• Nuclear Engineering and Technology
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• v.56 no.8
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• pp.2948-2957
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• 2024

High-order harmonic techniques can be used to recreate neutron flux distributions in reactor cores using the neutron diffusion equation. However, traditional source iteration and source correction iteration techniques have sluggish convergence rates and protracted calculation periods. The correctness of the implicitly restarted Arnoldi method (IRAM) in resolving the eigenvalue problems of the one-dimensional and two-dimensional neutron diffusion equations was confirmed by computing the benchmark problems SLAB_1D_1G and two-dimensional steady-state TWIGL using IRAM. By integrating Galerkin projection with Proper Orthogonal Decomposition (POD) techniques, a POD-Galerkin reduced-order model was developed and the IRAM model was used as the full-order model. For 14 macroscopic cross-section values, the TWIGL benchmark problem was perturbed within a 20% range. We extracted 100 sample points using the Latin hypercube sampling method, and 70% of the samples were used as the testing set to assess the performance of the reduced-order model The remaining 30% were utilized as the training set to develop the reduced-order model, which was employed to rebuild the TWIGL benchmark problem. The reduced-order model demonstrates good flexibility and can efficiently and accurately forecast the effective multiplication factor and neutron flux distribution in the core. The reduced-order model predicts k_eff and neutron flux distribution with a high degree of agreement compared to the full-order model. Additionally, the reduced-order model's computation time is only 10.18% of that required by the full-order model.The neutron flux distribution of the steady-state TWIGL benchmark was recreated using the reduced-order model. The obtained results indicate that the reduced-order model can accurately predict the k_eff and neutron flux distribution of the steady-state TWIGL benchmark.Overall, the proposed technique not only has the potential to accurately project neutron flux distributions in transient settings, but is also relevant for reconstructing neutron flux distributions in steady-state conditions; thus, its applicability is bound to increase in the future.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.90.2-90.2
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• 2012

Geosynchronous electron flux dropouts are most likely due to fast drift loss of the particles to the magnetopause (or equivalently, the "magnetopause shadowing effect"). A possible effect related to the drift loss is the radial diffusion of PSD due to gradient of PSD set by the drift loss effect at an outer L region. This possibly implies that the drift loss can affect the flux levels even inside the trapping boundary. We recently investigated the details of such diffusion process by solving the diffusion equation with a set of initial and boundary conditions set by the drift loss. Motivated by the simulation work, we have examined observationally the energy spectrum and pitch angle distribution near trapping boundary during the geosynchronous flux dropouts. For this work, we have first identified a list of geosynchronous flux dropout events for 2007-2010 from GOES satellite electron measurements and solar wind pressures observed by ACE satellite. We have then used the electron data from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft measurements to investigate the particle fluxes. The five THEMIS spacecraft sufficiently cover the inner magnetospheric regions near the equatorial plane and thus provide us with data of much higher spatial resolution. In this paper, we report the results of our investigations on the energy spectrum and pitch angle distribution near trapping boundary during the geosynchronous flux dropout events and discuss implications on the effects of the drift loss on the flux levels at inner L regions.

• Nuclear Engineering and Technology
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• v.21 no.1
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• pp.56-61
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• 1989

A simple, approximate method for determining the two-group adjoint flux based on the Borresen's coarse-mesh 1.5 group diffusion theory scheme is proposed. With the principle of the 1.5 group diffusion theory scheme, the method describes the thermal leakage term of the adjoint flux approximately by the geomerical buckling determined from the fast adjoint flux. The accuracy of the adjoint flux is investigated tv the comparison of the adjoint flux constructed from this method with a fine-mesh finite-difference KIDD computations. It is shown that the proposed method can predict the adjoint flux as good as the KIDD results. Possible applications of the present method are then suggested in conjunction with the application of the perturbation theory.

• Journal of Energy Engineering
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• v.17 no.4
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• pp.233-240
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• 2008

Conventionally, the second-order self-adjoint neutron transport equations have been studied using the even parity and the odd parity equations. Recently, however, the SAAF(self-adjoint angular flux) form of neutron transport equation has been introduced as a new option for the second-order self-adjoint equations. In this paper we validated the SAAF equation mathematically and clarified how it relates with the existing even and odd parity equations. We also developed a second-order SAAF differencing formula including DSA(diffusion synthetic acceleration) from the first-order difference equations. Numerical result is attached to show that the proposed methods increases accuracy with effective computational effort.

