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.

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.

Investigations of an Axial Compressor End-Wall Boundary Layer Prediction Method

1981 ◽  
Vol 103 (1) ◽  
pp. 20-33 ◽  
Author(s):  
J. De Ruyck ◽  
C. Hirsch
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Diffusion Factor ◽  
Profile Model ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
End Wall

A previously developed axial compressor end-wall boundary layer calculation method which requires the introduction of three-dimensional velocity profile models is summarized. In this method the classical three-dimensional velocity profile models were shown to present inherent limitations at stall limit, with regard to the range of transverse boundary layer thicknesses they are able to represent. A corrected profile model is presented which contains no more limitations without affecting the previous found overall results. Stall limit is predicted by limiting values of shape factor and/or diffusion factor. The new profile model containing also compressibility effects allows the calculation of boundary layers in machines with shrouded blades, by simulating the jump between rotating and non rotating parts of the walls. A corrected version of a force defect correlation is presented which is shown to give better agreement at high incidences. Some results on high and low speed machines are discussed. The model is applied to obtain an end-wall blockage correlation depending on geometry, flow coefficient, AVR, aspect ratio, solidity, diffusion factor, Reynolds number, axial blade spacing, tip clearance and inlet boundary layer thickness. A quantitative estimation of the losses associated with the end-wall boundary layers can be obtained using this analysis and therefore can be a useful tool in the design of an axial compressor stage.

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.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

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.

Investigation of the Dihedral Angle Effect on the Boundary Layer Development Using Special-Shaped Expansion Pipes

2018 ◽  
Author(s):  
Teng Fei ◽  
Lucheng Ji ◽  
Weilin Yi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Dihedral Angle ◽  
Adverse Pressure Gradient ◽  
Secondary Flows ◽  
Flow Structures ◽  
Wall Surface ◽  
Geometric Structures ◽  
Corner Region ◽  
End Wall

The corners between the blades and end walls are common geometric structures in turbomachinery, where boundary layers on the blade and end wall surface interact with each other. This boundary layer interaction enlarges the region of low momentum fluid which leads to the boundary layers grow thicker at the corner region. Then the corner separation is likely to occur, and even worse by the adverse pressure gradient along the streamwise as well as secondary flows along the pitchwise. The key issue to design the geometric structures of the corner region is to control the dihedral angle between the blade and end wall surface. However, from the current published literature, few researchers have studied the influence of dihedral angle on the flow structures at the corner region in detail. In this paper, a series of expansion pipes with different cross sections which represent different dihedral angles are simulated. Then, some useful conclusions about how the dihedral angle affects the flow structures at the corner region are drawn. Moreover, a new method to predict the boundary layer thickness at the corner region is introduced, and the predicted results are in good agreement with simulation results.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

An Axial Compressor End-Wall Boundary Layer Theory

1971 ◽  
Vol 93 (2) ◽  
pp. 300-314 ◽  
Author(s):  
G. L. Mellor ◽  
G. M. Wood
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Axial Compressor ◽  
Jump Condition ◽  
Present Theory ◽  
Boundary Layer Theory ◽  
Tip Clearance ◽  
Main Stream ◽  
Wall Boundary ◽  
End Wall

The essential ingredient missing in existing prediction methods for the performance of multistage axial compressors is that which would account for the effect of end-wall boundary layers. It is, in fact, believed that end-wall boundary layers play a major role in compressor performance and the absence of an adequate theory represents a handicap to turbomachinery designers that might be likened to the handicap that designers of wings, for example, would face if Prandtl had not introduced the idea of a boundary layer. In this paper a new theory is developed which retains all elements of classical boundary layer theory; for example, we discuss variables such as momentum thickness and wall shear stress. However, the present theory introduces new concepts such as axial and tangential defect force thickness, a rotor exit-stator inlet “jump condition” and the importance of these concepts is demonstrated. Inherent in the derivation is an identification of the role of secondary flow and tip clearance flow. A proper means of matching the boundary layer calculations to conventional main stream calculations is suggested. Independent of empirical parametization it appears that the theory is capable of correctly modeling boundary layer blockage, losses, and end-wall stall. Near stall, the main stream-boundary layer interaction is very strong.

Interaction of Compressor Rotor Blade Wake With Wall Boundary Layer/Vortex in the End-Wall Region

1982 ◽  
Vol 104 (2) ◽  
pp. 467-478 ◽  
Author(s):  
B. Lakshminarayana ◽  
A. Ravindranath
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Boundary Layers ◽  
Substantial Effect ◽  
Wall Region ◽  
Tip Leakage Flow ◽  
Mean Velocity ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
End Wall

This paper reports the experimental study of the three-dimensional characteristics of the mean velocity of the rotor wake inside the annulus- and hub-wall boundary layers. The measurements were taken with a rotating three-sensor hot wire behind the rotor. This set of measurements probably represents the first set of comprehensive measurements taken inside the annulus- and hub-wall boundary layers. The wake was surveyed at several radial locations inside the boundary layer region and at several axial locations. Interaction of the wake with the annulus-wall boundary layer, secondary flow, tip-leakage flow, and the trailing vortex system results in slower decay and larger width of the wake. The presence of a strong vortex and its merger with the wake is also observed. The end-wall boundary layers and the secondary flow were found to have a substantial effect on both the decay characteristics and the profile of the wake. These and other measurements are reported and interpreted in this paper.

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