Koopman spectral analysis of separated flow over a finite-thickness flat plate with elliptical leading edge

2011 ◽  
Author(s):  
Jonathan Tu ◽  
Clarence Rowley ◽  
Ehsan Aram ◽  
Rajat Mittal
Keyword(s):  
Spectral Analysis ◽  
Flat Plate ◽  
Finite Thickness ◽  
Separated Flow ◽  
Leading Edge

Turbulence Measurements in a Separated and Reattached Flow Over a Blunt Flat Plate

1978 ◽  
Vol 100 (2) ◽  
pp. 224-228 ◽  
Author(s):  
Terukazu Ota ◽  
Masashi Narita
Keyword(s):  
Kinetic Energy ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Finite Thickness ◽  
Leading Edge ◽  
Turbulent Shear ◽  
Turbulence Measurements ◽  
Turbulent Shear Stress ◽  
Separated And Reattached Flow ◽  
Blunt Leading Edge

Turbulence measurements were made in the separated, reattached, and redeveloped regions of a two-dimensional incompressible air flow over a flat plate with finite thickness and blunt leading edge. In the boundary layer downstream of the reattachment point, Prandtl’s mixing length and turbulent kinetic energy length scale are estimated, and the correlation between the turbulent shear stress and the turbulent kinetic energy is described.

A theoretical investigation of enhanced lift in the presence of thin aerofoil stall

1999 ◽  
Vol 103 (1023) ◽  
pp. 237-244 ◽  
Author(s):  
W. W. H. Yeung ◽  
G. V. Parkinson
Keyword(s):  
Flat Plate ◽  
Flow Model ◽  
Separated Flow ◽  
Leading Edge ◽  
Geometrical Parameters ◽  
Separation Flow ◽  
Attached Flow ◽  
Positive Angle ◽  
Edge Separation ◽  
Potential Flow Model

Abstract A theoretical study is presented for the investigation of a potential-flow model for enhancing lift over a flat-plate aerofoil experiencing thin aerofoil stall. Rather than suppressing the leading-edge separation, flow is assumed to separate tangentially at the leading edge and made to reattach smoothly at the tip of a forward-facing fence joining the plate tangentially on its upper surface to avoid any unnecessary stagnated flow. The length of the fence and its location from the leading edge form two geometrical parameters. At any positive angle of attack, the resulting bounding streamline emanating from the leading edge and terminating at the tip of the fence is simulated by using suitable mathematical singularities subject to boundary conditions such as attaining a finite velocity at each critical point of the conformal mapping involved, and the condition of finite pressure gradient at reattachment, when applicable. Computational results from varying these two geometrical parameters indicate that the lift from each model is enhanced, as compared with the attached flow model around a simple flat plate and the original separated flow model by Kirchhoff.

On the steady separated flow around an inclined flat plate

1997 ◽  
Vol 333 ◽  
pp. 403-413 ◽  
Author(s):  
W. W. H. YEUNG ◽  
G. V. PARKINSON
Keyword(s):  
Flat Plate ◽  
Bluff Body ◽  
Separation Bubble ◽  
Separated Flow ◽  
Leading Edge ◽  
Source Model ◽  
Pressure Distributions ◽  
Wide Range ◽  
Trailing Edges ◽  
Edge Separation

An inviscid analytic model is proposed for the steady separated flow around an inclined flat plate. With the plate normal to the stream, the model reduces to the wake-source model of Parkinson & Jandali originally developed for flow external to a symmetrical two-dimensional bluff body and its wake. At any other inclination, the Kutta condition is satisfied at both leading and trailing edges of the plate, and, in the limit that the angle of attack approaches zero, classical airfoil theory is recovered. A boundary condition is formulated based on some experimental results of Abernathy, but no additional empirical information is required. The predicted pressure distributions on the wetted surface for a wide range of angle attack are found to be in good agreement with experimental data, especially at smaller angles of attack. An extension to include a leading-edge separation bubble is explored and results are satisfactory.

scholarly journals Flow Past a Flat Plate With a Vortex/Sink Combination

1996 ◽  
Vol 63 (2) ◽  
pp. 543-550 ◽  
Author(s):  
N. J. Mourtos ◽  
M. Brooks
Keyword(s):  
Flat Plate ◽  
Current Model ◽  
Angle Of Attack ◽  
Separated Flow ◽  
Leading Edge ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Attached Flow

This paper presents a potential flow model for the leading edge vortex over a two-dimensional flat plate at an angle of attack. The paper is an extension of a model by Saffman and Sheffield (1977). A sink has been added in this model in an effort to satisfy the Kutta condition at both the leading edge and the trailing edge of the plate. The introduction of the sink was inspired by the fact that most steady vortices in nature appear in combination with a flow feature which can be interpreted as a sink at their cores when the flow is analyzed in a two-dimensional observation plane. As in the Saffman and Sheffield model, the presence of a vortex results in increased lift; however, in the current model a unique vortex/sink position is found at each angle of attack. A comparison has also been made between the lift and the drag of this model and the corresponding results for two classical solutions of flow over a flat plate: (a) the fully attached flow with the Kutta condition satisfied at the trailing edge only and (b) the Helmholtz solution of fully separated flow.

Acoustic receptivity simulations of flow past a flat plate with elliptic leading edge

2016 ◽  
Vol 800 ◽  
Author(s):  
Nima Shahriari ◽  
Daniel J. Bodony ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Numerical Methods ◽  
Numerical Simulations ◽  
Flat Plate ◽  
Incompressible Flow ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Finite Thickness ◽  
Leading Edge ◽  
High Accuracy ◽  
Order Of Magnitude

We present results of numerical simulations of leading-edge acoustic receptivity for acoustic waves impinging on the leading edge of a finite-thickness flat plate. We use both compressible and incompressible flow solvers fitted with high-order high-accuracy numerical methods and independent methods of estimating the receptivity coefficient. The results show that the level of acoustic receptivity in the existing literature appears to be one order of magnitude too high. Our review of previous numerical simulations and experiments clearly identifies some contradictory trends. In the limit of an infinitely thin flat plate, our results are consistent with asymptotic theory and numerical simulations.

