Numerical simulation of cavitation and atomization using a fully compressible three-phase model

The aim of this paper is to present a fully compressible three-phase (liquid, vapor, and air) model and its application to the simulation of in-nozzle cavitation effects on liquid atomization. The model employs a combination of the homogeneous equilibrium barotropic cavitation model with an implicit sharp interface capturing volume of fluid (VOF) approximation. The numerical predictions are validated against the experimental results obtained for injection of water into the air from a step nozzle, which is designed to produce asymmetric cavitation along its two sides. Simulations are performed for three injection pressures, corresponding to three different cavitation regimes, referred to as cavitation inception, developing cavitation, and hydraulic flip. Model validation is achieved by qualitative comparison of the cavitation, spray pattern, and spray cone angles. The flow turbulence in this study is resolved using the large-eddy simulation approach. The simulation results indicate that the major parameters that influence the primary atomization are cavitation, liquid turbulence, and, to a smaller extent, the Rayleigh-Taylor and Kelvin-Helmholtz aerodynamic instabilities developing on the liquid-air interface. Moreover, the simulations performed indicate that periodic entrainment of air into the nozzle occurs at intermediate cavitation numbers, corresponding to developing cavitation (as opposed to incipient and fully developed cavitation regimes); this transient effect causes a periodic shedding of the cavitation and air clouds and contributes to improved primary atomization. Finally, the cone angle of the spray is found to increase with increased injection pressure but drops drastically when hydraulic flip occurs, in agreement with the relevant experiments.

Figure 1

Two-phase barotropic relation (plot in logarithmic scale).

Figure 2

(a) Step-nozzle geometry as reported by Abderrezzak and Huang [46]. Here $W_u$ denotes the upstream width, $W_n$ denotes the nozzle width, and $L_n$ denotes the nozzle length. (b) Computational domain with boundary conditions: walls (gray), inlet (red), and outlet (blue). All dimensions are in millimeters.

Figure 3

Details of the computational mesh.

Figure 4

Comparison of in-nozzle cavitation and near-exit spray formation between experimental results from Abderrezzak and Huang [46] and the present numerical study for inlet pressures of (a) and (b) 2 bars, (c) and (d) 3 bars, and (e) and (f) 5 bars. Isosurfaces of the mixture density at $100\text{kg}/{\mathrm{m}}^3$ are shown at a random time instant.

Figure 5

Spray cone angle for injection pressures of (a) 2 bars, (b) 3 bars, and (c) 5 bars with a transparent isosurface of 95% gas volume fraction and (d) comparison with the experiments from Abderrezzak and Huang [46].

Figure 6

Instances of the evolution of in-nozzle cavitation and liquid jet disintegration at $p_{\mathrm{inj}}=2$ bars. Isosurfaces of 50% vapor (cyan) and 95% gas (white) volume fraction are shown. The instances are chosen randomly over the evolution to highlight the main features. (The nondimensional time is given in parentheses.)

Figure 7

Instances of the evolution of in-nozzle cavitation and liquid jet disintegration at $p_{\mathrm{inj}}=3$ bars. Isosurfaces of 50% vapor (cyan) and 95% gas (white) volume fraction are shown. The instances are chosen randomly over the evolution to highlight the main features. The thinning and widening of the liquid jet are highlighted using red and blue circles, respectively. (The nondimensional time is given in parentheses.)

Figure 8

Instances of the evolution of in-nozzle cavitation and liquid jet disintegration at $p_{\mathrm{inj}}=5$ bars. Isosurfaces of 50% vapor (cyan) and 95% gas (white) volume fraction are shown. (The nondimensional time is given in parentheses.)

Figure 9

Instantaneous isosurface of the $Q$ criterion showing vortex cores (value of ${10}^9$) colored by nondimensional velocity magnitude at $p_{\mathrm{inj}}=2$ bars. (The jet interface close to the nozzle exit is shown in the inset.)

Figure 10

Instantaneous isosurface of the $Q$ criterion showing vortex cores (value of ${10}^9$) colored by nondimensional velocity magnitude at $p_{\mathrm{inj}}=3$ bars. (The jet interface close to the nozzle exit is shown in the inset.)

Figure 11

Instantaneous isosurface of the $Q$ criterion showing vortex cores (value of ${10}^9$) colored by nondimensional velocity magnitude at $p_{\mathrm{inj}}=5$ bars. (The jet interface close to the nozzle exit is shown in the inset.)

Figure 12

Contours of nondimensional velocity magnitude with isolines of $95–99\%$ gas volume fraction. (a) Pictorial representation of the first spray widening event. (b) and (d) Widening of the spray. (c) Reduction in spray width. (The vectors shown are not to scale; they are used as an indicator of flow direction.)

Figure 13

Contours of (a)–(c) average and (d)–(f) rms vapor volume fraction with isolines of mean and rms gas volume fractions, respectively, ranging from 0.1 to 0.5 at injection pressures of (a) and (d) 2 bars, (b) and (e) 3 bars, and (c) and (f) 5 bars.

Figure 14

Contours of mean and rms absolute pressure normalized with the injection pressure and isolines of gas volume fraction ranging from 0.1 to 0.5 at injection pressures of (a) and (d) 2 bars, (b) and (e) 3 bars, and (c) and (f) 5 bars.

Figure 15

Contours of average velocity magnitude and $z$ vorticity for injection pressures of (a) and (d) 2 bars, (b) and (e) 3 bars, and (c) and (f) 5 bars. Also shown are (g)–(i) the mean streamwise velocity distribution and (j)–(l) the rms of streamwise velocity at locations Y0, Y2, and Y4.

Figure 16

Instantaneous contours of (a) and (c) flow velocity in the $y$ direction showing the flow separation of liquid from the inlet edge and ambient gas from the exit edge of the bottom wall and (b) the instantaneous vorticity contours at an injection pressure of 5 bars.

Figure 17

Nondimensional surface area generation (an approximate measure of primary atomization) at different injection pressures. The region where integration is performed is highlighted in blue (in the inset).

Figure 18

The LES mesh resolution assessment using (a) the ratio between the resolved and total turbulent kinetic energy along the lines shown in the inset, and (b) the wall $Y^{+}$ values. All plots are for the extreme condition considered in this study ($P_{\mathrm{inj}}=5$ bars).

Figure 19

Turbulent energy spectra (a), (c), and (e) at the midsection of the nozzle and (b), (d), and (f) 5 mm downstream the nozzle exit in the spray region for injection pressures of (a) and (b) 2 bars, (c) and (d) 3 bars, and (e) and (f) 5 bars.

Figure 20

Comparison between the (a) mixture approach and (b) VOF approach for modeling atomization. Contours of mixture density are normalized with the water density.

Figure 21

Instantaneous contours of (a) vorticity and (b) velocity magnitude from two-dimensional simulation using the mixture model (without surface tension effects). (c) Calculated Weber numbers at the highlighted regions.