Pool Rotation Research Articles

Effect of Slag Pool Rotation on the Structure of a High-Speed Steel in a Current-Supplying Mold

Effect of Slag Pool Rotation on the Structure of a High-Speed Steel in a Current-Supplying Mold

Instabilities of thermocapillary-buoyancy flow in a rotating annular pool for medium-Prandtl-number fluid.

The instabilities of the steady axisymmetric thermocapillary-buoyancy flow in a rotating annular pool were investigated by linear stability analysis. The critical instability parameters for the thermocapillary-buoyancy flow (normal gravity) and the pure thermocapillary flow (microgravity) were compared under different pool depths and rotation rates. The results show that the thermocapillary-buoyancy flow is more stable than the pure thermocapillary flow due to the stabilizing effect of the gravity (buoyancy) force. Two types of oscillatory instabilities were observed depending on the different rotation rates, and the propagation direction of the hydrothermal wave is also affected by the rotation rate.

Water entry of spheres into a rotating liquid

Abstract

Thermocapillary Flow Instabilities in a Rotating Annular Pool for Moderate-Prandtl-number Fluid

The linear stability of thermocapillary flow in a rotating annular pool at intermediate Prandtl number (Pr = 1.4) was studied over a wide range of rotation rate. The critical Marangoni number for the onset of flow instability was determined using linear stability analysis based on the spectral element method. The results indicate that the pool rotation can stabilize the thermocapillary flow and affect the instability mechanism. Specially, three bifurcations were observed with increasing Marangoni number when the rotation rate is small, and this peculiar phenomenon is believed to be the competition result of the inertial instability mechanism and the thermocapillary mechanism. Moreover, the steady axisymmetric basic flow was found to be extraordinarily stable in a certain range of rotation rate.

The effect of rotation on the thermal-solutal capillary-buoyancy flow in a shallow annular pool with various capillary ratios

In order to understand the effect of pool rotation on the thermal-solutal capillary-buoyancy convection at various capillary ratios, a series of three-dimensional simulations are performed in a rotating shallow annular pool filled with silicon-germanium melt and subjected to radial temperature and solute concentration gradients under normal gravity. The capillary ratios are Rσ=−0.5, −0.8, −1.25 and −2, while Taylor number ranges from Ta = 0 to 1200. Three types of basic flows are obtained at different capillary ratios. The pool rotation diversely affects the structures of the basic flow and further varies the destabilization mechanisms. The pool rotation enhances the flow stability at Ta < 400 and reduces the flow stability at Ta > 400 with Rσ=−0.5 and −0.8, while it always stabilizes the basic flow at Rσ=−1.25 and −2. The evolution of flow pattern depends remarkably on the Taylor number and the capillary ratio. Multiple flow bifurcations occur at small capillary ratios or high Taylor numbers, which results from the coupling of various driven forces. The reverse transition process is observed at Rσ=−0.5 and −0.8 with Taylor numbers slightly larger than the turning point. Meanwhile, abundant oscillatory flow patterns are shown. The effects of pool rotation on their characteristics are discussed.

Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.

Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

Thermocapillary flow of silicon melt (Pr=0.011) in shallow annular pool heated from inner wall was simulated at the dimensionless rotation rate ω ranging from 0~7000. The effect of pool rotation on the stability of the thermocapillary flow was investigated. The steady axisymmetric basic state was solved by using the spectral element method; the critical stability parameters were determined by linear stability analysis; the mechanism of the flow instability was explored by the analysis of energy balance. A stability diagram, exhibiting the variation of the critical Marangoni number versus the dimensionless rotation rate ω was presented. The results reveal that only one Hopf bifurcation point appeared in the intervals of ω 3965, and the corresponding instability was caused by the shear energy, which was provided by the thermocapillary force and pool rotation, respectively. In addition, the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

Oscillatory flow in a rotating annular pool with radial temperature and solute concentration gradients

