“…Another advantage is that LBM or LK methods were designed for high efficient parallel computation [53]. The fluid mass and momentum conservation equations are coupled with energy equations [54] to solve the heat transfer in both liquid and solid phase for crystal growth models. The energy equation can be numerically solved by the traditional methods, such as the FD, FV, and FE method, and it also can be solved in lattice-based schemes.…”
Section: Governing Equations For Continuum Crystal Growth Modelsmentioning
confidence: 99%
“…A series of experimental studies of ACRT has been conducted by Caper and coworkers [77][78][79][80], and they observed Ekman flow and a sidewall instability, which is identified as a Couette instability. A. Yeckel and J. J. Derby [54] used continuum crystal growth models to numerically simulated the ACRT applied to the vertical solidification system, and sidewall instability was shown in their results and identified as a Taylor-Görtler boundary layer instability [82]. It was shown that changing of acceleration in the rotation cycle can dramatically affect the radial and axial segregation in crystal growth system [83].…”
Section: Applications Of Continuum Crystal Growth Modelsmentioning
“…Another advantage is that LBM or LK methods were designed for high efficient parallel computation [53]. The fluid mass and momentum conservation equations are coupled with energy equations [54] to solve the heat transfer in both liquid and solid phase for crystal growth models. The energy equation can be numerically solved by the traditional methods, such as the FD, FV, and FE method, and it also can be solved in lattice-based schemes.…”
Section: Governing Equations For Continuum Crystal Growth Modelsmentioning
confidence: 99%
“…A series of experimental studies of ACRT has been conducted by Caper and coworkers [77][78][79][80], and they observed Ekman flow and a sidewall instability, which is identified as a Couette instability. A. Yeckel and J. J. Derby [54] used continuum crystal growth models to numerically simulated the ACRT applied to the vertical solidification system, and sidewall instability was shown in their results and identified as a Taylor-Görtler boundary layer instability [82]. It was shown that changing of acceleration in the rotation cycle can dramatically affect the radial and axial segregation in crystal growth system [83].…”
Section: Applications Of Continuum Crystal Growth Modelsmentioning
“…3.1a. Both steady [101,102] and accelerated rotation [103][104][105] have been studied using computer modelling. Steady rotation is not favored in this situation because it tends to suppress mixing by damping convective flows in the meriodonal plane (the r, z plane in an r, θ , z cylindrical coordinate system).…”
Section: Bridgman Growth Of Czt: Axisymmetric Analysismentioning
confidence: 99%
“…The equations are solved using Cats2D with the same methods described in the previous section, using up to 40 734 degrees of freedom. We have studied two growth systems, distinguished primarily by size: a large system for growth of 10-cm diameter crystals [103], and a small system for growth of 1.5-cm diameter crystals [104]. Experimental data suitable for constructing a furnace temperature profile for Equation (3.10) are available for both systems.…”
Section: Bridgman Growth Of Czt: Axisymmetric Analysismentioning
“…In Bridgman crystal growth only two melt stirring techniques have been studied, accelerated crucible rotation (20)(21)(22) and low frequency vibrational stirring (23)(24)(25). In this laboratory we have been studying the latter technique and started to do some experiments toward the end of this program to see if we could improve the crystal uniformity.…”
Section: Segregation Problem In Pmnt Growthmentioning
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