Isothermal Cavitation in a Throttle Nozzle

Cavitation and turbulence inside a diesel and gasoline injectors play a critical role in primary spray breakup and development processes. In this validation example we consider Flow Simulation capabilities to simulate cavitation in industrial liquid flows using the Isothermal Cavitation Model.

The problem studied here validates this model by considering a 3D diesel fuel flow in a throttle channel that was studied experimentally in Ref. 26. According to this work, thermal effects in the considered flow are negligible. Therefore, it is reasonable to apply the Isothermal Cavitation Model.

Throttle channel geometry with its main dimensions is shown in Figure 1.

Figure 1. The channel geometry: (s) symmetry plane, L = 1 mm, H = 0.299 mm, W = 0.3 mm, Rin = 0.02 mm.

Diesel fuel at 30°C is supplied to the inlet under the pressure (Pin) of 100 bar. The outlet pressure (Pout) varies from 10 to 70 bar. The properties of the analyzed fuel for the given temperature are presented in the following table:

Table 1. Properties of the diesel fuel (2-D) at 30°C
Density (kg/m3)	836
Molar Mass (kg/mol)	0.198
Dynamic Viscosity (Pa∙s)	0.0025
Saturation Pressure (Pa)	2000

It is assumed that fuel contains dissolved air. The mass fraction of dissolved air is set to 0.001 to conform with the experimental data.

The objective of the calculations is to obtain channel characteristic under cavitation conditions and compare it with the experimental measurements. Because throttle channel has a symmetry plane, only a half of the model is used to generate the computational mesh. A finer local mesh is used to resolve the flow in the narrow channel and the adjacent regions providing about 15 mesh cells across the channel half-height. Additional refinement is performed in the region near the small fillet Rin. The resulting mesh are shown in Figure 2.

Figure 2. The computational mesh (zoom-view).

Figure 3 shows the distribution of the vapor volume fraction at different pressure drop. This figure provides a view of the initiation and development of the cavitation area.

Figure 3. Cavitation fields at symmetry plane.

The dependency of the pressure drop on the mass flow rate both predicted by Flow Simulation and determined experimentally are shown on Figure 4. The difference between the calculations and the experimental measurements is less than 5%. Also, as it can be seen from the Figure 3 and Figure 4, the critical cavitation point corresponds to the pressure drop of about 70 bar. This point defines the transition from a pressure-dependent mass flow to choked mass flow that is induced by cavitation.

Figure 4. Mass flow rate versus pressure drop at 100 bar inlet pressure in comparison with the experimental data.

The comparison of the Flow Simulation calculations with the experimental data shows that the application of the Isothermal cavitation model that employs a limited set of fluid properties allows to predict cavitating flow characteristics with the sufficient accuracy.