| Project/Area Number |
08458127
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
エネルギー学一般・原子力学
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| Research Institution | Saitama Institute of Technology |
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Principal Investigator |
SAKAI Katsuhiro Saitama Institute of Technology, Faculty of Eng.Prof., 工学部, 教授 (60153839)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | finite difference method / numerical analysis / transport equation / high-order numerical scheme / numerical oscillations / natural convection / cavity flow / spectrum analysis / 自然対流 / 特性多項式 |
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| Research Abstract |
1) A numerical method on the concept of nonlocally exact numerical differencing is presented. The essence of this method consists in determining the coefficients of the difference scheme such that the resulting equation interpolating numerical fluxes at the control volume surface satisfies the analytical solution of transport equations with absorption and source terms. The spatial distribution of the coefficients of transport equations is taken into consideration based on a four- region model among adjacent three control volumes, in which continuous conditions for solutions are imposed on the boundary between adjacent two regions.
2) The analysis on nonoscillation properties of the present scheme was performed using the characteristic polynomial analysis method. It was found that the present scheme possesses potential of nonoscillation properties for stationary convection- diffusion equations with absorption. The present scheme is examined through numerical experiments, and shows good s
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olutions for transport equations with absorption and source terms.
3) Numerical experiments for transport equations with strongly spatially dependent coefficients show that the present SDCLENS scheme gives solutions distinctly better than solutions with the locally exact scheme LENS and the QUICK scheme.
4) The mass, momentum and energy equations were discretized using the SDCLENS scheme and a 2- D thermal hydraulics analysis program has been developed.
5) The above computer program was validated through numerical experiments for the shear-driven cavity flow with the exact solution.
6) The numerical simulation using the present computer program was performed for naturally circulating flows with high Rayleigh numbers Ra 10^5-10^9 in a square cavity, where conventional numerical methods tend to suffer from large numerical diffusions and unstable solutions because of thermohydraulically coupling in multidimensional fields. Steady laminar solutions were obtained up to Ra = 10^9. However, in case of Ra = 10^8the solutions were not steady but temporally dependent. Developing of vortex formation and the chaotic structure of vortex after the temperature difference was imposed on the walls are made numerically investigated. Further, as results of statistical analysis in case of Ra = 10^9, a Reynolds stress and a fluctuation energy spectrum were evaluated. It was shown that the energy spectrum is roughly 1/f spectrum, which is different from the Kolmogorov's (-5/3) power spectrum in case of fully developed turbulent flows. Less
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