Sound diffraction at a trailing edge

1981 ◽  
Vol 108 ◽  
pp. 443-460 ◽  
Author(s):  
S. W. Rienstra
Keyword(s):  
Vortex Shedding ◽  
Pulse Wave ◽  
Layer Structure ◽  
Harmonic Wave ◽  
Sound Field ◽  
Edge Condition ◽  
Trailing Edge ◽  
Kutta Condition ◽  
High Reynolds ◽  
Sound Diffraction

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

Sound generation by a supersonic aerofoil cutting through a steady jet flow

1990 ◽  
Vol 216 ◽  
pp. 193-212 ◽  
Author(s):  
Y. P. Guo
Keyword(s):  
Vortex Shedding ◽  
Sound Field ◽  
Leading Edge ◽  
Jet Flow ◽  
Generation Process ◽  
Sound Waves ◽  
Leading Order ◽  
Sound Generation ◽  
Trailing Edge ◽  
Kutta Condition

This paper examines the sound generation process when a supersonic aerofoil cuts through a steady jet flow. It is shown that the principal sound is generated by the leading edge of the aerofoil when it interacts with the streaming jet. To the leading order in terms of the jet velocity, no trailing-edge sound is generated. This is not the result of the cancellation of a trailing-edge sound by that from vortex shedding through the imposition of the Kutta condition. Instead, the null acoustic radiation from the trailing edge is entirely because, to the leading order, there is no interaction between the trailing edge and the jet. The effect of the trailing edge is to diffract sound waves generated by the leading edge. It is shown that the diffracted field (as well as the incident field) is regular at the trailing edge and the issue of satisfying the Kutta condition does not arise during the diffraction process. Thus, there is no extra vortex shedding from the trailing edge owing to its interaction with the flow, apart from those resulting from the discontinuity across the aerofoil, generated by the flow-leading edge interaction. This is in sharp contrast to the case of subsonic aerofoils where the removal of the singularity in the diffracted field at the trailing edge through the imposition of the Kutta condition results in vortex shedding from the sharp edge and energy exchange between the sound field and the vortical wake.

The influence of vortex shedding on the generation of sound by convected turbulence

1976 ◽  
Vol 76 (4) ◽  
pp. 711-740 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Vortex Shedding ◽  
Infinite Plate ◽  
Vortex Sheet ◽  
Realistic Model ◽  
Diffraction Field ◽  
Mean Flow ◽  
Turbulent Eddy ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Mathematical Problems

This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

Vorticity and Kutta Condition for Unsteady Multienergy Flows

1969 ◽  
Vol 36 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. P. Giesing
Keyword(s):  
Vortex Shedding ◽  
Pressure Difference ◽  
Total Pressure ◽  
Vortex Sheet ◽  
Rate Of Change ◽  
The Other ◽  
Numerical Calculations ◽  
Time Rate ◽  
Trailing Edge ◽  
Kutta Condition

The dynamical conditions for vortex shedding in unsteady multienergy flows are given: It is shown that the vorticity shed is composed of an unsteady part, which is proportional to the time rate of change of the circulation, and a steady part, which is proportional to the total-pressure difference across the vortex sheet. The kinematics of vortex shedding are also investigated. It is determined that the vortex sheet is shed parallel to one side of the trailing edge or the other depending on the sense of the shed vorticity. It is further determined that the shedding velocity is equal to one half of the strength of the vorticity at the trailing edge (except for trailing-edge angles of zero). Numerical calculations are presented to illustrate the results.

Experimental Investigation of the Vortex Shedding in the Wake of Oblique and Blunt Trailing Edge Hydrofoils Using PIV-POD Method

2010 ◽  
Author(s):  
Amirreza Zobeiri ◽  
Philippe Ausoni ◽  
Franc¸ois Avellan ◽  
Mohamed Farhat
Keyword(s):  
Experimental Investigation ◽  
Phase Shift ◽  
Vortex Shedding ◽  
High Speed ◽  
Flow Induced Vibration ◽  
Trailing Edge ◽  
Blunt Trailing Edge ◽  
Vortex Induced Vibrations ◽  
Image Velocimetry ◽  
High Reynolds

