Similarity and stability of the laminar boundary layer in a streamwise corner

1981 ◽  
Vol 377 (1770) ◽  
pp. 269-288 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Conclusive Evidence ◽  
Experimental Results ◽  
Solid Surfaces ◽  
Boundary Layer Problem ◽  
Streamwise Pressure Gradient ◽  
The Stability ◽  
Limiting Case ◽  
Theoretical Results

The study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state, and out­standing differences between various experimental and theoretical results are analysed. New experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles. Conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the Reynolds number much above about 10 4 . The new results also help to explain the differences between various experimental results, and between theory and experi­ment, which have characterized the corner boundary layer problem for several years. By extrapolation, an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient, if the layer were stable in that state. The predicted profile is compared with the results of current theories.

Transition of streamwise streaks in zero-pressure-gradient boundary layers

2002 ◽  
Vol 472 ◽  
pp. 229-261 ◽  
Author(s):  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
High Speed ◽  
Plate Boundary ◽  
Transition Process ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Streamwise Streaks ◽  
The Stability ◽  
Optimal Disturbances

A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation (Andersson et al. 2001), the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. The main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low-speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern. The present scenario is compared with transition initiated by Tollmien–Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.

scholarly journals Stability of the laminar boundary layer in a streamwise corner

1984 ◽  
Vol 393 (1804) ◽  
pp. 101-116 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Viscous Incompressible Flow ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Mean ◽  
Layer Region ◽  
The Stability ◽  
Infinite Boundary Value Problem ◽  
Layer Problem

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.

Influence of Stream Turbulence and Pressure Gradient upon Boundary Layer Transition

1972 ◽  
Vol 14 (2) ◽  
pp. 134-146 ◽  
Author(s):  
D. J. Hall ◽  
J. C. Gibbings
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Transition ◽  
Experimental Results ◽  
Prediction Methods ◽  
Layer Transition ◽  
Approximate Nature

In considering boundary layer transition, the available experimental data and prediction methods are reviewed and further experimental results are presented. Some empirical rules are suggested for the separate effects of stream turbulence and of pressure gradient and of both combined. The approximate nature of these rules is described and the causes indicated.

scholarly journals Application of the Method of Integral Relations to the Calculation of Two-Dimensional Incompressible Turbulent Boundary Layer

1981 ◽  
Vol 48 (4) ◽  
pp. 701-706 ◽  
Author(s):  
W.-S. Yeung ◽  
R.-J. Yang
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Experimental Results ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Method Of Integral Relations ◽  
Integral Relations

The orthonormal version of the Method of Integral Relations (MIR) was applied to solve for a two-dimensional incompressible turbulent boundary layer. The flow was assumed to be nonseparating. Flows with favorable, unfavorable, and zero pressure gradient were considered, and comparisons made with available experimental data. In general, the method predicted very well the experimental results for flows with favorable or zero pressure gradient; for flows with unfavorable pressure gradient, it predicted the experimental data well only up to a certain distance from the initial station. This result is due to the flow not being in equilibrium beyond that distance. Finally, the scheme was shown to be efficient in obtaining numerical solutions.

Direct Simulations of Wake-Perturbed Separated Boundary Layers

2011 ◽  
Author(s):  
Ayse G. Gungor ◽  
Mark P. Simens ◽  
Javier Jime´nez
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Separation Bubble ◽  
Turbine Blades ◽  
Plate Boundary ◽  
Maximum Velocity ◽  
Adverse Pressure Gradient ◽  
Suction Side ◽  
Single Experiment ◽  
The Stability

A wake-perturbed flat plate boundary layer with a stream-wise pressure distribution similar to those encountered on the suction side of typical low-pressure turbine blades is investigated by direct numerical simulation. The laminar boundary layer separates due to a strong adverse pressure gradient induced by suction along the upper simulation boundary, transitions and reattaches while still subject to the adverse pressure gradient. Various simulations are performed with different wake passing frequencies, corresponding to the Strouhal number 0.0043 < fθb/ΔU < 0.0496 and wake profiles. The wake profile is changed by varying its maximum velocity defect and its symmetry. Results indicate that the separation and reattachment points, as well as the subsequent boundary layer development, are mainly affected by the frequency, but that the wake shape and intensity have little effect. Moreover, the effect of the different frequencies can be predicted from a single experiment in which the separation bubble is allowed to reform after having been reduced by wake perturbations. The stability characteristics of the mean flows resulting from the forcing at different frequencies are evaluated in terms of local linear stability analysis based on the Orr-Sommerfeld equation.

Experimental Investigation of a Turbulent Compressible Boundary Layer

2009 ◽  
Author(s):  
Todd Reedy
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Pressure Gradient ◽  
Static Pressure ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Experimental Results ◽  
Compressible Boundary Layer ◽  
Law Of The Wall ◽  
Displacement Thickness

A turbulent compressible boundary layer in a nominally Mach 4.2 flow was investigated experimentally. Pitot, wall-static pressure, total pressure and temperature measurements were utilized to determine Mach number, temperature, and velocity profiles within the boundary layer. An adverse pressure gradient was observed, resulting in non-uniform flow in the streamwise direction of the test section during development. Alterations were made to the tunnel top and bottom walls to account for the growing boundary layer displacement thickness, resulting in a much improved, uniform Mach number in the freestream and boundary layer. The existence of a slight adverse pressure gradient remained. Flow visualization was conducted via the Schlieren imaging technique. Experimental results were compared against turbulent compressible flow theory and were found to be in excellent agreement, based on an extension of the law-of-the-wall and law-of-the-wake. Velocity profiles and boundary layer thicknesses of the theoretical and experimental results aligned satisfactorily.

Experiments on the Laminar Flow in a Rectangular Streamwise Corner

1978 ◽  
Vol 29 (2) ◽  
pp. 75-97 ◽  
Author(s):  
H.A. El-Gamal ◽  
W.H. Barclay
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Experimental Work ◽  
Marked Effect ◽  
Leading Edge ◽  
Experimental Results ◽  
Edge Geometry ◽  
Significant Difference ◽  
Streamwise Pressure Gradient ◽  
Corner Layer

SummaryThe results of measurements in the flow along a rectangular corner are presented in the form of velocity profiles. The profiles form two sets: one for flow in a slightly favourable streamwise pressure gradient and one for flow when the pressure gradient is ‘practically zero’. The appearance of the profiles is quite different from that of previously reported experimental work and it is suggested here that the primary cause of this is the different type of corner leading edges used in each case. The flow appears to be only marginally stable and even very slightly changed entry conditions caused by alterations in the leading edge geometry may have a marked effect on the profiles further downstream. The new results are consistent with the notion of corner layer similarity (an implication in every attempted theoretical solution) but there remains a significant difference between the experimental results and the more reliable theoretical solutions available.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

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