*2.5. Multiphase Nozzle Flow Modeling*

The internal nozzle flow is simulated through the Eulerian multi-fluid method, Equations (4)–(7). In the current application, the flow is supposed to be isothermal and comprises *n* = 3 phases, namely, the liquid fuel, its vapor and air. The flow model is based on the RANS approach with k–ζ–f turbulence closure model, with a standard wall function. The turbulent stresses in the continuous phases are computed by adding to the standard turbulent viscosity a bubble-induced viscosity term, according to the Sato model [43]. The interfacial exchange terms, relevant for cavitation between liquid and fuel vapor, are represented by the mass- and momentum-exchange terms, which take into account the microscopic effects at the interface between the phases. Concerning the mass exchange term between liquid fuel and vapor, the non-linear form of the Rayleigh–Plesset equation is used to describe bubble growth dynamics. The interfacial momentum exchange (between liquid fuel and vapor) is modeled taking drag and turbulent dispersion effects into account, while neglecting inertia and lift effects. The drag model on the bubbles uses drag coefficient *C*D, based on spherical shape and is dependent on Reynolds number. The turbulent mixing process between phases relies on the momentum interaction at the interface, which induces turbulence production on the liquid phase through the Sato model [43]. The state of bubble diameter is a function of position and time (poly-dispersed diameter); coalescence due to turbulent random collisions, breakup (induced by turbulent impact) and bubble generation due to cavitation are the mechanisms taken into account. The complete mathematical description of this approach in the modeling of multiphase nozzle flow has been published and can be found in [44,45]; these authors also report the model validation against several reference flows.
