Mathematical Simulation Methods Research Articles

Modeling of heat and mass transfer and aerodynamics in a bulk of stored agricultural raw material

Methods of mathematical and computer simulation of the microclimate in storehouses for juicy agricultural raw material are suggested. The calculation algorithms developed allow one to determine the aerodynamic and temperature-moisture characteristics with account for natural convection and arbitrary shape of storehouses in order to optimize the storing of biological products.

Mechanisms of reference posture correction in the system of upright posture control

It was earlier shown that ultraslow tilts of the support under quiet standing conditions evoke an unusual response reflecting the operation of compensatory mechanisms: postural sway is a superposition of postural oscillations typical of quiet standing and greater, slower inclinations of the body caused by the tilt. This may be explained by the presence of two hierarchical levels of upright posture control: real-time control compensates for small deviations of the body from the reference posture prescribed by presetting control. Mathematical simulation methods have been used to study the mechanisms of reference posture control. The results are compared with available experimental data. It is demonstrated that the reference posture can be corrected according to the gravitational vertical with the use of a kinesthetic reference alone. It is hypothesized that, when correcting the reference posture, the nervous system “assumes” the support to be immobile. The afferent input from sole pressure receptors is an important factor in reference posture correction. The advantages of the putative two-level control over control based on an explicit internal model are discussed.

Optimum thickness of a cooled wall subjected to local frictional heating in the regime of spinning friction

Using the methods of mathematical simulation, the characteristic features of a stationary temperature field in a cooled plane isotropic wall subjected to local frictional heating from a circular source in the regime of spinning friction are investigated. The possibility of the existence of an optimal wall thickness which ensures a minimum temperature of its most heated point has been established.

On the distribution of preliminary stresses and the optimal shape of an anchor joint for reinforced concrete

By the methods of mathematical simulation and optimization, we determine the optimal geometry of the anchor with regard for its action upon reinforced concrete.

Fluid Flow in A Four-strand Bloom Continuous Casting Tundish with Different Flow Modifiers

Fluid flows in a four-strand tundish for bloom continuous casting have been investigated with physical modeling and mathematical simulation methods. The liquid steel flow velocity fields in the former tundish and the optimal one with a turbulence inhibitor and newly-designed baffles were numerically calculated and the flow characteristics in the two cases and other tundish configurations were measured in the physical modeling. The results in the physical modeling experiments showed that large difference in the Residence Time Distribution (RTD) curves of two outlets in one side of the former configuration tundish existed. It was found from the numerical calculation of the velocity fields in the tundishes that with the former tundish configuration velocities and turbulent degree of the liquid steel flow in the impact zone of the tundish were large due to the high velocities of liquid steel from the long shroud of the ladle, which caused in lining corrosion and slag entrapment due to the surface eddies. Asymmetric velocity field in the tundish with the former baffles formed and short circuit flow existed in one side of the four-strand tundish. For the optimal configuration of the tundish with a turbulence inhibitor and newly-designed baffles, very similar RTD curves of the two outlets in the same side of the tundish were achieved. The velocities and turbulent degree in the impacting zone of the tundish were depressed and quiet and symmetric molten steel flow was obtained. Eddies on surface and short circuit flow in the optimal tundish disappeared. Such improvement of liquid steel flow in the tundish would increase the ability of inclusion removal. Turbulence inhibitors should be used with other well-designed flow control devices for effective improvement to fluid flow characteristics in tundishes.

Simulation of surge phenomena in a bounded sea basin

By using the method of mathematical simulation, we study surge oscillations caused by the action of tangential wind stresses in a bounded basin whose geometric parameters correspond to Lake Donuzlav. The dependences of the amplitudes of surges on the magnitude and direction of the wind velocity are analyzed at several points of the coast.

“Gradual cut-off” method of the sequential procedure in the case of a Rayleigh distribution

The effectiveness of optimum statistical sequential criteria for signal detection on the background of noise is studied when the signal and noise have a Rayleigh distribution. A sequential criterion with parabolic boundaries of zones that is sometimes more economic is suggested. The properties of criteria are compared by a mathematical simulation method.

