The boundary layer beneath a Rankine-like vortex

1987 ◽  
Vol 411 (1840) ◽  
pp. 177-192 ◽  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Reynolds Numbers ◽  
Tangential Component ◽  
Plane Boundary ◽  
Outer Flow ◽  
Law Of The Wall ◽  
Dimensional Boundary ◽  
Transitory State

An experimental investigation is made of the three-dimensional boundary layer that results when a Rankine-like vortex is bounded by a fixed plane boundary, in particular by a horizontal disc coaxial with, and perpendicular to, the axis of rotation of the vortex. A laser-Doppler anemometer is used to make velocity traverses through both the vortex and the boundary layer, for Reynolds numbers, Re , ranging from 5000 to 30000, where Re is based on velocity and radius at the disc edge. The boundary layer is laminar at Re = 5000 and the data agree well with the theory of Belcher et al . ( J . Fluid Mech . 52, 753-780 (1972)); at Re = 10000 the layer is in a transitory state, while for Re ≽ 15000 it is turbulent over some of the disc. The radial pressure gradient associated with the outer flow has a stabilizing effect on the boundary layer and, for 10000 ≼ Re ≼ 30000, acts to revert it to a laminar state, but with diminishing effect as Re increases. In spite of the high threedimensionality of the layer, the tangential component of velocity conforms to the same law-of-the-wall as its streamwise counterpart in two-dimensional turbulent boundary layers.

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.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

scholarly journals Behavior of Three-Dimensional Boundary Layers in a Radial Inflow Turbine Scroll

1993 ◽  
Author(s):  
Kazuo Hara ◽  
Masato Furukawa ◽  
Masahiro Inoue
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Inlet Region ◽  
Flow Phenomena ◽  
Dimensional Boundary ◽  
Radial Inflow Turbine ◽  
The One ◽  
Circumferential Nonuniformity

A detailed experimental investigation was carried out to examine the three-dimensional boundary layer characteristics in a radial inflow turbine scroll. Some basic flow phenomena and growth of secondary flow were also investigated. In the inlet region of the scroll, the incoming boundary layer begins to have the skewed nature, namely the radially inward secondary flow caused by the radial pressure gradient. From the inlet region to the one third of the scroll circumference, the secondary flow grows so strongly that the most of the low momentum fluid in the incoming boundary layer are transported to the nozzle region. The succeeding elimination of the low momentum fluid in the boundary layer suppresses growth of the boundary layer further downstream, where the boundary layer shows a similarity of velocity profile. The distributions of the boundary layer properties in the scroll correspond well to those of the flow properties at the nozzle. The behavior of the boundary layer in the scroll is found to affect the circumferential nonuniformity of the nozzle flow field.

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.

Behavior of Three-Dimensional Boundary Layers in a Radial Inflow Turbine Scroll

1994 ◽  
Vol 116 (3) ◽  
pp. 446-452 ◽  
Author(s):  
K. Hara ◽  
M. Furukawa ◽  
M. Inoue
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Flow Properties ◽  
Inlet Region ◽  
Flow Phenomena ◽  
Dimensional Boundary ◽  
Radial Inflow Turbine ◽  
Circumferential Nonuniformity

A detailed experimental investigation was carried out to examine the three-dimensional boundary layer characteristics in a radial inflow turbine scroll. Some basic flow phenomena and growth of secondary flow were also investigated. In the inlet region of the scroll, the incoming boundary layer begins to have a skewed nature, namely the radially inward secondary flow caused by the radial pressure gradient. From the inlet region to one third of the scroll circumference, the secondary flow grows so strongly that most of the low-momentum fluid in the incoming boundary layer is transported to the nozzle region. The succeeding elimination of the low-momentum fluid in the boundary layer suppresses growth of the boundary layer farther downstream, where the boundary layer shows a similar velocity profile. The distributions of the boundary layer properties in the scroll correspond well to those of the flow properties at the nozzle. The behavior of the boundary layer in the scroll is found to affect the circumferential nonuniformity of the nozzle flow field.

Three-Dimensional Blade Boundary Layer and Endwall Flow Development in the Nozzle Passage of a Single Stage Turbine

1998 ◽  
Vol 120 (3) ◽  
pp. 570-578 ◽  
Author(s):  
D. Ristic ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Axial Flow ◽  
Flow Region ◽  
Radial Pressure ◽  
Suction Surface ◽  
Field Development ◽  
Dimensional Boundary

