The paper presents modeling and simulation results of the operation of a three-phase fluidized bed bioreactorwith partial recirculation of biomass. The proposed quantitative description of the bioreactor takes into account biomass growth on inert carriers, microorganisms decay and interphase biomass transfer. Stationary characteristics of the bioreactor and local stability of steady-stateswere determined. The influence of microbiological growth kinetics on the multiplicity of steady-states was discussed. The relationship between biofilm growth and boundaries of fluidized bed existence was shown.
Rock excavation is a basic technological operation during tunnelling and drilling roadways in underground mines. Tunnels and roadways in underground mines are driven into a rock mass, which in the particular case of sedimentary rocks, often have a layered structure and complicated tectonics. For this reason, rock strata often have highly differentiated mechanical properties, diverse deposition patterns and varied thicknesses in the cross sections of such headings. In the field of roadheader technology applied to drilling headings, the structure of a rock mass is highly relevant when selecting the appropriate cutting method for the heading face. Decidedly differentiated values of the parameters which describe the mechanical properties of a particular rock layer deposited in the cross section of the drilled tunnel heading will influence the value and character of the load on the cutting system, generated by the cutting process, power demand, efficiency and energy consumption of the cutting process. The article presents a mathematical modelling process for cutting a layered structure rock mass with the transverse head of a boom-type roadheader. The assumption was made that the rock mass being cut consists of a certain number of rock layers with predefined mechanical properties, a specific thickness and deposition pattern. The mathematical model created was executed through a computer programme. It was used for analysing the impact deposition patterns of rock layers with varied mechanical properties, have on the amount of cutting power consumed and load placed on a roadheader cutting system. The article presents an example of the results attained from computer simulations. They indicate that variations in the properties of the rock cut – as cutting heads are moving along the surface of the heading face – may have, apart from multiple other factors, a significant impact on the value of the power consumed by the cutting process.
Comparative calculations with a mathematical model designed by the authors, which takes into consideration energy transfer from gas flowing through a given channel to gas which penetrates this channel from an adjacent channel, as well as a model which omits this phenomenon, respectively, were made for the process of separating gas mixtures carried out with an inert sweep gas in the fourend capillary membrane module. Calculations were made for the process of biogas separation using a PMSP polymer membrane, relative to helium as the sweep gas. It was demonstrated that omitting the energy transfer in the mathematical model might lead to obtaining results which indicate that the capacity of the process expressed by the value of feed flux subjected to separation is by several percent higher than in reality.
Optimization of dialysis needs methods for quantitative assessment of fluid and solutes transport in body compartments and solute and fluid exchange between body and dialysate. A mathematical model describing the dynamics of these quantities during dialysis is presented. This model is first and foremost based on the existing models, but also includes some new solutions. All parts were combined and extended by the detailed descriptions of selected aspects. The virtual patient model was applied to simulate and test different methods of treatment and their influence on the condition of the patient. The purpose of this model is to serve as a decision support system for selection of optimal treatment options for particular patient.
The article presents a zero-dimensional mathematical model of a tubular fuel cell and its verification on four experiments. Despite the fact that fuel cells are still rarely used in commercial applications, their use has become increasingly more common. Computational Flow Mechanics codes allow to predict basic parameters of a cell such as current, voltage, combustion composition, exhaust temperature, etc. Precise models are particularly important for a complex energy system, where fuel cells cooperate with gas, gas-steam cycles or ORCs and their thermodynamic parameters affect those systems. The proposed model employs extended Nernst equation to determine the fuel cell voltage and steadystate shifting reaction equilibrium to calculate the exhaust composition. Additionally, the reaction of methane reforming and the electrochemical reaction of hydrogen and oxygen have been implemented into the model. The numerical simulation results were compared with available experiment results and the differences, with the exception of the Tomlin experiment, are below 5%. It has been proven that the increase in current density lowers the electrical efficiency of SOFCs, hence fuel cells typically work at low current density, with a corresponding efficiency of 45–50% and with a low emission level (zero emissions in case of hydrogen combustion).
