The resonant-triad nonlinear interaction in boundary-layer transition

1987 ◽  
Vol 179 ◽  
pp. 227-252 ◽  
Author(s):  
F. T. Smith ◽  
P. A. Stewart
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Finite Amplitude ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Layer Transition ◽  
Structured Analysis

Recent controlled experiments by Kachanov & Levchenko (1984) and others indicate that, during some slower kinds of transition to turbulence in boundary layers, three-dimensionality can come into play initially as a resonant-triad phenomenon, depending on the disturbance sizes present. The triad interaction, suggested theoretically in the boundary-layer context by Craik (1971) and others, is studied in the present work by means of multi-structured analysis for high characteristic Reynolds numbers. A finite-amplitude/relatively high-frequency approach leads rationally to the nonlinear triad equations, solutions for which are then obtained analytically and computationally in certain central cases of interest (temporal and spatial). The solutions have a rather chaotic spiky appearance as continual energy exchange develops between the two- and three-dimensional nonlinear modes, whose large-scale response seems governed by inviscid dynamics but subject to important, continual ‘rejuvenation’ from small- (fast-) scale viscous action in-between. The three-dimensional growth rate is thereby increased, but not the two-dimensional. Subsequently the disturbed flow enters a higher-amplitude regime similar to that studied in some related papers by the authors and co-workers. Comparisons with the experiments are very supportive of the theory (in the small and in the large), yielding both qualitative and quantitative agreement.

Secondary instability of crossflow vortices and swept-wing boundary-layer transition

1999 ◽  
Vol 399 ◽  
pp. 85-115 ◽  
Author(s):  
MUJEEB R. MALIK ◽  
FEI LI ◽  
MEELAN M. CHOUDHARI ◽  
CHAU-LYAN CHANG
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Swept Wing ◽  
Layer Transition ◽  
Transition Prediction ◽  
Dimensional Boundary

Crossflow instability of a three-dimensional boundary layer is a common cause of transition in swept-wing flows. The boundary-layer flow modified by the presence of finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined for the recent swept-wing experimental data by Reibert et al. (1996). Exploiting the experimental observation that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the secondary instability analysis based on a two-dimensional eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is also confirmed. The analysis reveals a number of secondary instability modes belonging to two basic families which, in some sense, are akin to the ‘horseshoe’ and ‘sinuous’ modes of the Görtler vortex problem. The frequency range of the secondary instability is consistent with that measured in earlier experiments by Kohama et al. (1991), as is the overall growth of the secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996). Results indicate that the N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

Velocity and Pressure Measurements Along a Row of Confined Cylinders

2006 ◽  
Author(s):  
Barton L. Smith ◽  
Jack J. Stepan ◽  
Donald M. McEligot
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Symmetry Plane ◽  
Field Measurements ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Recirculation Region ◽  
Pressure Measurements ◽  
Layer Transition ◽  
Flow Experiments

The results of flow experiments performed in a cylinder array designed to mimic a VHTR Nuclear Plant lower plenum design are presented. Pressure drop and velocity field measurements were made. Based on these measurements, five regimes of behavior are identified that are found to depend on Reynolds number. It is found that the recirculation region behind the cylinders is shorter than that of half cylinders placed on the wall representing the symmetry plane. Unlike a single cylinder, the separation point is found to always be on the rear of the cylinders, even at very low Reynolds number. Boundary layer transition is found to occur at much lower Reynolds numbers than previously reported.

Numerical simulation of boundary-layer transition and transition control

1989 ◽  
Vol 199 ◽  
pp. 403-440 ◽  
Author(s):  
E. Laurien ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Transition Process ◽  
Numerical Results ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Longitudinal Vortices ◽  
Tollmien Schlichting

The laminar-turbulent transition process in a parallel boundary-layer with Blasius profile is simulated by numerical integration of the three-dimensional incompressible Navier-Stokes equations using a spectral method. The model of spatially periodic disturbances developing in time is used. Both the classical Klebanoff-type and the subharmonic type of transition are simulated. Maps of the three-dimensional velocity and vorticity fields and visualizations by integrated fluid markers are obtained. The numerical results are compared with experimental measurements and flow visualizations by other authors. Good qualitative and quantitative agreement is found at corresponding stages of development up to the one-spike stage. After the appearance of two-dimensional Tollmien-Schlichting waves of sufficiently large amplitude an increasing three-dimensionality is observed. In particular, a peak-valley structure of the velocity fluctuations, mean longitudinal vortices and sharp spike-like instantaneous velocity signals are formed. The flow field is dominated by a three-dimensional horseshoe vortex system connected with free high-shear layers. Visualizations by time-lines show the formation of A-structures. Our numerical results connect various observations obtained with different experimental techniques. The initial three-dimensional steps of the transition process are consistent with the linear theory of secondary instability. In the later stages nonlinear interactions of the disturbance modes and the production of higher harmonics are essential.We also study the control of transition by local two-dimensional suction and blowing at the wall. It is shown that transition can be delayed or accelerated by superposing disturbances which are out of phase or in phase with oncoming Tollmien-Schlichting instability waves, respectively. Control is only effective if applied at an early, two-dimensional stage of transition. Mean longitudinal vortices remain even after successful control of the fluctuations.

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