Pool Rotation Research Articles

Stability of Thermocapillary Convection in Rotating Shallow Annular Pool of Silicon Melt

In order to understand the effect of pool rotation on stability of thermocapillary convection, the critical conditions for the incipience of oscillatory flow in rotating shallow annular pools of silicon melt (Pr = 0.011) are investigated by means of linear stability analysis (LSA) under different pool rotation rates ranging from Ta = 0 to 1,513.9 and under microgravity condition. The results indicate that with increase of Ta numbers, the critical Marangoni for the incipience of hydrothermal wave (HTW) increases, i.e., pool rotation stabilizes the steady axisymmetric thermocapillary convection of silicon melt. The critical azimuthal wave number mc decreases linearly with increase of Ta number when Ta ≤ 378.5. However, when Ta > 378.5, mc almost keeps constant with mc = 34. When Ta 550.

Three-dimensional flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface

In order to understand the fundamental characteristics of the forced flow driven by iso- and counter-rotation of a shallow pool and a disk on the free surface, we conducted a series of unsteady three-dimensional numerical simulations in a shallow pool. The ratio of the disk to pool radius is Rs=0.3 and the aspect ratio of pool is H=0.06. The results indicated that the forced flow driven by disk and pool rotation is axisymmetric and steady at the small rotation Reynolds number. However, when Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, which is characterized by the velocity fluctuation waves traveling in the azimuthal direction. The propagating direction and the velocity of the waves depend on the rotation rates and directions of the disk and pool. Besides, the critical conditions for the onset of the oscillatory flow were determined. The details of the flow fields were discussed and the mechanism of the flow pattern transition was also exhibited.

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.

Thermocapillary convection in a shallow annular pool heated from inner wall

In order to discover the effect of heating direction on the thermocapillary convection, three-dimensional numerical simulations have been conducted in a shallow annular pool (depth d=1 mm) of silicone oil (0.65 cSt, Pr=6.7) differentially heated from the inner wall. The linear stability analysis predicts a critical temperature difference (ΔTc) for the incipience of hydrothermal wave (HTW) is 4.58K, which is less than ΔTc=5.0K for a pool heated at the outer wall. Numerical simulations predict that two groups of HTWs, propagating in azimuthal directions opposite to each other, always coexist in the pool. Simulations with pool rotation around the axis elucidate that pool rotation up to 1.05 rad/s gives no distinguishable effect on the behavior of HTW in an inner heated pool, whereas the HTW patterns in an outer heated pool are significantly modified by rotation.

Effect of pool rotation on flow pattern transition of silicon melt thermocapillary flow in a slowly rotating shallow annular pool

In order to understand the mechanism of the flow pattern transitions on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a slowly rotating shallow annular pool in the counter-clockwise direction. The pool was heated from the outer cylinder and cooled at the inner cylinder. The temperature differences between the vertical outer and inner cylinders ranged from 5K to 28K and annular pool rotation rate from 0 and 2rpm. Bottom and top surfaces of the melt pool were adiabatic. The simulation results indicate that two flow transitions occur when increasing the radial temperature difference along the free surface. At first, the steady two-dimensional flow becomes the first hydrothermal wave and then the second hydrothermal wave with less wave number. The critical conditions for the onset of the instability and the transition zone between the first and the second hydrothermal wave are determined at various rotation rates. Characteristics of the steady and the three-dimensional flows are discussed.

Effect of pool rotation on thermocapillary convection in shallow annular pool of silicone oil

The influence of pool rotation on the thermocapillary flow in a shallow annular pool ( R i=20 mm, R 0=40 mm, and depth d=1 mm) of silicone oil (0.65 cSt, Pr=6.7), heated from the outer wall and cooled at the inner wall, is investigated by numerical simulations and linear stability analysis (LSA). The increase in Ta from 0 to 0.322 and 0.806 destabilizes the basic steady axisymmetric flow field against hydrothermal waves (HTW) and the critical Marangoni number Ma c decreases from 8.396×10 3 to 8.096×10 3 and 7.999×10 3, while the critical azimuthal wave number m c increases from 27 to 30 and 33. In rotating annular pool, the HTW propagates in the direction opposite to the pool rotation, when observed from a view point in the rotating coordinate. At Ma=1.34×10 4, the azimuthal wave number m increases up to 54 and branching of spiral arms occurs near the inner wall. This branching phenomenon occurs only at Ma=1.34×10 4 and disappears at larger values of Ma. However, at Ma=2×10 4, two groups of HTWs ( m=48 and m=5) coexist and the HTW with m=5 propagates in the same azimuthal direction as that of the pool rotation. Both the numerical simulation and LSA results indicate that the pool rotation destabilizes the basic steady axisymmetric thermocapillary flow in the present Ta range ( Ta⩽0.806). The influence of the pool rotation on the instability of the thermocapillary flow is distinguishable even for such a small rotating rate of the shallow annular pool. This can be explained by the additional energy supply from the azimuthal flow field induced by the Coriolis force.

Electrical and magnetic interactions in vacuum-arc remelting and their effect on the metallurgical quality of specialty steels

The principal interactions between melting current, self-generated magnetic fields, and structural parts of the vacuum arc furnace, and the effect of unsymmetrical stray fields on arc characteristics, pool behavior, and metallurgical quality are briefly reviewed. Various macrosegregation defects are caused by unbalanced electromagnetic interactions affecting pool rotation and the solidification process. The procedure for measuring magnetic-flux density is described, and the results obtained on a large vacuum arc furnace with different bus-bar arrangements are presented. These results, along with extensive operational observations, strongly pointed out the importance of properly located current connections and coaxial current flow on furnace operation and ingot quality. Corrective actions and modifications of the current transmission system to eliminate nonuniform magnetic stray fields from the arc and melting zone are outlined. A coaxial, electromagnetically “clean” configuration of the entire current circuit to and within the furnace is a most important requirement for consistent consumable-electrode melting operation and reliable avoidance of macrosegregations in specialty steels and alloys. A discussion of controlling electromagnetic interactions by careful engineering of the current supply layout and incorporation of these concepts into an advanced furnace design concludes the paper.