The three-dimensional viscous flow field development in the nozzle passage of an axial flow turbine stage was measured using a “x” hot-wire probe. The measurements were carried out at two axial stations on the endwall and vane surfaces and at several spanwise and pitchwise locations. Static pressure measurements and flow visualization, using a fluorescent oil technique, were also performed to obtain the location of transition and the endwall limiting streamlines. The boundary layers on the vane surface were found to be very thin and mostly laminar, except on the suction surface downstream of 70 percent axial chord. Strong radial pressure gradient, especially close to the suction surface, induces strong radial flow velocities in the trailing edge regions of the blade. On the endwalls, the boundary layers were much thicker, especially near the suction corner of the casing surface, caused by the secondary flow. The secondary flow region near the suction surface-casing corner indicated the presence of the passage vortex detached from the vane surface. The boundary layer code accurately predicts the three-dimensional boundary layers on both vane surfaces and endwall in the regions where the influence of the secondary flow is small.

scholarly journals Some similarity solutions for three-dimensional boundary layers

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190267 ◽  
Author(s):  
R. H. Vaz ◽  
A. J. Mestel
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Wall Jet ◽  
Dimensional Solution ◽  
Similarity Reduction ◽  
Outer Flow ◽  
Dimensional Boundary ◽  
Constant Potential

A similarity solution of a three-dimensional boundary layer is investigated. The outer flow is given by U  = ( −  xz , −  yz , z 2 ), corresponding to an axisymmetric poloidal circulation with constant potential vorticity. This flow is an exact solution of the Navier–Stokes. A wall is introduced at y  = 0 along which a boundary layer develops towards x  = 0. We show that a similarity reduction to a system of ODEs is possible. Two distinct solutions are found, one of them through numerical path-continuation, and their stability is investigated. A second three-dimensional solution is also identified for two-dimensional outer flow. The solutions are generalized for outer flows scaling with different powers of z and similar results are found. This behaviour is related to the non-uniqueness of the Falkner–Skan flows in a three-dimensional sense, with a transverse wall-jet.

The Law of the Wake and Plane of Symmetry Flows in Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Vol 88 (1) ◽  
pp. 101-108 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Three Dimensional Model ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
The Law

Coles’ model incorporating the law of the wall and the law of the wake, proposed for two and three-dimensional turbulent boundary-layer flows, is examined for the special case of plane of symmetry flows in collateral and skewed three-dimensional boundary layers. Contrary to other published results, it is shown that the model is appropriate for adverse pressure gradient plane of symmetry flows in collateral environments away from separation. Additional, it appears that the departure from Coles’ law of the wake for recently reported three-dimensional flows is of the same basic form as that observed for plane of symmetry flows in transient development or two-dimensional flow with imminent separation. Since the Coles’ model, as most velocity profile models, is proposed only in an asymptotic sense for a well-developed flow, the fact that most of the three-dimensional flows heretofore reported are in transient or undeveloped states, suggests that the three-dimensional model be examined in well-developed three-dimensional boundary-layer flows before the question of the model’s validity can be properly answered.

Streamwise absolute instability of a three-dimensional boundary layer at high Reynolds numbers

1998 ◽  
Vol 373 ◽  
pp. 111-153 ◽  
Author(s):  
OLEG S. RYZHOV ◽  
EUGENE D. TERENT'EV
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Wave Packets ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Streamwise Direction ◽  
High Reynolds Numbers ◽  
Dimensional Boundary ◽  
High Reynolds

The simplest receptivity problem of linear disturbances artificially excited in a three-dimensional boundary layer adjacent to a solid surface is studied in the framework of the generalized triple-deck theory. In order to provide a mathematical model to be compared with experimental data from wind-tunnel tests we consider the base flow over a swept flat plate. Then crossflow in the near-wall region originates owing to an almost constant pressure gradient induced from outside with a displacement body on top. A pulsed or vibrating ribbon installed on the solid surface serves as an external agency provoking initially weak pulsations. A periodic dependence of the ribbon shape on a coordinate normal to the streamwise direction makes the receptivity problem effectively two-dimensional, thereby allowing a rigorous analysis to be carried out without additional assumptions.The most striking result from the asymptotic theory is the discovery of streamwise absolute instability intrinsic to a three-dimensional boundary layer at high Reynolds numbers. However, due to limitations imposed on the receptivity problem no definite conclusions can be made with regard to possible continued convection of disturbances in the crossflow direction. An investigation of the dispersion-relation roots points to the fact that wave packets of different kinds can be generated by an external source operating in the pulse mode. Rapidly growing wave packets sweep downstream, weaker wave packets move against the oncoming stream. Insofar as the amplitude of all of the modulated signals increases exponentially in time and space, the excitation process gives rise to absolutely unstable disturbances in the streamwise direction. The computation confirms the theoretical prediction about the existence of upstream-advancing wave packets. They can be prevented from being persistently amplified only in a region ahead of the ribbon where nearly critical values of the Reynolds number are attained.The results achieved are shown to be broadly consistent with wind-tunnel measurements. Hence a conjecture is made that the onset of transition is probably associated, under some environmental conditions, with the mechanism of streamwise absolute instability in the supercritical range of the Reynolds numbers.

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