• 한국연소학회:학술대회논문집
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• 2003.05a
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• pp.143-150
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• 2003

The synthesis gas generated in waste pyrolysis melting process which consists of pyrolysis of waste and melting process of ash is known to be an alternative fuel. Since the compositopn of synthesis gas is much different from other synthesis gases, the fundamental combustion characteristics are analyzed in this study. The radiation heat heat flux is used to estimate the heat flux from flames made by many combinations of fuel and oxidant supply. The results show that the synthesis gas needs much more amount of oxidant for equivalent heat flux to methane flame and the inverse diffusion flame type for synthesis gas burner is suitable for better radiation heat transfer.

• Journal of computational fluids engineering
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• v.8 no.4
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• pp.34-40
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• 2003

The effect of nose radius on aerodynamic heating is investigated by using the Navier-Stokes code extended to thermochemical nonequilibrium airflow, Spherical blunt bodies, whose nose radius varies from 0.O03048 m to 0.6096 m, flying at Mach 25 at an altitude of 53.34 km are considered. Comparison of heat flux at stagnation point with the solution of Viscous Shock Layer and Fay-Riddell are made. Results show that the flow for very small radius is in a nearly frozen state, and therefore the heat flux due to diffusion is smaller than that due to translational energy. As the radius becomes larger, the portion of heat flux by diffusion becomes greater than that of heat flux by translational temperature and approaches to a constant value.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.109-114
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• 2002

The effect of nose radius on aerodynamic heating are investigated by using the Wavier-Stokes code extended to thermochemical nonequilibrium airflow. A spherical blunt body, whose radius varies from 0.003048 m to 0.6096 m, flying at Mach 25 at an altitude of 53.34 km is considered. Comparison of heat flux at stagnation point with the solution of Viscous Shock Layer and Fay-Riddell are made. Obtained result reveals that the flow chemistry for very small radius is nearly frozen, and therefore the contribution of heat flux due to chemical diffusion is smaller than that of translational energy. As the radius becomes larger, the portion of diffusion heat flux becomes greater than translational heat flux and approaches to a constant value.

• Progress in Superconductivity and Cryogenics
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• v.5 no.2
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• pp.66-70
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• 2003

Transient magnetic diffusion process in a melt-cast Bi2Sr2CaCu20X(Bi-2212) tube was studied by experimental and numerical analyses. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper. This experiment measure the magnetic flux density in the supercondutor after supply direct-current of Bi-2212 rounded by copper coil. This study was discussed of valid of a previous numerical solution which is compared by the penetrate time and the magnetic flux density difference of between the present results and the numerical solution.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.70.3-70.3
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• 2020

Previous numerical simulations on planet-disk interactions revealed a lot of interesting phenomena including the planetary migration and the formation of many sub-structures inside the disks. However, these simulations were limited to an isothermal or adiabatic equation of state which does not account for various heating and cooling processes in the disks. Recent studies showed that the behavior of the planet-disk interaction can be significantly influenced by the disk thermodynamics. We develop a radiative diffusion module based on the two-temperature flux-limited diffusion approximation accounting for viscous heating and the accretion feedback. In this presentation, we describe our radiative diffusion solver, present some test results, and discuss potential applications of the module to planet-disk interactions,

• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.1-11
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• 2003

A mathematical model was proposed to analyze the oxygen diffusion reaching the cornea through the tear layers and contact lens based on Fick's law and the principle of continuity of the diffusion flux through the each layers. The model predicts how the parameters such as the thickness of tear layer on the cornea, both the Dk and thickness of contact lenses etc., affect the oxygen tension at cornea and oxygen flux entering the cornea. It is found that either too flat or too tightly fitted contact lenses can cause the oxygen deficiency inside the periphery of the cornea because of the reduction of oxygen flux resulted from too thickened tear layer.