Laminar flow over a small hump on a flat plate

1973 ◽  
Vol 57 (4) ◽  
pp. 803-824 ◽  
Author(s):  
F. T. Smith
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Leading Edge ◽  
Main Stream ◽  
Pressure Force ◽  
Boundary Layer Flows ◽  
Local Flow ◽  
Wide Range ◽  
Layer Flow

A boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge. The description of the boundary-layer flow, based upon a triple-deck structure, shows how the presence of the hump generates an interaction between the inviscid region just outside the layer and the viscous region near the hump. The pressure force dominant in the boundary layer and the connexion of the local flow with the main stream develop together and are self-perpetuating, and both remain of primary significance for a wide range of hump sizes, even for a hump buried well inside the boundary layer. By consideration of the limiting cases of very small and very large humps, a consistent account of the nature of the disturbances due to the various sizes of hump is produced. The forces and couples on the hump are also evaluated.

The three-dimensional laminar boundary layer on a flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 587-598 ◽  
Author(s):  
L. Sowerby
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Leading Edge ◽  
Main Stream ◽  
Dimensional Parameter ◽  
Stress Components ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Limiting Streamlines

A series expansion is derived for the three-dimensional boundary-layer flow over a flat plate, arising from a general main-stream flow over the plate. The series involved are calculated as far as terms of order ξ2, where ξ is a non-dimensional parameter defining distance measured from the leading edge of the plate. The results are applied to an example in which the main stream arises from the disturbance of a uniform stream by a circular cylinder mounted downstream from the leading edge of the plate, the axis of the cylinder being normal to the plate. Calculations are made for shear stress components on the plate, and for the deviation of direction of the limiting streamlines from those in the main stream.

Keel Design for Low Viscous Drag

1987 ◽  
Author(s):  
Clifford J. Obara ◽  
C. P. van Dam
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Viscous Drag ◽  
Hydrodynamic Characteristics ◽  
Sweep Angle ◽  
Layer Transition ◽  
Layer Flow

In this paper, foil and planform parameters which govern the level of viscous drag produced by the keel of a sailing yacht are discussed. It is shown that the application of laminar boundary-Layer flow offers great potential for increased boat speed resulting from the reduction in viscous drag. Three foil shapes have been designed and it is shown that their hydro­dynamic characteristics are very much dependent on location and mode of boundary-Layer transition. The planform parameter which strongly affects the capabilities of the keel to achieve laminar flow is lea ding-edge sweep angle. The two significant phenomena related to keel sweep angle which can cause premature transition of the laminar boundary layer are crossflow instability and turbulent contamination of the leading-edge attachment line. These flow phenomena and methods to control them are discussed in detail. The remaining factors that affect the maintainability of laminar flow include surface roughness, surface waviness, and freestream turbulence. Recommended limits for these factors are given to insure achievability of laminar flow on the keel. In addition, the application of a simple trailing-edge flap to improve the hydrodynamic characteristics of a foil at moderate-to-high leeway angles is studied.

The Evolution of Streamwise Counter-Rotating Vortices in Flat Plate Boundary Layer With Leading Edge Pattern

2015 ◽  
Author(s):  
Seyed Mohammad Hasheminejad ◽  
Hatsari Mitsudharmadi ◽  
S. H. Winoto ◽  
Kim Boon Lua ◽  
Hong Tong Low
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Plate Boundary ◽  
Leading Edge ◽  
Streamwise Vortex ◽  
Streamwise Velocity ◽  
Stream Velocity ◽  
Hot Wire ◽  
Layer Flow ◽  
Different Characteristics

The evolution of streamwise counter-rotating vortices induced by different leading edge patterns is investigated quantitatively using hot-wire anemometer. A notched and triangular leading edge with the same wavelength and amplitude were designed to induce streamwise vortices over a flat plate at Reynolds number (based on the wavelength of the leading edge patterns) of 3080 corresponding to free-stream velocity of 3 m/s. The streamwise velocity at different streamwise locations collected and analyzed using a single wire probe hot-wire anemometer showed reveal different characteristics of boundary layer flow due to the presence of these two leading edge patterns. The major difference is the appearance of an additional streamwise vortex between the troughs of the notched pattern. Such vortices increase the mixing effect in the boundary layer as well as the velocity profile.

