Dynamics and Optimal Control of Self-Sustained Instabilities in Laminar and Turbulent Swirling Flows: Application to the Part Load Vortex Rope in Francis Turbines

In 2050, the European commission plans to achieve actual energetic transition, which contributes in meeting the climate change challenges by moving away from the fossil fuels and by developing a competitive low-carbon economy. As a consequence, a foreseeable massive introduction of intermittent renewable energy sources in the transmission and distribution systems is going to occur, which will impact randomly the balance of the electric consumption and production, and could jeopardize the electric grid stability. In this context, the present research work aims at increasing the operation flexibility of Francis turbines at part load regime, which is thought to be one of the main solutions to mitigate the large power fluctuations of the electric grid arising from these intermittent power productions. An intense cavitation vortex rope is however known to appear in these operating conditions and to prohibit power generation due to large pressure fluctuations at a well-defined frequency, which causes risks of operating instability, and fatigue of the mechanical structures. The control of the part load vortex rope is therefore addressed in this research work using optimal flow control techniques. Minimization algorithms need a physically-based target characterizing this single helical structure, which is obtained by investigating the hydrodynamic instability properties of this turbulent open swirling flow. This approach is first developed on a benchmark open flow, the spiral vortex breakdown in laminar swirling flow. Global stability analysis about the mean flow is computed and reveals up to two unstable eigenmodes, which well predict the frequencies of the vortical structures of the nonlinear dynamics. Moreover, the computations of the nonlinear interactions of these purely hydrodynamic self-sustained instabilities help identifying a Ruelle-Takens-Newhouse route to chaos as the Reynolds number increases. The optimal control of spiral vortex breakdown, implemented through a minimization algorithm targeting the largest eigenvalue growth rate of the mean flow, results in a distributed force which succeeds in stabilizing the self-sustained instability. This promising approach next requires to transpose the uncluttered theoretical framework of laminar swirling flow to the complexity inherent to industrial design, including in particular turbulence modeling to reach high Reynolds number flows, Re = O(10^6). The present work bridges this gap and presents an optimal control technique suitable for stabilizing the flow in hydraulic turbines. The part load vortex rope is identified as a global unstable eigenmode which originates from a single helical disturbance of the mean flow. This first result provides a linear framework to investigate the flow in hydraulic turbines and enables us to obtain the generation mechanism of the synchronous pressure fluctuations as a fluid-solid interaction using an asymptotic expansion. Based on the hydrodynamic instability properties of the part load vortex rope, the predictive control of this vortex is performed by targeting the most unstable eigenvalue growth rate of the draft tube mean turbulent flow. We determine an optimal force distribution that successfully quenches the vortex rope and sketches the design of a realistic control appendage. This result brings a promising solution to control the part load vortex rope and increase the operation flexibility of Francis turbines.

Turbulent vortex shedding from a blunt trailing edge hydrofoil

Philippe Ausoni

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.

EPFL2009

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

Unsteady Numerical Simulations of the Flow Related to the Unstable Energy-Discharge Characteristic of a Medium Specific Speed Double Suction Pump

François Avellan, Olivier Braun, Philippe Dupont

Regions of positive slope in the pressure-discharge characteristics can result in a reduction or even lack of damping of system instabilities. They are therefore one of the major concerns in design and operation of centrifugal pumps as they are limiting the admissible operating range. The considered preliminary hydraulic design of an industrial double suction pump of medium specific speed n = 0.410 (0.205 per impeller side) shows a marked saddle in the energydischarge characteristic associated to a sudden drop of efficiency versus discharge at part load. Unsteady RANS type flow simulations are performed using hexahedral meshes with 2.5 million nodes to model the inlet casing, the shrouded double sided impeller with 2 x 7 blades, the diffuser with 12 blades and the volute. In unsteady solution monitoring, low frequency (below blade passing frequencies) phenomena are noticed. Therefore, simulation times of up to 10 impeller revolutions at each flow rate are requested to achieve statistically steady behavior of the flow judged on global performance numbers and circumferential flow rate distribution. The numerical simulations emphasize a drop in the characteristic, though at a lower flow rate than found on the test rig. It is shown to be associated to a one-sided separation in the diffuser, further leading to an unbalanced flow rate distribution of about 10% of flow rate between both sides of the impeller. There is a region of hysteresis, where both configurations with balanced and unbalanced flow rate distributions can be obtained for the same global flow rate. The asymmetric flow distribution leads to asymmetric velocity profiles at the impeller-diffuser interface which results in a strongly vortical flow in the diffuser channels, where an important amount of energy is dissipated in regions of increased viscous and turbulent shear.

2007

Turbulent vortex shedding from a blunt trailing edge hydrofoil

Philippe Ausoni

EPFL2009

Unsteady Numerical Simulations of the Flow Related to the Unstable Energy-Discharge Characteristic of a Medium Specific Speed Double Suction Pump

François Avellan, Olivier Braun, Philippe Dupont

2007

Cavitation Influence on Kármán Vortex Shedding and Induced Hydrofoil Vibrations

Philippe Ausoni, François Avellan, Eduard Egusquiza, Mohamed Farhat

2007