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This article presents an investigation of fluid flow and natural convection heat transfer in a cylindrical enclosure heated laterally. Two-dimensional (2D) Reynolds-averaged Navier-Stokes (RANS) equations and three-dimensional (3D) Large Eddy Simulation (LES) calculations are conducted using commercial computational fluid dynamics (CFD) software, ANSYS FLUENT. The Rayleigh number (Ra) = 2E+7 is constant in all of the simulations and is based on a length scale that is equal to the ratio of volume to the lateral area of the reactor, i.e., R/2, where R is the radius of the reactor. The validity of the Boussinesq approximation is analyzed by comparing calculations using both the Boussinesq approximation and temperature-dependent properties (non-Boussinesq approach) using 2D RANS and 3D LES (Dynamic Smagorinsky) formulations. Moreover, 2D axisymmetric k-ω SST RANS model will be implemented to investigate whether the 2D axisymmetric model can give results that are comparable to those of the 3D LES (Dynamic Smagorinsky) model when the corresponding longitudinal or azimuthal cross section are compared. In other words, the validity of using a 2D model instead of a 3D model for the current geometry, flow regime and thermal boundary conditions will be discussed. The flow and temperature contours of these two types of simulations are analyzed, compared to determine the various aspects of each case and discussed for deeper physical insight. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of flow and heat transfer in a large diameter (6.25 in) cylindrical enclosure heated laterally and containing a porous block that simulates the basket of nutrients used in a crystal growth reactor. The numerical model entails the use of a commercially available computational engine provided by ANSYS FLUENT, and based on a two-dimensional (2D) axisymmetric Reynolds-averaged Navier Stokes (RANS) equations. The porous medium is simulated using the Brinkman-extended model accounting for the Darcy and Forchheimer induced pressure drops. The porous ‘plug’ effects are analyzed as both its permeability/inertial resistance and locations in the reactor are changed on a parametric basis, while the Rayleigh number ( Ra = g β Δ TL 3 ν α ) is kept constant at 1.98 × 10 9 . Additionally, the effect of different ratios of the hot to the cold zone lengths are investigated as a part of the current effort. For all cases, the velocity and temperature distributions in the reactor are analyzed together with the flow patterns in, and around the porous block. A comprehensive discussion is provided with regard to the effects of the position of the porous block and its permeability on both the immediately adjacent, and far flows. The consequences on the temperature distribution in the enclosure, when the ratio of the length of the hot-to-cold zones is changed, are also analyzed. [ABSTRACT FROM AUTHOR]

An enhancement to the pressure-decay leak-rate method with mass-point analysis solved deficiencies with the standard method. By adding a control system, a constant gas pressure differential across the test article was maintained. As a result, the desired pressure condition was met at the onset of the test, and the mass leak rate and measurement uncertainty were computed in real time. Data acquisition and control systems were programmed to automatically end the test when specified criteria were met. Typically, the test was stopped when a specified level of measurement uncertainty was attained. Using silicone O-ring test articles, the enhanced method was compared with the standard method that permitted the downstream pressure to be nonconstant atmospheric pressure. Two example cases were presented: one case had a low leak rate, whereas the second leak rate was three orders of magnitude higher. The two methods recorded comparable leak rates, but the enhanced method resulted in significantly lower measurement uncertainty, statistical variance, and test duration. Utilizing this enhancement in leak-rate quantification, projects will realize reduced cost and schedule, improved test results, and easier interpretation between data sets. [ABSTRACT FROM AUTHOR]

This study presents a physics-based cavitation model solving the coupled Rayleigh–Plesset (RP) and Reynolds (RE) equations in a fully transient environment. Inclusion of the surface dilatational viscosity within the interfacial stress balance of a dynamically growing bubble is discussed at length and detailed physical insight into its mechanism adds significantly to the existing body of literature. A parametric study establishes the importance of the surface dilatational viscosity and values on the order of 10 −2 to 10 −4 [N s/m] are shown to establish upper and lower bounds on tensile stresses producing the full and half-Sommerfeld-like solutions respectively. Interactions between rotational speed and eccentricity ratio are elucidated with the overall effect of increasing surface dilatational viscosity shown to be de-stabilizing. [ABSTRACT FROM AUTHOR]

