Turbulent vortex shedding from a blunt trailing edge hydrofoil

Placed in a fluid stream, solid bodies can exhibit a separated flow that extends to their wake. The detachment of the boundary layer on both upper and lower surfaces forms two shear layers which generate above a critical value of Reynolds number a periodic array of discrete vortices termed von Kármán street. The body experiences a fluctuating lift force transverse to the flow caused by the asymmetric formation of vortices. The structural vibration amplitude is significantly amplified when the vortex shedding frequency lies close to a resonance frequency of the combined fluid-structure system. For resonance condition, fatigue cracks are likely to occur and lead to the premature failure of the mechanical system. Despite numerous and extensive studies on the topic, the periodic vortex shedding is considered to be a primary damage mechanism. The wake produced by a streamlined body, such as a hydrofoil, is an important issue for a variety of applications, including hydropower generation and marine vessel propulsion. However, the current state of the laboratory art focuses mainly in the wakes produced by hydraulically smooth bluff bodies at low Reynolds numbers. The present work considers a blunt trailing edge symmetric hydrofoil operating at zero angle of attack in a uniform high speed flow, Reh = 16.1·103 - 96.6·103 where the reference length h is the trailing edge thickness. Experiments are performed in the test section of the EPFL-LMH high speed cavitation tunnel. With the help of various measurement devices including laser Doppler vibrometer, particle image velocimetry, laser Doppler velocimetry and high speed digital camera, the effects of cavitation on the generation mechanism of the vortex street are investigated. Furthermore, the effects of a tripped turbulent boundary layer on the wake characteristics are analyzed and compared with the condition of a natural turbulent transition. In cavitation free regime and according to the Strouhal law, the vortex shedding frequency is found to vary quasi-linearly with the free-stream velocity provided that no hydrofoil resonance frequency is excited, the so-called lock-off condition. For such regime, the shed vortices exhibit strong span-wise instabilities and dislocations. A direct relation between vortex span-wise organization and vortex-induced vibration amplitude is found. In the case of resonance, the coherence of the vortex shedding process is significantly enhanced. The eigen modes are identified so that the lock-in of the vortex shedding frequency on a free-stream velocity range occurs for the first torsional mode. In the case of liquid flows, when the pressure falls below the vapor pressure, cavitation occurs in the vortex core. For lock-off condition, the cavitation inception index is linearly dependent on the square root of the Reynolds number which is in accordance with former models. For lock-in, it is significantly increased and makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index and considering the trailing edge displacement velocity, a new correlation relationship that encompasses the lock-off and the lock-in conditions is proposed and validated. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. Therefore, the displacement velocity of the hydrofoil trailing edge increases the fluctuating forces on the body and this effect is additional to any increase of vortex span-wise organization, as observed for the lock-in condition. Cavitation developing in the vortex street cannot be considered as a passive agent for the visualization of the turbulent wake flow. The cavitation reacts on the wake as soon as it appears. At early stage of cavitation development, the vortex-induced vibration and flow velocity fluctuations are significantly increased. 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 stream-wise and cross-stream inter-vortex spacings. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation. Besides, it is shown that the cavitation does not obviously modify the vortex span-wise organization. Moreover, hydro-elastic couplings are found to be enabled/disabled by permitting a sufficient vortex cavitation development. The effects on the wake characteristics of a tripped turbulent boundary layer, as opposed to the natural turbulent transition, are investigated. The foil surface is hydraulically smooth and a fully effective boundary-layer tripping at the leading edge is achieved with the help of a distributed roughness. The vortex shedding process is found to be strongly influenced by the boundary-layer development. The tripped turbulent transition promotes the re-establishment of organized vortex shedding. In the context of the tripped transition and in comparison with the natural one, significant increases in the vortex span-wise organization, the induced hydrofoil vibration, the wake velocity fluctuations, the wake energies and the vortex strength are revealed. The vortex shedding process intermittency is decreased and the coherence is increased. Although the vortex shedding frequency is decreased, a modified Strouhal number based on the wake width at the end of the vortex formation region is constant and evidences the similarity of the wakes. This result leads to an effective estimation of the vortex shedding frequency.

Cavitation Influence on Kármán Vortex Shedding and Induced Hydrofoil Vibrations

Philippe Ausoni, François Avellan, Eduard Egusquiza, Mohamed Farhat

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. 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.

