The possibility to stabilize the oscillatory thermocapillaryconvection is demonstrated using a proportional feedbackcontrol. This topic has a strong industrial motivation inconnection with a container-less crystal growth method calledthe floating-zone technique. The thermocapillary oscillation isknown to cause detrimental striations, microscopicinhomogeneity of the dopant distribution, in the final productof the crystal growth process. The feedback control is realizedby locally modifying the surface temperature by using the localtemperature measured at dierent locations fed back through asimple control law. Placing sensor/actuator pairs (controllers)in a strategical manner using the knowledge of the modalstructures, a simple cancellation scheme can be constructedwith only a few controllers. In this method, the state can bestabilized without altering the base flow appreciably whichcould be advantageous compared with other available controlmethods targeting the base convection. As an initial study of such kind of control method, thisthesis work explores the possibility of applying the control insimplified geometries such as the annular configuration and thehalf-zone for high Prandtl number liquids by means ofexperiments, numerical simulations, and formulation of a simplemodel equation system. Successful suppression of theoscillation was obtained especially in the weakly nonlinearregime where the control completely suppresses theoscillations. With a right choice of actuators, even with thelocal control, it was shown that it is possible to modify thelinear and weakly-nonlinear properties of the three-dimensionalflow system with linear and weakly nonlinear control. On theother hand, the method exhibits certain limitations. Dependingon the geometry of the system and actuators, the limitation canbe caused by either the enhancement of nonlinear dynamics dueto the finite size of the actuators or the amplification of newlinear modes. The former case can be attenuated by increasingthe azimuthal length of the actuators to reduce the generationof broad wavenumber waves. In the latter case, having an ideaof the structures of the newly appearing modes, thedestabilization of those modes can be delayed by optimizing theconfiguration of controllers. On the whole, the oscillation canbe attenuated significantly in a range of supercritical Maup to almost twice the critical value. <b>Keywords:</b>Fluid mechanics, Marangoni convection,thermocapillary convection, annular configuration, half-zone,feedback control, flow visualization, low dimensional model,bifurcation.

<p>The possibility to stabilize the oscillatory thermocapillaryconvection is demonstrated using a proportional feedbackcontrol. This topic has a strong industrial motivation inconnection with a container-less crystal growth method calledthe floating-zone technique. The thermocapillary oscillation isknown to cause detrimental striations, microscopicinhomogeneity of the dopant distribution, in the final productof the crystal growth process. The feedback control is realizedby locally modifying the surface temperature by using the localtemperature measured at dierent locations fed back through asimple control law. Placing sensor/actuator pairs (controllers)in a strategical manner using the knowledge of the modalstructures, a simple cancellation scheme can be constructedwith only a few controllers. In this method, the state can bestabilized without altering the base flow appreciably whichcould be advantageous compared with other available controlmethods targeting the base convection.</p><p>As an initial study of such kind of control method, thisthesis work explores the possibility of applying the control insimplified geometries such as the annular configuration and thehalf-zone for high Prandtl number liquids by means ofexperiments, numerical simulations, and formulation of a simplemodel equation system. Successful suppression of theoscillation was obtained especially in the weakly nonlinearregime where the control completely suppresses theoscillations. With a right choice of actuators, even with thelocal control, it was shown that it is possible to modify thelinear and weakly-nonlinear properties of the three-dimensionalflow system with linear and weakly nonlinear control. On theother hand, the method exhibits certain limitations. Dependingon the geometry of the system and actuators, the limitation canbe caused by either the enhancement of nonlinear dynamics dueto the finite size of the actuators or the amplification of newlinear modes. The former case can be attenuated by increasingthe azimuthal length of the actuators to reduce the generationof broad wavenumber waves. In the latter case, having an ideaof the structures of the newly appearing modes, thedestabilization of those modes can be delayed by optimizing theconfiguration of controllers. On the whole, the oscillation canbe attenuated significantly in a range of supercritical M<i>a</i>up to almost twice the critical value.</p><p><b>Keywords:</b>Fluid mechanics, Marangoni convection,thermocapillary convection, annular configuration, half-zone,feedback control, flow visualization, low dimensional model,bifurcation.</p>

The transient two-dimensional thermocapillary convection and molten pool shape in melting or welding with a time-dependent and distributed incident flux are numerically predicted in this study. Determination of the molten pool shapes is crucial, because of its close relationships with the strength, microstructure, and mechanical properties of the fusion zone. In the work, the time-dependent incident flux is assumed to be a function of scanning speed and energy distribution parameter. Transport processes at the time corresponding to the maximum cross section can be identical to those under steady three-dimensional condition. The computed flow patterns and molten pool shapes under the flat free surface exhibits distinct regions for different Marangoni and Prandtl numbers. The effects of Peclet number and beam power on flow and temperature fields and fusion zone shapes are also presented. The computed results are confirmed by comparing the predicted peak speed on the free surface and molten pool width with those obtained from scale analysis provided in the literature.