Abstract: This paper is presenting a 3D, isothermal numerical analysis of a cylindrical porous journal bearing characterized by a self-circulating lubricating system that eliminates the necessity of an external circulating pump. The system includes a stationary porous bushing whose inner diameter faces the bearing clearance while the outer diameter faces a wrapped-around reservoir. The loaded, eccentric shaft is generating a high pressure zone in the convergent region followed by a low pressure zone in the divergent region causing the fluid to circulate naturally between the bearing clearance and the reservoir, as it passes through the porous bushing. The fundamental physics of the circulating mechanism are described, and its operation is numerically simulated. The study uses the complete 3D Navier–Stokes Equations (NSE) for the fluid motion in the bearing clearance and the adjacent reservoir. The flow inside the porous matrix is modeled using the Brinkman formulation with added pressure ‘penalties’ brought by the addition of the Darcy and Forchheimer terms. The bearing operates in the fully hydrodynamic lubricating regime disregarding surface roughness effects. A cavitation model proposed by Singhal et al. (2002 [1]) is utilized in the numerical simulation to account for flow and pressure characteristics in the divergent region. The parameters used during the simulations are angular velocity, permeability, porosity, reservoir depth and shaft eccentricity. The results which include the flow patterns, pressure maps and attitude angles, are presented on a parametric basis, and confirm the functionality of the proposed self-circulating system. It was found that the load capacity decreases and the attitude angle increase as permeability increases, and depending on permeability ranges, the increase in the reservoir depth may result in a reduction of the load capacity. Further, certain combinations of geometric parameters and permeability values render the pressure build-up independent of the reservoir depth. Because an optimal configuration requires both a large fluid mass flows through the porous bed (for cooling purposes) and a large load carrying capability, two variables at odds with each other in the present model, an interactive parametric analysis is essential in order to optimize the load carrying capacity versus geometric and operational parameters. [Copyright &y& Elsevier]

Abstract: Direct and cross-coupled damping coefficients are developed for the 2π-film, π-film (Gumbel cavitation condition) and homogeneous two-phase mixture films in a squeeze film damper. The numerical simulation uses the CFD-ACE+ commercial software, which employs a finite volume method for the discretization of the Navier–Stokes equations (NSE). In order to determine the dynamic coefficients, the NSE is combined with a finite perturbation method applied to the ‘equivalent journal’ of the damper. It was found that for the 2π-film and the Gumbel conditions, the damping coefficients exhibit linear characteristics, while the homogeneous cavitation model yields nonlinear coefficients. Using the CFD-ACE+, the inertia/added mass coefficients are derived for the limiting cases of the short and long dampers, respectively. The first set of forces is calculated by setting the fluid density to its actual value. The second set of forces is calculated when the density of the fluid is set close to zero (1E-10kg/m3), thus practically eliminating the effects of the inertia terms. Subtracting the two sets of forces from each other, allows the determination of the inertia component contribution and the corresponding inertia coefficients. By varying the density, dynamic viscosity and whirling speed, it was found that the inertia coefficients follow a single curve represented by a function dependent on the modified Reynolds number, Re*. The inertia coefficients presented in this study are compared with the ones reported by other researchers that used the modified Reynolds equation. Some differences were found between the NSE based results and the Reynolds equation based outcomes. This is attributed to the three-dimensional effects introduced by the totality of the terms comprised in the full NSE. [Copyright &y& Elsevier]

Abstract: This paper presents an experimental and numerical investigation on the natural convection in a rectangular enclosure with lower-half-heated, upper-half-cooled sidewalls. The flow structure contains thin wall-layers and large central vortical circulating zones. The mixing process and the fluid paths caused by the wall-layer head-on collisions and stream–stream interaction are fundamental to the development of the heat and fluid transport mechanisms. The understanding of the flow structures and their mutual interaction provides a guide leading to the optimization of the autoclave internal architecture and to practical suggestions for the design strategy of crystal growth vessels. [Copyright &y& Elsevier]

Abstract: Hydrothermal growth is the industrial method of preference to synthesize high-quality single crystals. The growth vessels, called autoclaves, are cylindrical containers filled with solutions of the crystal material. Under normal conditions, the fluid flows are three-dimensional. A baffle is used to partition the container into two chambers. This paper presents a systematic investigation on the transports through the baffle openings. Results indicate that a single-hole baffle is effective in controlling the fluid exchange and heat transfer between the two chambers. A smaller baffle opening establishes more uniform temperatures in the chambers. The flow structure shows that there is a pair of flow streams across the baffle opening. However, the heat exchange carried by this pair of streams, as well as heat exchange through molecular diffusion, is small. The transport through baffle opening is dominated by turbulence diffusion. Further heat transfer analysis shows that the characteristic length scale in industry growth vessels is a combination of the diameter of the baffle opening, the diameter of the autoclave, and the height of the chambers. [Copyright &y& Elsevier]

