• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.16 no.4
• /
• pp.149-156
• /
• 2006

For an aspect ratio (transport length-to-width) of 5, Pr = 2.89, Le = 0.018, Pe = 2.29, Cv = 1.11, $P_B$=40 Torr, solutally buoyancy-driven convection $(Gr_s=3.03{\times}10^5)$ due to the disparity in the molecular weights of the component A $(Hg_2Cl_2)$ and B (He) is stronger than thermally buoyancy-driven convection $(Cr_t=1.66{\times}10^4)$. The crystal growth rate is decreased exponentially for $2.5\;{\leq}\;Ar\;{\leq}\;5$, with (1) the linear temperature profile and a fixed temperature difference, (2) the imposed thermal profile, a fixed crystal region and varied temperature difference. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. But, with the imposed thermal profile, a fixed source region and varied temperature difference, the rate is increased far $2\;{\leq}\;Ar\;{\leq}\;3$, and remains nearly unchanged for $3\;{\leq}\;Ar\;{\leq}\;5$.

• Korean Chemical Engineering Research
• /
• v.57 no.5
• /
• pp.723-729
• /
• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.20 no.3
• /
• pp.117-124
• /
• 2010

For Ar=5, Pr=1.18, Le=0.15, Pe=2.89, Cv=1.06, $P_B$=20 Torr, the effects of impurity $(N_2)$ on thermally and solutally buoyancy-driven convection ($Gr_t=3.46{\times}10^4$ and $Gr_s=6.02{\times}10^5$, respectively) are theoretically investigated for further understanding and insight into an essence of thermo-solutal convection occurring in the vapor phase during the physical vapor transport. For $10K{\leq}{\Delta}T{\leq}50K$, the crystal growth rates are intimately related and linearly proportional to a temperature difference between the source and crystal region which is a driving force for thermally buoyancy-driven convection. Moreover, both the dimensionless Peclet number (Pe) and dimensional maximum velocity magnitudes are directly and linearly proportional to ${\Delta}T$. The growth rate is second order-exponentially decayed for $2{\leq}Ar{\leq}5$. This is related to a finding that the effects of side walls tend to stabilize the thermo-solutal convection in the growth reactor. Finally, the growth rate is found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.

• Korean Chemical Engineering Research
• /
• v.57 no.1
• /
• pp.142-147
• /
• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.8
• /
• pp.2069-2078
• /
• 1993

The buoyancy-driven turbulent thermal convection is predicted using an anisotropic hybrid turbulence model, which is incorporated with a low Reynolds k-.epsilon. turbulence model and an anisotropic buoyant part of algebraic stress model(ASM). The numerical predictions are compared with the Davidson's model,(1) the full ASM and the experimental results of Cheesewright et al.(2) All the models are shown to predict good agreements with the experiments for the averaged turbulence quantities. It is found that the effect of an anisotropic part on the Reynolds stress and the turbulent heat fluxes is substantial. In this study, the present hybrid model gives a fairly reasonable prediction in terms of the computational accuracy, convergence and stability. The contribution of an anisotropic buoyant part to turbulent heat fluxes are also scrutinized over the range of Rayleigh numbers $(4.79{\times}10^{10}{\le}Ra{\le}7.46{\times}10^{10}).$

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.3
• /
• pp.360-372
• /
• 1998

This study deals with the interaction between buoyancy-induced convection and externally imposed excitation in the form of harmonic rocking and the effect of the interaction upon heat transfer in low-Pr liquids. A wide array of system responses are discussed using the spectral collocation numerical technique. The superposition of buoyancy and Coriolis forces leads to complex fluid flow and heat transfer. The transition to chaotic convection is accelerated, and heat transfer rates are reduced as the enclosure is excited at the fundamental frequency of oscillation associated with the pure buoyancy-driven case. Average heat transfer rates are correlated for Pr=0.02 and 0.03. The heat transfer is affected more in the Pr=0.03 liquid than the case of Pr=0.02.

• Solar Energy
• /
• v.2 no.1
• /
• pp.9-16
• /
• 1982

The problem of transient laminar natural convection in compressible fluid in a rectangular enclosure is considered. The upper and lower boundaries of the enclosure are thermally insulating and the side boundaries are maintained at fixed temperatures. The fluid is considered to be a perfect gas with constant viscosity and thermal conductivity and the formulation differs from the boussinesq simplification in that the effects of variable density are completely retained. The motions are restricted to two dimensions. For incompressible fluid, the natural convection is driven mainly by buoyancy force. But the solutions show that for compressible fluid, the natural convection is driven by pressure and buoyancy forces and the thermally induced motion is acoustic in nature.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.20 no.3
• /
• pp.125-132
• /
• 2010

For typical governing dimensionless parameters of Ar = 5, Pr = 1.16, Le = 0.14, Pe = 3.57, Cv = 1.02, $Gr_s=2.65{\times}10^6$, the effects of thermo physical properties such as a molecular weight, a binary diffusivity coefficient, a partial pressure of component B on solutally buoyancy-driven convection (solutal Grashof number $Gr_s=2.65{\times}10^6$) are theoretically investigated for further understanding and insight into an essence of solutal convection occurring in the vapor phase during the physical vapor transport of a $Hg_2Cl_2-N_2$ system. The solutally buoyancy-driven convection is significantly affected by any significant disparity in the molecular weight of the crystal components and the impurity gas of nitrogen. The solutal convection in a vertical orientation is found to be more suppressed than a tenth reduction of gravitational accelerations in a horizontal orientation. For crystal growth parameters under consideration, the greater uniformity in the growth rate is obtained for either solutal convection mode in a vertical orientation or thermal convection mode in horizontal geometry. The growth rate is also found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.16 no.5
• /
• pp.203-209
• /
• 2006

For $P_B=50,\;{\Delta}T=10K$, Ar=5, Pr=2.36, Le=0.015, Pe=1.26, Cv=1.11, the intensity of solutal convection (solutal Grashof number $Grs=3.44x10^4$) is greater than that of thermal convection (thermal Grashof number $Grt=1.81x10^3$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A($Hg_2Cl_2$) and B(He). With increasing the partial pressure of component B from 10 up to 200 Torr, the rate is decreased exponentially. The convective transport decreases with lower g level and is changed to the diffusive mode at 0.1 $g_0$. In other words, for regions in which the g level is 0.1 $g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than 0.1 $g_0$ can be adequate to ensure purely diffusive transport.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.18 no.6
• /
• pp.225-231
• /
• 2008

For an aspect ratio (transport length-to-width) of 5, Pr=1.13, Le=1.91, Pe=4.3, Cv=1.01, $P_B=20\;Torr$, the effects of addition of inert gas Ne on thermally buoyancy-driven convection ($Gr=2.44{\times}10^3$) are numerically investigated for further understanding and insight into essence of transport phenomena in two dimensional horizontal enclosures. For $10K{\leq}{\Delta}T{\leq}50\;K$, the crystal growth rate increases from 10 K up to 20 K, and then is slowly decreased until ${\Delat}T=50\;K$, which is likely to be due to the effects of thermo-physical properties stronger than the temperature gradient corresponding to driving force for thermal convection. The dimensional maximum velocity gratitude reflecting the intensity of thermal convection is directly and linearly proportional to the temperature difference between the source and crystal regions. The rate is first order-exponentially decreased for $2{\leq}Ar{\leq}5$. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. In addition, the rate is first order exponentially decayed for $10{\leq}P_B{\leq}200\;Torr$.