ON THE GENERATION OF TOLLMIEN-SCHLICHTING WAVES IN THE BOUNDARY LAYER OF A FLAT PLATE BY THE DISTURBANCES IN THE FREE STREAM

1988 ◽  
pp. 237-242
Author(s):  
Luo Jisheng ◽  
Zhou Heng
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Tollmien Schlichting

The generation of Tollmien-Schlichting waves by free-stream turbulence

1996 ◽  
Vol 312 ◽  
pp. 341-371 ◽  
Author(s):  
P. W. Duck ◽  
A. I. Ruban ◽  
C. N. Zhikharev
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Stokes Equations ◽  
Leading Edge ◽  
Wave Generation ◽  
Generation Process ◽  
Viscous Boundary Layer ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting

The phenomenon of Tollmien-Schlichting wave generation in a boundary layer by free-stream turbulence is analysed theoretically by means of asymptotic solution of the Navier-Stokes equations at large Reynolds numbers (Re → ∞). For simplicity the basic flow is taken to be the Blasius boundary layer over a flat plate. Free-stream turbulence is taken to be uniform and thus may be represented by a superposition of vorticity waves. Interaction of these waves with the flat plate is investigated first. It is shown that apart from the conventional viscous boundary layer of thickness O(Re−1/2), a ‘vorticity deformation layer’ of thickness O(Re−1/4) forms along the flat-plate surface. Equations to describe the vorticity deformation process are derived, based on multiscale asymptotic techniques, and solved numerically. As a result it is shown that a strong singularity (in the form of a shock-like distribution in the wall vorticity) forms in the flow at some distance downstream of the leading edge, on the surface of the flat plate. This is likely to provoke abrupt transition in the boundary layer. With decreasing amplitude of free-stream turbulence perturbations, the singular point moves far away from the leading edge of the flat plate, and any roughness on the surface may cause Tollmien-Schlichting wave generation in the boundary layer. The theory describing the generation process is constructed on the basis of the ‘triple-deck’ concept of the boundary-layer interaction with the external inviscid flow. As a result, an explicit formula for the amplitude of Tollmien-Schlichting waves is obtained.

On the generation of Tollmien-Schlichting waves in the boundary layer of a flat plate by the disturbances in the free stream

1987 ◽  
Vol 413 (1845) ◽  
pp. 351-367 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Nonlinear Interaction ◽  
Free Stream ◽  
Velocity Spectrum ◽  
Free Stream Turbulence ◽  
Order Of Magnitude ◽  
Tollmien Schlichting ◽  
Harmonic Components

A model is proposed for the problem of ‘receptivity’ of the boundary layer of a flat plate to the free-stream turbulence. The basic idea is that two harmonic components of the turbulent velocity spectrum may generate Tollmien-Schlichting waves in the boundary layer through nonlinear interaction. The numerical calculations based on this model show that Tollmien-Schlichting waves can actually be generated and the amplitudes may have the same order of magnitude as the disturbance amplitude in the free stream, at least for certain ranges of the Reynolds number, wavenumber and frequency.

scholarly journals A Theory for Wake-Induced Transition

1989 ◽  
Author(s):  
R. E. Mayle ◽  
K. Dullenkopf
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flow ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Transition Model ◽  
Model Comparisons ◽  
Turbulent Wakes ◽  
Flat Plate Boundary Layer

A theory for transition from laminar to turbulent flow as the result of unsteady, periodic passing of turbulent wakes in the free stream is developed using Emmons’ transition model. Comparisons made to flat plate boundary layer measurements and airfoil heat transfer measurements confirm the theory.

scholarly journals Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

1992 ◽  
Vol 242 ◽  
pp. 701-720 ◽  
Author(s):  
M. Tadjfar ◽  
R. J. Bodonyi
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Flow ◽  
Free Stream ◽  
Flow Direction ◽  
Roughness Element ◽  
Three Dimensional ◽  
Unsteady Motion ◽  
Time Harmonic ◽  
Tollmien Schlichting

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.

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