parameters behave similarly on suction and pressure side with the exception of the cross-flow angle, the cross-wise momentun 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.

The Behavior of the Casing Boundary Layer With the Presence of Tip Leakage Vortex

2018 ◽  
Author(s):  
Xi Nan ◽  
Feng Lin ◽  
Takehiro Himeno ◽  
Toshinori Watanabe
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Transonic Compressor ◽  
Flow Loss ◽  
Produce Flow

Casing boundary layer effectively places a limit on the pressure rise capability achievable by the compressor. The separation of the casing boundary layer not only produce flow loss but also closely related to the compressor rotating stall. The motivation of this paper is to present a viewpoint that the casing boundary layer should be paid attention to in parallel with other flow factors on rotating stall trigger. This paper illustrates the casing boundary layer behavior by displaying its separation phenomena with the presence of tip leakage vortex at different flow conditions. Skin friction lines and the corresponding absolute streamlines are used to demonstrate the three-dimensional flow patterns on and near the casing. The results depict a Saddle, a Node and several tufts of skin friction lines dividing the passage into four zones. The tip leakage vortex is enfolded within one of the zones by the separated flows. All the flows in each blade passage are confined within the passage as long as the compressor is stable. The casing boundary layer of a transonic compressor is also examined in the same way, which results in qualitatively similar zonal flows that enfolds the tip leakage vortex. This research develops a new way to study the casing boundary layer in rotating compressors. The results may provide a first-principle based explanation to stalling mechanisms for compressors that are casing sensitive.

On Integral Methods for Predicting Shear Layer Behavior

1969 ◽  
Vol 36 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S. J. Shamroth
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Integral Equations ◽  
Boundary Layers ◽  
Specific Problem ◽  
Shear Layers ◽  
Near Wake ◽  
Integral Methods ◽  
Layer Behavior ◽  
Momentum Integral

The origin and consequences of a nonphysical constraint which may arise when boundary-layer momentum integral equations are used to predict the behavior of shear layers are examined. It is pointed out that should the constraint occur within the domain of integration of the momentum integral equations, the effect may either be catastrophic or significantly constrain the solution. Several methods of solution having the usual advantages associated with boundary-layer momentum integral equations, but free from this constraint, are proposed for the specific problem of the plane turbulent near wake. One method developed to avoid this constraint in the case of a plane turbulent near wake appears to be perfectly general, and therefore, it may be possible to apply this method to both boundary layers and wakes.

Smooth and Rough Turbulent Boundary Layers: A Look at Skin Friction, Pressure Gradient and Roughness

2006 ◽  
Author(s):  
Katherine A. Newhall ◽  
Raul Bayoan Cal ◽  
Brian Brzek ◽  
Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Rough Surfaces ◽  
Boundary Layer Equation ◽  
Roughness Parameter ◽  
Surface Boundary ◽  
Favorable Pressure Gradient ◽  
Momentum Integral

The skin friction for a turbulent boundary layer can be measured and calculated in several ways with varying degrees of accuracy. In particular, the methods of the velocity gradient at the wall, the integrated boundary layer equation and the momentum integral equation are evaluated for both smooth and rough surface boundary layers. These methods are compared to the oil film interferometry technique measurements for the case of smooth surface flows. The integrated boundary layer equation is found to be relatively reliable, and the values computed with this technique are used to investigate the effect of increasing external favorable pressure gradient for both smooth and rough surfaces, and increasing roughness parameter for the rough surfaces.

Boundary Layers over Infinite Yawed Wings

1960 ◽  
Vol 11 (4) ◽  
pp. 333-347 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Free Flow ◽  
Momentum Thickness ◽  
Displacement Thickness

SummaryA method of calculating turbulent boundary layers on infinite yawed wings is given, making use of a method of calculating turbulent boundary layers due to Spence and of an analogy between three-dimensional and axi-symmetric boundary layers. It is also shown that the displacement thickness is equal to that computed using chordwise components and that the streamwise momentum thickness is approximately equal to the chordwise momentum thickness. Shock-free flow and small boundary layer cross-flow are assumed.

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.

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.

Laminar Boundary Layer Swirling Flow with Heat and Mass Transfer in Conical Nozzles and Diffusers

1979 ◽  
Vol 101 (1) ◽  
pp. 151-156 ◽  
Author(s):  
B. K. Meena ◽  
G. Nath
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Skin Friction ◽  
Swirling Flow ◽  
Local Similarity ◽  
Integral Methods ◽  
Implicit Finite Difference Scheme ◽  
Incompressible Boundary ◽  
Momentum Integral

The flow and heat transfer for a steady axisymmetric laminar incompressible boundary layer swirling flow with mass transfer in a conical nozzle and a diffuser have been studied. The partial differential equations governing nonsimilar flow have been solved numerically using an implicit finite-difference scheme after transforming them into new coordinates having finite ranges. The results indicate that, both for the nozzle and diffuser, swirl exerts a strong influence on the longitudinal skin friction, but its effect on the tangential skin friction and heat transfer is comparatively small. In the case of the nozzle, even for a small value of the dissipation parameter at the inlet, the heat transfer rapidly increases near the end of the nozzle; whereas in the case of the diffuser, no such trend is observed. Suction increases the skin friction and heat transfer, but injection does the reverse. The results are found to be in good agreement with those of the local nonsimilarity and momentum integral methods except near the end of the nozzle or diffuser, but they differ appreciably from those of the local similarity method except near the inlet.

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 Solution of a Three-Dimensional Turbulent Boundary Layer

1972 ◽  
Vol 94 (4) ◽  
pp. 795-800
Author(s):  
F. J. Pierce ◽  
W. F. Klinksiek
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Integral Solution ◽  
Edge Condition ◽  
Integral Methods ◽  
Flow Parameters ◽  
Layer Flow ◽  
Momentum Integral

The results of a momentum integral solution of the three-dimensional turbulent boundary layer on the confining wall of an impinging jet are presented. This geometry provides a boundary layer where large gradients in the streamwise and especially the transverse direction occur and hence is a severe test of momentum integral methods. The solution utilizes the Head entrainment function and the Ludwieg and Tillmann wall shear law, with no restriction on cross flows. An extensive comparison with experimental results show good to moderate agreement in the integrated flow parameters, with a strong dependence on the free-stream or edge condition to the boundary layer flow.

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