This paper presents a series of three-dimensional numerical simulations to investigate the oscillatory flow induced by the surface tension, buoyancy and rotation in an annular pool. The annular pool is filled with the silicon-germanium melt and rotates around the vertical axis at different Taylor numbers ranging from 0 to 1200. The surface tension gradient is induced by the temperature and solute concentration differences. It is assumed that the thermal and solutal capillary effects are opposite and of equal magnitude. Results reveal that the pool rotation can suppress the radial flow by changing the solute concentration distribution. It remarkably influences the flow structure and the flow stability of the basic flow. When the thermal capillary Reynolds number exceeds a critical value, the basic flow would bifurcate to two types of oscillatory convection, depending on the Taylor number. With the increase of Taylor number, the critical thermal capillary Reynolds number increases first, then decreases rapidly once it reaches the inflection point. At last, it keeps at almost a constant level. The evolutions of flow pattern with thermal capillary Reynolds number at different Taylor numbers are obtained. It reveals that the characteristics of these flow patterns are strongly dependent on the Taylor number and the thermal capillary Reynolds number. Corresponding formation mechanisms of these flow patterns are also discussed.

Экспериментальное изучение вращения шлаковой и металлической ванн при электрошлаковом процессе в токоподводящем кристаллизаторе

Экспериментальное изучение вращения шлаковой и металлической ванн при электрошлаковом процессе в токоподводящем кристаллизаторе

Experimental study of slag and metal pool rotation during the electroslag process in current-supplying mould

Experimental study of slag and metal pool rotation during the electroslag process in current-supplying mould

Влияние электрических параметров наплавки дискретной присадкой в токоподводящем кристаллизаторе на скорость вращения шлаковой ванны

Влияние электрических параметров наплавки дискретной присадкой в токоподводящем кристаллизаторе на скорость вращения шлаковой ванны

Influence of electric parameters of surfacing with discrete filler in current-supplying mould on speed of slag pool rotation

Influence of electric parameters of surfacing with discrete filler in current-supplying mould on speed of slag pool rotation

Simulation results of influence of constricted arc column on anode deformation and melting pool swirl in vacuum arcs with AMF contacts

In the process of vacuum arc breaking, the energy injected into the anode will cause anode melting, evaporation, and deformation, resulting in the formation of the anode melting pool. The anode activities have great influence on the arc behavior. When the arc current is large enough, even the influence of axial magnetic field is considered, the arc column still is in contraction state, which means the arc burns only on a part of the electrode. In this paper, the model of anode melting pool deformation and rotation is used, and the model includes anode melting and solidification module, magneto-hydro-dynamic module of the anode melting pool, the volume of fraction method, and the current continuity equation. In this paper, the diffuse arc area is selected as 100%, 75%, and 50%, respectively. The anode temperature and deformation, the anode melting layer thickness, and the rotational velocity of the anode melting pool are obtained. The results show that when the current is at 17.5 kA (rms) and the diffuse arc area is 100%, the anode's maximum temperature is 1477 K and the crater depth is 0.83 mm. But when the diffuse arc areas are 75% and 50%, the anode's maximum temperatures reach 1500 K and 1761 K, and the crater depths reach 1.2 mm and 3 mm, respectively. Arc contraction will lead to more serious anode deformation. A similar result is obtained when the simulation current is 12.5 kA. Under the similar situation, the simulation results in the crater depth, the residual melt layer thickness, the rotational speed of the melting pool, and the maximum temperature of the anode at current zero are in good agreement with the experimental results.

Thermocapillary flow instabilities of medium Prandtl number liquid in rotating annular pools

The linear stability of thermocapillary flow for a medium Prandtl number liquid (Pr = 6.7) is investigated in the annular pools rotating along counterclockwise direction. The neutral Reynolds numbers for the incipience of instabilities are determined by linear stability analysis and the underlying mechanisms are analyzed by energy budgets. Four types of oscillatory instabilities are predicted for different aspect ratios over a wide range of Taylor number. The energy budgets reveal that all the instabilities are basically driven by the hydrothermal wave instability mechanism of moderately large-Prandtl-number liquid. The pool rotation influences the basic flow and enables the disturbances to receive energy in different ways. When the system rotation is initiated, the axisymmetric steady thermocapillary flow becomes unstable typically by a hydrothermal wave instability (type I) for all aspect ratios. The slow rotation destabilizes the basic flow whereas the fast rotation stabilizes it when the Taylor number exceeds a certain threshold value. For large Taylor numbers, two types of flow instabilities (types II and III) occur in sequence with increasing aspect ratio. While type IV arises in a range of Taylor number between those of the type I and type II for the layer of A = 0.25. The critical Reynolds numbers for the onset of the later three oscillatory bifurcations all increase with increasing Taylor number.

