Novel Blade Design Strategy to Control the Erosion Aggressiveness of Cavitation

With the reduction in size of turbomachinery systems, cavitation aggressiveness is intensified. Erosion, caused by the repeated collapse of gaseous bubbles in proximity to solid surfaces, occurs at rates that dramatically downgrade the life expectancy of rotating parts. As a result, the compacting strategy, meant to reduce cost and improve efficiency, fails for liquid flows. The research undertaken here proposes a novel design method aimed at controlling the erosion aggressiveness of cavitation. The underlying idea is that the cavity closure shock is a determining factor in the intensity of bubble collapse mechanisms: sharp and high amplitude shocks give rise to strong erosion, while low gradient and low amplitude recoveries reduce the erosive intensity. The working hypothesis is tested here, first, by developing a novel inverse design algorithm capable of handling cavitating flow. The code solves the inviscid Euler equations and models blade cavitation using the Tohoku-Ebara barotropic equation of state. Bespoke preconditioning and multigrid procedures are constructed to handle the large amplitudes in flow regime (from hypersonic in the cavity to very low Mach number in the liquid phase). The inverse solver is then used to produce a set of 2D cascade hydrofoil geometries with smoothed shock profiles at cavity closure. The blades are assessed numerically using both steady state and time-resolved approaches. Both hydrodynamic performance, given in terms of swirl, lift and drag, and cavitation dynamics are evaluated. Recently developed erosion prediction methodologies are implemented and demonstrate compelling correlations between the erosion patterns and shock profile. Finally, experimental testing is carried out using a purposefully developed observation platform. The erosive performance of two of the geometries is measured using the paint removal technique. Results reveal a significant improvement in erosive response for the shock smoothed design, thus confirming the numerical findings as well as the validity of the design hypothesis

Systematic validation study of an unsteady cavitating flow over a hydrofoil uising conditional averaging: LES and PIV

We present results of Large-eddy simulations (LES) modeling of steady sheet and unsteady cloud cavitation on a two-dimensional hydrofoil which are validated against Particle image velocimetry (PIV) data. The study is performed for the angle of attack of 9° and high Reynolds numbers ReC of the order of 106 providing a strong adverse pressure gradient along the surface. We employ the Schnerr–Sauer and Kunz cavitation models together with the adaptive mesh refinement in critical flow regions where intensive phase transitions occur. Comparison of the LES and visualization results confirms that the flow dynamics is adequately reproduced in the calculations. To correctly match averaged velocity distributions, we propose a new methodology based on conditional averaging of instantaneous velocity fields measured by PIV which only provides information on the liquid phase. This approach leads to an excellent overall agreement between the conditionally averaged fields of the mean velocity and turbulence intensity obtained experimentally and numerically. The benefits of second-order discretization schemes are highlighted as opposed to the lower-order TVD scheme

Multiscale Computational Methodology Applied to Hydroacoustic Resonance in Cavitating Pipe Flow

