In the present paper, Lie group symmetry method is used to obtain some exact solutions for a hyperbolic system of partial differential equations （PDEs）, which governs an isothermal no-slip drift-flux model for multi...In the present paper, Lie group symmetry method is used to obtain some exact solutions for a hyperbolic system of partial differential equations （PDEs）, which governs an isothermal no-slip drift-flux model for multiphase flow problem. Those sym- metries are used for the governing system of equations to obtain infinitesimal transforma- tions, which consequently reduces the governing system of PDEs to a system of ODEs. Further, the solutions of the system of ODEs which in turn produces some exact solutions for the PDEs are presented. Finally, the evolutionary behavior of weak discontinuity is discussed.展开更多
To investigate the steady thermal hydraulic characteristics of U-tube steam generator(SG), a 1D simulation code based on the four-equation drift flux model is developed. The U-tube channels presumably consist mainly o...To investigate the steady thermal hydraulic characteristics of U-tube steam generator(SG), a 1D simulation code based on the four-equation drift flux model is developed. The U-tube channels presumably consist mainly of the primary channel, secondary channel, and tube wall. In the sub-cooling regions of the primary and secondary channels, flow is simulated using the single-phase flow model, whereas that in the boiling regions of the secondary channels is simulated using the four-equation drift flux model. The first-order equations of upwind difference are derived based on the staggered grid. Steady-state thermal hydraulic parameters are obtained with a cross-iteration scheme of heat balance and natural circulation requirement. The developed code is applied to analyze the SG behavior of the Qinshan I Nuclear Power Plant under 100%, 75%, 50%, 30%, and 15% power conditions. Analysis results are then compared with the simulation results obtained using RELAP5.展开更多
The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional sys...The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.展开更多
基金Project supported by the Ministry of Minority Affairs through UGC,Government of India(No.F1-17.1/2010/MANF-CHR-ORI-1839)the Industrial Consultancy,IIT Kharagpur(No.IIT/SRIC/ISIRD/2013-14)
文摘In the present paper, Lie group symmetry method is used to obtain some exact solutions for a hyperbolic system of partial differential equations （PDEs）, which governs an isothermal no-slip drift-flux model for multiphase flow problem. Those sym- metries are used for the governing system of equations to obtain infinitesimal transforma- tions, which consequently reduces the governing system of PDEs to a system of ODEs. Further, the solutions of the system of ODEs which in turn produces some exact solutions for the PDEs are presented. Finally, the evolutionary behavior of weak discontinuity is discussed.
基金Supported by the National Natural Science Foundation of China(Nos.51376065 and 51176052)
文摘To investigate the steady thermal hydraulic characteristics of U-tube steam generator(SG), a 1D simulation code based on the four-equation drift flux model is developed. The U-tube channels presumably consist mainly of the primary channel, secondary channel, and tube wall. In the sub-cooling regions of the primary and secondary channels, flow is simulated using the single-phase flow model, whereas that in the boiling regions of the secondary channels is simulated using the four-equation drift flux model. The first-order equations of upwind difference are derived based on the staggered grid. Steady-state thermal hydraulic parameters are obtained with a cross-iteration scheme of heat balance and natural circulation requirement. The developed code is applied to analyze the SG behavior of the Qinshan I Nuclear Power Plant under 100%, 75%, 50%, 30%, and 15% power conditions. Analysis results are then compared with the simulation results obtained using RELAP5.
基金supported by the National Natural Science Foundation of China(11172210)the Shuguang Program of Shanghai City(11SG21)
文摘The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.
