scholarly journals The generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow

2021 ◽  
Vol 129 (1) ◽  
Author(s):  
A. I. Ruban ◽  
H. Broadley
Keyword(s):  
Boundary Layer ◽  
Transonic Flow ◽  
Free Stream ◽  
Roughness Element ◽  
Free Stream Turbulence ◽  
Upper Deck ◽  
Classical Boundary ◽  
Tollmien Schlichting ◽  
Deformation Layer ◽  
Interaction Problem

AbstractThis paper studies the generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow over a half-infinite flat plate with a roughness element using an asymptotic approach. It is assumed that the Reynolds number (denoted Re) is large, and that the free-stream turbulence is uniform so it can be modelled as vorticity waves. Close to the plate, a Blasius boundary layer forms at a thickness of $$O(\mathrm{{Re}}^{-{1}/{2}})$$ O ( Re - 1 / 2 ) , and a vorticity deformation layer is also present with thickness $$O(\mathrm{{Re}}^{-{1}/{4}})$$ O ( Re - 1 / 4 ) . The report shows that there is no mechanism by which the vorticity waves can penetrate from the vorticity deformation layer into the classical boundary layer; therefore, a transitional layer is introduced between them in order to prevent a discontinuity in vorticity. The flow in the interaction region in the vicinity of the roughness element is then analysed using the triple-deck model for transonic flow. A novel asymptotic expansion is used to analyse the upper deck, which enables a viscous–inviscid interaction problem to be derived. In order to make analytical progress, the height of the roughness element is assumed to be small, and from this, we find an explicit formula for the receptivity coefficient of the Tollmien–Schlichting wave far downstream of the roughness.

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.

Effects of Weak Free Stream Nonuniformity on Boundary Layer Transition (Keynote Paper)

2003 ◽  
Author(s):  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Mean Flow ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Distorted Waves ◽  
Thickness Variations

Experiments are described in which well-defined FSN (Free Stream Nonuniformity) distributions are introduced by placing fine wires upstream of the leading edge of a flat plate. Large amplitude spanwise thickness variations are present in the downstream boundary layer resulting from the interaction of the laminar wakes with the leading edge. Regions of elevated background unsteadiness appear on either side of the peak layer thickness, which share many of the characteristics of Klebanoff modes, observed at elevated Free Stream Turbulence (FST) levels. However, for the low background disturbance level of the free stream, the layer remains laminar to the end of the test section (Rx ≈ l.4×106) and there is no evidence of bursting or other phenomena associated with breakdown to turbulence. A vibrating ribbon apparatus is used to demonstrate that the deformation of the mean flow is responsible for substantial phase and amplitude distortion of Tollmien-Schlichting (TS) waves. Pseudo-flow visualization of hot-wire data shows that the breakdown of the distorted waves is more complex and occurs at a lower Reynolds number than the breakdown of the K-type secondary instability observed when the FSN is not present.

Experiments in a boundary layer subjected to free stream turbulence. Part 2. The role of TS-waves in the transition process

1994 ◽  
Vol 281 ◽  
pp. 219-245 ◽  
Author(s):  
A. V. Boiko ◽  
K. J. A. Westin ◽  
B. G. B. Klingmann ◽  
V. V. Kozlov ◽  
P. H. Alfredsson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Small Amplitude ◽  
Free Stream ◽  
Transition Process ◽  
Natural Occurrence ◽  
Free Stream Turbulence ◽  
Onset Of Turbulence ◽  
Tollmien Schlichting

The natural occurrence of Tollmien-Schlichting (TS) waves has so far only been observed in boundary layers subjected to moderate levels of free stream turbulence (Tu < 1%), owing to the difficulty in detecting small-amplitude waves in highly perturbed boundary layers. By introducing controlled oscillations with a vibrating ribbon, it is possible to study small-amplitude waves using phase-selective filtering techniques. In the present work, the effect of TS-waves on the transition is studied at Tu = 1.5%. It is demonstrated that TS-waves can exist and develop in a similar way as in an undisturbed boundary layer. It is also found that TS-waves with quite small amplitudes are involved in nonlinear interactions which lead to a regeneration of TS-waves in the whole unstable frequency band. This results in a significant increase in the number of turbulent spots, which promote the onset of turbulence.

scholarly journals Boundary layer stabilization using free-stream vortices

2014 ◽  
Vol 764 ◽  
Author(s):  
L. Siconolfi ◽  
S. Camarri ◽  
J. H. M. Fransson
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Control Method ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Free Stream Turbulence ◽  
Passive Flow Control ◽  
Tollmien Schlichting ◽  
Transition Delay

