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Robert A Brown - One of the best experts on this subject based on the ideXlab platform.
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dynamic simulation of czochralski crystal growth using an integrated thermal Capillary Model
Journal of Crystal Growth, 1994Co-Authors: W Zhou, D E Bornside, Robert A BrownAbstract:Abstract A transient simulation of the Czochralski (CZ) crystal growth of silicon is presented that is based on the integrated thermal-Capillary Model (ITCM) which includes conductive heat transport in the melt, crystal and all other components of a prototypical Czochralski system, diffuse, grey radiation between these components, and the dynamics of the melt/crystal interface, the meniscus and the crystal shape. Time-dependent simulations are carried out using the finite-element method and fully implicit time integration. The utility of the transient analysis is demonstrated by the calculation of operating states and their temporal stability for a quasi-steady-state Model. Multiple operating states are computed for a given crystal growth rate and a limiting value of the power to the heater is found below which no steady-state solutions exist. Transient simulations connect the existence of the multiple states to long time-scale instabilities in the CZ system, which have implications for the control of the batchwise process.
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application of turbulence Modeling to the integrated hydrodynamic thermal Capillary Model of czochralski crystal growth of silicon
Journal of Crystal Growth, 1993Co-Authors: T A Kinney, Robert A BrownAbstract:Abstract The integrated hydrodynamic thermal-Capillary Model (IHTCM) of Czochralski growth for large-diameter silicon crystals is extended to include a k -ϵ Model for turbulence in the melt implemented in a form appropriate for capturing the transition to nearly laminar flow near solid boundaries. Calculations are presented for buoyancy-driven flow alone and for the flow driven by a combination of crystal and crucible rotation, buoyancy and surface tension gradients. These results predict the enhancement in the heat and mass transfer seen in experiments with increased crucible rotation rate, which is not predicted by laminar flow simulatons. The computed temperature fields and interface shapes compare well with measurements reported before (Kinney, Bornside, Brown and Kim, J. Crystal Growth 126 (1992) 413). The use of the k -ϵ/IHTCM for optimization of operating conditions is demonstrated by calculations for varying crystal and crucible rotation rates using an objective function that attempts to optimize oxygen concentration in the crystal, to minimize the radial variation of oxygen and to reduce the magnitude of the thermoelastic stress.
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quantitative assessment of an integrated hydrodynamic thermal Capillary Model for large diameter czochralski growth of silicon comparison of predicted temperature field with experiment
Journal of Crystal Growth, 1993Co-Authors: T A Kinney, Robert A Brown, D E Bornside, K M KimAbstract:Abstract Accuracy in the prediction of the thermal field in a Czochralski (CZ) crystal growth system is crucial for quantitative application of Models. Predictions of the integrated hydrodynamic thermal-Capillary Model (IHTCM) are compared to experimental measurements of the thermal field from growth of 83 mm diameter crystals and the melt/crystal interface shape of a 100 mm diameter crystal obtained in a conventional CZ system. The temperature measurements show good quantitative agreement with predictions irrespective of the Model for melt convection. However, the predicted melt/crystal interface shape is much more sensitive to the type and state of convection in the melt. The IHTCM includes steady-state laminar flows driven by crystal and crucible rotation, natural convection and thermocapillarity. Although flows at the correct intensity can be computed for each mechanism separately, solutions for the combined driving forces only are found when the viscosity of the melt is set artificially high. Calculated values of the thermal stress in the crystal exceed the critical resolved shear stress near the melt/solid interface for all flow conditions. The maximum stress at the melt/solid interface depends on the interface shape and varies between 2.8 and 6.2 times the critical resolved shear stress, depending on the flow.
Suresh G Advani - One of the best experts on this subject based on the ideXlab platform.
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flow of generalized newtonian fluids across a periodic array of cylinders
Journal of Rheology, 1993Co-Authors: M V Bruschke, Suresh G AdvaniAbstract:Traditionally, the Capillary Model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to Model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell Model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell Model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the ef...
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flow of generalized newtonian fluids across a periodic array of cylinders
Journal of Rheology, 1993Co-Authors: M V Bruschke, Suresh G AdvaniAbstract:Traditionally, the Capillary Model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to Model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell Model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell Model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the effect of the fluid rheology and the porosity on the resistance to flow.
Jeffrey J Derby - One of the best experts on this subject based on the ideXlab platform.
