TWO PHASE FLOWS
Example 1 ¡ª Thermo-induced Marangoni effects
  • One of two-phase fluids flow example, is two-fluid Marangoni convection in which the heated boundary is embedded in the free surface between two liquid with different densities (with the lighter one on the top), the induced temperature gradient on the surface drives convective motion, and induces vorticity in the bulk fluid. This motion deforms the free surface and lead to a complicated flow pattern. Preliminary numerical experiments for a two dimensional model have already been performed using grid adaptation techniques
  • The experimental counter part has been constructed in the Pritchard Lab by Belmonte.
Example 2 ¡ª Gel fingering phenomenon
The Dynamics Of Gelation And Its Interaction With The Flow Fields
Participants: Andrew Belmonte, Chun Liu, Pengtao Sun , Jinchao Xu
  • The experiments in the Pritchard's Lab show some very interesting phenomena in the process of the gelation between diluted salt water and certain surfactant polymer fluid. Most notably are their special rheological properties, among them, the gel concentration-dependent diffusion of the two fluids and the concentration-dependent surface tensions.
  • Using an energetic variational method with a phase field formulation, we derived the full hydrodynamic system that takes into account the reaction-diffusion of the gelation, they non-homogeneous surface tension and their interactions.?
  • Numerical simulations using multilevel adaptive finite element methods were performed in order to validate the model and compare with the experiments.
Example 3 ¡ª Surface water waves
  • Another even more challenging example is in the area of surface water waves. The Pritchard Lab contains a wave basin with a segmented, programmable wave-maker system that is capable of generating both 2D and 3D water waves. These wave motions are typically modeled by the (inviscid) Euler equations assuming the flow to be irrotational. Yet, both viscous and rotational effects have been observed in many experiments. In particular, a remarkably stable 2D vortex has been observed in 2D and weakly 3D experiments carried out by J. Hammack and D. Henderson. The vortex forms near the center of the basin, spanning its width,and then propagates slowly to the wave-maker where it is extinguished.
  • We will use our grid adaptation and multigrid techniques to develop a \numerical wave basin" based on the Navier-Stokes equations that will be used to predict wave motions as well as resulting vortical motions.

 

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