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.

scholarly journals Boundary-layer receptivity for a parabolic leading edge. Part 2. The small-Strouhal-number limit

1997 ◽  
Vol 353 ◽  
pp. 205-220 ◽  
Author(s):  
P. W. HAMMERTON ◽  
E. J. KERSCHEN
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Free Stream ◽  
Leading Edge ◽  
Numerical Results ◽  
Two Dimensional ◽  
Mean Flow ◽  
The Mean

In Hammerton & Kerschen (1996), the effect of the nose radius of a body on boundary-layer receptivity was analysed for the case of a symmetric mean flow past a two-dimensional body with a parabolic leading edge. A low-Mach-number two-dimensional flow was considered. The radius of curvature of the leading edge, rn, enters the theory through a Strouhal number, S=ωrn/U, where ω is the frequency of the unsteady free-stream disturbance and U is the mean flow speed. Numerical results revealed that the variation of receptivity for small S was very different for free-stream acoustic waves propagating parallel to the mean flow and those free-stream waves propagating at an angle to the mean flow. In this paper the small-S asymptotic theory is presented. For free-stream acoustic waves propagating parallel to the symmetric mean flow, the receptivity is found to vary linearly with S, giving a small increase in the amplitude of the receptivity coefficient for small S compared to the flat-plate value. In contrast, for oblique free-stream acoustic waves, the receptivity varies with S1/2, leading to a sharp decrease in the amplitude of the receptivity coefficient relative to the flat-plate value. Comparison of the asymptotic theory with numerical results obtained in the earlier paper confirms the asymptotic results but reveals that the numerical results diverge from the asymptotic result for unexpectedly small values of S.

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.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

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.

Some Boundary Layer Measurements on a Slender Wing at Supersonic Speeds

1963 ◽  
Vol 67 (629) ◽  
pp. 291-295
Author(s):  
R. T. Griffiths
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Aspect Ratio ◽  
Flat Plate ◽  
Layer Thickness ◽  
Incompressible Flow ◽  
Boundary Layer Thickness ◽  
Static Pressure ◽  
Leading Edge ◽  
Slender Wing

SummaryBoundary layer measurements have been made at four positions on a slender gothic wing of aspect ratio 0·75. Test's were made over a range of incidence at M=1·42 and 1·82. With transition fixed by roughness near the leading edge the boundary layer thickness varied little with small positive or negative incidence but was reduced at larger incidences, this being most marked at positive incidence for positions nearest the leading edge due to the influence of the wing vortex. With the exception of positions in the vicinity of the vortex, a good estimate of the boundary layer thickness was given by the theory for incompressible flow over a flat plate and an excellent estimate of the variation of local static pressure and Mach number with incidence was given by not-so-slender wing theory.

Boundary layer receptivity to free-stream sound on elliptic leading edges of flat plates

2001 ◽  
Vol 429 ◽  
pp. 1-21 ◽  
Author(s):  
JUAN B. V. WANDERLEY ◽  
THOMAS C. CORKE
Keyword(s):  
Flat Plate ◽  
Acoustic Waves ◽  
Free Stream ◽  
Stokes Equations ◽  
Leading Edge ◽  
Neutral Curve ◽  
Curvilinear Coordinates ◽  
Flat Plates ◽  
Linear Superposition ◽  
Leading Edges

The leading-edge receptivity to acoustic waves of two-dimensional bodies is investigated using a spatial solution of the Navier–Stokes equations in vorticity/stream function form in general curvilinear coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998), in which the solution for the basic flow and the linearized perturbation flow are solved separately. The initial motivation for the work comes from past physical experiments for flat plates with elliptic leading edges, which indicated narrow frequency bands of higher neutral-curve Branch I receptivity. We investigate the same conditions in our simulations, as well as on a parabolic leading edge. The results document the importance of the leading edge, junction between the ellipse and flat plate, and pressure gradient to the receptivity coefficient at Branch I. Comparisons to the past experiments and other numerical simulations showed the influence of the elliptic leading-edge/flat-plate joint as an additional site of receptivity which, along with the leading edge, provides a wavelength selection mechanism which favours certain frequencies through linear superposition.

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.

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