AbstractIn this numerical investigation we explore the possibility of applying free-stream vortices as a passive flow control method for delaying the transition to turbulence. The work is motivated by previous experimental studies demonstrating that stable streamwise boundary layer (BL) streaks can attenuate both two- and three-dimensional disturbances inside the BL, leading to transition delay, with the implication of reducing skin-friction drag. To date, successful control has been obtained using physical BL modulators mounted on the surface in order to generate stable streaks. However, surface mounted BL modulators are doomed to failure when the BL is subject to free-stream turbulence (FST), since a destructive interaction between the two is inevitable. In order to tackle free-stream disturbances, such as FST, a smooth surface is desired, which has motivated us to seek new methods to induce streamwise streaks inside the BL. A first step, in a systematic order, is taken in the present paper to prove the control idea of generating free-stream vortices for the attenuation of ordinary Tollmien–Schlichting waves inside the BL. In this proof-of-concept study we show that, by applying a spanwise array of counter-rotating free-stream vortices, inducing streamwise BL streaks further downstream, it is possible to alter the BL stability characteristics to such a degree that transition delay may be accomplished. For the demonstration we use direct numerical simulations along with stability analysis.

Development and use of a vane device for boundary-layer measurements

1959 ◽  
Vol 6 (1) ◽  
pp. 97-112 ◽  
Author(s):  
J. G. Burns ◽  
W. H. J. Childs ◽  
A. A. Nicol ◽  
M. A. S. Ross
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Boundary Layers ◽  
Free Stream ◽  
Neutral Curve ◽  
Approximate Theory ◽  
Electrical System ◽  
Natural Oscillations ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting

A hinged vane and a sensitive electrical system for recording the motion of the vane have been developed for the observation of fluctuating y-components of velocity in boundary layers. An approximate theory of the natural oscillations of such vanes is presented and experimentally verified. Using vanes as resonant detectors, meassurements have been made of oscillations injected into the laminar boundary layer on a flat plate in a wind tunnel with 0·3% free-stream turbulence. Points on the neutral Tollmien-Schlichting curve have thereby been obtained which lie close to the theoretical neutral curve.

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 Instability Tollmien-Schlichting Waves by Free-Stream Turbulence

2017 ◽  
Vol 9 (2) ◽  
pp. 429-438
Author(s):  
Luyu Shen ◽  
Changgen Lu
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Free Stream ◽  
Leading Edge ◽  
S Wave ◽  
S Waves ◽  
Free Stream Turbulence ◽  
Temporal Mode ◽  
Tollmien Schlichting ◽  
Experimental Researches

AbstractThe beginning of the transition from the laminar to a turbulent flow is usually the generation of instability Tollmien-Schlichting (T-S) waves in the boundary layer. Previously, most numerical and experimental researches focused on generating instability T-S waves through the external disturbances such as acoustic waves and vortical disturbances interacting with wall roughness or at the leading-edge of flatplate, whereas only a few paid attention to the excitation of the T-S waves directly by free-stream turbulence (FST). In this study, the generating mechanism of the temporal mode T-S waves under free-stream turbulence is investigated by using direct numerical simulation (DNS) and fast Fourier transform. Wave packets superposed by a group of stability, neutral and instability T-S waves are discovered in the boundary layer. In addition, the relation between the amplitude of the imposed free-stream turbulence and the amplitude of the excited T-S wave is also 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.

Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity

1994 ◽  
Vol 281 ◽  
pp. 193-218 ◽  
Author(s):  
K. J. A. Westin ◽  
A. V. Boiko ◽  
B. G. B. Klingmann ◽  
V. V. Kozlov ◽  
P. H. Alfredsson
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Layer Structure ◽  
Present Report ◽  
Plate Boundary ◽  
Transition Process ◽  
Wave Instability ◽  
Free Stream Turbulence ◽  
The Mean ◽  
Tollmien Schlichting

The modification of the mean and fluctuating characteristics of a flat-plate boundary layer subjected to nearly isotropic free stream turbulence (FST) is studied experimentally using hot-wire anemometry. The study is focussed on the region upstream of the transition onset, where the fluctuations inside the boundary layer are dominated by elongated flow structures which grow downstream both in amplitude and length. Their downstream development and scaling are investigated and the results are compared with those obtained by previous authors. This allows some conclusions about the parameters which are relevant for the modelling of the transition process. The mechanisms underlying the transition process and the relative importance of the Tollmien–Schlichting wave instability in this flow are treated in an accompanying paper (part 2 of the present report).

Sign in / Sign up

Export Citation Format

Share Document