• Korean Journal of Agricultural and Forest Meteorology
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• v.17 no.3
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• pp.227-235
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• 2015

Using eddy covariance method, net ecosystem exchange (NEE) of $CO_2$ ($F_{CO_2}$), $H_2O$ (LE), and sensible heat (H) can be approximated as the sum of eddy flux ($F_c$) and storage flux term ($F_s$). Depending on strength and distribution of sink/source of scalars and magnitude of vertical turbulence mixing, the rates of changes in scalars are different with height. In order to calculate $F_s$ accurately, the differences should be considered using scalar profile measurement. However, most of flux sites for agricultural lands in Asia do not operate profile system and estimate $F_s$ using single-level scalars from eddy covariance system under the assumption that the rates of changes in scalars are constant regardless of the height. In this study, we measured $F_c$ and $F_s$ of $CO_2$, $H_2O$, and air temperature ($T_a$) using eddy covariance and profile system (i.e., the multi-level measurement system in scalars from eddy covariance measurement height to the land surface) at the Chengmicheon farmland site in Korea (CFK) in order to quantify the differences between $F_s$ calculated by single-level measurements ($F_s_{-single}$ i.e., $F_s$ from scalars measured by profile system only at eddy covariance system measurement height) and $F_s$ calculated by profile measurements and verify the errors of NEE caused by $F_s_{-single}$. The rate of change in $CO_2$, $H_2O$, and Ta were varied with height depending on the magnitudes and distribution of sink and source and the stability in the atmospheric boundary layer. Thus, $F_s_{-single}$ underestimated or overestimated $F_s$ (especially 21% underestimation in $F_s$ of $CO_2$ around sunrise and sunset (0430-0800 h and 1630-2000 h)). For $F_{CO_2}$, the errors in $F_s_{-single}$ generated 3% and 2% underestimation of $F_{CO_2}$ during nighttime (2030-0400 h) and around sunrise and sunset, respectively. In the process of nighttime correction and partitioning of $F_{CO_2}$, these differences would cause an underestimation in carbon balance at the rice paddy. In contrast, there were little differences at the errors in LE and H caused by the error in $F_s_{-single}$, irrespective of time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.218-225
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• 1999

Flow visualization study has been conducted to simulate the turbulent dispersion behavior of a crossflow jet physically under the conditions of various thermal stratification in a wind tunnel. A smoke jet with the constant ratio of the jet to freestream velocity is injected normally to the cross flow of the thermally stratified wind tunnel(TSWT) for flow visualization. The typical natures of the smoke dispersion under different thermal stratifications such as neutral, weakly stable, strongly stable, weakly unstable, strongly unstable and inversion layer are successfully reproduced in the TSWT. The Instantaneous velocity and temperature fluctuations are measured by using a cold and hot-wire combination probe. The time averaged dispersion behaviors, the centerline trajectories, the spreading angles and the virtual origins of the cross jet are deduced from the edge detected images with respect to the stability parameter. All the general characteristics of the turbulent dispersion behavior reveal that the definitely different dispersion mechanisms are inherent in both stable and unstable conditions. It is conjectured that the turbulent statistics obtained in the various stability conditions quantitatively demonstrate the vertical scalar flux plays a key role in the turbulent dispersion behavior.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.5
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• pp.1300-1307
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• 1995

The effect of thermal stratification on the turbulent dispersion from a fine cylindrical heat source was experimentally examined in a wind tunnel with and without a strong temperature gradient. A 0.5 mm dia. nichrome wire was used as a line heat source. Turbulent intensities, r.m.s. value of temperature and convective heat fluxes were measured by using a hot-wire and cold-wire combination probe. The results show that the peack value and the spread of the vertical turbulent intensity for the stratified case are far lower than those in the neutral case, which indicates that the stable temperature gradient suppresses the vertical velocity component. All of the third order moments including heat fluxes measured in the stable condition have very small values than those of the neutral case. This nature suggests that the decrease of scalar fluctuations in the stably stratified flow is mainly due to the suppression ofthe turbulent diffusion processes by the stable stratification. A simple gradient model with a composite timescale which has a simple weighted algebraic mean between dynamic and thermal time scale yields reasonably good numerical values in comparison with the experimental data.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.16 no.2
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• pp.203-209
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• 2018

To correctly predict the neutron behavior based on diffusion calculations, it is necessary to adopt well-specified boundary conditions using suitable diffusion approximations to transport boundary conditions. Boundary conditions such as the zero net-current, the Marshak, the Mark, the zero scalar flux, and the Albedo condition have been used extensively in diffusion theory to approximate the reflective and vacuum conditions in transport theory. In this paper, we derive and analyze these conditions to prove their mathematical validity and to understand their physical implications, as well as their relationships with one another. To show the validity of these diffusion boundary conditions, we solve a sample problem. The results show that solutions of the diffusion equation with these well-formulated boundary conditions are very close to the solution of the transport equation with transport boundary conditions.

