Interaction between Supersonic Disintegrating Liquid Jets and Their Shock Waves

We used ultrafast x radiography and developed a novel multiphase numerical simulation to reveal the origin and the unique dynamics of the liquid-jet-generated shock waves and their interactions with the jets. Liquid-jet-generated shock waves are transiently correlated to the structural evolution of the disintegrating jets. The multiphase simulation revealed that the aerodynamic interaction between the liquid jet and the shock waves results in an intriguing ambient gas distribution in the vicinity of the shock front, as validated by the ultrafast x-radiography measurements. The excellent agreement between the data and the simulation suggests the combined experimental and computational approach should find broader applications in predicting and understanding dynamics of highly transient multiphase flows.

Figure 1

Shock wave generated by a transonic liquid jet: X-radiographic images of the liquid jet with injecting pressure of 40 MPa at 223 (a) and $338\mu \mathrm{s}$ (b) after SOI, and jet leading-edge speed at various injection pressures: 40, 100, and 135 MPa (c). The line indicates the sonic speed of $138\mathrm{m}/\mathrm{s}$ of ambient gas ${\mathrm{SF}}_6$. The speed is calculated by measuring the jet leading-edge position at various times [18].

Figure 2

Comparison between shock waves measured by microsecond radiography (a)–(c) and computational fluid dynamics simulation (d)–(f). (a) X radiographs reveal the shock waves generated by the liquid jet injected at 135 (top), 100 (middle), and 40 MPa (bottom) at 161, 177, and $330\mu \mathrm{s}$ after SOI, respectively. The color bar indicates the quantitative ambient gas distribution near the Mach cones. (b) Projected excess gas density profiles, in units of $\mu \mathrm{g}/{\mathrm{mm}}^2$, across the shock waves along lines 2.55 ($A\mathrm{\text{−}}A$) and 4.80 mm ($B\mathrm{\text{−}}B$) from the spray axis. (c) Reconstructed 3D gas density along the same lines across the Mach cone. The inset shows the model for the 3D reconstruction [19]. (d) Simulation of shock waves generated at the same injection conditions shown in (a). (e) Simulation results on projected excess gas density profiles along lines $A\mathrm{\text{−}}A$ and $B\mathrm{\text{−}}B$. (f) Simulation results of excess gas density distribution in 3D.

Figure 3

Simulation results of the shock waves generated by a liquid jet with different spray half-angles of (a) $\theta =1.66°$, (b) $2\theta$, and (c) $4\theta$, respectively, with injection pressure and time kept at 100 MPa and $177\mu \mathrm{s}$, after SOI. (d) Comparison of the projected excessive gas density profiles across the Mach cones at 2.55 mm from the cone axis for the three simulations.

Figure 4

Transient multiphase simulation results on aerodynamic behavior and internal structure of the shock waves superimposed with gas phase velocity vectors and gas density distribution: (a) The liquid jet, injected at 100-MPa pressure and $220\mu \mathrm{s}$ after SOI, is overlaid with the gas velocity and density map; (b) the liquid jet alone is replicated for clarity. Major features such as the separation line and rollback sprays are labeled.