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.

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.

Three-Dimensional Flow Field in the Tip Region of a Compressor Rotor Passage—Part I: Mean Velocity Profiles and Annulus Wall Boundary Layer

1982 ◽  
Vol 104 (4) ◽  
pp. 760-771 ◽  
Author(s):  
B. Lakshminarayana ◽  
M. Pouagare ◽  
R. Davino
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Three Dimensional ◽  
Leading Edge ◽  
Leakage Flow ◽  
Suction Surface ◽  
Mean Velocity ◽  
Wall Boundary Layer ◽  
Compressor Rotor ◽  
Wall Boundary

The flow field in the annulus wall and tip region of a compressor rotor was measured using a triaxial, hot-wire probe rotating with the rotor. The flow was surveyed across the entire passage at five axial locations (leading edge, 1/4 chord, 1/2 chord, 3/4 chord, and trailing edge locations) and at six radial locations inside the passage. The data derived include all three components of mean velocity. Blade-to-blade variations of the velocity components, pitch and yaw angles, as well as the passage-averaged mean properties of the annulus wall boundary layer, are derived from this data. The measurements indicate that the leakage flow starts beyond a quarter-chord and tends to roll up farther away from the suction surface than that observed in cascades. Substantial velocity deficiencies and radial inward velocities are observed in this region. The annulus wall boundary layer is well behaved up to half a chord, beyond which interactions with the leakage flow produce complex profiles.

Effects of Inlet Turbulence and End-Wall Boundary Layer on Aero-Thermal Performance of a Transonic Turbine Blade Tip

2013 ◽  
Author(s):  
Q. Zhang ◽  
L. He ◽  
A. Rawlinson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Freestream Turbulence ◽  
Suction Surface ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Passage Vortex ◽  
Blade Tip ◽  
Transonic Turbine ◽  
End Wall

Most of previous researches of inlet turbulence effects on blade tip have been carried out for low speed situations. Recent work has indicated that for a transonic turbine tip, turbulent diffusion tends to have distinctively different impact on tip heat transfer than for its subsonic counterpart. It is hence of interest to examine how inlet turbulence flow conditioning would affect heat transfer characteristics for a transonic tip. This present work is aimed to identify and understand the effects of both inlet freestream turbulence and end-wall boundary layer on a transonic turbine blade tip aero-thermal performance. Spatially-resolved heat transfer data are obtained at aerodynamic conditions representative of a high-pressure turbine, using the transient infrared thermography technique with the Oxford High-Speed Linear Cascade research facility. With and without turbulence grids, the turbulence levels achieved are 7–9% and 1% respectively. On the blade tip surface, no apparent change in heat transfer was observed with high and low turbulence intensity levels investigated. On the blade suction surface, however, substantially different local heat transfer for the suction side near tip surface have been observed, indicating a strong local dependence of the local vortical flow on the freestream turbulence. These experimentally observed trends have also been confirmed by CFD predictions using Rolls-Royce HYDRA. Further CFD analysis suggests that the level of inflow turbulence alters the balance between the passage vortex associated secondary flow and the OverTL flow. Consequently, enhanced inertia of near wall fluid at a higher inflow turbulence weakens the cross-passage flow. As such, the weaker passage vortex leads the tip leakage vortex to move further into the mid passage, with the less spanwise coverage on the suction surface, as consistently indicated by the heat transfer signature. Different inlet end-wall boundary layer profiles are employed in the HYDRA numerical study. All CFD results indicate the inlet boundary layer thickness has little impact on the heat transfer over the tip surface as well as the pressure side near-tip surface. However, noticeable changes in heat transfer are observed for the suction side near-tip surface. Similar to the freestream turbulence effect, such changes are attributed to the interaction between the passage vortex and the OTL flow.

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.

