Towards the Applicability of the Modified von Kármán Spectrum to Predict Trailing Edge Noise

The present study deals with the shedding process of the von Kármán vortices at the trailing edge of a 2D hydrofoil at high Reynolds number Reh=25×103–65×103. This research focuses mainly on the effects of cavitation and fluid-structure interaction on the mechanism of the vortex generation. The vortex shedding frequency, derived from the flow-induced vibration measurement, is found to follow the Strouhal law provided that no hydrofoil resonance frequencies are excited, i.e., lock-off. For such a regime, the von Kármán vortices exhibit strong spanwise 3D instabilities and the cavitation inception index is linearly dependent on the square root of the Reynolds number. In the case of resonance, the vortex shedding frequency is locked onto the hydrofoil eigenfrequency and the spatial coherence is enhanced with a quasi-2D shape. The measurements of the hydrofoil wall velocity amplitude and phase reveal the first torsion eigenmotion. In this case, the cavitation inception index is found to be significantly increased compared to lock-off conditions. It makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index, a new correlation relationship that encompasses the entire range of Reynolds numbers, including both the lock-off and the lock-in cases, is proposed and validated. In contrast to the earlier models, the new correlation takes into account the trailing edge displacement velocity. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. This effect is important in the context of the fluid-structure interaction, since it implies that the velocity of the hydrofoil trailing edge increases the fluctuating forces on the body. It is also demonstrated that cavitation developing in the vortex street cannot be considered as a passive agent for the turbulent wake flow. In fact, for fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the streamwise vortex spacing. In addition, a significant increase of the vortex-induced vibration level is found at cavitation onset. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation.

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Transonic Turbine Vane Wake Flows

Volume 1: Turbomachinery ◽

10.1115/96-gt-419 ◽

1996 ◽

Cited By ~ 11

Author(s):

W. E. Carscallen ◽

H. U. Fleige ◽

J. P. Gostelow

Keyword(s):

Mach Number ◽

Vortex Street ◽

Trailing Edge ◽

Karman Vortex Street ◽

Von Karman ◽

Von Karman Vortex Street ◽

Kármán Vortex Street ◽

Karman Vortex ◽

Total Temperature ◽

Von Kármán

This paper summarizes the research on transonic turbine vane wake flows carried out in a Transonic Planar Cascade at the National Research Council of Canada between 1987 and 1995. The cascade used in the research is a large scale, continuously operating, inflow facility which was developed to study both flow phenomena and aerodynamics of turbine vanes. Research was initially directed at investigating the apparent redistribution of total temperature (energy) from the centre to the edge of the vane wake. This redistribution was found to be a real physical phenomenon that correlated extremely well with wake total pressure distributions indicating that the mechanism which redistributes the energy also has a direct effect on the losses associated with the vane wake. Both phenomena were found to be a function of Mach number in that the losses and the time-averaged total temperature difference between the centre and edge of the wake increased to a maximum as the Mach number approached 0.95 and then decreased by half as the Mach number was raised to 1.3. Following Kurosaka et al (1987) conclusion that the redistribution of energy behind a circular cylinder was caused by the vortices which were shed from the trailing edge an additional experimental program was initiated to study the details of the unsteady vane wakes by the use of high speed schlieren photographs and high frequency response transducers to measure unsteady static and total pressures. This research has confirmed that over the range of Mach numbers, from low to high subsonic, a von Karman vortex street is shed continuously from the vanes. What this research has revealed is that as the transonic regime is traversed, the von Karman vortex street still occurs but only as one of a number of different and highly transient vortex shedding patterns. This breakdown of the stable von Karman vortex street is associated with the migration of the origin of the vortices from the trailing edge of the vane to the nodal point formed by the trailing edge shock waves and the confluence of the two trailing edge shear layers. The cause of the redistribution of energy within the wake and of the high wake losses is the shedding of a continuous von Karman vortex street from the vane. In the subsonic flow regime the presence of a stable von Karman vortex street leads to high wake losses due to the depression of the base pressure while the redistribution of total temperature (energy) is caused by the combined pumping action of the vortices. The strength of the vortices and the above phenomena increase with increasing Mach number. As the transonic flow regime is encountered and the supersonic flow regime entered the coherent structures in the wake become unstable, less von Karman-like, and occur less frequently and the origin of the vortices migrates downstream. This leads to a significant elevation in base pressure and redistribution of energy, thereby implying that significant gains in engine stage efficiency can be realized by the destabilization or elimination of the von Karman vortex street from the vane wake.

