A Scaling Law for Cavitation Inception in Circular Jet Flows

The historical data for circular jets indicates that the incipient cavitation number increases with the diameter of the jet. This trend is not explained by the classic cavitation theory which expects incipient cavitation number to remain constant regardless of the jet diameter, flow parameters, or water quality. This paper explores the origins of cavitation scale effects and explains the correlation between the incipient cavitation number, jet diameter, and nuclei size. This is accomplished through turbulence-resolving CFD simulations of the jet flow field at three length scales and Rayleigh-Plesset bubble dynamics for three nuclei sizes. The numerical simulations show that incipient cavitation number (σ_i) changes significantly as the size of the jet is altered while the Reynolds number and the value of the minimum pressure coefficient are held constant. Larger nuclei bubbles (100μm) exhibit an increase in σ_i with jet diameter, while moderate (50μm) and small (10μm) nuclei bubble exhibit a decrease in σ_i as jet diameter increases. The value of σ_i associated with a small jet was similar for all nuclei sizes. As the jet increased in size, the disparity between the values of σ_i associated with each nuclei size was found to increase substantially. The equilibrium form of the Rayleigh-Plesset equation was used to derive a correction to the classic theory of cavitation inception. This correction is a function of initial nuclei size and the dynamic head of the flow. As either the nuclei properties or dynamic head of the fluid change, the magnitude of the correction term will also change. This correction to the classic cavitation theory was used to make predictions of how σ_i will change as length scale and Reynolds number are altered. These equilibrium predictions were found to be in good agreement with the numerical simulations of cavitation inception for large and moderate (100μm and 50μm) nuclei bubbles. Comparisons with the small (10μm) nuclei bubbles indicate that the inertial terms are quite significant for these bubbles, resulting in large discrepancies between the full numerical solution and the equilibrium predictions. In general, the equilibrium scaling relations show that as the length scale of a flow is held constant and the Reynolds number is increased, σ_i will converge to −CP_min. The scaling relations also show that when Reynolds number is held constant and the length scale of a flow is increased, σ_i will depart from −CP_min.