Mathematical Model Of Dynamic Behavior Research Articles

Energy recovery of solid waste disposal in Russia, State of the Art and operation experience

For Russia, there is no alternative way of a civilized solution to the problem of municipal solid wastes (MSW): through combustion (energy utilization) to complex processing. The government of the Russian Federation in 2017 adopted some decisions aimed at thermal processing of MSW. The order defines the construction of renewable energy facilities on the basis of MSW with a total electric capacity of 280 MW in Moscow region and one object with an electric capacity of 55 MW in the Republic of Tatarstan. In Russia, only three plants where the energy potential of MSW is converted into electricity were built. The results of the operation experience of fluidized bed furnaces for MSW incineration at Rudnevo plant in Russia are done. The main problems were connected with ash properties, deposit formation, and corrosion of superheater tubes. Also, the data of mathematical modeling of dynamic behavior near gas burners, chemical composition and material balance of solids, and the influence of secondary air injection on NOx formation are given. A special test rig was designed for the investigation of the corrosion mechanism. Also, the main corrosion factors (temperature of the tube surface, rates of O2, HCl, SO2, and H2O in flue gas, contains chloride and alkali metals in deposits) were found during the tests. Experience of energy recovery from waste incineration of pulp and paper mill plants is presented. Considerable attention is paid to improving the efficiency of waste incineration and bed particle agglomeration. Special experiments were carried out to optimize the bed drain flow rate. The influence of secondary air supply improvement on mixing with the main flow and boiler efficiency is given. Semi-empirical three-zone method of engineering heat calculations for fluidized bed furnaces of biomass boilers was proposed to predict both the value of outlet furnace temperature and the value of fluidized bed temperature. The method based on empirical values and relationships of the share of heat release in fluidized bed zone.

Dynamic interaction of a thin metallic inclusion with a piezoceramic matrix

A mathematical model of dynamic behavior of a thin metallic inclusion or a layer in a piezoelectric medium subjected to longitudinal shear load is constructed. At the boundary of inclusion and matrix, the conditions of perfect mechanical contact and zero electric potential are prescribed. Modeling is performed using the apparatus of the theory of singular perturbations. Cite as: Yu. I. Maksymiv, Yu. V. Porokhovsky, R. V. Rabosh, V. O. Mishchenko, Ya. I. Kunets, “Dynamic interaction of a thin metallic inclusion with a piezoceramic matrix,” Prykl. Probl. Mekh. Mat. , Issue 17, 134–138 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.134-138

Mathematical modeling of dynamic behavior of fluid bilayer membranes under the effect of density asymmetry

Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases.

Analysis of Fan Waves in a Laboratory Model Simulating the Propagation of Shear Ruptures in Rocks

The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth’s crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

Analysis of fan waves in a laboratory model simulating the propagation of shear ruptures in rocks

The fan-shaped mechanism of rotational motion transmission in a system of elastically bonded slabs on flat surface, simulating the propagation of shear ruptures in super brittle rocks, is analyzed. Such ruptures appear in the Earth’s crust at seismogenic depths. They propagate due to the nucleation of oblique tensile microcracks, leading to the formation of a fan domino-structure in the rupture head. A laboratory physical model was created which demonstrates the process of fan-structure wave propagation. Equations of the dynamics of rotational motion of slabs as a mechanical system with a finite number of degrees of freedom are obtained. Based on the Merson method of solving the Cauchy problem for systems of ordinary differential equations, the computational algorithm taking into account contact interaction of slabs is developed. Within the framework of a simplified mathematical model of dynamic behavior of a fan-shaped system in the approximation of a continuous medium, the approximate estimates of the length of a fan depending on the velocity of its motion are obtained. It is shown that in the absence of friction a fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of slabs, the initial angle and the elasticity coefficient of bonds. In the presence of friction a fan stops. On the basis of discrete and continuous models, the main qualitative features of the behavior of a fan-structure moving under the action of applied tangential forces, whose values in a laboratory physical model are regulated by a change in the inclination angle of the rupture plane, are analyzed. Comparison of computations and laboratory measurements and observations shows good correspondence between the results.

Mathematical model of dynamic behavior of microbial desalination cells for simultaneous wastewater treatment and water desalination.

