Effect of Adverse Pressure Gradients on Turbulent Boundary Layers in Axisymmetric Conduits

1957 ◽  
Vol 24 (2) ◽  
pp. 191-196
Author(s):  
J. M. Robertson ◽  
J. W. Holl
Keyword(s):  
Boundary Layer ◽  
Flow Parameter ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Straight Pipe ◽  
Outer Flow ◽  
Dimensional Boundary

Abstract The development of the three-dimensional boundary layer in a diffuser with several discharge arrangements has been studied for air flow, in continuation of the work of Uram (1). The flow conditions in a diffuser when followed by a straight pipe, an additional length of the diffuser, or a jet, are compared. Extension of the method of analysis developed by Ross for two-dimensional layers is presented. In some cases the use of three-dimensionally defined parameters leads to different results. Ross’s (2) unique outer-flow parameter is found to be no longer satisfactory. Other outer parameters are presented as possible substitutes.

The measurement of skin friction in turbulent boundary layers with adverse pressure gradients

1969 ◽  
Vol 35 (4) ◽  
pp. 737-757 ◽  
Author(s):  
K. C. Brown ◽  
P. N. Joubert
Keyword(s):  
Shear Stress ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Direct Measurements ◽  
Floating Element ◽  
Dimensional Boundary

This paper describes a floating-element skin friction meter which has been designed for use in adverse pressure gradients. The effects of secondary forces on the element, which arise from the pressure gradient, are examined in some detail. The limitations of various methods of measuring wall shear stress are discussed and the results from the floating element device are compared with measurements taken in a two-dimensional boundary layer using Preston tubes and velocity profiles. As it is planned to use the instrument later for direct measurements of the shear stress in three-dimensional boundary layers, the relevance of the instrument to this situation is also discussed.

Equilibrium turbulent boundary layers with lateral streamline convergence or divergence

2009 ◽  
Vol 623 ◽  
pp. 273-282 ◽  
Author(s):  
T. B. NICKELS
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Convergence And Divergence ◽  
Necessary Constraints

The constraints necessary for equilibrium solutions of the boundary layer equations are explored for turbulent boundary layers subject to lateral convergence and divergence and with longitudinal pressure gradients. It is shown that in addition to the well-known equilibrium solutions for two-dimensional boundary layers there are additionalpossibleequilibrium states for boundary layers with these extra rates-of-strain acting. The necessary constraints for equilibrium are derived and discussed.

A two-dimensional boundary layer encountering a three-dimensional hump

1977 ◽  
Vol 83 (1) ◽  
pp. 163-176 ◽  
Author(s):  
F. T. Smith ◽  
R. I. Sykes ◽  
P. W. M. Brighton
Keyword(s):  
Boundary Layer ◽  
Constant Width ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flow Properties ◽  
Nonlinear Motion ◽  
Dimensional Boundary ◽  
Incompressible Boundary ◽  
Insight Into ◽  
Steady Laminar

A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.

On vortex boundary layers

1985 ◽  
Vol 400 (1819) ◽  
pp. 253-261 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Outer Flow ◽  
The Core ◽  
Dimensional Boundary ◽  
Radial Pressure Gradient ◽  
Potential Vortex ◽  
Vortex Axis

Flow visualization is used to study the flow that results when a potential vortex rotates normal to a stationary horizontal disc. Viscosity is seen to remove the singularity on the vortex axis and lead to the development of a three-dimensional boundary layer. The flow remains laminar below a Reynolds number, Re , of about 10 4 , where Re is based on radius and velocity at the disc edge. With further increases in Re the boundary layer becomes turbulent but relaminarizes as it is advected radially inwards by the highly favourable radial pressure gradient associated with the outer flow. The radius of the zone of relaminarized fluid decreases with increasing Re . Close to the axis the flow effuses vertically to form the core of the vortex which, for Re < 10 4 , is observed to undergo a massive disruption, either of the axisymmetric or helical form. The sense of the helix was observed on some occasions to be with that of the outer flow and on others to be opposite that of the outer flow.

Modelling the calmed region behind a spot

2005 ◽  
Vol 363 (1830) ◽  
pp. 1069-1078 ◽  
Author(s):  
S.N Brown ◽  
F.T Smith
Keyword(s):  
Boundary Layer ◽  
Theoretical Model ◽  
Slip Velocity ◽  
Three Dimensional ◽  
Cross Flow ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Flow Surface ◽  
Dimensional Boundary

A theoretical model of the laminar ‘calmed region’ following a three-dimensional turbulent spot within a transitioning two-dimensional boundary layer is formulated and discussed. The flow is taken to be inviscid, and the perturbation mean flow surface streamlines calculated represent disturbances to the basic slip velocity. Available experimental evidence shows a fuller, more stable, streamwise profile in a considerable region trailing the spot, with cross-flow ‘inwash’ towards the line of symmetry. Present results are in qualitative agreement with this evidence.

Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

1989 ◽  
Vol 202 ◽  
pp. 263-294 ◽  
Author(s):  
Shawn D. Anderson ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Free Stream ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Stress Vector ◽  
Dimensional Boundary ◽  
Cross Wire

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

scholarly journals Cancellation of Tollmien–Schlichting waves with surface heating

2021 ◽  
Vol 128 (1) ◽  
Author(s):  
Georgia S. Brennan ◽  
Jitesh S. B. Gajjar ◽  
Richard E. Hewitt
Keyword(s):  
Boundary Layer ◽  
Asymptotic Methods ◽  
Three Dimensional ◽  
Exact Formula ◽  
Surface Heating ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Dimensional Boundary ◽  
Tollmien Schlichting ◽  
Layer Flow

AbstractTwo-dimensional boundary layer flows in quiet disturbance environments are known to become unstable to Tollmien–Schlichting waves. The experimental work of Liepmann et al. (J Fluid Mech 118:187–200, 1982), Liepmann and Nosenchuck (J Fluid Mech 118:201–204, 1982) showed how it is possible to control and reduce unstable Tollmien–Schlichting wave amplitudes using unsteady surface heating. We consider the problem of an oncoming planar compressible subsonic boundary layer flow with a three-dimensional vibrator mounted on a flat plate, and with surface heating present. It is shown using asymptotic methods based on triple-deck theory that it is possible to choose an unsteady surface heating distribution to cancel out the response due to the vibrator. An approximation based on the exact formula is used successfully in numerical computations to confirm the findings. The results presented here are a generalisation of the analogous results for the two-dimensional problem in Brennan et al. (J Fluid Mech 909:A16-1, 2020).

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