Mechanical and Civil Engineering Seminar

  Direct numerical simulation (DNS) studies of droplet-laden turbulent flows have mostly been limited to sub-Kolmogorov (d < η) size droplets using the point-particle approach. DNS of finite-size droplets (d > η), characteristic of the size of fuel droplets during secondary atomization, requires fully-resolving the flow inside and around the droplets while accounting for the effects of surface tension. The main goal of the present study is to investigate via DNS the effects of finite-size deformable droplets on decaying isotropic turbulence. 

In order to achieve this objective, first, we have developed a three-dimensional volume of fluid (VoF) method for tracking droplets accurately and efficiently in incompressible velocity fields. The novelty of the developed approach is that besides conserving mass globally, a condition not always satisfied by VoF methods, mass conservation is also ensured locally while requiring half the number of advection and reconstruction steps of conventional methods. Then, we have developed and coupled a new pressure-correction method with the VoF method for simulating incompressible two-fluid flows. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation. This equation can then be solved directly using, e.g., the FFT-based parallel Poisson solver that we have developed for petascale supercomputers. For a 10243 mesh, our new pressure-correction method using the FFT-based parallel Poisson solver is ten to forty times faster than the standard pressure-correction method using multigrid. In general, the new pressure correction method could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking.

Our new pressure-correction/VoF flow solver has been verified up to density and viscosity ratios of 10,000 against theoretical results, validated against experimental results, and shown to conserve mass, momentum, and kinetic energy in the inviscid limit. Finally, I will present results from DNS of non-evaporating droplet-laden isotropic turbulence and the effects of varying the droplet Weber number and the density ratio on the time development of the turbulence kinetic energy budget.