Marginal separation of a three-dimensional boundary layer on a line of symmetry

1985 ◽  
Vol 158 ◽  
pp. 95-111 ◽  
Author(s):  
S. N. Brown
Keyword(s):  
Boundary Layer ◽  
Asymptotic Form ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Additional Parameter ◽  
Analytical Prediction ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Incompressible Boundary

The marginal separation of a laminar incompressible boundary layer on the line of symmetry of a three-dimensional body is discussed. The interaction itself is taken to be quasi-two-dimensional but the results differ from those for a two-dimensional boundary layer in that the effect of the gradient of the crossflow is included. Solutions of the resulting integral equation are computed for two values of the additional parameter, and comparisons made with an analytical prediction of the asymptotic form as the length of the separation bubble tends to infinity. The occurrence of the phenomenon is confirmed by an examination of the results of an existing numerical integration of the boundary-layer equations for the line of symmetry of a paraboloid.

A two-dimensional boundary layer encountering a three-dimensional hump

1977 ◽  
Vol 83 (1) ◽  
pp. 163-176 ◽  
Author(s):  
F. T. Smith ◽  
R. I. Sykes ◽  
P. W. M. Brighton
Keyword(s):  
Boundary Layer ◽  
Constant Width ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flow Properties ◽  
Nonlinear Motion ◽  
Dimensional Boundary ◽  
Incompressible Boundary ◽  
Insight Into ◽  
Steady Laminar

A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.

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.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

On three-dimensional boundary layer flow over surface irregularities

1980 ◽  
Vol 373 (1754) ◽  
pp. 311-329 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Solution Technique ◽  
Parabolic Boundary ◽  
Boundary Layer Equations ◽  
Surface Irregularities ◽  
Dimensional Boundary ◽  
Layer Flow

The three-dimensional pipeflow boundary layer equations of Smith (1976) are shown to apply to certain external flow problems, and a numerical method for their solution is developed. The method is used to study flow over surface irregularities, and some three-dimensional separated flows are calculated. Upstream influence in the form of so-called ‘free interactions’ requires an iterative solution technique, in which the initial conditions for the parabolic boundary layer equations must be determined to satisfy a downstream condition

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