Two- and three-dimensional simulation of a rising bubble and falling droplet using level set method

Two- and three-dimensional simulation of a rising bubble and falling droplet using level set method

Liao, C.B.
Chen, C.H.

2006-09-05

The numerical simulation of a rising bubble in liquid and falling droplet is presented. The two- and three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phases flow system with free surfaces. A sharp interface separates fluids of different density and viscosity. The interface between gas and liquid is described as the zero level set of a smooth function. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The staggered grid system is used in the numerical model. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. The effect of deformation and motion of a riging bubble is investigated by changing the Reynolds numbers and Weber numbers. A droplet falls into a tank of a quiescent fluid is also simulated. Complex numerical simulations show the capability of our numerical model. Our model can be used to simulate a number of problems and to investigate many physical phenomena involving multi-fluid flows that consider the free surfaces.

level set method
rising bubble
droplet
Runge-Kutta scheme
WENO

http://resolver.tudelft.nl/uuid:2c50954a-eaa9-4924-b496-de642ca132e1

Conference proceedings

conference paper

(c) 2006 Liao, C.B.; Chen, C.H.