A Three-Dimensional Hypersonic Viscous Interaction

1970 ◽  
Vol 37 (2) ◽  
pp. 467-474
Author(s):  
F. X. Hurley
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Delta Wing ◽  
Control Volume ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Region ◽  
Transfer Coefficients ◽  
Elevated Pressures

The displacement-interacting boundary layer in the symmetry plane region of a flat hypersonic delta wing is studied through a method of control volume balances for mass, momentum, and energy. Free-parameter-bearing expressions for the velocity components, density, and boundary-layer thickness are postulated and substituted into the integral balance equations. The resulting algebraic system for the free parameters is a very complicated one, but solutions are readily extracted by means of iterative machine computations. Answers for the assumed set of flight conditions indicate that the inboard drift of boundary-layer fluid from both sides gives rise to a center-plane region which is three-dimensional in character and which exhibits increased boundary-layer thickness, elevated pressures, and reduced skin-friction and heat-transfer coefficients.

Singularities encountered in three-dimensional boundary layers under an adverse or favourable pressure gradient

1995 ◽  
Vol 352 (1698) ◽  
pp. 45-87 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Plane Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary

Singularities in solutions of the classical boundary-layer equations are considered, numerically and analytically, in an example of steady hypersonic flow along a flat plate with three-dimensional surface roughness. First, a wide parametric study of the breakdown of symmetry-plane flow is performed for two particular cases of the surface geometry. Emphasis is put on the structural stability of the singularities’ development to local/global variation of the pressure distribution. It is found that, as usual, the solution behaviour under an adverse pressure gradient involves the Goldstein- or marginal-type singularity at a point of zero streamwise skin friction. As the main alternative, typical of configurations with favourable or zero pressure forcing, an inviscid breakdown in the middle of the flow is identified. Similarly to unsteady flows, the main features of the novel singularity include infinitely growing boundary-layer thickness and finite limiting values of the skin-friction components. Subsequent analytical extensions of the singular symmetry-plane solution then suggest two different scenarios for the global boundary-layer behaviour: one implies inviscid breakdown of the flow at some singular line, the other describes the development of a boundary-layer collision at a downstream portion of the symmetry plane. In contrast with previous studies of the collision phenomenon in steady flows, the present theory suggests logarithmic growth of boundary-layer thickness on both sides of the discontinuity. Finally, an example of numerical solution of the full three dimensional boundary layer equations is given. The flow régime chosen corresponds to inviscid breakdown of a centreplane flow under a favourable pressure gradient and development of the discontinuity/collision downstream. The numerical results near the origin of the discontinuity are found to be supportive, producing quantitative agreement with the local analytical description.

Secondary Losses in a Large Deflection Annular Turbine Cascade: Effect of the Entry Boundary Layer Thickness

1986 ◽  
Author(s):  
M. Govardhan ◽  
N. Venkatrayulu ◽  
D. Prithvi Raj
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Impulse Turbine ◽  
Flow Measurements ◽  
Local Loss ◽  
Trailing Edges ◽  
Annular Cascade

The paper presents the results of three dimensional flow measurements behind the trailing edges of an impulse turbine blade row of 120° deflection in an annular cascade. The entry boundary layer thickness was systematically varied on the hub and casing walls separately and its effect on secondary flows and losses is investigated. With the increase of entry boundary layer thickness, it has been found that (i) the contours of local loss coefficient show that the magnitude of the hub loss core increased, (ii) the loss cores near the hub and casing wall are convected away from the walls, (iii) the spanwise variation of the pitchwise averaged losses indicate that the position of large loss peak near the hub wall remains the same, but the magnitude of the loss increases, (iv) the exit static pressure increases and the exit velocity in general decreases, (v) the degree of underturning of flow increases and (vi) the net secondary losses do not change appreciably.

205 Three Dimensional Separated Flow with Spiral-Focus in the Wind Tunnel : Effect of Inlet Boundary Layer Thickness

2000 ◽  
Vol 2000.53 (0) ◽  
pp. 25-26
Author(s):  
Yoichi KINOUE ◽  
Toshiaki SETOGUCHI ◽  
Kenji KANEKO ◽  
Takeshi MURASAKI ◽  
Masahiro INOUE
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Separated Flow ◽  
Tunnel Effect

Three dimensional separation with spiral-focus in a decelerating duct flow (effect of asymmetric inlet boundary layer thickness)

2003 ◽  
Vol 12 (1) ◽  
pp. 27-32
Author(s):  
Yoichi Kinoue ◽  
Toshiaki Setoguchi ◽  
Kenji Kaneko ◽  
Mamun Mohammad ◽  
Masahiro Inoue
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Duct Flow ◽  
Flow Effect

Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink

2015 ◽  
Vol 25 (4) ◽  
pp. 762-781 ◽  
Author(s):  
Tasawar Hayat ◽  
Taseer Muhammad ◽  
Sabir Ali Shehzad ◽  
A. Alsaedi
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Stretching Surface ◽  
Three Dimensional Flow ◽  
Soret And Dufour Effects ◽  
Content Type ◽  
Dimensional Flow

Purpose – The purpose of this paper is to study the Soret and Dufour effects in three-dimensional flow induced by an exponential stretching surface in a porous medium. Design/methodology/approach – Series solutions are developed. Findings – The authors observed that the temperature profile and thermal boundary layer thickness are enhanced when the authors increase the values of Dufour number. It is also examined that the concentration field and its associated boundary layer thickness are higher for the larger values of Soret number. Originality/value – Such investigation is not available in the literature.

The Effect of Leading Edge Diameter on the Horse Shoe Vortex and Endwall Heat Transfer

2008 ◽  
Author(s):  
Satoshi Hada ◽  
Kenichiro Takeishi ◽  
Yutaka Oda ◽  
Seijiro Mori ◽  
Yoshihiro Nuta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Leading Edge ◽  
Marginal Effect ◽  
Transfer Coefficients ◽  
Film Cooling Effectiveness ◽  
Heat Transfer Coefficients ◽  
Horse Shoe Vortex

The endwall of the first stage vane / blade of modern high temperature gas turbine has been exposed to severe heat transfer environments. Due to the formation of a horse shoe vortex (HV), the flow field of a vane and blade leading edge juncture to endwall is especially complicated and it is difficult to estimate the heat transfer coefficients and the film cooling effectiveness levels in this area. This paper describes the results of experimental and numerical studies on the heat transfer and flow dynamics in the leading edge endwall region of a symmetric airfoil. The effects of inlet velocity, boundary layer thickness and leading edge diameter of a symmetric airfoil were investigated on the endwall heat transfer in a low speed wind tunnel facility. The time averaged local heat transfer coefficients were measured by naphthalene sublimation method and the instantaneous velocity field was obtained by Particle Image Velocimetry (PIV). As the leading edge diameter of symmetric airfoil decreases, the heat transfer coefficients on an endwall increases and is proportional to Re0.71 that is base on the leading edge diameter. However, the boundary layer thickness was found to have a marginal effect on the endwall heat transfer.

Design Point Variation of Three-Dimensional Loss and Deviation for Axial Compressor Middle Stages

1988 ◽  
Vol 110 (4) ◽  
pp. 426-433 ◽  
Author(s):  
W. B. Roberts ◽  
G. K. Serovy ◽  
D. M. Sandercock
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Tip Clearance ◽  
Flow Angle ◽  
Design Point ◽  
Blade Element Theory ◽  
The Difference

Three-dimensional spanwise pressure loss and flow angle deviation variations have been deduced from NASA, university, and industrial sources from middle-stage research compressors operating near design point. These variations are taken as the difference above or below that predicted by blade element theory at any spanwise location. It was observed that the magnitude of the three-dimensional loss and deviation in the endwall regions is affected by hub and casing boundary layer thickness, camber, solidity, and blade channel aspect ratio for stators and rotor hubs. Rotor tip variations were found to depend on casing boundary layer thickness and tip clearance. Simple design point loss models derived from these data can aid in the design of axial compressor middle stages.

scholarly journals An Analysis of the Turbine Endwall Boundary Layer and Aerodynamic Losses

1975 ◽  
Author(s):  
T. C. Booth
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Shape Factor ◽  
Boundary Layer Thickness ◽  
Energy Equation ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Aerodynamic Loss ◽  
Flow Configurations ◽  
Momentum Integral

A momentum-integral analysis of the three-dimensional flow on the turbine endwall is presented. The formulation is for a compressible turbulent boundary layer with a constant streamwise shape factor. The effect of compressibility enters through a coordinate transformation and an assumed energy equation. An aerodynamic loss model is derived using inner and outer expansions. The losses decompose into frictional losses on the annulus and a vortex loss. Results are predicted for four cascade tests. In addition, previously observed trends of loss versus inlet boundary layer thickness, blade height, and blade chord are predicted. To illustrate a possible application, a parametric study is presented showing the effect on losses and heat transfer of various inlet boundary layer thickness distributions, which simulates different secondary flow configurations.

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