Quasi-hydrodynamic simulation of the conductivity of heavily doped nanosize layered heterostructures in high electric fields

The electrical conductivity of nanosize-layered heterostructures in high electric fields is studied using the methods of mathematical simulation based on the equation of energy balance. It is shown that a characteristic feature of the corresponding current-voltage characteristics is a peak of the differential conductance, whose position and magnitude are determined by the heterobarrier height and steepness, as well as by the doping level of the structure. A physical model is suggested that accounts for the shape of the calculated characteristics by the combined effect of the electrostatic reduction in the heterobarrier height and the increase in the electronic temperature in the vicinity of the injecting heterointerfaces.

Automated design of exhaust systems

For some years, a significant proportion of the functional development of exhaust systems has been carried out by means of simulation programs. Nonetheless, the development process does not differ markedly from the traditional approach involving trial and error. Efficiency can only be further increased by combining the known mathematical simulation methods with modern optimisation processes. This paper presents the development methodology used at Eberspacher to optimise exhaust tailpipe noise and exhaust emission control. The capabilities and reliability of this optimisation program are illustrated by means of examples.

A van der Pol coupled-oscillator model as a basis for developing a system for suppressing MHD instabilities in a tokamak

The main parameters of tokamak discharges are known to be limited by large-scale MHD instabilities. Sometimes, the instabilities lead to a rapid (on time scales of tens of microseconds) disruption of the discharge current and to the release of all the energy stored in the plasma column at the discharge chamber wall. This process, which is called the disruptive instability, may have irreversible catastrophic consequences for the operation of a fusion reactor. In the present paper, a study is made of the dynamics of self-oscillations in systems of two and six van der Pol coupled oscillators. A van der Pol coupled-oscillator model is used to develop a multivariable feedback controller based on the combined principle of compensating for internal cross feedbacks within the object and introducing damping feedbacks in each control channel. By using mathematical simulation methods, it is shown that the controller designed guarantees the suppression of self-oscillations in a system of van der Pol oscillators over a fairly broad range of parameters of the object under control (and thereby provides the structural stability of the object). The nonlinear control system model makes it possible to suppress coupled MHD perturbations developing in a tokamak plasma.

Simulation of single slip in FCC metals

The study of single slip was performed by imitation simulation and mathematical simulation methods. In a modified barrier model of constant linear tension, all stages of the process of nucleation and propagation of single crystallographic slip to the field of discrete dislocation obstacles have been simulated and investigated. The equation of dynamics of expansion of an isolated closed planar dislocation loop, which restricts slipping, was used to perform a comparative study of the effect of the mechanisms of resistance to dislocation motion on the characteristics of the resulting single slip. Micromechanical characteristics of each dislocation loop emitted by a dislocation source after loss of stability have been calculated. The time it takes for single slip to propagate up to the barrier configurations that restrict slipping and the total formative time of the crystallographic shear zone have been estimated.

Investigation of Transformations of the Local Regions of Pollution in the Northwest Part of the Black Sea Caused by the Motion of a Cyclone

By the method of mathematical simulation, we study the evolution of local discharges of pollutants on the northwest shelf of the Black Sea induced by the motion of a cyclone. We use the nonlinear equations of motion of a homogeneous viscous fluid in the hydrostatic approximation and the equation of turbulent diffusion. A cyclonic formation is represented by a moving axisymmetric area of low pressures. The discharges of pollutants are caused by the action of instantaneous sources located on the sea surface. We perform the analysis of dependences of the paths of motion of polluted regions, the periods of their dissipation, and the depths of penetration of pollutants on the bottom topography and the intensity of diffusion processes.

Interplay of Darwinian and frequency-dependent selection in the host-associated microbial population

The method for mathematical simulation is suggested to analyze the balanced polymorphism in rhizobia population generated due to the interplay of Darwinian and frequency-dependent selection. Analysis of the model suggested that this polymorphism is determined not only by the selection pressures but also by the capacities of ecological niches occupied by bacteria in the «plant-soil» system. The model may be used for analyzing the selective processes in various symbiotic systems and for predicting the consequences of releasing of genetically modified plant symbionts into environment.

