Cavitation is a complex multiphase hydrodynamics phenomenon that has received much attention over the past several decades. In a cavitation flow, a gas phase can be generated in the liquid phase if the local pressure drops below the vapor pressure. In such flow condition, the fluid densities are rapidly changed from the liquid (~ 880 kg/m3 in the case of diesel fuel) to vapor phase (~ 1.2 kg/m3). Such a low-pressure condition can be generated in a liquid flow, for example, due to abrupt turning of the flow direction.
To capture the multiphase nature of the flow, a calculation model must take into account the major physics involved in the cavitating flow. One of most important and critical phenomena is the changing of the speed of sound in the cavitating flow. Figure 1 shows the variation of the speed of sound for the mixture of nitrogen gas and liquid(water) as a function of their volume fraction, assuming that in the pure gas and liquid phases, the values are 340 m/s and 1450 m/s, respectively. In the mixture, the speed of sound can drop to a value significantly less than either, for example, 10 m/s. Therefore, supersonic flow can happen and should be taken into consideration in the model, especially, for the high-pressure, high-speed internal flow as shown in Fig. 2.
A number of approaches were made to model the complex cavitating flows, which can be classified in two major categories. The first approach starts with constructing an equation of state (EOS) corresponding to the liquid, the gas, and the mixture phase, respectively. Since the EOSs in the gas and liquid phase are well defined, the well posed is always guaranteed when a valid EOS in the mixture phase is provided. The second approach is the non-equilibrium multiphase flow model, which does not need to use the EOS for the mixture phase. Rather, the interface variables in the mixture must calculate through the relaxation process, which accompanies an auxiliary equation to closure the systems. Also, the coupling process between the governing equations would be required.
So far, in LS-DYNA, a simple but robust barotropic model is implemented by describing an EOS in the gas, liquid, and mixture (homogeneous equilibrium model, HEM).