The three-dimensional laminar boundary layer on a flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 587-598 ◽  
Author(s):  
L. Sowerby
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Leading Edge ◽  
Main Stream ◽  
Dimensional Parameter ◽  
Stress Components ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Limiting Streamlines

A series expansion is derived for the three-dimensional boundary-layer flow over a flat plate, arising from a general main-stream flow over the plate. The series involved are calculated as far as terms of order ξ2, where ξ is a non-dimensional parameter defining distance measured from the leading edge of the plate. The results are applied to an example in which the main stream arises from the disturbance of a uniform stream by a circular cylinder mounted downstream from the leading edge of the plate, the axis of the cylinder being normal to the plate. Calculations are made for shear stress components on the plate, and for the deviation of direction of the limiting streamlines from those in the main stream.

Receptivity mechanisms in three-dimensional boundary-layer flows

2009 ◽  
Vol 618 ◽  
pp. 209-241 ◽  
Author(s):  
LARS-UVE SCHRADER ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Three Dimensional ◽  
Leading Edge ◽  
Nonlinear Process ◽  
Transition To Turbulence ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
Dimensional Boundary ◽  
Layer Flow

Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.

Three-dimensional boundary-layer instability and separation induced by small-amplitude streamwise vorticity in the upstream flow

1993 ◽  
Vol 246 ◽  
pp. 21-41 ◽  
Author(s):  
M. E. Goldstein ◽  
S. J. Leib
Keyword(s):  
Boundary Layer ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Cross Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
Linear Perturbation ◽  
Streamwise Vorticity ◽  
Dimensional Boundary ◽  
Layer Flow

We consider the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. We show how the initially linear perturbation, ultimately leads to a small-amplitude but nonlinear cross-flow far downstream from the leading edge. This motion is imposed on the boundary-layer flow and eventually causes the boundary layer to separate. The streamwise velocity profiles within the boundary layer become inflexional in localized spanwise regions just upstream of the separation point. The flow in these regions is therefore susceptible to rapidly growing inviscid instabilities.

Laminar flow over a small hump on a flat plate

1973 ◽  
Vol 57 (4) ◽  
pp. 803-824 ◽  
Author(s):  
F. T. Smith
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Leading Edge ◽  
Main Stream ◽  
Pressure Force ◽  
Boundary Layer Flows ◽  
Local Flow ◽  
Wide Range ◽  
Layer Flow

A boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge. The description of the boundary-layer flow, based upon a triple-deck structure, shows how the presence of the hump generates an interaction between the inviscid region just outside the layer and the viscous region near the hump. The pressure force dominant in the boundary layer and the connexion of the local flow with the main stream develop together and are self-perpetuating, and both remain of primary significance for a wide range of hump sizes, even for a hump buried well inside the boundary layer. By consideration of the limiting cases of very small and very large humps, a consistent account of the nature of the disturbances due to the various sizes of hump is produced. The forces and couples on the hump are also evaluated.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Prediction of Steady Propeller Performance with a Nonlinear Slipstream and Boundary-Layer Effect

1995 ◽  
Vol 39 (04) ◽  
pp. 297-312
Author(s):  
You-Hua Liu
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Viscous Drag ◽  
Viscous Effects ◽  
Lattice Method ◽  
Suction Force ◽  
Layer Effect ◽  
Dimensional Boundary ◽  
Propeller Performance

Both slipstream deformation and viscous effects are factors that affect the performance of a rotating marine propeller but neither of them has been properly treated in most of the current lifting-surface methods and surface panel theories. With the introduction of a partial roll-up wake model that is flexible to various cases of propeller geometry and loading condition, this paper presents a vortex-lattice method that can improve propeller performance prediction especially at heavy loading conditions. Some observations on the calculation of the blade leading-edge suction force and how to deduct it to account for the viscous drag increasing are given. The scale effect of propeller performance can be readily predicted by the quasi-three-dimensional boundary-layer calculation presented in this paper. Some patterns of the limiting streamlines on blade surfaces are also illustrated and compared with experimental results.

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