Rapid tooling by laser powder deposition: Process simulation using finite element analysis

Laser powder deposition (LPD) is a rapid manufacturing process, whereby near-net-shape components are fabricated by the successive overlapping of layers of laser melted and resolidified material. As new layers of material are deposited, heat is conducted away from recently resolidified material, through the previously deposited layers, inducing cyclic thermal fluctuations in the part as it is built up. These thermal cycles can activate a variety of metallurgical phenomena, such as solid-state transformations, leading to a progressive modification of the material’s microstructure and properties. Since the thermal history of the material in the deposited part will differ from point to point and depends on the deposition parameters and build-up strategy, the finished part may present complex distributions of microstructure and properties. In order to achieve the best properties, the deposition process must be optimized and, given its complexity, this optimization can only be effectively done using mathematical simulation methods. In this paper a thermo-kinetic LPD model coupling finite element heat transfer calculations with transformation kinetics and quantitative property–structure relationships is presented. This model was applied to the study of the influence of substrate size and idle time between the deposition of consecutive layers on the microstructure and hardness of a ten-layer AISI 420 steel wall built by LPD. The results show that the thermal history and, hence, the microstructure and properties of the final part, depend significantly on these parameters.

The role of spatio-temporal effects in anaerobic digestion of solid waste

Using methods of mathematical modelling and computer simulation, we study the effect that spatial distribution of material has on the process duration of anaerobic digestion of solid waste. The need for a spatio-temporal model is demonstrated by analysis of the solutions of an ODE model in dependence of model parameters and initial data. The spatio-temporal model is obtained by inclusion of mass transfer processes. This leads to a semi-linear diffusion–reaction system, the transient behavior of which we study numerically. Our focus is on the temporal spreading of so-called methanogenic pockets in bounded domains. These are regions, in which the qualitative behavior of the model solution is different than in their neighborhood.

Optimum Thickness of a Cooled Wall in Local Pulse-Periodic Heating

Using the methods of mathematical simulation. We investigated the characteristic features of formation of a stationary temperature field in a cooled plane isotropic wall subjected to local pulse-periodic heating. The possibility of the existence of an optimum wall thickness that ensures a minimum stationary temperature of its most heated point has been established.

Mathematical simulation of a belt crystallizer for molding of coagulants

The existing methods for mathematical simulation of the bulk crystallization of supersaturated solutions (pastes) are analyzed. A method for calculating the characteristics of paste drying on a belt conveyor is developed. This method is necessary to analyze proposals of process equipment manufacturers and also serves as the basis for calculating the optimal operating conditions and intensifying the preparation of a granulated coagulant.

Simulation of Special Features of the Drift-Mobility Saturation in Submicrometer Silicon Structures

Special characteristics of the high-field drift of electrons in submicrometer n+-n-n+ structures are studied by mathematical simulation methods in the quasi-hydrodynamic approximation. Alternative dependences of the mobility and energy-relaxation time on the electron temperature are used to calculate the profiles of the potential, temperature, drift mobility, and density of the thermal-energy flux of electrons. It is shown that, in a submicrometer configuration, a large part of the thermal energy acquired by an electron in a high-resistivity n-type region is dissipated in a low-resistivity n+-type contact. This effect reduces the rate of increase in the electron temperature in the drift region as the voltage increases, brings about an increase in the effective mobility, and prevents saturation of the drift velocity, as is shown by the calculated current-voltage characteristics.

Fluorination of a depleted uranium-plutonium-nitride fuel with elemental fluorine

A physical and a mathematical model have been developed to describe the physicochemical process of torch fluorination of an uranium-plutonium-nitride fuel. An algorithm for calculating the velocity, temperature, and concentration of the chemical components has been constructed which makes it possible to optimize the parameters and operating modes of a torch reactor based on mathematical simulation methods.

Modeling Water Flow in the Presence of Higher Vegetation

The notions of hydromechanics of continuum with a complicated structure are used to formulate a closed spatially homogeneous mathematical model of water flow within higher aquatic vegetation (HAV) canopy. Model equations are applied to the analysis of the vertical structure of a turbulent flow in a vegetated open channel. Test calculations are made. The results of calculations and experimental studies of water flow characteristics within vegetation communities in some water bodies [1, 6–8, 10, 14] are shown. The difficulties in implementing such experiments require improving the methods of mathematical simulation of water flows through HAV.