Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow

Abstract

A liquid spherical droplet impulsively accelerated by a gaseous flow is simulated in order to investigate the drag force and the deformation. The dynamics of the droplet immersed in a gaseous flow are investigated by solving the incompressible Navier-Stokes equations using a finite volume staggered mesh method coupled with a moving mesh interface tracking scheme. The benefit of the current scheme is that the interface conditions are implemented directly on an explicitly located interface with zero thickness. The droplet shape changes as it is accelerated, and the deformation factor of the droplet is as small as 0.2, so mesh adaptation methods are employed to achieve good mesh quality and to capture the interface curvature. The total drag coefficients are found to be larger than typical steady-state drag coefficients of solid spheres at the same Reynolds numbers. This agrees with the observation of Temkin et al. [ J. Fluid Mech. 96, 133 (1980)] that the unsteady drag of decelerating relative flows was always larger than the steady drag. The large recirculation region behind the deformed droplet may explain this greater drag force. The effects of the viscosity ratio, density ratio, and initial Weber number on the droplet dynamics are also studied. It is found that the initial Weber number and the viscosity ratio have significant effects on the droplet dynamics, while the density ratio does not. A liquid spherical droplet impulsively accelerated by a gaseous flow is simulated in order to investigate the drag force and the deformation. The dynamics of the droplet immersed in a gaseous flow are investigated by solving the incompressible Navier-Stokes equations using a finite volume staggered mesh method coupled with a moving mesh interface tracking scheme. The benefit of the current scheme is that the interface conditions are implemented directly on an explicitly located interface with zero thickness. The droplet shape changes as it is accelerated, and the deformation factor of the droplet is as small as 0.2, so mesh adaptation methods are employed to achieve good mesh quality and to capture the interface curvature. The total drag coefficients are found to be larger than typical steady-state drag coefficients of solid spheres at the same Reynolds numbers. This agrees with the observation of Temkin et al. ͓J. Fluid Mech. 96, 133 ͑1980͔͒ that the unsteady drag of decelerating relative flows was always larger than the steady drag. The large recirculation region behind the deformed droplet may explain this greater drag force. The effects of the viscosity ratio, density ratio, and initial Weber number on the droplet dynamics are also studied. It is found that the initial Weber number and the viscosity ratio have significant effects on the droplet dynamics, while the density ratio does not.

Predicting droplet deformation and breakup for moderate Weber numbers

“…After validating their model qualitatively against experimental data, they concluded that droplet breakup in air crossflow is ought to surface waves instead of the boundary layer stripping mechanism. (Quan and Schmidt, 2006) used a moving mesh interface tracking scheme with mesh adaption techniques to simulate impulsively accelerated droplets. They found that the total drag coefficients are larger than typical steady-state drag coefficients of solid spheres at the same Re numbers which is explained by the A C C E P T E D M A N U S C R I P T 10 large recirculation region behind the deformed droplet.…”

Numerical investigation of the aerodynamic breakup of diesel droplets under various gas pressures

“…The work of [10] used the Level-Set method in a 2-D axisymmetric domain to investigate the deformation of droplets at small Re numbers and density ratios (2-32); they found that for density ratios above 32 the boundaries of the breakup regimes are almost unaffected by the density ratio. Furthermore, [11] simulated impulsively accelerated drops using a moving mesh interface tracking scheme and found that the drag coefficient is not affected much by the density ratio although it is larger than those of solid spheres at the same Re numbers. In [12] they used the Level Set method to simulate in a 2-D axisymmetric domain the deformation and breakup of liquid drops under the effect of gas flow.…”

Validated simulation of droplet sedimentation with finite-element and level-set methods

“…Their results for the sedimentation velocities are in good agreement with the experiments, but only a small range of dra oplet diameters was investigated in which the droplets are not expected to exhibit strong interfacial movement (Mack, 2001). The ''moving grid'' front-tracking technique was used by Quan and Schmidt (2006) for the simulation of a liquid droplet in a gaseous current. An implementation of the ''marker point'' front-tracking method (Cristini et al, 1998) was compared to experimental results for droplet breakup by Patel et al (2003).…”