At the Kielce University of Technology a new concept of accurate measurements of sphericity deviations of machine parts has been developed. The concept is based upon measurement of roundness profiles in many clearly defined cross-sections of the workpiece. Measurements are performed with the use of typical radial measuring instrument equipped with a unit allowing accurate positioning of the ball. The developed concept required finding a solution to numerous problems relating to the principle of the radial measurement. One of the problems to be solved was matching of measured roundness profiles. The paper presents an outline of the developed concept of sphericity measurement, a mathematical model of profile matching and results of the verification of the model.
The paper presents a description of used methods and exemplary mathematical models which are classified into theoretical-empirical models of thermal processes. Such models encompass equations resulting from the laws of physics and additional empirical functions describing processes for which analytical models are complex and difficult to develop. The principle of developing, advantages and disadvantages of presented models as well as quality prediction assessment were presented. Mathematical models of a steam boiler, a steam turbine as well as a heat recovery steam generator were described. Exemplary calculation results were presented and compared with measurements.
The generic mathematical model and computational algorithm considering hydrodynamics, heat and mass transfer processes during casting and forming steel ingots and castings are offered. Usage domains for turbulent, convective and non-convective models are determined depending on ingot geometry and thermal overheating of the poured melt. The expert system is developed, enabling to choose a mathematical model depending on the physical statement of a problem.
Postharvest processing of grain is an important step in the overall grain production process. It makes possible not only quantitative and qualitative preservation of the harvest, but also ensures maximum profit from its sale at the most favorable market conditions. Convective heat treatment (drying, cooling) guarantees commercial harvest conservation, prevents its loss, and in some cases improves the quality of the finished product. The necessity of intensification and automation of technological processes of postharvest grain processing requires the development of methods of mathematical modeling of energy-intensive processes of convective heat treatment. The determination and substantiation of optimum modes and parameters of equipment operation to ensure the preservation of grain quality is possible only when applying mathematical modeling techniques. In this work, a mathematical model of particulate material drying is presented through a system of differential equations in partial derivatives of which the variable in time and space relationship between heat and mass transfer processes in the material and a drying agent is reflected. The aim of the research was to determine the dynamics of the interrelated fields of unsteady temperature and moisture content of the material and the drying agent on the basis of mathematical models of heat and mass transfer in the layer of particulate material in convective heat approach or heat retraction. The implementation of the mathematical model proposed in the standard mathematical set allows analyzing efficiency of machines and equipment for the convective heat treatment of particulate agricultural materials in a dense layer, according the determinant technological parameters and operating modes.
The results of bearing capacity, deformability and fracture toughness of reinforced concrete beams with the external reinforcement in the form of steel cut and stretchy sheet, obtained due to the conducting of the experiment and mathematical simulation which were made of concrete of C40/50 class are given in the article. Mathematical simulation of beam structures is done on the basis of the deformation model which allows to conduct calculations of the unified methodological positions of different elements with diverse configuration of cross section and reinforcement as well as take into consideration elastic and plastic properties of concrete and reinforcement, assessing the actual stress-strain state of sections of reinforced concrete elements at different loading levels, including ultimate one. The deformation model is based on the actual diagrams use of concrete and reinforcement materials deformation and conditions of efforts balance in the normal section and hypothesis of flat sections. The theoretical value of bearing capacity and deformability, obtained as a result of the mathematical simulation was compared to the experimental data. The satisfactory coincidence of the mathematical calculation of bearing capacity, deformability, fracture toughness and experimental data gives an opportunity to use the algorithm not only for beam structures with bar reinforcement but also for beam structures with the external reinforcement in the form of steel cut and stretchy sheet.
This paper presents a design of a tracked in-pipe inspection mobile robot with an adaptive drive positioning system. The robot is intended to operate in circular and rectangular pipes and ducts, oriented horizontally and vertically. The paper covers a design process of a virtual prototype, focusing on track adaptation to work environment. A mathematical description of a kinematic model of the robot is presented. Operation of the prototype in pipes with a cross-section greater than 210 mm is described. Laboratory tests that validate the design and enable determination of energy consumption of the robot are presented.