Development and Validation of a Reduced Critical Radius Model for Cryogenic Cavitation

Cryogenic fluids such as liquid hydrogen, liquid oxygen, and liquid methane have often been used as liquid rocket propellants, and it is well known that the suction performance of turbopump inducers is better in cryogenic fluids than it is in cold water due to the so-called “thermodynamic effect.” The origin of the thermodynamic effect is the temperature change inside a cavity region that arises from the latent heat transfer across the interface of a cavity. To better understand the suction performance of cavitating cryogenic inducers, we must take into account the temperature changes that take place due to the thermodynamic effect; computational fluid dynamics (CFD) analysis coupled with an energy equation is one of the most powerful tools for this purpose. The computational cost, however, becomes an obstacle for its application to the design phase, so a reduction in the number of governing equations is often preferable. In the present study, a cryogenic cavitation model that does not need to solve an energy equation is proposed as a reduced model; the model is named the “reduced critical radius model.” This model assumes that the temperature change due to the latent heat transfer can be analytically well estimated on the basis of an approximation of the local equilibrium when the pressure inside a cavity is always kept at a saturation vapor pressure at every temperature (at least on the time scale of the flow field). The proposed method was validated carefully for a variety of objects: blunt headforms, hydrofoils, a two-dimensional blunt wing, and Laval nozzles. The results obtained during the validation were in good agreement with the experimental results, except in the case of strong unsteady cavitation. This indicates that the present method, which does not involve solving an energy equation, offers good potential for application to the design phase of cryogenic cavitating inducers.