A Correlation of End Wall Losses in Plane Compressor Cascades

1968 ◽  
Vol 90 (3) ◽  
pp. 251-257 ◽  
Author(s):  
W. T. Hanley
Keyword(s):  
Boundary Layer ◽  
Integral Equations ◽  
Free Stream ◽  
Wall Boundary Layer ◽  
Profile Parameter ◽  
Displacement Thickness ◽  
Wall Losses ◽  
Wall Loss ◽  
Momentum Integral ◽  
End Wall

Consideration of parameters suggested by the momentum integral equations has lead to a successful correlation relating (a) the change of the free stream component of the end wall boundary layer displacement thickness to chord ratio, and (b) a profile parameter as functions of free stream loading. For the range of investigation, both correlations were found to be insensitive to gap-chord ratio, camber, stagger, incidence, and airfoil shape. Maximum permissible loading limits for operation without excessive end wall loss are shown to decrease with increasing inlet displacement thickness to chord ratio.

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.

Wall Boundary Layers in Turbomachines

1972 ◽  
Vol 14 (6) ◽  
pp. 411-423 ◽  
Author(s):  
H. Marsh ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Integral Equations ◽  
Cross Flow ◽  
Inlet Guide Vanes ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Alternative Approach ◽  
Flow Through ◽  
The Many ◽  
Momentum Integral

Equations for the passage-averaged flow in a cascade are used to derive the momentum integral equations governing the development of the wall boundary layer in turbomachines. Several existing methods of analysis are discussed and an alternative approach is given which is based on the passage-averaged momentum integral equations. The analysis leads to an anomaly in the prediction of the cross flow and to avoid this it is suggested that for the many-bladed cascade there should be a variation of the blade force through the boundary layer. This variation of the blade force can be included in the analysis as a force deficit integral. The growth of the wall boundary layer has been calculated by four methods and the predictions are compared with two sets of published experimental results for flow through inlet guide vanes.

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.

The Effect of a Wall Boundary Layer on Local Mass Transfer From a Cylinder in Crossflow

1984 ◽  
Vol 106 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. J. Goldstein ◽  
J. Karni
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Tunnel Wall ◽  
Wall Boundary Layer ◽  
Naphthalene Sublimation Technique ◽  
Displacement Thickness ◽  
Two Dimensional Flow

A naphthalene sublimation technique is used to determine the circumferential and longitudinal variations of mass transfer from a smooth circular cylinder in a crossflow of air. The effect of the three-dimensional secondary flows near the wall-attached ends of a cylinder is discussed. For a cylinder Reynolds number of 19000, local enhancement of the mass transfer over values in the center of the tunnel are observed up to a distance of 3.5 cylinder diameters from the tunnel wall. In a narrow span extending from the tunnel wall to about 0.066 cylinder diameters above it (about 0.75 of the mainstream boundary layer displacement thickness), increases of 90 to 700 percent over the two-dimensional flow mass transfer are measured on the front portion of the cylinder. Farther from the wall, local increases of up to 38 percent over the two-dimensional values are measured. In this region, increases of mass transfer in the rear portion of the cylinder, downstream of separation, are, in general, larger and cover a greater span than the increases in the front portion of the cylinder.

scholarly journals LES and RANS Analysis of the End-Wall Flow in a Linear LPT Cascade: Part I — Flow and Secondary Vorticity Fields Under Varying Inlet Condition

2018 ◽  
Author(s):  
R. Pichler ◽  
Yaomin Zhao ◽  
R. D. Sandberg ◽  
V. Michelassi ◽  
R. Pacciani ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Flow Characteristics ◽  
Flow Region ◽  
Secondary Flows ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Wall Flow ◽  
End Wall ◽  
The Impact

