Numerical simulation of droplet dynamics using level set method

Full text of publication follows: A levitated liquid droplet is used to measure the properties of molten metal at high temperature. Viscosity is, for instance, obtained from the damping of an oscillation of the droplet. The levitation of droplets is controlled by using electrostatic force or ultrasonic wave under the gravitational condition. The droplet is not in contact with a container, and the effect of the container wall is eliminated for a detailed measurement. Small disturbances such as an initial deformation or rotation, which can not be neglected completely in the measurement, however, still have a large effect on the measurement, since the relation between the properties and the oscillation parameters is given by the linear theory. In order to study the effect of initial disturbances and nonlinearity of the droplet dynamics on the measurement, numerical simulations of a liquid droplet are performed. Three-dimensional Navier- Stokes equations are solved using the level set method. The level set function, which is the distance from the droplet surface, is calculated by solving the transport equation to obtain the position of the surface. Mass conservation of the droplet is especially taken into account in the calculation of the level set function. The staggered mesh system is used and the second-order upwind differencing scheme is applied for convective terms. The second-order Adams-Bashforth method is used for time integration. Differences between two-dimensional and three-dimensional calculations are shown first, and it is found that the two-dimensional calculation is not suitable for simulating the droplet dynamics. The nonlinearity effect is studied next. The oscillation of the droplet is simulated by changing the amplitude of the initial deformation, which is given by the Legendre polynomial. The period and the damping of the oscillation are obtained, and the effect of the amplitude on the measurement of surface tension and viscosity is discussed. The effect of initial rotation is also studied. (author)