• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.7-14
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• 1997

Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission produce such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low bum-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.327-364
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• 2015

In this paper, a generalized guidance law with an arbitrary pair of guidance coefficients for impact angle control is proposed. Under the assumptions of a stationary target and a lag-free missile with constant speed, necessary conditions for the guidance coefficients to satisfy the required terminal constraints are obtained by deriving an explicit closed-form solution. Moreover, optimality of the generalized impact-angle control guidance law is discussed. By solving an inverse optimal control problem for the guidance law, it is found that the generalized guidance law can minimize a certain quadratic performance index. Finally, analytic solutions of the generalized guidance law for a first-order lag system are investigated. By solving a third-order linear time-varying ordinary differential equation, the blowing-up phenomenon of the guidance loop as the missile approaches the target is mathematically proved. Moreover, it is found that terminal misses due to the system lag are expressed in terms of the guidance coefficients, homing geometry, and the ratio of time-to-go to system time constant.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Journal of the Korean Society of Groundwater Environment
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• v.2 no.1
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• pp.14-21
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• 1995

Colloids such as exogenous biocolloids in a bioremediation operation can enhance the transport of contaminant in ground water by reducing retardation effects. Because of their colloidal size and favorable surface conditions in addition to their low density, bacteria can act as efficient contaminant carriers. When mobile bacteria are present in a subsurface environment, the system can be treated as consisting of three phases: water phase, bacterial phase, and the stationary solid matrix phase. In this work, a mathematical model based on mass balances is developed to describe the facilitated transport and fate of a contaminant in a porous medium. Bacterial partition between the bulk solution and the stationary solid matrix, and the contaminant partition among the three phases are represented by the equilibrium relationships. Solutions were obtained to provide estimates of contaminant and bacterial concentrations. A dimensionless analysis of the transport model was utilized to estimate model parameters from the experimental data. The model results matched with experimental data of Jenkins and Lion (1993). The presence of mobile bacteria enhances the contaminant transport. However, bacterial consumption of the contaminant which serves as a bacterial nutrient, can attenuate the contaminant concentration.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.05a
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• pp.707-712
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• 1995

Grain boundary diffusion plays significant role in the fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated inside fuel pellet have to diffuse in the lattice and in the grain boundary before they reach open space in the fuel rod. In the mean time, the grains in the fuel pellet grow and shrink according to grain growth kinetics, especially at elevated temperature at which nuclear reactors are operating. Thus the boundary movement ascribed to the grain growth greatly influences the fission gas release rate by lengthening or shortening the lattice diffusion distance, which is the rate limiting step. Sweeping fission gases by the moving boundary contributes to the increment of the fission gas release as well. Lattice and grain boundary diffusion processes in the fission gas release can be studied by 'tracer diffusion' technique, by which grain boundary diffusion can be estimated and used directly for low burn-up fission gas release analysis. However, even for tracer diffusion analysis, taking both the intragranular grain growth and the diffusion processes simultaneously into consideration is not easy. Only a few models accounting for the both processes are available and mostly handle them numerically. Numerical solutions are limited in the practical use. Here in this paper, an approximate analytical solution of the lattice and stationary grain boundary diffusion in a polycrystalline solid is developed for the tracer diffusion techniques. This short closed-form solution is compared to available exact and numerical solutions and turns out to be acceptably accurate. It can be applied to the theoretical modeling and the experimental analysis, especially PIE (post irradiation examination), of low burn up fission. gas release.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.222-228
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• 2004

The effects of rotation on the unsteady laminar flow past a circular cylinder is numerically investigated in the present study. We obtained the numerical solutions for unsteady two-dimensional governing equation for the flow using two different numerical schemes. One is an accurate spectral method and another is finite volume method. Above all, the flow around a stationary circular cylinder is investigated to understand the basic phenomenon of flow separation, bluff body wake. Also, the validation of our own codes, expecially based on FVM, is carried out by the comparison of results obtained from our simulations using two different schemes and previous numerical and experimental studies. By the effect of rotation, the mean lift increases and drag deceases, which well represent the previous study.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.49.2-49.2
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• 2015