A numerical code for solving the time-dependent incompressible 3D Navier-Stokes equations with finite volumes on overlapping staggered grids in cylindrical and rectangular geometry is developed. In the code, written in FORTRAN, the momentum equation for the velocity is solved by projection method and Poisson equation for the pressure is solved by ADI implicit method in two directions combined with discrete fast Fourier transform in the third direction. A special technique for overcoming the singularity on the cylinder's axis is developed. This code, taking into account dependence upon temperature of the viscosity, density and surface tension of the liquid, is used to study the fluid motion in a cylinder with free cylindrical surface (under normal and zero-gravity conditions); and in a rectangular closed cell with a source of thermocapillary convection (bubble inside attached to one of the cell's faces). They are significant problems in crystal growth and in general experiments in fluid dynamics respectively. Nevertheless, the main study is dedicated to the liquid bridge problem. The development of thermocapillary convection inside a cylindrical liquid bridge is investigated by using a direct numerical simulation of the 3D, time-dependent problem for a wide range of Prandtl numbers, Pr = 0.01 - 108. For Pr > 0.08 (e.g. silicon oils), above the critical value of temperature difference between the supporting disks, two counter propagating hydrothermal waves bifurcate from the 2D steady state. The existence of standing and traveling waves is discussed. The dependence of viscosity upon temperature is taken into account. For Pr = 4, 0-g conditions, and for Pr = 18.8, 1-g case with unit aspect ratio an investigation of the onset of chaos was numerically carried out. For a Pr = 108 liquid bridge under terrestrial conditions , the appearance and the development of thermoconvective oscillatory flows were investigated for different ambient conditions around the free surface. Transition from 2D thermoconvective steady flow to a 3D flow is considered for low-Prandtl fluids (Pr = 0.01) in a liquid bridge with a non-cylindrical free surface. For Pr < 0.08 (e.g. liquid metals), in supercritical region of parameters 3D but non-oscillatory convective flow is observed. The computer program developed for this simulation transforms the original non-rectangular physical domain into a rectangular computational domain. A study of how presence of a bubble in experimental rectangular cell influences the convective flow when carrying out microgravity experiments. As a model, a real experiment called TRAMP is numerically simulated. The obtained results were very different from what was expected. First, because of residual gravity taking place on board any spacecraft; second, due to presence of a bubble having appeared on the experimental cell's wall. Real data obtained from experimental observations were taken for the calculations.

A droplet may be prevented from wetting a solid surface by the existence of a lubricating film of air, driven by theromcapillary convection, between liquid and solid surfaces. The noncontact nature and the load-carrying capability of a nonwetting droplet lead to potential engineering applications, e.g., low-friction bearings. The present research consists of two thrusts. The first is aimed at quantifying nonwetting-system failures (film and pinning) triggered by application of a mechanical load, gaining insights to failure mechanisms. Experimental results show that film failure occurs over a wide range of droplet volumes when the temperature difference between the droplet and the plate, the driving potential of the free-surface motion, is small. Interferometric observations reveal flow instability just prior to film failure, with the growth of a nonaxisymmetric disturbance on a free surface (m = 1). Pinning failure becomes more prevalent as the temperature difference is increased, stabilizing the film flow. As part of the present investigation, a system was devised, allowing an oscillating free-surface to be reconstructed from a series of interferograms. The dynamic responses of the free surface reveal mode coupling, with harmonics of the input frequency excited through nonlinearity. The second thrust of the research succeeded in levitating and translating a droplet using the mechanism of permanent nonwetting. In this scheme, the droplet is heated by a CO2 laser and is placed above a cooled glass surface in order to drive the lubricating film that supports the weight of the drop. Furthermore, the position of the droplet can be controlled by moving the heating location, which leads to an asymmetry of the flow fields, driving air from the cooler-end of the droplet and propelling it towards the heat source. These demonstrations suggest the techniques potential use as a liquid-delivery scheme in a Lab-On-a-Chip system. Modeling is carried out to estimate propulsive forces on the droplet and to explain oscillatory behavior observed when excessive heating is applied on the drop. The concept to sandwich a droplet between two plates, a necessary configuration for levitating smaller droplets (less than mm-scale), is also discussed.