Thermocapillary convection in a differentially heated two-layer annular system with and without rotation

Thermocapillary convection in a differentially heated bilayer annular pool consisting of 5cS silicone oil and HT-70 is investigated by a series of three-dimensional numerical simulations. Both systems with and without rotation are considered. The results indicate that the thermocapillary convection is steady and axisymmetric when the Marangoni number is small. The system rotation suppresses the radial flow in the lower layer. Once the Marangoni number exceeds a threshold value, three-dimensional oscillatory flow occurs in both layers simultaneously. The stability diagram reveals that weak rotation destabilizes the axisymmetric flow, while stronger rotation retards the onset of oscillatory flow. The wave patterns for oscillatory flow appear in the form of blade-like waves propagating outward. The surface oscillation and the interface oscillation always share a common frequency but have about a half-period phase lag. In the rotating pool, single group of curved hydrothermal waves propagates in the azimuthal direction opposite to the pool rotation. As the rotation rate increases, the wave number increases while the oscillation frequency decreases.

Inferring in-situ floc size, predicting solids recovery, and scaling-up using the Leung number in separating flocculated suspension in decanter centrifuges

Abstract Centrifugation accompanied by flocculation of fine biosolids is often utilized in wastewater treatment. Unfortunately, commonly used laboratory jar tests often over-estimate the size of the flocculated solids (flocs) that can be realized in-situ in the centrifuge as the fragile flocs can be easily broken by shear and turbulence during feed acceleration in the centrifuge. Currently, there is no satisfactory method to predict in-situ floc size in the centrifuge, despite the floc size is critical to separation and solids recovery. The difficulty in making predictions also leads to inaccuracy in predicting solids recovery by decanter centrifuge and scale-up between centrifuges of different sizes, designs, and operating conditions, which is an even more serious issue. This study attempts to address these hurdles. In this study, first the flow pattern in a decanter centrifuge in form of moving layer at the pool surface is demonstrated by two different experiments. Second, a model on separation of suspended flocs in the moving layer in a centrifuge is developed. Further, a two-parameter model is proposed to represent the floc size distribution wherein the first parameter represents the minimum floc size (primary particle without coagulation or flocculation) and the second parameter represents the median floc size. A closed form analytical solution for the model is obtained with results expressed by the ratio of minimum-to-median floc size and a dimensionless Leung number which measures feed rate to the clarification rate of the centrifuge. Third, a Buckingham-π analysis has been conducted on separation in a moving layer under centrifugal field confirming these two governing dimensionless parameters can also be derived independently from the more basic dimensionless π groups. Fourth, by matching the solids recovery obtained from field tests with the model prediction, the median floc size can be inferred. In this matching process, the minimum floc size is assumed to be equal to the size of the primary, unflocculated solids. Fifth, four sets of tests (over 20 runs) have been carried out using two decanter centrifuges of different sizes and designs operating, respectively, under different pool depths, feed rates, polymer dosages and rotation speeds in a wastewater treatment plant processing mixed sludge with 48% primary sludge and 52% waste activated sludge. The median floc size inferred from the present method is in the range of 4–9 mm from the three series of tests (14 tests). The improved feed acceleration design with speed matching closely that of the rotating pool results in less pool turbulence, larger flocs, and lower polymer dosage (7 kg polymer/ton sludge); while the poorer feed acceleration with more pool disturbance from the under-accelerated feed results in smaller flocs, and higher polymer dosage (9 kg/t). Sixth, an important application of the model is to predict solids recovery using an estimated median floc size and this approach has predicted the solids recovery reasonably well on the fourth set of tests (9 tests). Seventh, the scale-up for predicting solids recovery of flocculated suspension from decanter centrifuges of different sizes, designs, and operating conditions has been demonstrated using the dimensionless Leung number and the minimum-to-median floc size ratio.

