Charn-Jung Kim

Two-dimensional freezing of water filled between vertical concentric tubes involving density anomaly and volume expansion

Abstract Freezing of an initially superheated water filled within an axisymmetric enclosure is studied numerically. Simulation is carried out using a computational method recently developed by the authors to treat moving boundary problems in axisymmetric geometries. Emphasized is the influence of both volume expansion and density anomaly upon freezing via natural convection. Two distinctive types of thermal boundary conditions are identified and utilized to guide our efforts to investigate the freezing process. Due to the density anomaly of pure water, fluid flow direction reverses depending on the initial superheat of water and thereby the interface slope exhibits an inversion behavior. By assuming that the water does not flood over the ice surface, the volume-change-induced rise of ice formed results in a substantially curved surface. Effects of several parameters characterizing phase-change process of interest are investigated. Numerical results clearly reveal that freezing undergoes multiple stages and proceeds in a complicated manner especially when the water is superheated over the density-extremum temperature.

Effects of buoyancy and periodic rotation on the melt flow in a vertical Bridgman configuration

The effects of thermal gravitational and periodically varying centrifugal forces on the fluid flow and heat transfer are investigated based on a simulation model for the vertical Bridgman crystal growth system with the accelerated crucible rotation technique (ACRT). The principal role of the crucible rotation is analyzed in a sequential manner by varying the complexities of rotating motion; long-time spin-up and ACRT. The long-time spin-up is found to enhance the heat transfer rate in the vicinity of the center. In light of the crystal-growth, this is considered to promote the concavity in the melt/crystal interface shape. By contrast, ACRT is observed to be conductive to maintaining the convexity of the interface through the periodic interaction between the Ekman layers and the inner fluid core. Overall, the present investigation confirms the available results from simulation experiments and crystal-growth runs in that ACRT can improve the melt stirring and the crystal growth rate.

EFFICIENT AND ROBUST MATRIX SOLVER FOR THE PRESSURE CORRECTION EQUATIONS IN TWO- AND THREE-DIMENSIONAL FLUID FLOW PROBLEMS

When fluid flow problems are solved by the SIMPLE-like sequential procedures, most of the computing time is spent on handling the pressure-correction equation. As a result, the overall efficiency of those sequential procedures is strongly dependent on how good is the matrix solver for the pressure correction equation. In this article, a modified conjugate gradient solver (MCGS) is presented that is specially tuned to solve the pressure-correction equations arising from both two- and three-dimensional fluid flow problems. A new solver described here lakes the advantages of conjugate gradient solver (CGS) and strongly implicit procedure (SIP) but eliminates the disadvantages of each. In contrast to the SIP, the present MCGS adopts the partial cancellation of zeroth order and is insensitive to variation of the cancellation parameter. In general, MCGS can be two or three times faster than CGS but is an order of magnitude faster than SIP and block-corrected ADI in treating large-scale problems.

Parametric Study of the Two-Dimensional Keyhole Model for High Power Density Welding Processes

This study presents a parametric study of the two-dimensional steady-state keyhole model for high power density welding processes. Keyhole formation is common to electron beam welding, laser welding, and plasma arc welding, all of which are important techniques for high-quality, high-precision welding. Computation was performed by adopting a recently developed concept of the position correction and modifying it suitably for the problem of interest. The dimensionless parameters pertaining to the model were identified and the influence of each parameter was investigated separately. Although the mathematical model employed here has been used in previous studies, a thorough investigation successfully revealed new features that have not been previously recognized in the literature.

A block-correction aided strongly implicit solver for the five-point formulation of elliptic differential equations

Abstract An efficient and robust iterative solver was proposed to solve the five-diagonal matrix equations that arise from implicit discretization of two-dimensional thermal and fluid flow problems. By regarding the well-known ADI solver and the direct solver as the lowest and the highest levels of matrix decomposition, a systematic investigation was carried out to identify which level of matrix decomposition is then most suitable for the five-point formulation currently in use. Also, the existing block-correction procedure is implemented by deliberately evaluating the residual. In this way, both the high- and low-frequency errors are efficiently reduced so that the new iterative solver provides savings of about an order of magnitude in the computational cost. As the grid size increases, the new solver presented here turns out to be more powerful and more robust than other iterative solvers previously available.