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a thinner thickness of the thermal boundary layer than that of momentum boundary layer. Since Marangoni number is usually very high, the domain of scaling is divided into the hot, intermediate and cold corner regions, boundary layers on the solid-liquid interface and ahead of the melting front. The results find that the width and depth of the pool, peak and secondary surface velocity, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical data, different combinations among scaled equations, and available experimental data.

The molten pool shape and thermocapillary convection in melting or welding of metals or alloys having negative surface tension coefficients and Prandtl number greater than unity are determined from a scale analysis. Negative surface tension coefficient indicates that the surface flow is in outward direction, while Prandtl number greater than unity represents that boundary layer thickness of conduction is less than that of momentum. Determination of the molten pool shape is crucial due to its close relationship with the strength, microstructure and properties of the fusion zone. Since Marangoni and Reynolds number are usually greater than ten thousands, transport processes can be determined by scale analysis. In this work, the molten pool is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front for analysis. The results find that the pool shape, surface speed and temperature profiles can be self-consistently evaluated as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and experimental data in the literature.

No description available.

A parallel finite element code with adaptive meshing was developed and used to study three dimensional, time-dependent fluid flows caused by thermocapillary convection as well as temperature and dopant distribution in fusion welding and floating zone crystal growth. A comprehensive numerical model of the three dimensional time-dependent fluid flows in a weld pool had been developed. This model considered most of the physical mechanisms involved in gas tungsten arc welding. The model helped obtaining the actual chaotic time-dependent melt flow. It was found that the fluid flow in the weld pool was highly complex and influenced the weld pool’s depth and width. The physicochemical model had also been studied and applied numerically in order to simulate the surfactant adsorption onto the surface effect to the surface tension of the metal liquid in a weld pool. Another model, a three dimensional time-dependent, with adaptive mesh refinement and coarsening was applied for simulating the effect of weak flow on the radial segregation in floating zone crystal growth. The phase change equation was also included in this model in order to simulate the real interface shape of floating zone. In the new parallel code, a scheme that keeps the level of node and face instead of the complete history of refinements was utilized to facilitate derefinement. The information was now local and the exchange of information between each and every processor during the derefinement process was minimized. This scheme helped to improve the efficiency of the parallel adaptive solver. / QC 20100527

Recently the computational speed and the functions of the numerical methods are advancing rapidly. It is the future trend that using the computational fluid dynamics (CFD) to perform simulation for making up the experimental deficiency, reducing the risk, improving the quality of the product, and saving the cost of research and development. A two-dimensional simulation was employed to study the melt/air and melt/solid interface shapes of the miniature molten zone formed in the laser-heated pedestal growth (LHPG) system. Using non-orthogonal body-fitting grid system with control-volume finite difference method, the interface shape can be determined both efficiently and accurately. During stable growth, the dependence of the molten-zone length and shape on the heating CO2 laser is examined in detail under both the maximum and the minimum allowed powers with various growth speeds. The effect of gravity for the miniature molten zone is also simulated, which reveals the possibility for a horizontally oriented LHPG system. Such a horizontal system is good for the growth of long crystal fibers. After comparing with the shape of the molten zone in terms of the experiment and the analysis of the simulation shown as above. Heat transfer and fluid flow in the LHPG system are analyzed near the deformed interfaces. The global thermal distributions of the crystal fiber, the melt, and the source rod are described by temperature and its axial gradient within length of ~10 mm. As compared with the growth of bulk crystal of several centimeters in dimension, natural convection drops six orders in magnitude due to smaller melt volume; therefore, conduction rather than convection determines the temperature distribution in the molten zone. Moreover, thermocapillary convection rather than mass-transfer convection becomes dominant. The symmetry and mass flow rate of double eddy pattern are significantly influenced by the molten-zone shape due to the diameter reduction and the large surface-tension-temperature coefficient in the order of 10-4~10-3. According to the analysis shown as above, the results could be further extended for the analysis of the concentration profile and study of horizontal growth.