In low-pressure-turbines (LPT) around 60–70% of losses are generated away from end-walls, while the remaining 30–40% is controlled by the interaction of the blade profile with the end-wall boundary layer. Experimental and numerical studies have shown how the strength and penetration of the secondary flow depends on the characteristics of the incoming end-wall boundary layer. Experimental techniques did shed light on the mechanism that controls the growth of the secondary vortices, and scale-resolving CFD allowed to dive deep into the details of the vorticity generation. Along these lines, this paper discusses the end-wall flow characteristics of the T106 LPT profile at Re = 120K and M = 0.59 by benchmarking with experiments and investigating the impact of the incoming boundary layer state. The simulations are carried out with proven Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) solvers to determine if Reynolds Averaged models can capture the relevant flow details with enough accuracy to drive the design of this flow region. Part I of the paper focuses on the critical grid needs to ensure accurate LES, and on the analysis of the overall time averaged flow field and comparison between RANS, LES and measurements when available. In particular, the growth of secondary flow features, the trace and strength of the secondary vortex system, its impact on the blade load variation along the span and end-wall flow visualizations are analysed. The ability of LES and RANS to accurately predict the secondary flows is discussed together with the implications this has on design.

The Removal of the Boundary Layer of a Supersonic Flow by Means of a Slot

1963 ◽  
Vol 30 (2) ◽  
pp. 275-278
Author(s):  
M. Cloutier
Keyword(s):  
Boundary Layer ◽  
Mass Flow ◽  
Static Pressure ◽  
Free Stream ◽  
Subsequent Development ◽  
Displacement Thickness ◽  
Free Stream Mach Number ◽  
Slot Opening ◽  
Flow Through ◽  
Transverse Slot

The influence of slot opening and of suction pressure upon the mass flow through the slot and the subsequent development of the boundary layer has been studied for the case of a single transverse slot opening into a boundary layer with a displacement thickness of 0.168 in. at a free-stream Mach number of 2.92. The results show that as much as 85 percent of the mass flow in the boundary layer between the wall and the position of the slot lip enters the slot, and that this result is independent of the slot reservoir pressure, providing the latter is less than approximately twice the tunnel static pressure.

Eddy Viscosity Distributions in Compressible Turbulent Boundary Layers with Injection

1971 ◽  
Vol 22 (2) ◽  
pp. 169-182 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mixing Length ◽  
Carbon Dioxide Injection ◽  
Displacement Thickness ◽  
Porous Surfaces ◽  
Injection Ratio

SummaryShear stress, eddy viscosity and mixing length distributions have been obtained from measured boundary-layer developments over porous surfaces with air and carbon dioxide injection at Mach numbers up to M=3·6. It is found that, if the eddy viscosity is non-dimensionalised by dividing by the product of the free-stream velocity and the kinematic displacement thickness then this non-dimensional ratio is almost independent of injection ratio, but decreases slightly with Mach number.

Boundary Layer Effects in the Turbulent Spiral Vortex Flow of a Compressible Fluid

1968 ◽  
Vol 183 (1) ◽  
pp. 179-188 ◽  
Author(s):  
B. F. Scott
Keyword(s):  
Boundary Layer ◽  
Vortex Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Radial Pressure ◽  
Vortex Chamber ◽  
Adiabatic Wall ◽  
Spiral Vortex ◽  
Momentum Integral

Because of the characteristically narrow impeller tip width in a proposed supersonic centrifugal compressor design, boundary layer effects in the vortex chamber are likely to be significant. The radial pressure gradient in the chambers sweeps retarded fluid towards the centre of curvature of the streamlines, thereby creating a ‘cross-flow’ in the boundary layer which is three-dimensional. Although the flow geometry has axial symmetry, the cross-flow is not independent of the streamwise flow. The momentum—integral method is adopted, together with assumptions concerning the velocity profiles; the energy equation is solved with the assumption of an adiabatic wall. Simultaneous solution of the free stream and boundary layer equations yields results emphasizing the critical dependence of the transverse deflection and growth of the boundary layer on the whirl component of the velocity. Separation cannot be predicted, but effects in the free stream can be estimated when the perturbations are small. Although the results are related to compressor performance, the method is generally applicable in situations where the idealizing assumption of spiral vortex flow is acceptable.

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