On the propulsion efficiency of swimming flexible hydrofoils of finite thickness

1968 ◽  
Vol 32 (1) ◽  
pp. 29-53 ◽  
Author(s):  
J. P. Uldrick
Keyword(s):  
Kinetic Energy ◽  
Flat Plate ◽  
Finite Thickness ◽  
Leading Edge ◽  
The Body ◽  
Suction Force ◽  
Inviscid Incompressible Fluid ◽  
Reduced Frequency ◽  
Non Linear ◽  
Order Of Magnitude

This paper presents some recent theoretical results on the energy exchange between a swimming flexible two-dimensional hydrofoil of finite profile thickness and the inviscid incompressible fluid in which the body swims. The rate at which kinetic energy is transferred to the fluid by the undulating hydrofoil, the power required to maintain the prescribed motion, and the resulting power available for propulsion are calculated in terms of the thickness to chord ratio and the displacement and rate of displacement of the hydrofoil. With a small unsteady perturbation theory, the analysis is decomposed to show separately the effects of the circulatory and non-circulatory flows, both depending on the first-order terms of the unsteady perturbation velocity components. In addition, an analysis is presented showing the effect of the non-linear unsteady pressure distribution on the surface of the hydrofoil. Contrary to what might be expected, this latter effect is of the same order of magnitude for a thick rounded-nose profile as for the flat plate where the effect is concentrated at the sharp leading edge and is related to the so-called suction force. However, except for small values of the reduced frequency, the non-linear contribution is negligible in comparison with the linear contribution.New functions associated with the retarded flow in the wake are introduced and special techniques for their solution are presented, these being related to Theodorsen's function of unsteady airfoil theory for the special case of the undulating flat plate.The numerical results reveal that the kinetic energy imparted to the fluid, the power required to maintain the motion, and the resulting propulsive power, follow closely those of an infinitesimal model for small values of the reduced frequency of oscillation, but diverge somewhat from the classical thin plate analysis for large reduced frequencies. Of particular interest is the fact that a very large percentage of the power required to maintain the motion is used in the generation of the wake, whereas a very small percentage of the power available for propulsion comes from the wake. This indicates that, if some mechanism could be devised to control the wake, very high swimming efficiencies could be attained. Fish, in all probability, have been succeeding in doing this for millions of years.

Turbulent Transfer of Momentum and Heat in a Separated and Reattached Flow over a Blunt Flat Plate

1980 ◽  
Vol 102 (4) ◽  
pp. 749-754 ◽  
Author(s):  
Terukazu Ota ◽  
Nobuhiko Kon
Keyword(s):  
Heat Flux ◽  
Shear Stress ◽  
Flat Plate ◽  
Finite Thickness ◽  
Leading Edge ◽  
Turbulent Heat Flux ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Turbulent Shear Stress ◽  
Separated And Reattached Flow

Turbulent shear stress and heat flux were measured with a hot-wire anemometer in the separated, reattached, and redeveloped regions of a two-dimensional incompressible air flow over a flat plate of finite thickness having blunt leading edge. The characteristic features of the turbulent heat flux are found to be nearly equal to those of the turbulent shear stress in the separated and reattached flow regions. However, in the turbulent boundary layer downstream from the reattachment point, the development of turbulent heat flux appears to be much quicker than that of turbulent shear stress. Eddy diffusivities of momentum and heat are evaluated and then the turbulent Prandtl number is estimated in the thermal layer downstream of reattachment. These results are compared with the available previous data.

Boundary layer receptivity to free-stream sound on parabolic bodies

1998 ◽  
Vol 368 ◽  
pp. 1-26 ◽  
Author(s):  
OSAMAH M. HADDAD ◽  
THOMAS C. CORKE
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Flow ◽  
Finite Thickness ◽  
Leading Edge ◽  
The Body ◽  
Nonlinear Flow ◽  
Radius Of Curvature ◽  
Nose Radius ◽  
Unsteady Stokes Flow

We use a numerical approach to study the receptivity of the boundary layer flow over a slender body with a leading edge of finite radius of curvature to small streamwise velocity fluctuations of a given frequency. The body of interest is a parabola in order to exclude jumps in curvature, which are known sites of receptivity and which occur on elliptic leading edges matched to finite-thickness at plates. The infinitesimally thin flat plate is the limiting solution for the parabola as the nose radius of curvature goes to zero. The formulation of the problem allows the two-dimensional unsteady Navier–Stokes equations in stream function and vorticity form to be converted to two steady systems of equations describing the basic (nonlinear) flow and the perturbation (linear) flow. The results for the basic flow are in excellent agreement with those in the literature. As expected, the perturbation flow was found to be a combination of an unsteady Stokes flow and Orr–Sommerfeld modes. To separate these, the unsteady Stokes flow was solved separately and subtracted from the total perturbation flow. We found agreement with the streamwise wavelengths and locations of Branches I and II of the linear stability neutral growth curve for Tollmien–Schlichting waves. The results showed an increase in the leading-edge receptivity with decreasing nose radius, with the maximum occurring for an infinitely sharp flat plate. The receptivity coefficient was also found to increase with angle of attack. These results were in qualitative agreement with the asymptotic analysis of Hammerton & Kerschen (1992). Good quantitative agreement was also found with the recent numerical results of Fuciarelli (1997), and the experimental results of Saric, Wei & Rasmussen (1994).

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