Abstract: Achieving better thermal environment for the growth of high quality single crystals has been the focus of numerous investigations. However, a literature review reveals that the topics of research dealt either with turbulent flow in industry size cylindrical hydrothermal autoclaves, or laminar flows in rectangular enclosures. This paper attempts to add new insight to the above-mentioned state of the art. The flow and heat transfer in a lower-half heated, upper-half cooled cylindrical model hydrothermal reactor are studied experimentally and numerically. Results show that for the parameters chosen, the flow in the model reactor is transient. The unsteady jet-like flow in each of the chambers originates from the fluid exchange at the baffle opening. The time-averaged temperature and flow profiles appear to be axially symmetric. The temperature and velocity fluctuations in the near-baffle region are significantly larger than in the rest of the chambers. The total heat flow rate is instrumental on the thermal environment in the upper chamber, while the heating conditions on the lower chamber wall have only minor effects. [Copyright &y& Elsevier]

Abstract: Due to the experimental difficulties brought about by high pressure and temperature growth conditions, flow and heat transfer in industrial hydrothermal autoclaves for the growth of single quartz crystals have been studied mostly numerically. To date, most of the numerical models and associated results are not experimentally validated; only qualitative validation data from experiments done during actual crystal growth production is partly available. In this study, the authors used a model simulated reactor represented by an enclosure with two lower half sidewalls uniformly heated while the upper half sidewalls are uniformly cooled. Flow structures in the reactor are qualitatively visualized using full field flow tracking; particle image velocimetry (PIV) is used for quantitative velocity pattern evaluation. Based on the physical setup and experimentally determined boundary conditions, flow is numerically simulated and the corresponding model is validated through comparison to the experimental results. The ensuing parametric studies show the changing of flow patterns and velocity magnitudes for a variety of enclosure aspect ratios. [Copyright &y& Elsevier]

This paper presents three-dimensional (3D) large eddy simulation (LES) calculations of natural convection in laterally-heated cylindrical enclosures using ANSYS FLUENT. The problem considered here is at a Rayleigh number, ( R a ) of 8.8 × 10 6 , based on a characteristic length scale defined by the ratio of the reactor's volume to the lateral area. The numerical simulations are carried out for three different geometrical configurations: an empty reactor, a reactor with a rack and 32 seeds, and thirdly, a reactor with a rack and 80 seeds mounted inside. The objective of the current study is to understand the effects of the rack and seeds on the flow patterns and thermal distribution inside the reactor. In order to investigate these effects, a comprehensive analysis of velocity and temperature on the selected planes and points inside the domain were performed. Results showed that with an increase in seeds within the reactor, the flow slowed down more, the turbulence intensity reduced, and the extent of temperature inversion increased. These have important implications for the choice of ammonothermal method in terms of acidic or basic, and also for species transport and reactions, which eventually affect the deposition rates of GaN crystals in autoclaves. [ABSTRACT FROM AUTHOR]

The ammonothermal crystal growth technique is one of the most effective methods used for growing Gallium Nitride (GaN) crystals in terms of the final product quality and manufacturing efficiency. Popular applications of GaN crystals include light emitting diodes (LEDs) and high-frequency electronic devices. A laterally-heated cylindrical enclosure with a top to bottom temperature gradient is considered in this study to investigate the fluid mechanics and heat transfer in an ammonothermal crystal growth reactor. Three-dimensional (3D) large eddy simulations (LES) results of natural convection in a laterally heated cylindrical reactor, using the commercial computational fluid dynamics (CFD) software, ANSYS FLUENT, are presented in this paper for a Rayleigh number ( R a ) of 8.8 × 10 6 . The R a is defined based on a length scale that is equal to the ratio of volume to the lateral area of the cylinder ( R / 2 ). In addition, an experiment of a geometrically- and dynamically-similar geometry is developed, and particle image velocimetry (PIV)-based flow visualizations are carried out for the purpose of validating the numerical model. Comparisons between experiments and numerical simulations showed that flow patterns were qualitatively similar, and Fourier transforms of velocity magnitudes at selected points in the domain matched reasonably well. An added interesting observation in the simulation was the existence of temperature inversion, which has potential implications on the choice of mineralizer (acidic/basic). [ABSTRACT FROM AUTHOR]

The present numerical work, the first of its kind, aims at establishing the threshold parameters for dynamic similitude (based on the Rayleigh number (Ra)), for free convection in a cylindrical enclosure heated laterally.Raconsidered in this study spanned a range between 750 and 8.8 × 108, where the characteristic length,L, used in its definition is represented by the ratio of cylindrical enclosure’s volume to its lateral surface area. The commercial code, ANSYS FLUENT, is used to model a 2-D axisymmetric cylindrical geometry. When comparatively analyzed, the results allowed conclusions associating values of theRawith flow development from laminar to turbulent. [ABSTRACT FROM PUBLISHER]