• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.435-443
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• 2007

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax\;=\;{\lambda}Bx$, where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.175-184
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• 1999

A theoretical study on the turbulent round jet diffusion flame impinging on the wall was carried out to predict the characteristics and structure of Impinging jet flame and heat transfer to the wall. Finite chemistry via Arrhenius equation and eddy dissipation model was adopted as a combustion model, and the Favre averaging and $k-{\varepsilon}$ model were Introduced In the theoretical modeling. The SIMPLE algorithm was applied to the calculation. All the transport properties were considered as the variable depending on the temperature and composition. For the parametric study, the distance from nozzle to impinging wall and Reynolds number at nozzle exit were chosen 88 the major parameters. As the results of the present study, the characteristics of flow fields, the distributions of main variables and each chemical species and the flame shapes were obtained. The heat transfer rate from the flame to the wall and the effective heating area were calculated to investigate the Influences of the major parameters on the heat transfer characteristics.

• Journal of Environmental Impact Assessment
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• v.8 no.3
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• pp.13-22
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• 1999

Tidal flow and water quality were simulated in this paper to assess environmental impact caused by pier construction projects in Onsan harbor system. The Surfacewater Modeling System (SMS) was applied to the Onsan harbor system, where coastal reclamation and dredging were planned to build the piers. A finite element mesh was constructed and refined to cover the complicated geometry of the Onsan harbor and the proposed reclamation area. The time variable change of tidal height at harbor inlet was given as an input condition to tidal simulation. The water quality simulation was based on the discharge rate of suspended solids at the reclamation area. The simulation results have shown reasonable agreements with real situations in both tidal flow and water quality. According to the proposed plan, tidal flow and water quality were predicted during and after the pier construction. The tidal simulation study showed that there would be no discernible change of tidal current in the harbor except for the dredged area. The water quality simulation, however, predicted that suspended solids would increase significantly near the reclaimed and dredged areas during construction.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.9
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• pp.879-888
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• 2009

Unsteady three-dimensional reacting flowfield generated by transverse hydrogen injection into a supersonic mainstream is numerically investigated using DES and finite-rate chemistry model. Comparisons are made with experimental results to investigate the turbulent reacting flow physics. The numerical OH distribution describes well the experimental OH-PLIF result, while the numerical ignition delay time shows some disparity due to the restricted available experimental data. The intermittency phenomena are identified by the comparative analysis between RANS and DES. Those effects are also quantified by the temperature distributions along streamlines and superimposed OH mass fraction along with time.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.1
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• pp.68-75
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• 2005

By utilizing a semi-empirical soot model, the applicability of the laminar flamelet concept fur simulating the formation and oxidation of soot in the laminar diffusion flame has been studied. The source terms for two transport equations of the soot formation and oxidation are calculated in the mixture fraction/scalar dissipation rate space for laminar flamelets and stored in a library. In this study, emphasis is given to the interaction associated with radiation and soot formation. The radiative heat loss is obtained by solving the radiative transfer equation using the unstructured grid finite volume method with the WSGGM. The calculated temperatures and soot volume fractions agree relatively well with the experimental data and the previous numerical results of Kaplan et al. using the detailed chemistry.

• Nuclear Engineering and Technology
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• v.41 no.10
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• pp.1275-1284
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• 2009

A directly heated $SO_3$ decomposer for the sulfur-iodine and hybrid-sulfur processes has been introduced and analyzed using the computational fluid dynamics (CFD) code CFX 11. The use of a directly heated decomposition reactor in conjunction with a very high temperature reactor (VHTR) allows for higher decomposition reactor operating temperatures. However, the high temperatures and strongly corrosive operating conditions associated with $SO_3$ decomposition present challenges for the structural materials of decomposition reactors. In order to resolve these problems, we have designed a directly heated $SO_3$ decomposer using RA330 alloy as a structural material and have performed a CFD analysis of the design based on the finite rate chemistry model. The CFD results show the maximum temperature of the structural material could be maintained sufficiently below 1073 K, which is considered the target temperature for RA 330. The CFD simulations also indicated good performance in terms of $SO_3$ decomposition for the design parameters of the present study.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.62-68
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• 2004

A comprehensive numerical analysis has been carried out for both non-reacting and reacting flows in a scramjet engine combustor with and without a cavity. The theoretical formulation treats the complete conservation equations of chemically reacting flows with finite-rate chemistry of hydrogen-air. Turbulence closure is achieved by means of a k-$\omega$ two-equation model. The governing equations are discretized using a MUSCL-type TVD scheme, and temporally integrated by a second-order accurate implicit scheme. Transverse injection of hydrogen is considered over a broad range of injection pressure. The corresponding equivalence ratio of the overall fuel/air mixture ranges from 0.167 to 0.50. The work features detailed resolution of the flow and flame dynamics in the combustor, which was not typically available in most of the previous studies. In particular, the oscillatory flow characteristics are captured at a scale sufficient to identify the .underlying physical mechanisms. Much of the flow unsteadiness is related not only to the cavity, but also to the intrinsic unsteadiness in the flow-field. The interactions between the unsteady flow and flame evolution may cause a large excursion of flow oscillation. The roles of the cavity, injection pressure, and heat release in determining the flow dynamics are examined systematically.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.1
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• pp.1-8
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• 2012

Acoustic-pressure response of diluted hydrogen-air diffusion flames is investigated numerically by adopting a fully unsteady analysis of flame structures in low and high pressure regimes. As acoustic frequency increases, finite-rate chemistry is enhanced through a nonlinear accumulation of heat release rate for any pressure regime, leading to a high amplification index. Same numerical results are analyzed with application of a pressure-sensitive time lag model, and thereby, interaction index and time lag are calculated for each pressure regime. The interaction index has the largest value in each pressure regime at an acoustic frequency near 1000 Hz. In a high-pressure regime, flames are more unstable than in a low-pressure regime. The interaction index shows a good agreement with the amplification index.