scholarly journals Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat plate

1988 ◽  
Vol 186 ◽  
pp. 223-241 ◽  
Author(s):  
B. Y. Wang ◽  
I. I. Glass
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Expansion Method ◽  
Boundary Layer Flows ◽  
Two Phase ◽  
Displacement Thickness ◽  
Slip Region ◽  
Two Phases

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Numerical Simulation of Laminar Boundary Layer Flow Over a Horizontal Flat Plate in External Incompressible Viscous Fluid

2021 ◽  
Author(s):  
Ali Belhocine ◽  
Nadica Stojanovic ◽  
Oday Ibraheem Abdullah
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Solution Procedure ◽  
Dimensionless Temperature ◽  
Plane Plate ◽  
Fluid Properties ◽  
Layer Flow

In this paper, steady laminar boundary layer flow of a Newtonian fluid over a flat plate in a uniform free stream was investigated numerically when the surface plate is heated by forced convection from the hot fluid. This flow is a good model of many situations involving flow over fins that are relatively widely spaced. All the solutions given here were with constant fluid properties and negligible viscous dissipation for two-dimensional, steady, incompressible laminar flow with zero pressure gradient. The similarity solution has shown its efficiency here to transform the governing equations of the thermal boundary layer into a nonlinear, third-order ordinary differential equation and solved numerically by using 4th-order Runge-Kutta method which in turn was programmed in FORTRAN language. The dimensionless temperature, velocity, and all boundary layer functions profiles were obtained and plotted in figures for different parameters entering into the problem. Several results of best approximations and expressions of important correlations relating to heat transfer rates were drawn in this study of which Prandtl’s number to the plate for physical interest was also discussed across the tables. The same case of solution procedure was made for a plane plate subjected to other thermal boundary conditions in a laminar flow. Finally, for the validation of the treated numerical model, the results obtained are in good agreement with those of the specialized literature, and comparison with available results in certain cases is excellent.

Keel Design for Low Viscous Drag

1989 ◽  
Vol 33 (02) ◽  
pp. 145-155
Author(s):  
Clifford J. Obara ◽  
C. P. van Dam
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Viscous Drag ◽  
Hydrodynamic Characteristics ◽  
Sweep Angle ◽  
Layer Transition ◽  
Layer Flow

Foil and planform parameters which govern the level of viscous drag produced by the keel of a sailing yacht are discussed. It is shown that the application of laminar boundary-layer flow offers great potential for increased boat speed resulting from the reduction in viscous drag. Three foil shapes have been designed and it is shown that their hydrodynamic characteristics are very much dependent on location and mode of boundary-layer transition. The planform parameter which strongly affects the capabilities of the keel to achieve laminar flow is leading-edge sweep angle. The two significant phenomena related to keel sweep angle which can cause premature transition of the laminar boundary layer are crossflow instability and turbulent contamination of the leading-edge attachment line. These flow phenomena and methods to control them are discussed in detail. The remaining factors that affect the maintainability of laminar flow include surface roughness, surface waviness, and freestream turbulence. Recommended limits for these factors are given to insure achievability of laminar flow on the keel. In addition, the application of a simple trailing-edge flap to improve the hydrodynamic characteristics of a foil at moderate-to-high leeway angles is studied.

Receptivity mechanisms in three-dimensional boundary-layer flows

2009 ◽  
Vol 618 ◽  
pp. 209-241 ◽  
Author(s):  
LARS-UVE SCHRADER ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Three Dimensional ◽  
Leading Edge ◽  
Nonlinear Process ◽  
Transition To Turbulence ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
Dimensional Boundary ◽  
Layer Flow

Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.

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