Thermocapillary convection with bidirectional temperature gradients in a shallow annular pool of silicon melt: Effects of ambient temperature and pool rotation

In order to understand the characteristics and instability of thermocapillary convection of silicon melt with bidirectional temperature gradients, a series of unsteady three-dimensional numerical simulations were carried out in a shallow annular pool. The imposed radial temperature gradient is established by the temperature difference between the outer and inner walls, while the imposed vertical temperature gradient is formed by adding a constant heat flux at the bottom and the thermal radiation on the top free surface. Two kinds of critical heat fluxes are determined. The first type is to ensure the whole silicon in the pool is in the molten state, and the second type is to judge the onset of oscillatory flow. When Marangoni number is small, a three-dimensional steady flow is common without pool rotation, but it becomes oscillatory at a higher ambient temperature or a small rotation Reynolds number. An axisymmetric steady flow can be observed at a large rotation Reynolds number in the case of small or moderate Marangoni number. Furthermore, the transition from the radial temperature gradient dominated flow to the vertical temperature gradient dominated flow is discussed.

Effect of pool rotation on three-dimensional flow in a shallow annular pool of silicon melt with bidirectional temperature gradients

In order to understand the effect of pool rotation on silicon melt flow with the bidirectional temperature gradients, we conducted a series of unsteady three-dimensional (3D) numerical simulations in a shallow annular pool. The bidirectional temperature gradients are produced by the temperature difference between outer and inner walls as well as a constant heat flux at the bottom. Results show that when Marangoni number is small, a 3D steady flow is common without pool rotation. But it bifurcates to a 3D oscillatory flow at a low rotation Reynolds number. Subsequently, the flow becomes steady and axisymmetric at a high rotation Reynolds number. When the Marangoni number is large, pool rotation can effectively suppress the temperature fluctuation on the free surface, meanwhile, it improves the flow stability. The critical heat flux density diagrams are mapped, and the effects of radial and vertical temperature gradients on the flow are discussed. Additionally, the transition process from the flow dominated by the radial temperature gradient to the one dominated by the vertical temperature gradient is presented.

Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method

The stability of thermocapillary flow in a slowly rotating shallow annular pool was investigated by using the Legendre spectral element method. The silicon melt (Pr=0.011), filling in a pool with adiabatic free surface and bottom, was heated at the outer cylindrical wall and cooled at the inner cylindrical wall. The critical stability conditions for different dimensionless rotation rates ω, ranging from 0 to 2000, were determined by linear stability analysis. Moreover, the energy analysis was applied to further illustrate the underlying mechanism of the flow instability. The results indicate that there is one Hopf bifurcation for ω<940 and ω>1185. Thermocapillary flow is the dominant factor of the instability for ω<940, and the pool rotation becomes the key role for the first instability for ω>1185. Three turning points were observed in the interval 940⩽ω⩽1185, corresponding to three transitions between two-dimensional steady flow and three-dimensional oscillatory flow, owing to the competition of two driving forces with increasing Marangoni number at a fixed ω. With pool rotation, the results exhibit that the flow instability is deduced to occur initially in the zone near the cold wall with the evidence of the extreme velocity gradient and also the distribution of the local kinetic energy.

Numerical simulation of influence of anode current density distributions on anode melting pool flow in high-current vacuum arc subjected to axial magnetic fields

In order to investigate the formation reason and influence factors of anode melting pool rotation in high-current vacuum arcs (HCVAs) subjected to axial magnetic field (AMF), the rotational symmetric magnetohydrodynamic (MHD) model of anode melting pool flow (AMPF) phenomena in HCVA is established. Based on this model, the influence of different anode current density distributions (ACDDs) on AMPF is simulated and analyzed. Simulation results show that the influence of ACDDs on rotational velocity of AMPF is significant. According to simulation results, the more nonuniform ACDDs can lead to the more rotational velocity. That is to say, the more serious current constriction in HCVA will lead to the larger rotational velocity of AMPF. The changing trend of rotational velocity in simulation results at different moments is in agreement with the experimental observation. Experimental and simulation results both show that the maximal rotational velocity appears at 9–10 ms moments.