Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach

A droplet exposed to a high-speed gas flow is subject to a rapid and violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet imposed by three different intensity shock waves, with Mach numbers of 1.21, 1.46, and 2.64, under the shear-induced entrainment regime. The numerical investigation is conducted within a physically consistent and computationally efficient multiscale framework, using the Σ-Υ two-fluid model with dynamic local topology detection. Overall, the breakup of the deforming droplet and the subsequent dispersion of the produced mist show good agreement with available experimental studies in the literature. The major features and physical mechanisms of breakup, including the incident shock wave dynamics and the vortices development, are discussed, and verified against the experiments and the theory. While the experimental visualizations inside the dense mist are restricted by the capabilities of the diagnostic methods, the multiscale two-fluid approach provides insight into the mist dynamics and the distribution of the secondary droplets under different postshock conditions.

Figure 1

Initial configuration and information regarding the computational mesh for the simulation of droplet aerobreakup.

Figure 2

Droplet aerobreakup in case 1. (i) Comparison between the experimental visualizations of Theofanous et al. [22] ($t^{*}=0.20$, 0.38) and Theofanous [16] ($t^{*}=0.53$), the simulation results of the deforming coherent droplet (red isoline for water volume fraction value 0.5), and the produced water mist (yellow isosurface for water volume fraction values higher than ${10}^{ndash;5}$). (ii) 3D reconstructed results. (iii) Dimensions of the secondary droplets inside the mist. (iv) Air and water velocity magnitudes (top) and vorticity streams (bottom).

Figure 3

Droplet aerobreakup in case 2. (i) Comparison between the experimental visualizations of Theofanous et al. [22] ($t^{*}=0.23$) and Theofanous [16] ($t^{*}=0.29,0.43$), the simulation results of the deforming coherent droplet (red isoline for water volume fraction value 0.5), and the produced water mist (yellow isosurface for water volume fraction values higher than ${10}^{ndash;5}$). (ii) 3D reconstructed results. (iii) Dimensions of the secondary droplets inside the mist. (iv) Air and water velocity magnitudes (top) and vorticity streams (bottom).

Figure 4

Droplet aerobreakup in case 3. (i) Comparison between the experimental visualizations of Theofanous et al. [22] ($t^{*}=0.18,0.29$) and Theofanous [16] ($t^{*}=0.52$), the simulation results of the deforming coherent droplet (red isoline for water volume fraction value 0.5), and the produced water mist (yellow isosurface for water volume fraction values higher than ${10}^{ndash;5}$). (ii) 3D reconstructed results. (iii) Dimensions of the secondary droplets inside the mist. (iv) Air and water velocity magnitudes (top) and vorticity streams (bottom).

Figure 5

Coherent droplet isolines. Comparison between the experimental isolines of Theofanous et al. [22] (black dashed line) and the simulation isolines for volume fraction value 0.5 using a computational mesh with 100 (red solid line) and 200 (blue solid line) cells per initial droplet diameter. The arrows point to the small deviations between the experimental and simulation isolines.

Figure 6

Coherent droplet isolines for different water volume fraction values, using a computational mesh with 100 cells per initial droplet diameter. Produced water mist isosurface for water volume fraction values higher than ${10}^{ndash;5}$ (gray). Comparison between cases 1, 2, and 3 at time instances that correspond to a decrease for the width of the deforming droplet by 10%, 25%, and 50%. The arrows point to the small deviations in interface sharpness with different volume fraction values.

Figure 7

Gas stream conditions during the droplet aerobreakup, while the incident shock wave lies at the same distance from the center of the droplet. Pressure field and produced water mist evolution (top). Numerical schlieren images and Mach number isolines (bottom).

Figure 8

Volume concentration of the secondary droplets with diameters between 5 and 19 μm (gray), 1 and 5 μm (blue), and lower than 1 μm (yellow) over the total volume of the dispersed region. The volume concentration of the dispersed region over the total volume of the water phase is plotted in red. The green vertical lines correspond to a decrease for the width of the deforming droplet by 10%, 25%, and 50%.

Figure 9

Volume concentration of the subgrid scale mechanisms, namely, turbulence, droplet collision, and secondary breakup, that contribute positively to the local interface surface area production and the creation of smaller-scaled droplets over the total volume of the dispersed region. The green vertical lines correspond to a decrease for the width of the deforming droplet by 10%, 25%, and 50%.

Figure 10

Droplet aerobreakup in case 3 at time instances that correspond to a decrease for the width of the deforming droplet by 10%, 25%, and 50%. Regions in the dispersed mist where the droplet coalescence (purple) and secondary breakup (red) are present (top). Dimensions of the secondary droplets inside the mist (bottom).

Figure 11

Compressibility effects at the early stages of aerobreakup, namely, the incident shock wave downstream propagation, the reflected shock wave in the free gas stream, and the transmitted shock wave into the liquid droplet. Pressure field (top) and numerical schlieren images (bottom).

Figure 12

Demonstration of the upper limit for the secondary droplets' diameters modeled within the diffuse mist, using a computational mesh with a resolution of 100 and 200 cells per original diameter. Illustrated in blue are the secondary droplets inside the mist, captured with both mesh resolutions. Illustrated in red are the droplets that are modeled inside the mist with the coarse mesh but are resolved by the mesh resolution with the fine mesh, shown inside the green box. The arrows point to areas where the coarse mesh detects fragments due to the unresolved interface sharpness.

Figure 13

Volume concentration of the dispersed region over the total volume of the water phase for a mesh resolution of 100 (red solid line) and 200 (blue solid line) cells per initial droplet diameter. The green vertical lines correspond to a decrease for the width of the deforming droplet by 10%, 25%, and 50%.