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stabilizing detached bridgman melt crystal growth Model based nonlinear feedback control
Journal of Crystal Growth, 2012Co-Authors: Andrew Yeckel, Prodromos Daoutidis, Jeffrey J DerbyAbstract:Abstract The dynamics and operability limits of a nonlinear-proportional-integral controller designed to stabilize detached vertical Bridgman crystal growth are studied. The manipulated variable is the pressure difference between upper and lower vapor spaces, and the controlled variable is the gap width at the triple-phase line. The controller consists of a Model-based nonlinear component coupled with a standard proportional-integral controller. The nonlinear component is based on a Capillary Model of shape stability. Perturbations to gap width, pressure difference, wetting angle, and growth angle are studied under both shape stable and shape unstable conditions. The nonlinear-PI controller allows a wider operating range of gain than a standard PI controller used alone, is easier to tune, and eliminates solution multiplicity from closed-loop operation.
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stabilizing detached bridgman melt crystal growth proportional integral feedback control
Journal of Crystal Growth, 2012Co-Authors: Andrew Yeckel, Prodromos Daoutidis, Jeffrey J DerbyAbstract:Abstract The dynamics, operability limits, and tuning of a proportional-integral feedback controller to stabilize detached vertical Bridgman crystal growth are analyzed using a Capillary Model of shape stability. The manipulated variable is the pressure difference between upper and lower vapor spaces, and the controlled variable is the gap width at the triple-phase line. Open and closed loop dynamics of step changes in these state variables are analyzed under both shape stable and shape unstable growth conditions. Effects of step changes in static contact angle and growth angle are also studied. Proportional and proportional-integral control can stabilize unstable growth, but only within tight operability limits imposed by the narrow range of allowed meniscus shapes. These limits are used to establish safe operating ranges of controller gain. Strong nonlinearity of the Capillary Model restricts the range of perturbations that can be stabilized, and under some circumstances, stabilizes a spurious operating state far from the set point. Stabilizing detachment at low growth angle proves difficult and becomes impossible at zero growth angle.
M V Bruschke - One of the best experts on this subject based on the ideXlab platform.
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flow of generalized newtonian fluids across a periodic array of cylinders
Journal of Rheology, 1993Co-Authors: M V Bruschke, Suresh G AdvaniAbstract:Traditionally, the Capillary Model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to Model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell Model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell Model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the ef...
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flow of generalized newtonian fluids across a periodic array of cylinders
Journal of Rheology, 1993Co-Authors: M V Bruschke, Suresh G AdvaniAbstract:Traditionally, the Capillary Model has been used to describe the permeability–porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to Model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell Model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell Model solution about the Newtonian point, and extending the lubrication approach to power‐law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations in square and hexagonal arrangements of cylinders for Newtonian and mildly shear‐thinning fluids. A scaling is suggested which allows one to separate the effect of the fluid rheology and the porosity on the resistance to flow.
Cheng Zhang - One of the best experts on this subject based on the ideXlab platform.
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the effects of quartz content on the formation of residual water in a brine co2 quartz system an experimental study
Journal of Natural Gas Science and Engineering, 2015Co-Authors: Cheng ZhangAbstract:Abstract Geo-sequestration of CO2 in deep saline aquifers is achieved by injecting CO2 into the aquifers and displacing brine. The residual water formed during the drainage process has a strong influence on traps of residual-gas. Moreover, in the context of CO2 geological storage, the characteristics of the brine–CO2–quartz system directly impact residual trapping capacities. We conducted experiments to investigate the influence of quartz content in the rocks on the formation of residual water and how much of this residual water remains after CO2 is injected. Three sandstone core samples were all saturated with 35 g/L NaCl brine. Supercritical CO2 was injected into the samples at aquifer temperature and pressure and the displaced water and water-gas mixtures were collected and measured. The results show that the irreducible water saturation was lower with higher quartz content in the rock core. The permeability of rock cores can only influence the drainage efficiency; it does not have a decisive impact on the irreducible water saturation. Based on drainage flow rates, the process of drainage can be divided into three stages termed: Pushing Drainage, Portable Drainage and Dissolved Drainage. This terminology differs slightly from previous time-frame characterizations. Note that we have used a Capillary Model to interpret the mechanisms that characterize the three stages in these experiments.
