Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction a...Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction and alumina content distributions. An Euler–Euler two-fluid model was employed coupled with a species transport equation for alumina content. Three different anode configurations such as anode without a slot, anode with a longitudinal slot and anode with a transversal slot were studied in the simulation. The simulation results clearly show that the slots can reduce the bath velocity and promote the releasing of the anode gas, but can not contribute to the uniformity of the alumina content. Comparisons of the effects between the longitudinal and transversal slots indicate that the longitudinal slot is better in terms of gas–liquid flow but is disadvantageous for alumina mixing and transport process due to a decrease of anode gas under the anode bottom surface. It is demonstrated from the simulations that the mixing and transfer characteristics of alumina are controlled to great extent by the anode gas forces while the electromagnetic forces(EMFs) play the second role.展开更多
For fully understanding the hydrological dynamics of an infinite terraced slope, the infiltration process was studied by employing the Green and Ampt infiltration model. The limit equilibrium method and the Mohr-Coulo...For fully understanding the hydrological dynamics of an infinite terraced slope, the infiltration process was studied by employing the Green and Ampt infiltration model. The limit equilibrium method and the Mohr-Coulomb failure criterion were adopted to derive a stability model for the infinite terraced slope subjected to an intense rainfall. Numerical simulation was performed for verifying its applicability. The results of numerical simulation indicate that a set of stepped wetting fronts are found during infiltration, and the infiltration of terraced slope covered by coarse-textured soils can be approximated as one-dimensional infiltration. The potential sliding surfaces from the numerical method are all parallel to the slope line, and the proposed model and framework can provide an approximate method of estimating how the infiltration affects the stability of an infinite terraced slope.展开更多
For a transient Bessel process X let I(t) = in fs＞tX(s) and§(t) = inf{u≥ 2 t: X(u) = I(t)}. In this note we compute the joint distribution of I(t),§(t) and Xt.
The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion ...The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti- mizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and iso- thermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation ex- tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremam principle are emphasized.展开更多
Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the th...Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.展开更多
In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
基金Project(2010AA065201)supported by the High Technology Research and Development Program of ChinaProject(2013zzts038)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(ZB2011CBBCe1)supported by the Major Program for Aluminum Corporation of China Limited,China
文摘Numerical simulations of gas–liquid two-phase flow and alumina transport process in an aluminum reduction cell were conducted to investigate the effects of anode configurations on the bath flow, gas volume fraction and alumina content distributions. An Euler–Euler two-fluid model was employed coupled with a species transport equation for alumina content. Three different anode configurations such as anode without a slot, anode with a longitudinal slot and anode with a transversal slot were studied in the simulation. The simulation results clearly show that the slots can reduce the bath velocity and promote the releasing of the anode gas, but can not contribute to the uniformity of the alumina content. Comparisons of the effects between the longitudinal and transversal slots indicate that the longitudinal slot is better in terms of gas–liquid flow but is disadvantageous for alumina mixing and transport process due to a decrease of anode gas under the anode bottom surface. It is demonstrated from the simulations that the mixing and transfer characteristics of alumina are controlled to great extent by the anode gas forces while the electromagnetic forces(EMFs) play the second role.
基金Project(51178423)supported by the National Natural Science Foundation of China
文摘For fully understanding the hydrological dynamics of an infinite terraced slope, the infiltration process was studied by employing the Green and Ampt infiltration model. The limit equilibrium method and the Mohr-Coulomb failure criterion were adopted to derive a stability model for the infinite terraced slope subjected to an intense rainfall. Numerical simulation was performed for verifying its applicability. The results of numerical simulation indicate that a set of stepped wetting fronts are found during infiltration, and the infiltration of terraced slope covered by coarse-textured soils can be approximated as one-dimensional infiltration. The potential sliding surfaces from the numerical method are all parallel to the slope line, and the proposed model and framework can provide an approximate method of estimating how the infiltration affects the stability of an infinite terraced slope.
基金Supported by National Natural Science Foundation of China (19801020)
文摘For a transient Bessel process X let I(t) = in fs＞tX(s) and§(t) = inf{u≥ 2 t: X(u) = I(t)}. In this note we compute the joint distribution of I(t),§(t) and Xt.
基金supported by the National Natural Science Foundation China(Grant Nos.51176203 and 10905093)
文摘The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti- mizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and iso- thermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation ex- tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremam principle are emphasized.
基金supported by the National Key Basic Research and Development Program of China (‘973’ Program) (Grant No. 2012CB720405)the National Natural Science Foundation of China (Grant No. 51176203)the Natural Science Foundation for Youngsters of Naval University of Engineering (Grant No. HGDQNJJ11008)
文摘Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
