Computation of a Wall Boundary Layer With Discrete Jet Injections

1992 ◽  
Vol 114 (4) ◽  
pp. 756-764 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
G. Perrin
Keyword(s):  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Conservation Equations ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Jet Interactions

Cooling of turbine blades is often achieved with cold discrete jets introduced at the wall. In this paper, a new method for computation of a wall boundary layer with discrete jet interactions is presented. The jets are assumed to be arranged in rows and the flow is assumed locally periodic in the row direction. The conservation equations are spatially averaged between two jet orifices. The resulting equations look like two-dimensional boundary layer equations, but with three-dimensional jet source terms. The numerical method solves the boundary layer equations with a Keller box method. A strong interaction with inviscid flow is also introduced in order to avoid numerical difficulty in the jet region. Three-dimensional jet conservation equations are solved with an integral method, under the boundary layer influence. A coupling of the two methods is performed. Comparisons with low-speed experimental data are presented, particularly near the jet orifices. It is shown that the agreement between the results of computation and the experiments depends on the jet behavior very near the jet exit.

scholarly journals Computation of a Wall Boundary Layer With Discrete Jet Injections

1991 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
G. Perrin
Keyword(s):  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Conservation Equations ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Jet Interactions

Cooling of turbine blades is often achieved with cold discrete jets introduced at the wall. In this paper, a new method for computation of a wall boundary layer with discrete jet interactions is presented. The jets are assumed to be arranged in rows and the flow is assumed locally periodic in the row direction. The conservation equations are spatially averaged between two jet orifices. The resulting equations look like two-dimensional boundary layer equations, but with three-dimensional jet source terms. The numerical method solves the boundary layer equations with a Keller box method. A strong interaction with inviscid flow is also introduced in order to avoid numerical difficulty in the jet region. Three-dimensional jet conservation equations are solved with an integral method, under the boundary layer influence. A coupling of the two methods is performed. Comparisons with low speed experimental data are presented, particularly near the jet orifices. It is shown that the agreement between the results of computation and the experiments depends on the jet behaviour very near to the jet exit.

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.

Wall Boundary Layer Development Near the Tip Region of an IGV of an Axial Flow Compressor

1984 ◽  
Vol 106 (2) ◽  
pp. 337-345
Author(s):  
B. Lakshminarayana ◽  
N. Sitaram
Keyword(s):  
Boundary Layer ◽  
Guide Vane ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Axial Flow ◽  
Inlet Guide Vane ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Boundary Layer Development ◽  
Flow Compressor

The annulus wall boundary layer inside the blade passage of the inlet guide vane (IGV) passage of a low-speed axial compressor stage was measured with a miniature five-hole probe. The three-dimensional velocity and pressure fields were measured at various axial and tangential locations. Limiting streamline angles and static pressures were also measured on the casing of the IGV passage. Strong secondary vorticity was developed. The data were analyzed and correlated with the existing velocity profile correlations. The end wall losses were also derived from these data.

Treatment of the Annulus Wall Boundary Layer Using a Secondary Flow Hypothesis

1977 ◽  
Vol 99 (1) ◽  
pp. 29-36 ◽  
Author(s):  
J. W. Railly ◽  
P. B. Sharma
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Wire Array ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Collateral Flow ◽  
Axially Symmetric ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Blade Row

Hitherto, theories of annulus wall boundary layer development in axial compressors have assumed an axially-symmetric flow in which the blade action has been replaced by a force field. A more rigorous treatment of the momentum equations in the annulus boundary layer by Mellor and Wood demonstrated the presence of certain terms, after the equations had been averaged in the pitch-wise direction, which arise from the truly three-dimensional character of the flow. These terms, which may be described as the gradients of apparent stresses, were not regarded by them (apart from a discussion of tip clearance) as having importance for the problem. In the present work a second equation of the annulus wall boundary layer is obtained by consideration of the work of these apparent stresses. By integration of the system of equations over a single blade row, two equations are obtained relating various integral quantities at inlet to and exit from the row. Each equation contains terms which depend upon apparent stresses connected with the relative velocity field at the exit plane. An experiment is described in which the six turbulent stresses in the stationary frame downstream of a single rotor, determined by means of a multiple hot wire array, are used to evaluate each term of the aforementioned equations. The integral quantities thus determined are shown to be reasonably consistent with the predictions from the two equations, in particular, for the case of the hub boundary layer. Theoretical solutions of the two integral equations require a secondary flow hypothesis so that the departure from collateral flow at blade row exit is determined by the solution.

The boundary-layer flow due to a vortex approaching a cylinder

1994 ◽  
Vol 275 ◽  
pp. 33-57 ◽  
Author(s):  
H. Affes ◽  
Z. Xiao ◽  
A. T. Conlisk
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Inviscid Flow ◽  
Main Stream ◽  
Boundary Layer Equations ◽  
Narrow Region ◽  
Secondary Flow Structure ◽  
Layer Flow

The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.

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.

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.

Prediction of Film Cooling by a Row of Holes With a Two-Dimensional Boundary-Layer Procedure

1987 ◽  
Vol 109 (4) ◽  
pp. 579-587 ◽  
Author(s):  
B. Scho¨nung ◽  
W. Rodi
Keyword(s):  
Boundary Layer ◽  
Film Cooling ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flat Plates ◽  
Specific Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Dispersion Terms

The present paper describes predictions of film cooling by a row of holes. The calculations have been performed by a two-dimensional boundary-layer code with special modifications that account for the basically three-dimensional, elliptic nature of the flow after injection. The elliptic reverse-flow region near the injection is leapt over and new boundary-layer profiles are set up after the blowing region. They take into account the oncoming boundary layer as well as the characteristics of the injected jets. The three dimensionality of the flow, which is very strong near the injection and decreases further downstream, is modeled by so-called dispersion terms, which are added to the two-dimensional boundary-layer equations. These terms describe additional mixing by the laterally nonuniform flow. Information on the modeling of the profiles after injection and of the dispersion terms has been extracted from three-dimensional fully elliptic calculations for specific flow configurations. The modified two-dimensional boundary-layer equations are solved by a forward-marching finite-volume method. A coordinate system is used that stretches with the growth of the boundary layer. The turbulent stresses and heat fluxes are obtained from the k-ε turbulence model. Results are given for flows over flat plates as well as for flows over gas turbine blades for different injection angles, relative spacings, blowing rates, and injection temperatures. The predicted cooling effectiveness and heat transfer coefficients are compared with experimental data and show generally fairly good agreement.

scholarly journals Viscous Flow Field Calculations in High-Loaded Centrifugal Compressor Diffusers

1990 ◽  
Author(s):  
Ingolf Teipel ◽  
Alexander Wiedermann
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Side Wall ◽  
Flow Fields ◽  
Wall Boundary Layer ◽  
Wall Boundary

The topic of this paper is the computation of transonic turbulent flow fields in high-loaded centrifugal compressor diffusers with a time-marching scheme. A thin-layer approximation is introduced into the time-dependent Navier-Stokes equations and the turbulent quantities are provided by a zero-equation eddy-viscosity model due to Baldwin and Lomax. For solving the governing equations an explicit-implicit MacCormack scheme is applied. The effect of the side wall boundary layer can be employed globally by variable stream sheet thickness. The present code has been verified by comparison of calculated and measured data. Pressure and velocity fields as well as global results like diffuser efficiency have been considered. The code is very efficient at a CRAY-XMP vector computer. Hence, two-dimensional and quasi-three-dimensional turbulent flow fields can be obtained with a reasonable effort. However, one has to be very careful concerning the modelling of the effect of the side-wall boundary layer by variable stream sheet thickness.

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