• Applied Biological Chemistry
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• v.43 no.2
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• pp.116-123
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• 2000

A numerical model of three-dimensional soil water distribution for drip irrigation management under cropped conditions was developed using Richards equation in Cartesian coordinates. The model accounts for both seasonal and diurnal changes in evaporation and transpiration, and the growth of plant root and the shape of root zone. Solutions were numerically approximated using the Crank-Nicolson implicit finite difference technique on the block-centered grid system and the Gauss-Seidel elimination in tandem. The model was tested under several conditions to allow the flow rates and configurations of drip emitters vary. In general, simulation results agreed well with experimental results and were as follows. The velocity of soil-water flow decreased drastically with distance from the drip source, and the rate of expansion of the wetted zone decreased rapidly during irrigation. The wetting front of wetted zone from a surface drip emitter traveled farther in vertical direction than in horizontal direction. Under this experimental weather condition, water use efficiency of a drip-irrigated apple field was greatest for 4-drip-emitter system buried at 25 cm, resulting from 10% increase in transpiration but 20% reduction in soil evaporation compared to those for surface 1-drip emitter system. Soil moisture retention curve obtained using disk tension infiltrometer showed significant difference from the curve obtained with pressure plate extractor.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.05a
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• pp.91-93
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• 2003

A comprehensive numerical study is carried out to investigate for the understanding of the flow evolution and flame development in a supersonic combustor with normal injection of ncumally injecting hydrogen in airsupersonic flows. The formulation treats the complete conservation equations of mass, momentum, energy, and species concentration for a multi-component chemically reacting system. For the numerical simulation of supersonic combustion, multi-species Navier-Stokes equations and detailed chemistry of H2-Air is considered. It also accommodates a finite-rate chemical kinetics mechanism of hydrogen-air combustion GRI-Mech. 2.11[1], which consists of nine species and twenty-five reaction steps. Turbulence closure is achieved by means of a k-two-equation model (2). The governing equations are spatially discretized using a finite-volume approach, and temporally integrated by means of a second-order accurate implicit scheme (3-5).The supersonic combustor consists of a flat channel of 10 cm height and a fuel-injection slit of 0.1 cm width located at 10 cm downstream of the inlet. A cavity of 5 cm height and 20 cm width is installed at 15 cm downstream of the injection slit. A total of 936160 grids are used for the main-combustor flow passage, and 159161 grids for the cavity. The grids are clustered in the flow direction near the fuel injector and cavity, as well as in the vertical direction near the bottom wall. The no-slip and adiabatic conditions are assumed throughout the entire wall boundary. As a specific example, the inflow Mach number is assumed to be 3, and the temperature and pressure are 600 K and 0.1 MPa, respectively. Gaseous hydrogen at a temperature of 151.5 K is injected normal to the wall from a choked injector.A series of calculations were carried out by varying the fuel injection pressure from 0.5 to 1.5MPa. This amounts to changing the fuel mass flow rate or the overall equivalence ratio for different operating regimes. Figure 1 shows the instantaneous temperature fields in the supersonic combustor at four different conditions. The dark blue region represents the hot burned gases. At the fuel injection pressure of 0.5 MPa, the flame is stably anchored, but the flow field exhibits a high-amplitude oscillation. At the fuel injection pressure of 1.0 MPa, the Mach reflection occurs ahead of the injector. The interaction between the incoming air and the injection flow becomes much more complex, and the fuel/air mixing is strongly enhanced. The Mach reflection oscillates and results in a strong fluctuation in the combustor wall pressure. At the fuel injection pressure of 1.5MPa, the flow inside the combustor becomes nearly choked and the Mach reflection is displaced forward. The leading shock wave moves slowly toward the inlet, and eventually causes the combustor-upstart due to the thermal choking. The cavity appears to play a secondary role in driving the flow unsteadiness, in spite of its influence on the fuel/air mixing and flame evolution. Further investigation is necessary on this issue. The present study features detailed resolution of the flow and flame dynamics in the combustor, which was not typically available in most of the previous works. In particular, the oscillatory flow characteristics are captured at a scale sufficient to identify the underlying physical mechanisms. Much of the flow unsteadiness is not related to the cavity, but rather to the intrinsic unsteadiness in the flowfield, as also shown experimentally by Ben-Yakar et al. [6], The interactions between the unsteady flow and flame evolution may cause a large excursion of flow oscillation. The work appears to be the first of its kind in the numerical study of combustion oscillations in a supersonic combustor, although a similar phenomenon was previously reported experimentally. A more comprehensive discussion will be given in the final paper presented at the colloquium.