The present work is a contribution to the physical analysis and numerical simulation of the pressure surges in hydraulic machinery and connected conduit systems. Localized hydrodynamic instabilities including cavitation are prone to interact with the entire conduit through the propagation of acoustic plane waves. At resonance, the superimposition of the acoustic waves leads to the formation of large amplitudes standing waves along the entire conduit. The resulting fluctuation of velocity and pressure in the source region may have a significant role on the hydrodynamic instability. A computational methodology based on two fields is proposed to simulate this interaction in the time domain: a 1D hydroacoustic model (HA model) is selected to analyze the entire acoustic field including the source region, a 3D incompressible hydrodynamic model (HD model) is used to describe the flow in the source region. The acoustic perturbation due to the instability is precisely evaluated with the HD model and injected in the HA model through discrete sources. To describe the complete interaction between the fields, two methods are proposed: the acoustic feedback is either fully modeled (two way coupled simulation) or accounted for using interaction parameters (one way concurrent simulation). In the first method, the boundary conditions of the HD model are adjusted dynamically using the solution field of the HA model and all components of the sources are evaluated in the HD model. In the second method, the acoustics and hydrodynamics components of the sources are considered as independent. The components due to the hydrodynamic field are evaluated in the HD model with steady boundary conditions and injected in HA model through discrete sources. The components of the sources due to the acoustic fluctuations are accounted for with specific parameters of the HA model; those interaction parameters, i.e. cavity compliance and mass flow gain factor, are evaluated with the help of the HD model. A reference case study has been setup; video analysis and dynamic pressure measurement have been performed to validate the simulations. The case study consists in a straight pipe connecting two constant pressure tanks. A bluff body is placed at 3/4 of the pipe length, the resulting flow instability is characterized by the alternate shedding of vortices at a frequency proportional to the flow velocity. The hydroacoustic resonator is the pipe itself. Measurements have been performed for resonant and non-resonant conditions in cavitating and cavitation free flow regime. In cavitation free flow regime, the hydrodynamic source is identified as a pure momentum source associated with the drag force on the bluff body. The flow conditions leading to resonance can be evaluated with the two way coupled simulation. At resonance, the distribution, frequency and amplitude of pressure fluctuation predicted in the simulation is in good agreement with the measurement. For the selected case study, the acoustic feedback is very weak and has no significant effect on the momentum source. In cavitating flow regime, two hydrodynamic sources have been identified, the momentum source and the mass source. The momentum source is associated with the drag force on the bluff body, the mass source is associated with the volume fluctuation of the fl vapor phase in the wake of the bluff body. The strength of the mass source is orders of magnitude larger and the momentum source can therefore be neglected. One way concurrent simulations using dynamic update of the interaction parameters have been performed. Fair agreement is obtained between the simulations and the measurements. The amplification of the fluctuation observed experimentally below incipient cavitation is reproduced. At intermediate cavitation index, the pressure fluctuation amplitude and the spectral energy distribution is in fair agreement with the experiment. The modifications of the pipe eigenmodes and eigenfrequencies due to cavitation is satisfactorily reproduced with the cavity compliance

Physical modelling of leading edge cavitation:computational methodologies and application to hydraulic machinery

Cavitation is usually the main physical phenomenon behind performance alterations in hydraulic machinery. For this reason, it is crucial to accurately predict its inception and development and to highlight a comprehensive relation between the cavitation development and the performances drop associated. The common cavitation models, based on numerical flow simulations, are intended to reproduce the general cavitation behavior, and their major focus is the cavitation onset and developed cavity shape prediction. In the present study, various methods in cavitation modelling are investigated. Specific computational methods are outlined for the two sensitive zones of cavity detachment and closure. Finally, an industrial case is investigated in order to highlight the mechanisms of head drop phenomenon in hydraulic machines. Current modelling techniques are reviewed together with physical arguments concerning the cavitation phenomenon, and a 2D hydrofoil test case is used to evaluate the models. A mono-fluid interface tracking model, a multiphase state-equation based model, and a multiphase transport-equation based model are discussed in terms of reproducing the cavitation flow characteristics as the cavitation inception, development, pressure distribution and velocity profiles in cavitation regimes. An innovative approach based on the local stress formulation is proposed. The non-viscous anisotropic stress is taken into account through the maximum tensile stress criterion for cavitation inception instead of the classical pressure threshold. The maximum tensile stress criterion, formulated using the shear strain rate formulation is used for CFD computations. The method is evaluated with the case of a parabolic nose leading edge flow with comparison to the boundary layer computations. The developed model is tested in the case of a 2D hydrofoil in both smooth and rough walls under different flow conditions. The ability of the model to take into account Reynolds and surface roughness effects, as observed in experimental investigations, is demonstrated. A comparative study of turbulence modelling for unsteady cavitation is presented which indicates a strong correlation between the cavitation unsteadiness predictions and the turbulence modelling. The adapted techniques in reproducing the unsteady cavitation flow are found to be either using an accurate filtering turbulence model to correctly capture the large eddies, or to modify the turbulent viscosity function, and thereby introducing an artificial compressibility effect. The simulated leading edge cavitation instability, in our case, occurs at a certain cavity length where the cavity closure corresponds to the high pressure gradient region and is governed mainly by the occurrence of the reentrant jet at the cavity closure. This phenomenon is found to be periodic and the shedding frequencies matches to the Strouhal law as observed in experiments. Finally, the multiphase mixture model is used in the case of an industrial inducer. The model provides satisfactory results for the prediction of the cavitation flow behavior and performance drop estimation for the operating points studied. An analysis based on global energy balance and local flow analysis demonstrates that the head drop is mainly caused by the lower torque generation and the hydraulic losses induced by the secondary flows. These phenomena occur when the cavity extends towards the throat region, leading to important changes in the flow structure