• Nuclear Engineering and Technology
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• v.54 no.9
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• pp.3478-3487
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• 2022

In this study, we incorporate an anisotropic scattering scheme involving spherical harmonics into the method of characteristics (MOC). The neutron transport solution in a light water reactor can be significantly improved because of the impact of an anisotropic scattering source with the MOC flat source approximation. Several problems are selected to verify the proposed scheme and investigate its effects and accuracy. The MOC anisotropic scattering source is based on the expansion of spherical harmonics with Legendre polynomial functions. The angular flux, scattering source, and cross section are expanded in terms of the surface spherical harmonics. Later, the polynomial is expanded to achieve the odd and even parity of the source components. Ultimately, the MOC angular and scalar fluxes are calculated from a combination of two sources. This paper presents various numerical examples that represent the hot and cold conditions of a reactor core with boron concentration, burnable absorbers, and control rod materials, with and without a reflector or baffle. Moreover, a small critical core problem is considered which involves significant neutron leakage at room temperature. We demonstrate that an anisotropic scattering source significantly improves solution accuracy for the small core high-leakage problem, as well as for practical large core analyses.

• Nuclear Engineering and Technology
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• v.55 no.4
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• pp.1428-1438
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• 2023

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is developed and implemented as a part of a hybrid neutronics method for source convergence acceleration and variance reduction in Monte Carlo (MC) criticality calculations. The acceleration of the MC calculation stems from constructing a synthetic operator and solving a low-order problem using information obtained from previous MC calculations. By applying the P₁ approximation, two correction terms, one for the scalar flux and the other for the current, can be solved in the low-order problem and applied to the transport solution. A variety of one-dimensional (1-D) and two-dimensional (2-D) numerical tests are constructed to demonstrate the performance of FDSA in comparison with the standalone MC method and the coupled MC and Coarse Mesh Finite Difference (MC-CMFD) method on both intended purposes. The comparison results show that the acceleration by a factor of 3-10 can be expected for source convergence and the reduction in MC variance is comparable to CMFD in both slab and full core geometries, although the effectiveness of such hybrid methods is limited to systems with small dominance ratios.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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• pp.1434-1443
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• 1999

The turbulent fluctuations of temperature and two components of velocity have been measured with hot- and cold-wires in the Thermally Stratified Wind Tunnel(TSWT). Using the fin-tube heat exchanger type heaters and the neural network control algorithm, both stable ($dT/dz=109.4^{\circ}C$) and unstable ($dT/dz=-49.1^{\circ}C$) stratifications were realized. An ambient air jet was issued normally into the cross flow($U_{\infty}=1.0 m/s$) from a round nozzle(d = 6 mm) flushed at the bottom waII of the wind tunnel with the velocity ratio of $5.8(U_{jet}/U_{\infty})$. The characteristics of turbulent dispersion in the cross flow jet are found to change drastically depending on the thermal stratification. Especially, in the unstable condition, the vertical velocity fluctuation increases very rapidly at downstream of jet. The fluctuation velocity spectra and velocity-temperature cospectra along the jet centerline were obtained and compared. In the case of stable stratification, the heat flux cospectra changes Its sign from a certain point at the far field because of the restratification phenomenon. It is inferred that the main reason in the difference between the vertical heat fluxes is caused by the different length scales of the large eddy motions. The turbulent kinetic energy and scalar dissipation rates were estimated using partially non-isotropic and isotropic turbulent approximation. In the unstable case, the turbulent energy dissipation decreases more rapidly with the downstream distance than in the stable case.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.669-689
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• 2011

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic geometric properties of such a manifold are obtained. The applications of Lorentzian quasi-Einstein manifolds to the general relativity and cosmology are investigated. Theories of gravitational collapse and models of Supernova explosions [5] are based on a relativistic fluid model for the star. In the theories of galaxy formation, relativistic fluid models have been used in order to describe the evolution of perturbations of the baryon and radiation components of the cosmic medium [32]. Theories of the structure and stability of neutron stars assume that the medium can be treated as a relativistic perfectly conducting magneto fluid. Theories of relativistic stars (which would be models for supermassive stars) are also based on relativistic fluid models. The problem of accretion onto a neutron star or a black hole is usually set in the framework of relativistic fluid models. Among others it is shown that a quasi-Einstein spacetime represents perfect fluid spacetime model in cosmology and consequently such a spacetime determines the final phase in the evolution of the universe. Finally the existence of such manifolds is ensured by several examples constructed from various well known geometric structures.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.