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The suitability of the von Karman spectrum for the structure of turbulence in a complex terrain wind farm

Journal of Wind Engineering and Industrial Aerodynamics ◽

10.1016/s0167-6105(96)00059-1 ◽

1996 ◽

Vol 62 (2-3) ◽

pp. 237-257 ◽

Cited By ~ 25

Author(s):

E.E. Morfiadakis ◽

G.L. Glinou ◽

M.J. Koulouvari

Keyword(s):

Complex Terrain ◽

Wind Farm ◽

Von Karman ◽

Von Kármán Spectrum ◽

Von Kármán

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Vortex wakes of a flapping foil

Journal of Fluid Mechanics ◽

10.1017/s0022112009007964 ◽

2009 ◽

Vol 633 ◽

pp. 411-423 ◽

Cited By ~ 107

Author(s):

TEIS SCHNIPPER ◽

ANDERS ANDERSEN ◽

TOMAS BOHR

Keyword(s):

Phase Diagram ◽

Leading Edge ◽

Vortex Street ◽

Trailing Edge ◽

Karman Vortex Street ◽

Von Karman ◽

Von Karman Vortex Street ◽

Kármán Vortex Street ◽

Karman Vortex ◽

Von Kármán

We present an experimental study of a symmetric foil performing pitching oscillations in a vertically flowing soap film. By varying the frequency and amplitude of the oscillation we visualize a variety of wakes with up to 16 vortices per oscillation period, including von Kármán vortex street, inverted von Kármán vortex street, 2P wake, 2P+2S wake and novel wakes ranging from 4P to 8P. We map out the wake types in a phase diagram spanned by the width-based Strouhal number and the dimensionless amplitude. We follow the time evolution of the vortex formation near the round leading edge and the shedding process at the sharp trailing edge in detail. This allows us to identify the origins of the vortices in the 2P wake, to understand that two distinct 2P regions are present in the phase diagram due to the timing of the vortex shedding at the leading edge and the trailing edge and to propose a simple model for the vorticity generation. We use the model to describe the transition from 2P wake to 2S wake with increasing oscillation frequency and the transition from the von Kármán wake, typically associated with drag, to the inverted von Kármán wake, typically associated with thrust generation.

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Golden Ratio Phenomenon of Random Data Obeying von Karman Spectrum

Mathematical Problems in Engineering ◽

10.1155/2013/130258 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 4

Author(s):

Ming Li ◽

Wei Zhao

Keyword(s):

Golden Ratio ◽

Point Of View ◽

Self Similarity ◽

Random Data ◽

Von Karman ◽

Speed Fluctuation ◽

Fractional Differential ◽

Navier Equation ◽

Von Kármán Spectrum ◽

Von Kármán

von Karman originally deduced his spectrum of wind speed fluctuation based on the Stokes-Navier equation. Taking into account, the practical issues of measurement and/or computation errors, we suggest that the spectrum can be described from the point of view of the golden ratio. We call it the golden ratio phenomenon of the von Karman spectrum. To depict that phenomenon, we derive the von Karman spectrum based on fractional differential equations, which bridges the golden ratio to the von Karman spectrum and consequently provides a new outlook of random data following the von Karman spectrum in turbulence. In addition, we express the fractal dimension, which is a measure of local self-similarity, using the golden ratio, of random data governed by the von Karman spectrum.

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