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.

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.

Passive pitching of splitters in the trailing edge of elliptic cylinders

2017 ◽  
Vol 826 ◽  
pp. 363-375 ◽  
Author(s):  
Y. Jin ◽  
L. P. Chamorro
Keyword(s):  
Vortex Shedding ◽  
Semimajor Axis ◽  
Wake Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Trailing Edge ◽  
Flow Measurements ◽  
High Background ◽  
Aspect Ratios ◽  
The Mean

The distinctive pitching of hinged splitters in the trailing edge of elliptic cylinders was experimentally studied at various angles of attack ($AoA$) of the cylinder, Reynolds numbers, splitter lengths, aspect ratios ($AR$) of the cylinder and freestream turbulence levels. High-resolution telemetry and hotwire anemometry were used to characterize and gain insight on the dynamics of splitters and wake flow. Results show that the motions of the splitters contain various dominating modes, e.g. $f_{p}$ and $f_{v}$, which are induced by the mean flow and wake dynamics. High background turbulence dampens the coherence of the regular vortex shedding leading to negligible $f_{v}$. For a sufficiently long splitter, namely twice the semimajor axis of the cylinder, dual vortex shedding mode exists close to the leading and trailing edges of the splitter. In general, the splitters oscillate around an equilibrium position nearly parallel to the mean direction of the flow; however, a skewed equilibrium is also possible with a strong recirculation region. This is the case with cylinders of low $AR$ and high $AoA$, where higher lift and drag occurs. Flow measurements at various transverse locations within the wake of the cylinder–splitter system indicate that the signature of the low-frequency splitter pitching is shifted in the wake in the cases with non-zero $AoA$ of the cylinder. Although the splitter pitching exhibits two dominant vortex shedding modes in various configurations, only the higher frequency is transmitted to the wake.

The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations

1981 ◽  
Vol 109 ◽  
pp. 125-146 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Leading Edge ◽  
Vortex Sheet ◽  
Mean Flow ◽  
Kutta Condition ◽  
Sustained Oscillations ◽  
Linearized Theory ◽  
Flow Through ◽  
The Mean ◽  
Theoretical Results ◽  
Disturbed Motion

This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.

Radiation properties of the semi-infinite vortex sheet

1972 ◽  
Vol 330 (1581) ◽  
pp. 185-198 ◽  
Keyword(s):  
Acoustic Radiation ◽  
Near Field ◽  
Infinite Plate ◽  
Sound Field ◽  
Vortex Sheet ◽  
Field Application ◽  
Kutta Condition ◽  
Radiation Properties ◽  
Loading Effects ◽  
Dependent Flow

An exact calculation is given of the acoustic radiation from a time dependent flow coupled to an inhomogeneous solid surface. Specifically, the flow consists of a vortex sheet leaving a semi-infinite plate and undergoing a two-dimensional spatial Kelvin-Helmholtz instability. In the absence of the plate, such an instability mode of the vortex sheet generates no sound. In the presence of a rigid plate, it is found that the intensity-directivity law is I ~ U 4 sin 2 1/2 θ , with θ measured from the downstream direction. If the plate is compliant and fluid loading effects high, the radiation is weaker, with I ~ U 5 sin 2 θ . These results agree completely with those predicted from general theories of the scattering of the near-field of point quadrupoles by large wedge-shaped surfaces (Ffowcs Williams & Hall 1970; Crighton & Leppington 1970, 1971). Imposition of the ‘rectified’ Kutta condition of Orszag & Crow (1970) does not modify the sound field. Application of the ‘full’ Kutta condition, that the sheet leaves the plate at zero gradient, results in an enormous increase in the radiation, with I ~ U 2 cosec 2 1/2 θ .

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.

scholarly journals Unsteady aerodynamics and vortex-sheet formation of a two-dimensional airfoil

2017 ◽  
Vol 830 ◽  
pp. 439-478 ◽  
Author(s):  
X. Xia ◽  
K. Mohseni
Keyword(s):  
Ad Hoc ◽  
Unsteady Aerodynamics ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
Formation Condition ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Flow Models ◽  
Edge Vortex

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modelling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical steady Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove any ad hoc implementation, the unsteady Kutta condition, the conservation of circulation as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for several airfoil motions in steady and unsteady background flows.

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.

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