A Numerical Investigation of the Effect of End-Wall Boundary Layer Skew on the Aerodynamic Performance of a Low Aspect Ratio, High Turning Compressor Cascade

2007 ◽  
Author(s):  
M. Boehle ◽  
U. Stark
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Numerical Investigation ◽  
Boundary Layers ◽  
Aerodynamic Performance ◽  
Compressor Cascade ◽  
Suction Surface ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
End Wall

The paper reports on a numerical investigation into the effects of inlet boundary layer skew on the aerodynamic performance of a high turning 50 deg, 2D compressor cascade. The cascade geometry is representative of stator hub sections in highly loaded single-stage axial-flow low-speed compressors. 2D blades with NACA 65 thickness distribution on circular arc camber lines were used. The blade aspect ratio was 1.0, the space/chord ratio 0.5 and the stagger angle 25 deg. The simulations were done with a commercially available, steady three-dimensional RANS solver with the Spalart-Allmaras turbulence model. The incoming end-wall boundary layers were assumed to be collateral or skewed. In both cases the profile boundary layers were fully turbulent. The Reynolds-number was fixed at 600000 and the thickness of the incoming end-wall boundary layer was 0.1. Results are shown for an inlet-air angle of 50 deg, representing the impact free inlet-air angle of a hypothetical cascade with zero-thickness blades. Contrary to what has been expected, the results do not show (hub) corner stall, neither with nor without end-wall boundary layer skew. Flow reversal happens to occur almost exclusively on the suction surface of the blades, not on the end-walls. The end-wall flow is highly overturned, when the incoming boundary layer is collateral and is much less curved when the incoming boundary layer is skewed and (re)energized. This in turn leads to an interaction between the end-wall and blade suction surface flow which is much stronger in the first than in the second case with corresponding higher and lower losses, respectively.

Effects of Inlet Turbulence and End-Wall Boundary Layer on Aerothermal Performance of a Transonic Turbine Blade Tip

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Q. Zhang ◽  
L. He ◽  
A. Rawlinson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Suction Side ◽  
Suction Surface ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Passage Vortex ◽  
Blade Tip ◽  
Transonic Turbine ◽  
End Wall

Most of the previous researches of inlet turbulence effects on blade tip have been carried out for low speed situations. Recent work has indicated that for a transonic turbine tip, turbulent diffusion tends to have a distinctively different impact on tip heat transfer than for its subsonic counterpart. It is hence of interest to examine how inlet turbulence flow conditioning would affect heat transfer characteristics for a transonic tip. The present work is aimed to identify and understand the effects of both inlet freestream turbulence and end wall boundary layer on a transonic turbine blade tip aerothermal performance. Spatially-resolved heat transfer data are obtained at aerodynamic conditions representative of a high-pressure turbine, using the transient infrared thermography technique with the Oxford High-Speed Linear Cascade research facility. With and without turbulence grids, the turbulence levels achieved are 7%–9% and 1%, respectively. On the blade tip surface, no apparent change in heat transfer was observed with high and low inlet turbulence intensity levels investigated. On the blade suction surface, however, substantially different local heat transfer distributions for the suction side near tip surface have been observed, indicating a strong local dependence of the local vortical flow structure on the freestream turbulence. These experimentally observed trends have also been confirmed by CFD examinations using the Rolls-Royce HYDRA. A further CFD analysis suggests that the level of inflow turbulence alters the balance between the passage vortex associated secondary flow and the over tip leakage (OTL) flow. Consequently, an enhanced inertia of near wall fluid at a higher inflow turbulence weakens the cross-passage flow. As such, the weaker passage vortex leads the tip leakage vortex to move further into the mid passage, with the less spanwise coverage on the suction surface, as consistently indicated by the heat transfer signature. Different inlet end wall boundary layer profiles are employed in the computational study with HYDRA. All CFD results indicate the inlet boundary layer thickness has little impact on the heat transfer over the tip surface as well as the pressure side near-tip surface. However, noticeable changes in heat transfer are observed for the suction side near-tip surface. Similar to the inlet turbulence effect, such changes can be attributed to the interaction between the passage vortex and the OTL flow.

An experimental study of the three dimensional boundary layer on the end wall of a vortex chamber

1976 ◽  
Vol 352 (1669) ◽  
pp. 169-187 ◽  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Vortex Chamber ◽  
Operating Conditions ◽  
Wall Friction ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
End Wall

Profiles of the radial and circumferential components of velocity have been measured in the end-wall boundary layer of a vortex chamber as part of an experimental and theoretical investigation of a confined, incompressible vortex flow. The profiles have been presented here for various radial positions and operating conditions and the main features of the boundary-layer have been discussed. Further, the circumferential profiles have been analysed by plotting them in two types of dimensionless coordinates. Also, the wall friction data corresponding to the circumferential direction have been plotted. Hence an empirical expression for the wall friction factor was obtained. The data presented here reveal some new features and provide new information on the end-wall boundary layer flow in a vortex chamber.

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.

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