2007

Effect of Hydrofoil Trailing Edge Geometry on the Wake Dynamics

Amirreza Zobeiri

In the present study, the effect of a hydrofoil trailing edge shape on the wake dynamic and its interaction with the mechanical structure is investigated. This would help better describe the physical reasons for vibration reduction when using oblique and Donaldson trailing edges in comparison to a truncated trailing edge and subsequently allow its further optimization. Thus, hydrofoils with oblique and Donaldson trailing edges are tested in a high-speed cavitation tunnel at zero angle of attack and high Reynolds numbers, ReL = 5·105 – 3·106. The truncated trailing edge hydrofoil is selected as reference. A velocity survey is performed via Laser Doppler Velocimetery, LDV, and Particle Image Velocimetry, PIV. Proper-Orthogonal-Decomposition, POD, is used to extract coherent structures from PIV data. In addition, flow induced vibration measurements and high-speed visualizations are performed. Finally, the effects of a tripped boundary layer transition on the wake are investigated and compared with the natural boundary layer transition. Vortex-induced vibration is found to decrease significantly for oblique and Donaldson trailing edges in comparison to the truncated case, specially under lock-off condition. However, minimum vibration corresponds to the Donaldson trailing edge. The high-speed videos clearly show that for three tested hydrofoils the alternate vortices clearly detach from suction and pressure sides of the trailing edge. However, for the oblique and Donaldson trailing edges the location of the lower vortex detachment is obviously shifted upstream with respect to the upper one. As a result, when the upper vortex rolls up, it coincides with the passage of the lower vortex, leading to their collision. This strong interaction leads to a redistribution of the vorticity, which does not concentrate within the core of Karman vortices any more. However, the spatial phase shift between the separation point of the upper and the lower vortices is different in the case of oblique and Donaldson trailing edges due to the being free the separation point on the Donaldson curve. LDV phase-locked averaging under lock-in condition is performed for truncated, oblique and Donaldson trailing edges. The truncated trailing edge exhibits a symmetric wake. However, in the case of the oblique and Donaldson trailing edges, an asymmetric thickening of the downward near wake is observed. The stream wise velocity fluctuation shows two peaks of different amplitudes. In the case of the truncated trailing edge, the upper and lower vortices have the same core diameter, contrary to the oblique trailing edge, where a larger vortex core diameter is found for the lower vortex. In the case of Donaldson trailing edge, the LDV phase-locked averaging is performed for the tripped transition where the vibration amplitude is high enough to perform the phase-locked average. The measurements show the passage of one vortex after the collision in the near wake contrary to the oblique one. However, the passage of two vortices corresponding to the upper and lower vortex is found far from the Donaldson trailing edge. LDV measurements show that the collision of the vortices for the oblique trailing edge, observed under lock-in conditions, also prevails for the lock-off condition in the case of oblique and Donaldson trailing edges. The velocity profile comparison at the vortex formation length for three trailing edges shows that in the case of the Donaldson trailing edge, the wake width increases significantly in comparison to two other trailing edges. Moreover, the minimum stream wise and transverse velocity fluctuation profiles obtained for the three trailing edges correspond to the Donaldson trailing edge. The strong similarity of results obtained for lock-in and lock-off conditions indicates that the collision between upper and lower vortices, clearly observed under lock-in, also occurs for lock-off condition. A thicker boundary layer with laminar-to-turbulent transition occurring further upstream is observed for the pressure side of the Donaldson trailing edge in comparison with the suction side. In contrast to the truncated trailing edge, both sides have a similar boundary layer structure and a similar transition location. Moreover, a thicker boundary layer is found for the Donaldson trailing edge in comparison to the truncated case. The collision between upper and lower vortices is also observed in the case of a tripped transition. However, the vortices are shed with a larger core diameter, greater strength, and lower frequency than for the natural transition. These investigations let us believe that the collision between upper and lower vortices and the resulting vorticity redistribution is the main reason for the vibration reduction obtained with oblique and Donaldson trailing edges. This result opens the way for more effective hydrofoil geometry optimization for further reduction of flow induced vibration.

EPFL2012

Kármán vortex shedding in the wake of a 2D hydrofoil: Measurement and numerical simulation

Youcef Ait Bouziad, Philippe Ausoni, François Avellan, Mohamed Farhat

The present study deals with the shedding process of the Kármán vortices at the trailing edge of a 2D hydrofoil at high Reynolds numbers. Investigations are performed in order to evaluate the ability of an unsteady numerical simulation to accurately reproduce the vortex shedding frequency. The vortex shedding frequency, derived from flow induced vibrations measurements, is found to follow the Strouhal law as long as none of the resonance frequencies of the hydrofoil is excited. For such lock-off conditions, the Kármán vortices exhibit a strong spanwise 3D instability. For Reynolds numbers ranging from 35’000 to 40’000, the torsion mode of the hydrofoil is excited with a substantial increase of the vibration level. In this case, the shedding frequency is locked onto the vibration frequency. The vortex roll-up, shedding and advection are well predicted by the computations as well as the 3D instability. Nevertheless, the numerical simulations underestimate the vortex shedding frequency of about 20%. No significant influence of the turbulence models, the incoming flow turbulence intensity and the mesh size is observed on the computed values. To investigate the issue of discrepancy between absolute values of measured and computed shedding frequency, we intend to address the sensitivity of the vortex shedding frequency to the boundary layer. It is indeed know that the boundary layer transition point to turbulence for this profile geometry is located slightly downstream of the midchord for an incidence angle of 0°. In contrast, the numerical simulation, as it solves the RANS equations, models the whole flow as being turbulent. Consequently, rough stripes are placed just behind the hydrofoil leading edge. For such a configuration, the boundary layer is turbulent from the leading edge in a similar way to the computations. Notable influence of the roughness is observed: The vortex shedding frequencies are significantly decreased in comparison to the smooth leading edge. The average Strouhal number St decreases from 0.24 to 0.18 and is nearly equal to the computational one, St=0.19. Kármán vortices being very sensitive to the boundary layer, differences in the transition points between experiments and computations have to be minimized in order to aspire good agreement.

2006