A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional t...A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional to the out-of-balance forces, acting on them. Numerical experiments show that if the liquid is confined within boundaries of a set of inter-communicating vessels, then the proposed method converges to a final equilibrium state. This incremental static analysis approximates dynamic behavior with strong damping and can provide information, as a first approximation to 2D movement of a liquid. In the initial arrangement of particles, a rhombic element is proposed, which assures satisfactory incompressibility of the fluid. Based on the proposed algorithm, a simple and short computer program (a “pocket” program) has been developed, with only about 120 Fortran instructions. This program is first applied to an amount of liquid, contained in a single vessel. A coarse and refined discretization is tried. In final equilibrium state of liquid, the distribution on hydro-static pressure on vessel boundaries, obtained by proposed computational model, is found in satisfactory approximation with corresponding theoretical data. Then, an opening is formed, at the bottom of a vertical boundary of initial vessel, and the liquid is allowed to flow gradually to an adjacent vessel. Almost whole amount of liquid is transferred, from first to second vessel, except of few drops-particles, which remain, in equilibrium, at the bottom of initial vessel. In the final equilibrium state of liquid, in the second vessel, the free surface level of the liquid confirms that the proposed rhombing element assures a satisfactory incompressibility of the fluid.展开更多
A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the batter...A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the battery are considered. A simple algorithm, with variable time step-length <span style="font-family:Verdana;">Δ</span><i><span style="font-family:Verdana;">t</span></i><span style="font-family:Verdana;">, is presented, for proposed model. The model is first applied to Daniel cell, in order to clar</span><span style="font-family:Verdana;">ify</span><span style="font-family:""><span style="font-family:Verdana;"> concepts and principles of battery operation. It is found that initial pinching, in time-history curve of voltage </span><i><span style="font-family:Verdana;">E-t</span></i><span style="font-family:Verdana;">, is due to initial under-concentration of product ion. Then, model is applied </span></span><span style="font-family:Verdana;">to</span><span> a lead-acid battery. In absence of an ion product, and in order to construct nominator of Nernst ratio, such an ion, with coefficient tending to zero, is assumed, thus yielding unity in nominator. Time-history curves of voltage, for various values of internal resistance, are compared with corresponding published experimental curves. Temperature effect on voltage-time curve is examined. Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too.</span>展开更多
文摘A simple method is proposed, for incremental static analysis of a set of inter-colliding particles, simulating 2D flow. Within each step of proposed algorithm, the particles perform small displacements, proportional to the out-of-balance forces, acting on them. Numerical experiments show that if the liquid is confined within boundaries of a set of inter-communicating vessels, then the proposed method converges to a final equilibrium state. This incremental static analysis approximates dynamic behavior with strong damping and can provide information, as a first approximation to 2D movement of a liquid. In the initial arrangement of particles, a rhombic element is proposed, which assures satisfactory incompressibility of the fluid. Based on the proposed algorithm, a simple and short computer program (a “pocket” program) has been developed, with only about 120 Fortran instructions. This program is first applied to an amount of liquid, contained in a single vessel. A coarse and refined discretization is tried. In final equilibrium state of liquid, the distribution on hydro-static pressure on vessel boundaries, obtained by proposed computational model, is found in satisfactory approximation with corresponding theoretical data. Then, an opening is formed, at the bottom of a vertical boundary of initial vessel, and the liquid is allowed to flow gradually to an adjacent vessel. Almost whole amount of liquid is transferred, from first to second vessel, except of few drops-particles, which remain, in equilibrium, at the bottom of initial vessel. In the final equilibrium state of liquid, in the second vessel, the free surface level of the liquid confirms that the proposed rhombing element assures a satisfactory incompressibility of the fluid.
文摘A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the battery are considered. A simple algorithm, with variable time step-length <span style="font-family:Verdana;">Δ</span><i><span style="font-family:Verdana;">t</span></i><span style="font-family:Verdana;">, is presented, for proposed model. The model is first applied to Daniel cell, in order to clar</span><span style="font-family:Verdana;">ify</span><span style="font-family:""><span style="font-family:Verdana;"> concepts and principles of battery operation. It is found that initial pinching, in time-history curve of voltage </span><i><span style="font-family:Verdana;">E-t</span></i><span style="font-family:Verdana;">, is due to initial under-concentration of product ion. Then, model is applied </span></span><span style="font-family:Verdana;">to</span><span> a lead-acid battery. In absence of an ion product, and in order to construct nominator of Nernst ratio, such an ion, with coefficient tending to zero, is assumed, thus yielding unity in nominator. Time-history curves of voltage, for various values of internal resistance, are compared with corresponding published experimental curves. Temperature effect on voltage-time curve is examined. Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too.</span>