Bifurcation phenomenon during the fixed-solid-mode melting inside a horizontal cylinder

Abstract As for the inward melting inside an isothermal horizontal cylinder, where the unmelted solid core is constrained from moving under gravity, two drastically different melting patterns have been reported in the literature; the shape of the melting surface in the bottom portion has been observed to be either concave or convex. The present work was motivated to elucidate the main cause of these conflicting results. This was done first by obtaining the full transient solutions conforming to the model equations, and then by introducing the bifurcation times as well as a pair of bifurcating solutions. It was found that the convex pear-like melting surface could be well explained in terms of the primary bifurcating solution. Another mode of melting, in which the concave crater shape of the melting surface was observed, turned out to be also a kind of branching solution to the melting process of interest.

On the selection of prognostic equations for the rotating motion in simulating Czochralski flow

Abstract When the fluid flow in the Czochralski crystal growth system involves swirling motion due to rotation effects, numerical simulation of the Czochralski flow can be performed using either the azimuthal velocity component or the angular momentum per unit mass, viz., the swirl, as the dependent variable to resolve the rotating motion. In the presence of a strong inward flow toward the axis, the Coriolis coupling in the azimuthal velocity equation can be a source of computational instability. This difficulty has been overcome by transforming the prognostic equation for the azimuthal velocity into the so-called swirl equation. In this article we show that although these two prognostic equations are mathematically identical to each other, numerical simulations based on them could yield appreciably different results under certain circumstances. This important as yet unresolved aspect of the Czochralski flow simulation is highlighted and the underlying cause of the discrepancy is addressed in the present ...

Computational Fluid Dynamics Study on Performance Variation of PEMFC with Serpentine Flow Fields According to Humidity Condition

Water management has been recognized as a crucial factor for achieving better performance and stability in polymer electrolyte membrane fuel cells (PEMFCs). Proper water management should provide favorable water conditions, including the local humidity, membrane water content, and liquid water saturation in PEMFCs, thereby leading to more uniform electrochemical reaction and current generation. In this study, computational fluid dynamics (CFD) simulation was conducted to investigate the effects of the cathode relative humidity (RH) on the performance of a 3 by 3 cm 2 PEMFC with serpentine flow fields. The CFD results showed that the best performance of the PEMFC was obtained for the cathode RH of 80%, but the performance variation was small for the cathode RH range of 60~100%. However, the loss of the PEMFC performance was significant when the cathode RH was reduced below 40%. The reason for such performance variation was investigated through the detailed inspection of ohmic loss, activation and concentration overpotential, and water and current distributions.

A BLOCK CORRECTION-AIDED, STRONGLY IMPLICIT PROCEDURE TO TREAT SIMULTANEOUS LINEAR EQUATIONS ARISING FROM IMPLICIT DISCRETIZATION OF THREE-DIMENSIONAL FIELD EQUATIONS

A block correction-aided, strongly implicit procedure (BASIP) is presented in this article to treat simultaneous linear equations arising from implicit discretization of three-dimensional field equations. In principle, the present BASIP solver is developed as a judicious combination of the strongly implicit procedure (SIP) and the block correction procedure. By introducing a simple order-of-magnitude analysis, computational efforts for the matrix decomposition are curtailed considerably in BASIP. A major advantage of the present BASIP over SIP lies in its stable operation in response to variation of the cancellation parameter. When tested with two example problems, the convergence rate of BASIP is found to be equivalent to that of an optimized SIP. Accordingly, a new solver presented here can be used as an alternative to an optimized SIP in treating three-dimensional problems.

A FULL NAVIER-STOKES ANALYSIS OF FLOW AND HEAT TRANSFER IN STEADY TWO-DIMENSIONAL TRANSONIC CASCADES

Fluid flow and heat transfer in a turbine blade row were investigated numerically using the two-dimensional, steady-state Navier-Stokes equations and the energy equation with dissipation. The finite-volume integration approach was employed to discretize the fully elliptic governing equations. A non-staggered grid system in the boundary-fitted coordinates was used and the compressible version of the SIMPLE was employed to solve extra equations. An ‘O-C-H’ type grid system was applied owing to its advantages of easily treating the blunt trailing edge and of producing less skewness in the boundary layer region. For an accurate prediction of the heat transfer coefficient at the turbine blade, the first numerical node from the wall was placed at y+∼3 so that it was embedded inside the viscous sublayer. The influence of the turbulence was analyzed with a new free-stream turbulence model which accounts for the free-stream turbulence and flow acceleration. Also the laminar-turbulent transition model was improved. Computations were performed for the low solidity Allison C3X turbine cascade. Present results showed good agreement with available experimental data in terms of the surface pressure and the heat transfer coefficient. Especially much improved distribution of the heat transfer coefficient was obtained in the vicinity of the leading and trailing edges. For practical purposes, the aerodynamic performance and the behavior of the heat transfer coefficient were analyzed by varying the inflow angle.© 1993 ASME