IntraCluster Medium (ICM) located at the galaxy cluster is in the state of very hot, tenuous, magnetized, and highly ionized X-ray emitting plasmas. High temperature and low density make ICM very viscous and conductive. In addition to the high conductivity, fluctuating random plasma motions in ICM, occurring at all evolution stages, generate and amplify the magnetic fields in such viscous ionized gas. The amplified magnetic fields in reverse drive and constrain the plasma motions beyond the viscous scale through the magnetic tension. Moreover, without the influence of resistivity viscous damping effect gets balanced only with the magnetic tension in the extended viscous scale leading to peculiar ICM energy spectra. This overall collisionless magnetohydrodynamic (MHD) turbulence in ICM was simulated using a hyper diffusivity method. The results show the plasma motions and frozen magnetic fields have power law of $E_V^k{\sim}k^{-3}$, $E_M^k{\sim}k^{-1}$. To explain these abnormal power spectra we set up two simultaneous differential equations for the kinetic and magnetic energy using an Eddy Damped Quasi Normal Markovianized (EDQNM) approximation. The solutions and dimensions of leading terms in the coupled equations derive the power spectra and tell us how the spectra are formed. We also derived the same results with a more intuitive balance relation and stationary energy transport rate.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.16-28
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• 2000

The steady rotating flows in eccentric annulus has been studied by a numerical method based on the spectral collocation method. The inner cylinder has a constant angular velocity while the outer on e is stationary. Flow between eccentric cylinders is of considerable technical importance as it occurs in journal bearings. In the present work, the governing equations for laminar flow are expressed as Navier-Stokes equations, including the non-linear convection terms. The solutions were utilized i, estimate the effects of the nonlinear terms on the load acting on the rotating cylinder. Based on the half and the full Sommerfeld methods, the load on the rotating cylinder is evaluated with eccentricity, by integrating the pressure and skin friction around the cylinder. The attitude angle and Sommerfeld reciprocal are calculated from the load. Also, the torque on the rotating inner cylinder was calculated. considering the skin friction. The attitude angle and Sommerfeld reciprocal are decreased with eccentricity. Viscous damping coefficient due to the skin friction becomes larger with decreasing the annular space. It is found the non-linear effects of the convection terms on the flow and the load are important. especially on the attitude angle, for relatively wide annular configurations however, the effects on those are minor for very narrow annular ones.

• Journal of Ocean Engineering and Technology
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• v.32 no.1
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• pp.68-75
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• 2018

This study deals with the heading angle and depth keeping control technique for an ROV with multiple horizontal and vertical thrusters by thrust allocation. The light work class ROV URI-L, which is under development at KRISO, is a redundant actuating system with multiple thrusters that are larger than the ROV's degree of freedom. In the redundant actuating system, there are several solutions for a specific ROV motion to be performed. Therefore, a thrust allocation algorithm that considers the entire propulsion system should be regarded as important. First, this paper describes the propulsion system of the ROV and introduces the thrust allocation method of each motion controller. In addition, the performance of the controller is examined using a heading angle and depth keeping control test in a stationary state.

• Journal of Ocean Engineering and Technology
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• v.19 no.3
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• pp.1-10
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• 2005

The effect of rotation on the unsteady laminar flaw past a circular cylinder is numerically investigated in the present study. The numerical solutions for the 2D Navier-Stokes equation obtained, using two different numerical methods. One is an accurate spectral method and the other is a finite volume method(FVM). First, the flaw around a stationary circular cylinder is investigated to understand the basic phenomenon of flaw separation and bluff body wake. Next, the flow characteristics of the laminar flow, past a rotating circular cylinder, are investigated, using a FVM developed in this study. By the effect of rotation, it is seen that values of lift increase, while the values of mean drag decrease. Further, the criteria of angular velocity, at which the Karman vorteces disappear, is also determined.