Microbial desalination cells (MDCs) are an emerging concept for simultaneous wastewater treatment and water desalination. This work presents a mathematical model to simulate dynamic behavior of MDCs for the first time through evaluating multiple factors such as organic supply, salt loading, and current generation. Ordinary differential equations were applied to describe the substrate as well as bacterial concentrations in the anode compartment. Local sensitivity analysis was employed to select model parameters that needed to be re-estimated from the previous studies. This model was validated by experimental data from both a bench- and a large-scale MDC system. It could fit current generation fairly well and simulate the change of salt concentration. It was able to predict the response of the MDC with time under various conditions, and also provide information for analyzing the effects of different operating conditions. Furthermore, optimal operating conditions for the MDC used in this study were estimated to have an acetate flow rate of 0.8 mL·min(-1), influent salt concentration of 15 g·L(-1) and salt solution flow rate of 0.04 mL·min(-1), and to be operated with an external resistor less than 30 Ω. The MDC model will be helpful with determining operational parameters to achieve optimal desalination in MDCs.

State equations in the mathematical model of dynamic behaviour of multihull floating unit

State equations in the mathematical model of dynamic behaviour of multihull floating unit This paper concerns dynamic behaviour of multihull floating unit of catamaran type exposed to excitations due to irregular sea waves. Dynamic analysis of multihull floating unit necessitates, in its initial stage, to determine physical model of the unit and next to assume an identified mathematical model. Correctly elaborated physical models should contain information on the basis of which a mathematical model could be built. Mathematical models describe mutual relations between crucial quantities which characterize a given system in time domain. The dynamic analysis of multihull unit was performed under assumption that the unit's model has been linear and exposed to action of irregular sea waves. Mathematical model of such dynamic system is represented by state equations. The formulated equations take into account encounter of head wave which generates symmetrical motions of the unit, i.e. surge, heave and pitch. For solving the equations the following three wave spectra were taken into consideration: - ISSC (International Ship Structures Congress) spectrum - Pierson-Moskowitz spectrum - Paszkiewicz spectrum.

A Wavelet Approach for the Analysis of Bending Waves in a Beam on Viscoelastic Random Foundation

This paper deals with the mathematical model of dynamic behaviour of a beam resting on viscoelastic random foundation for which the modulus of subgrade reaction is assumed to be a homogeneous random function of the space variable. An approximate analytical solution for the fourth-order differential equation with random parameters is obtained in the case of a ∞ C -class correlation function. This higher order regularity of correlation function implies the regularity of associated stochastic function [1] in the sense of the mean-square analysis [2]. The numerical results for the average displacement have been obtained by using Bourret’s approximation method. A special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in the numerical examples.

Analysis of bending waves in beam on viscoelastic random foundation using wavelet technique

This paper deals with the mathematical model of dynamic behaviour of the beam resting on viscoelastic random foundation. It is considered by assuming the modulus of subgrade reaction to be a homogeneous random function of space variable. The problem is governed by the fourth-order differential equation with random parameters. The main results of this article are the approximate analytical solutions for the displacement field, variance and dynamic-stiffness coefficient. It has been made a comparison of numerical results obtained by using two different methods: Adomian’s decomposition and Bourret’s approximation. The special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in numerical examples. For making numerical calculations and plots the programs in MATHEMATICA have been prepared.

Study On Model Predictive Control Of Plate-finHeat Exchangers

Heat exchangers are important pieces of equipment to transfer heat between process fluid media. In some processes the working fluid temperatures must be exactly controlled. The common control method such as PID feedback control might not provide high control quality because such a control is based on the deviation between inputs and outputs, and therefore the disturbances in the outputs cannot be eliminated if disturbances in the inputs occur. To overcome the disadvantages of traditional control methods, a model predictive control method is developed. A mathematical model for dynamic behaviour of one-dimensional flow multistream plate-fin heat exchangers is proposed to calculate the adjustment parameters. A model predictive control method is put forward by introducing a feed-forward controller. Experiments are carried out to compare the model predictive control with the PID feedback control method, which shows that the adjustment time and fluctuations of the controlled outputs of model predictive control are much smaller than those of PID feedback control.