Numerical investigation on cavitation flow of hydrofoil and its flow noise with emphasis on turbulence models

Abstract

In this study, cavitation flow of hydrofoils is numerically investigated to characterize the effects of turbulence models on cavitation-flow patterns and the corresponding radiated sound waves. The two distinct flow conditions are considered by varying the mean flow velocity and angle of attack, which are categorized under the experimentally observed unstable or stable cavitation flows. To consider the phase interchanges between the vapor and the liquid, the flow fields around the hydrofoil are analyzed by solving the unsteady compressible Reynolds-averaged Navier–Stokes equations coupled with a mass-transfer model, also referred to as the cavitation model. In the numerical solver, a preconditioning algorithm with dual-time stepping techniques is employed in generalized curvilinear coordinates. The following three types of turbulence models are employed: the laminar-flow model, standard k − ε turbulent model, and filter-based model. Hydro-acoustic field formed by the cavitation flow of the hydrofoil is predicted by applying the Ffowcs Williams and Hawkings equation to the predicted flow field. From the predicted results, the effects of the turbulences on the cavitation flow pattern and radiated flow noise are quantitatively assessed in terms of the void fraction, sound-pressure-propagation directivities, and spectrum.

Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

“…The accurate and effective numerical simulation of a multi-phase problem is challenging, as numerical instability issues arise from the large variations in the speed of sound with rapid local density changes [9,11,12,[16][17][18][19]. To resolve these problems, the preconditioned and dual-time stepping numerical methods are employed.…”

“…Based on the results from a previous study [16], the filter-based turbulent viscosity modification proposed by Johansen et al [13] is adopted to predict unstable cavitation flows more accurately. The transport equations of the low Reynolds number k-ε turbulence model, and the modified turbulent viscosity, are written as follows…”

“…The monotonic upstream-centered scheme for conservation laws (MUSCL), and the 2nd order central difference schemes, are applied to the convective and viscous flux terms, respectively. For more detailed descriptions of the numerical methodologies, except for the additional linearization terms of the viscous flux that are the main subject of this study, the studies conducted by Ha and Park [12] and Kim et al [16] can be referred to.…”

“…Lighthill's stress tensor, T ij , is defined as T ij = ρu i u j + p − c 2 0 ρ δ ij − τ ij . By following the procedure from a previous study (Kim et al [16]), the FW-H equation can be rewritten in a form appropriate to account for flow noise, due to cavitation flow, over an acoustically compact stationary body, as follows…”

“…Kunz et al [9], Huang [10], Esfahanian and Akbarzadeh [11], and Ha and Park [12] proposed preconditioning methods to resolve numerical instability issues, that arise from large disparities between the acoustic and convective wave speeds. Johansen et al [13] developed a filter-based turbulence model that was applied across a wide range of multi-phase problems [14][15][16].…”