Assessment of the λ coefficient in an interface-effect eddy-viscosity correction for unsteady cavitating flow over a Delft Twist 11 hydrofoil

Abstract

Unsteady cavitation affects the hydraulic performance and reliability of mechanical engineering components such as hydrofoils, pumps, and turbines. Its numerical prediction remains challenging because standard one-fluid RANS simulations may overpredict eddy viscosity in the vapor–liquid transition region and suppress cloud-cavity shedding. This study evaluates the empirical coefficient λ within an existing interface-effect eddy-viscosity correction for cavitating flow over the Delft Twist 11 hydrofoil. The simulations are performed using the SST k-ω turbulence model and the Zwart–Gerber–Belamri cavitation model. In the correction method, the vapor–liquid transition region is identified from the density gradient, and the local eddy viscosity is reduced within the numerically resolved diffuse interface. Four values of the correction coefficient λ , namely 0.001, 0.02, 0.05, and 0.07, are examined under the documented Delft Twist 11 operating condition. The numerical setup is assessed using grid-convergence and time-step sensitivity analyses. The mean pressure distribution is validated against experimental measurements, while the cavity morphology is evaluated using visual comparison and phase-matched projected cavity-area fractions. Time-resolved total-vapor-volume, cavity-count, and perimeter-based fractal-dimension signals are used to quantify the macroscopic vapor response, cloud breakup, boundary complexity, and dominant shedding time scale. The results show that λ affects cavity closure, reverse-flow development, cloud fragmentation, and shedding frequency. Insufficient correction weakens periodic cloud detachment, whereas excessive correction promotes overly rapid shedding and stronger fragmentation. Among the tested values, λ  = 0.02 gives the closest agreement with the experiment. The dominant frequency obtained from the fractal-dimension signal is 30 Hz, compared with the measured value of 32.2 Hz. The results indicate that the interface-effect correction can improve SST k-ω -based prediction of three-dimensional hydrofoil cavitation when the coefficient is selected appropriately. The value λ = 0.02 should be interpreted as a case-supported coefficient for the present hydrofoil and operating condition.