Abstract
Cavitation is the formation of vapor bubbles within a liquid where the flow dynamics causes the local static pressure to drop below the vapor pressure. The so-called full cavitation model (FCM) developed by Singhal has been widely used in numerical modeling of the cavitation flow for thermosensible and non-thermosensible fluids. Within the FCM, the bubble size is taken to be equivalent to the maximum possible value to forego the calculation of bubble number density. We developed a new cavitation model by re-calculating the bubble radius in FCM to account for the effects of local pressure. The new model was obtained by combining the thermodynamic phase-change theory and the Young-Laplace equation with the assumption of thermodynamic equilibrium during the cavitation process. The cavitation calculations were performed based on the mathematical framework of the homogeneous equilibrium flow model and the transport-equation-based model for vapor phase mass fraction. The model was validated by modeling the cavitating flow of liquid nitrogen and liquid hydrogen through NASA hydrofoil and Ogive with consideration of the phase-change thermal effects. The temperature and pressure distributions with the new model are found to agree well with data from existing experimental studies, as well as the simulations with the FCM.
Highlights
The cavitation phenomenon happens in a liquid when the local static pressure drops below the vapor pressure, where the generated vapor sustains the pressure dynamic balance
The present paper introduces a new cavitation model, named the “dynamic cavitation model” (DCM), in which we re-calculate the bubble size in full cavitation model” (FCM) by taking the effect of local pressure into account
The thermodynamic equilibrium assumption for LN2 and LH2 cavitation modeling was validated by Hosangadi and Ahuja [8]
Summary
The set of governing equations for cavitation based on the HEFM comprises the conservative form of the NavierStokes equations, the energy equation, the κ-ε two-equation turbulence closure, and a transport equation for the vapor mass fraction. The continuity, momentum, and energy equations for steady flow are given below, respectively [12]: mu j 0 ,. The effect of slip velocity between the liquid and vapor phases on the momentum exchange has been neglected in eq (2) because cavitation often occurs in regions of high-speed flow. The - two-equation turbulence model has been widely used in simulating the quasi-steady cavitating flow of cryogenic fluids [8,12,19]. Compared with the standard - model, the realizable - turbulence model has shown substantial improvements in computing flows with sharp streamline curvature or vortices. We employ the realizable - model to investigate turbulent mixing, and SWF to account for boundary layer effects, whose detailed formulations are detailed in [16]
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