Direct Numerical Study of a Liquid Droplet Impulsively Accelerated by Gaseous Flow

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. Disciplines Engineering Comments Suggested Citation: Quan, S. and Schmidt, D.P. (2006). Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow. Physics of Fluids 18, 103103. © 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids and may be found at http://dx.doi.org/10.1063/1.2363216. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/275 Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow Shaoping Quan Department of Mechanical Engineering and Applied Mechanics, The University of Pennsylvania, Towne Building, Philadelphia, Pennsylvania 19104 David P. Schmidt Department of Mechanical and Industrial Engineering, The University of Massachusetts at Amherst, Engineering Laboratory, Amherst, Massachusetts 01003 Received 15 June 2006; accepted 24 August 2006; published online 31 October 2006 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. © 2006 American Institute of Physics. DOI: 10.1063/1.2363216