This paper presents an experimental investigation of the vortex shedding in the wake of blunt and oblique trailing edge hydrofoils at high Reynolds number, Re = 5 105 − 2.9 106. The velocity field in the wake is surveyed with the help of Particle-Image-Velocimetry, PIV, using Proper-Orthogonal-Decomposition, POD. Besides, flow induced vibration measurements and high-speed visualization are performed. The high-speed visualization clearly shows that the oblique trailing edge leads to a spatial phase shift of the upper and lower vortices at their generation stage, resulting their partial cancellation. For the oblique trailing edge geometry and in comparison with the blunt one, the vortex-induced vibrations are significantly reduced. Moreover, PIV data reveals a lower vorticity for the oblique trailing edge. The phase shift between upper and lower vortices, introduced by the oblique truncation of the trailing edge, is found to vanish in the far wake, where alternate shedding is recovered as observed with the blunt trailing edge. The phase shift generated by the oblique trailing edge and the resulting partial cancellation of the vortices is believed to be the main reason of the vibration reduction.

Emendation of the Brown & Michael equation, with application to sound generation by vortex motion near a half-plane

1996 ◽  
Vol 329 ◽  
pp. 89-101 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Half Plane ◽  
Vortex Shedding ◽  
Vortex Motion ◽  
Flow Characteristics ◽  
Surface Force ◽  
Two Dimensions ◽  
Wake Flow ◽  
Kutta Condition ◽  
Radiated Sound ◽  
High Reynolds

A reappraisal is made of the Brown & Michael (1954, 1955) equation that is widely used to model high-Reynolds-number vortex shedding in two dimensions by rectilinear vortices of time-dependent circulations. It is concluded that the equation introduces an unbalanced and unacceptable surface force that can significantly influence predicted flow characteristics. A corrected equation is derived which removes this force, and is applied to determine the sound generated at low Mach numbers when a line vortex translates around the edge of a rigid half-plane. The solution of this problem in the absence of vortex shedding (Crighton 1972) is extended by permitting shedding to occur at the edge in accordance with the unsteady Kutta condition. The shed vorticity is assumed to roll-up into a concentrated core whose motion is calculated by both the emended and original Brown & Michael equations. The two models exhibit large qualitative differences in the predicted wake flow near the edge; both predict significant reductions in the radiated sound, but the reduction is smaller by about 4 dB for the emended Brown & Michael equation.

Some modeling issues on trailing-edge vortex shedding

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 787-793
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Vortex Shedding ◽  
Trailing Edge ◽  
Edge Vortex

Viscous tails in Hele-Shaw flow

1971 ◽  
Vol 46 (3) ◽  
pp. 569-576
Author(s):  
C. J. Wood
Keyword(s):  
Reynolds Number ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Quantitative Discrepancy ◽  
Edge Flow ◽  
Hele Shaw Cell

An experiment has been performed, using pulsed dye injection on an aerofoil in a Hele-Shaw cell. The purpose was to observe the form of the trailing-edge flow when the Reynolds number was high enough to permit separation and the initiation of a Kutta condition. The experiment provides a successful confirmation of the existence of a ‘viscous tail’ as predicted by Buckmaster (1970) although there is an unexplained quantitative discrepancy.

Influence of Trailing-Edge Geometry on Hydraulic-Turbine-Blade Vibration Resulting From Vortex Excitation

1960 ◽  
Vol 82 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Gunnar Heskestad ◽  
D. R. Olberts
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Vortex Shedding ◽  
Hydraulic Turbine ◽  
Trailing Edge ◽  
Blade Vibration ◽  
Edge Geometry ◽  
Blade Thickness ◽  
Vortex Induced Vibrations ◽  
Approach Velocity

A study was made to determine effects of trailing-edge geometry on the vortex-induced vibrations of a model blade designed to simulate the conditions at the trailing edge of a hydraulic-turbine blade. For the type of trailing-edge flow encountered, characterized by a thick boundary layer relative to the blade thickness, the vortex-shedding frequency could not be represented by any modification of the Strouhal formula. The amplitude of the induced vibrations increased with the strength of a vortex in the von Karman vortex street of the wake; one exception was provided by a grooved edge, which is discussed in some detail. For a particular approach velocity, the vortex strength is primarily a function of the ratio of distance between separation points to boundary-layer thickness, the degree of “shielding” between regions of vortex growth, and frequency of vortex shedding.

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