The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

Experimental approaches towards interpreting dolphin-stimulated bioluminescence.

1998 ◽  
Vol 201 (9) ◽  
pp. 1447-1460 ◽  
Author(s):  
J Rohr ◽  
M I Latz ◽  
S Fallon ◽  
J C Nauen ◽  
E Hendricks
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Visualization ◽  
Leading Edge ◽  
Field Studies ◽  
Flow Speed ◽  
The Body ◽  
Surface Shear Stress ◽  
Literature Report ◽  
Surface Shear

Flow-induced bioluminescence provides a unique opportunity for visualizing the flow field around a swimming dolphin. Unfortunately, previous descriptions of dolphin-stimulated bioluminescence have been largely anecdotal and often conflicting. Most references in the scientific literature report an absence of bioluminescence on the dolphin body, which has been invariably assumed to be indicative of laminar flow. However, hydrodynamicists have yet to find compelling evidence that the flow remains laminar over most of the body. The present study integrates laboratory, computational and field approaches to begin to assess the utility of using bioluminescence as a method for flow visualization by relating fundamental characteristics of the flow to the stimulation of naturally occurring luminescent plankton. Laboratory experiments using fully developed pipe flow revealed that the bioluminescent organisms identified in the field studies can be stimulated in both laminar and turbulent flow when shear stress values exceed approximately 0.1 N m-2. Computational studies of an idealized hydrodynamic representation of a dolphin (modeled as a 6:1 ellipsoid), gliding at a speed of 2 m s-1, predicted suprathreshold surface shear stress values everywhere on the model, regardless of whether the boundary layer flow was laminar or turbulent. Laboratory flow visualization of a sphere demonstrated that the intensity of bioluminescence decreased with increasing flow speed due to the thinning of the boundary layer, while flow separation caused a dramatic increase in intensity due to the significantly greater volume of stimulating flow in the wake. Intensified video recordings of dolphins gliding at speeds of approximately 2 m s-1 confirmed that brilliant displays of bioluminescence occurred on the body of the dolphin. The distribution and intensity of bioluminescence suggest that the flow remained attached over most of the body. A conspicuous lack of bioluminescence was often observed on the dolphin rostrum and melon and on the leading edge of the dorsal and pectoral fins, where the boundary layer is thought to be thinnest. To differentiate between effects related to the thickness of the stimulatory boundary layer and those due to the latency of the bioluminescence response and the upstream depletion of bioluminescence, laboratory and dolphin studies of forced separation and laminar-to-turbulent transition were conducted. The observed pattern of stimulated bioluminescence is consistent with the hypothesis that bioluminescent intensity is directly related to the thickness of the boundary layer.

Compressor Wake/Leading-Edge Interactions at Off Design Incidences

2008 ◽  
Author(s):  
Andrew P. S. Wheeler ◽  
Robert J. Miller
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Field ◽  
Leading Edge ◽  
Flow Coefficient ◽  
Surface Shear Stress ◽  
Momentum Thickness ◽  
Surface Shear ◽  
Time Resolved ◽  
Edge Flow

In this paper, the effects of wake/leading-edge interactions were studied at off-design conditions. Measurements were performed on the stator-blade suction surface at midspan. The leading-edge flow-field was investigated using hotwire micro-traverses, hotfilm surface shear-stress sensors and pressure micro-tappings. The trailing-edge flow-field was investigated using hotwire boundary-layer traverses. Unsteady CFD calculations were also performed to aid the interpretation of the results. At low flow coefficients, the time-averaged momentum thickness of the leading-edge boundary layer was found to rise as the flow coefficient was reduced. The time-resolved momentum-thickness rose due to the interaction of the incoming rotor wake. As the flow coefficient was reduced, the incoming wakes increased in pitch-wise extent, velocity deficit and turbulence intensity. This increased both the time-resolved rise in the momentum thickness and the turbulent spot production within the wake affected boundary-layer. Close to stall, a drop in the leading-edge momentum thickness was observed in-between wake events. This was associated with the formation of a leading-edge separation bubble in-between wake events. The wake interaction with the bubble gave rise to a shedding phenomenon, which produced large length scale disturbances in the surface shear stress.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

scholarly journals Simultaneous Free Convection and Heat Generation on a Horizontal Isothermal Circular Cylinder

2015 ◽  
Vol 9 (12) ◽  
pp. 21 ◽  
Author(s):  
Sajjad Sedighi ◽  
Mohammad Saeed Aghighi
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Generation ◽  
Heat Rate ◽  
Horizontal Cylinder ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Boundary Layer Equations ◽  
Linear Partial Differential Equations ◽  
Dimensional Boundary

<p class="zhengwen"><span lang="EN-GB">The linear boundary layer of the free flow around a circular horizontal cylinder with uniform surface temperature in the presence of heat generation was studied. Upon obtaining the non-dimensional boundary layer equations, the Runge-Kutta series method was used to solve the non-linear partial differential equations numerically. The surface shear stress results and surface heat rate were subsequently obtained in terms of the internal shell friction and the local Nusselt number respectively. The following heat generation parameters (C) were selected:  0.0, 0.2, 0.5, 0.8, and 1.0. The following results were obtained: 1) increasing C led to a corresponding increase u, v , VM , and θ , 2) Increasing i led to a corresponding increase in u, v , and VM, and 3) increasing C increased velocity variations and, naturally, the value of Cf, and 4) increasing i from i=0 to i=100 led to a decrease in the Nusselt number (Nu). </span></p>

The Effects of Localized Blade Endwall Suction on Secondary Flows and Heat Transfer

2010 ◽  
Author(s):  
Rebecca Hollis ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
High Surface ◽  
Surface Heat ◽  
Secondary Flows ◽  
Surface Shear Stress ◽  
Mean Velocity ◽  
Surface Shear ◽  
Surface Heat Transfer ◽  
High Heat Transfer

Two methods of flow control were designed to mitigate the effects of the horseshoe vortex structure (HV) at an airfoil/endwall junction. An experimental study was conducted to quantify the effects of localized boundary layer removal on surface heat transfer in a low-speed wind tunnel. A transient infrared technique was used to measure the convective heat transfer values along the surface surrounding the juncture. Particle image velocimetry was used to collect the time-mean velocity vectors of the flow field across three planes of interest. Boundary layer suction was applied through a thin slot cut into the leading edge of the airfoil at two locations. The first, referred to as Method 1, was directly along the endwall, the second, Method 2, was located at a height ∼1/3 of the approaching boundary layer height. Five suction rates were tested; 0%, 6.5%, 11%, 15% and 20% of the approaching boundary layer mass flow was removed at a constant rate. Both methods reduced the effects of the HV with increasing suction on the symmetry, 0.5-D and 1-D planes. Method 2 yielded a greater reduction in surface heat transfer but Method 1 outperformed Method 2 aerodynamically by completely removing the HV structure when 11% suction was applied. This method however produced other adverse effects such as high surface shear stress and localized areas of high heat transfer near the slot edges at high suction rates.

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