Wanyuan Shi

Hydrothermal waves in rotating annular pools of silicon melt

Influences of pool rotation on thermocapillary convection in shallow annular pools (ri=20 mm, ro=40 mm, and depth ranging from 1 mm to 3 mm) of silicon melt (Pr=0.011), differentially heated from the outer wall, are investigated by numerical simulations. In non-rotating pool, the hydrothermal wave (HTW) appears with characteristic spoke-like pattern. The spoke pattern is stationary or pulsating according to layer depth. However, in the rotating pool, curved HTW pattern propagates in the same azimuthal direction as the pool rotation direction, when observed from a fixed point in the rotating coordinate system. Most important effect of pool rotation is that even low pool rotation rate such as Ω=0.21rad/s weakens the HTW. Further increase of pool rotation rate up to Ω=0.52 rad/s can fully suppress the HTW in the pools of d=2 mm and 3mm, i.e., the pool rotation stabilizes the basic steady axisymmetric thermocapillary flow in annular pool of silicon melt against hydrothermal wave.

Effect of crystal rotation on thermocapillary flow in a shallow molten silicon pool

In order to understand the effect of crystal rotation on thermocapillary flow, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary flow in a shallow molten silicon pool with Czochralski configuration. The crucible sidewall is maintained at constant temperature. Bottom and free surfaces are adiabatic. The temperature difference between the crucible and the crystal is 16 K and crystal rotation rate varies from −10 and 10 rpm. The simulation results indicate that the spoken pattern rotates slowly with the crystal rotation at low rotation rate. When rotation rate exceeds a critical value, the spoken pattern becomes the hydrothermal waves. This transition exists hysteresis.

Experimental investigation on hydrothermal wave in a shallow annular pool

An on-ground experiment was conducted for observation of pattern formation in thermocapillary convection in an annular pool (ri=20 mm, ro=40 mm, and depth d=1.4 mm) of silicone oil (0.65 cSt, Pr=10.1). By a shadowgraph technique, curved traveling hydrothermal waves (HTW) were observed in liquid pools differentially heated at the outer wall. The critical temperature differences (ΔTc) for the incipience of HTW were measured and were semi-quantitatively consistent with our numerical analysis for d=1.0mm and Pr=6.7.

Numerical simulation of thermocapillary convection in an annular pool of silicone oil heated from inner wall

Thermocapillary convection in a shallow annular pool (depth d = 1 mm) of silicone oil (0.65 cSt, Pr = 6.7), heated from the inner wall, is investigated by numerical simulations. Under a fixed value of temperature difference between the outer and inner walls, surface temperature gradient in the inner heated pool is about 10% higher than that in the outer heated pool. Accordingly, the critical temperature difference for the incipience of HTW (ΔTc = 4.58K) is smaller than that (ΔTc = 5.0K) in the outer heated pool. Numerical simulations indicate that two groups of HTW, propagating in opposite azimuthal directions to each other, coexist and produce interference patterns in the inner heated pool. Rotation of the pool around its axis gives no significant influence on the behavior of HTW in the inner heated pool. The characteristics of HTW are discussed in contrast with those in the outer heated pool.Copyright