Numerical Study of Cavitation in Cryogenic Fluids

Abstract

Numerical simulations of cavitation in liquid nitrogen and liquid hydrogen are presented; they represent a broader class of problems where the fluid is operating close to its critical temperature and thermal effects of cavitation are important. A compressible, multiphase formulation that accounts for the energy balance and variable thermodynamic properties of the fluid is described. Fundamental changes in the physical characteristics of the cavity when thermal effects become significant are identified; the cavity becomes more porous, the interface less distinct, and it shows increased spreading while getting shorter in length. The heat transfer model postulated in variants of the B-factor theory, where viscous thermal diffusion at the vapor-liquid interface governs the vaporization, is shown to be a poor approximation for cryogenic fluids. In contrast the results presented here indicate that the cavity is sustained by mass directly convecting into it and vaporization occurring as the liquid crosses the cavity interface. Parametric studies for flow over a hydrofoil are presented and compared with experimental data of Hord (1973, “Cavitation in Liquid Cryogens II—Hydrofoil,” NASA CR-2156); free-stream velocity is shown to be an independent parameter that affects the level of thermal depression.

Numerical simulation of unsteady three-dimensional sheet cavitation

“…With the unlimited extrapolated values U ij defined by equation (4.85), let ∆ − be equal to 96) and let ∆ + be defined by…”

Modeling cavitation flow of cryogenic fluids with thermodynamic phase-change theory

“…Efforts have been made to model cavitating flow with the homogenous equilibrium flow model (HEFM), in which the single-fluid modeling approach is employed for both phases [3][4][5][6][7][8][9][10]. The key for implementation of the HEFM is to calculate the variable density field.…”

“…Wang et al [11] and Wu et al [12] have reviewed these calculation models in detail. Among the various modeling approaches, the transport equation-based cavitation models (TEM) have been widely used recently [6][7][8][9][10][11][12]. The TEM solves the transport equation of vapor volume (or mass) fraction, whose source terms are the condensation and evaporation rate in the liquid-vapor conversion.…”

“…The model combines the classical thermodynamic phase-change theory and YoungLaplace equations under the assumption of thermodynamic equilibrium during the cavitation process. The thermodynamic equilibrium assumption for LN 2 and LH 2 cavitation modeling was validated by Hosangadi and Ahuja [8]. Afterwards, the model was implemented as a resource term into transport equations of the gas mass fraction, which were solved together within the mathematical framework of the homogeneous equilibrium model in multiple-phase CFD calculations.…”

Thermal Effects on Cryogenic Cavitating Flows around an Axisymmetric Ogive

“…Despite the improvements in the approach, it is important to underscore the limitation that the above studies does not solve the energy equation in the domain. Ahuja [8] and Utturkar [9] recently solve the energy equation in the entire domain with dynamic update of material properties and reported numerical studies on cavitation using liquid hydrogen and liquid nitrogen. For the former, their pressure and temperature predictions over a hydrofoil geometry is not obtained well with the experiment in the leading edge.…”