Numerical investigations on the deformation and breakup of an n-decane droplet induced by a shock wave

Abstract

This paper adopts the coupled level-set and volume-of-fluid (CLSVOF) and the large eddy simulation (LES) methods to simulate the deformation and breakup of an n-Decane droplet under the action of shock wave. We aim to investigate the effects of the shock Mach number and droplet diameter on temporary deformation and breakup characteristics at high Weber numbers from 5813 to 22380. Additionally, special attention is paid to subsequent sub-droplet size distributions, which many researchers generally ignore. The results indicate that the evolution of droplet deformation and breakup in the shear breakup regime generally agrees with the obtained experimental data. Based on the present methods, the physical mechanisms for variations of multiple recirculation zones and the development of Kelvin-Helmholtz instability in wave formation are discussed. Larger shock Mach number and smaller droplet diameter can significantly increase the cross-stream and stream-wise deformations. Moreover, both relaxation and breakup times are directly proportional to the initial droplet diameters but inversely proportional to the shock Mach numbers. Eventually, as the shock Mach number increases, the superficial area and mass ratios of sub-droplets to parent droplets all increase from 5.596 to 8.278 and from 23.38% to 38.38%, while the ratios respectively increase from 2.652 to 18.523 and from 4.63% to 92.7% as the droplet diameter decreases.

Scale-Resolving Simulation of Shock-Induced Aerobreakup of Water Droplet

“…The temporal integration was performed using the bounded second-order time integration scheme, where the maximum Courant-Friedrichs-Lewy (CFL) number 0.5 was prescribed. As a result, an average time-step of the order of 0.04 µs was obtained, con-sistent with similar studies [33]. Moreover, as sketched in Figure 1, pressure inlet and pressure outlet boundary conditions were prescribed in the stream-wise direction, employing the thermo-fluid dynamic variables reported in Table 1, while symmetry conditions were imposed at the four lateral faces of the computational domain, assuming zero normal gradients of all balanced variables.…”

“…The reference coordinates system (x, y, z) ≡ (x 1 , x 2 , x 3 ) has the first axis aligned with the stream-wise direction, while the origin corresponds to the leading edge of the spherical water body in its initial position. Here, different from previous similar studies [12,33], the shock tube flow was not explicitly simulated, but the discontinuous airflow conditions across the moving shock front were directly imposed. The simulations were initiated with the planar shock front being positioned one diameter away from the droplet leading edge, namely, at x/D 0 = −1, separating the two domain sections with post-shock and pre-shock conditions.…”

Hybrid VOF–Lagrangian CFD Modeling of Droplet Aerobreakup

“…The numerical simulations are conducted by using the industrial solver Ansys Fluent, which has been successfully employed for droplet breakup investigations [12,14], as well as in applied CFD studies of bluff body flows by the present research group [21]. The solver utilizes the finite volume (FV) method to approximate the compressible flow, with the conservation principles being applied over each control volume [37,38].…”

“…From a numerical point of view, since the droplet aerobreakup under the SIE regime is characterized by a very broad range of spatial and temporal scales, the accurate prediction of the droplet deformation and fragmentation is particularly demanding in terms of computing power. Due to the high computational cost of fully three-dimensional (3D) simulations, several CFD studies have been conducted in two spatial dimensions, by considering that the shear-induced breakup of a cylindrical liquid column [10][11][12]. Twodimensional simulations have been mostly focused on the early stages of the breakup process, without investigating the droplet fragmentation and the subsequent mist development [13,14].…”