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.
The implementation of EU environmental regulations in the energy sector is challenging for the power industry of its member states. The main role is played by documents such as the Winter Package and, especially, the Directive of the European Parliament and of the Council on the emission limits of certain pollutants and the implementation of BAT conclusions in order to achieve the EU’s decarbonization objectives. These regulations impose a greater need to control harmful substances emitted to the atmosphere while using fossil fuels, including hard coal, which is the main fuel for domestic units. At the same time, the decline in domestic fossil fuel production and decrease in the quality of parameters of the hard coal makes it difficult to purchase the proper fuel for power plants. As a consequence, the costs of hard coal increase. The article presents the concept of a mathematical model that can be applied for the optimization of coal supplies. The employment of this model allows one to achieve cost reductions. One of the advantages of the proposed tool, in addition to minimizing the cost of purchase and use of hard coal, is its rational management, especially for companies producing and using hard coal.
The economic envelopes obtained by optimization techniques in open pit mining are transformed into operational phases that are suitable for extraction through ramp designs. This process is performed with the aid of specialized design software, which is still very manual, time consuming and highly dependent on the expertise of the planner. In this paper, we introduce a new methodology based on a mathematical model to automatically propose the design of ramps from the economic envelope of a pushback, with the resulting envelope having the maximum value. The developed model was tested against a real case scenario showing reasonable and useable solutions for the planner. Using this approach, a planner can evaluate several alternatives in a reasonable time before selecting the final design.
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 enzymatic synthesis of a highly hydrophobic product (dipeptide precursor) in which the reaction is accompanied by the mass transfer of the reaction product to the organic phase and the substrates to the water phase is considered. Equations describing both continuous and batch processes are formulated. The range of variability in the operating parameters of such a bioreactor is specified, and the correlations reported in the literature to describe mass transfer in the membrane contactor are validated. The proposed process was verified experimentally, and good agreement between the determined and calculated concentrations was obtained in both phases.
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.
Protection of the environment and counteracting global warming require finding alternative sources of energy. One of the methods of generating energy from environmentally friendly sources is increasing the share of gaseous fuels in the total energy balance. The use of these fuels in compression-ignition (CI) engines is difficult due to their relatively high autoignition temperature. One solution for using these fuels in CI engines is operating in a dualfuel mode, where the air and gas mixture is ignited with a liquid fuel dose. In this method, a series of relatively complex chemical processes occur in the engine's combustion chamber, related to the combustion of individual fuel fractions that interact with one another. Analysis of combustion of specific fuels in this type of fuel injection to the engine is difficult due to the fact that combustion of both fuel fractions takes place simultaneously. Simulation experiments can be used to analyse the impact of diesel fuel combustion on gaseous fuel combustion. In this paper, we discuss the results of simulation tests of combustion, based on the proprietary multiphase model of a dual-fuel engine. The results obtained from the simulation allow for analysis of the combustion process of individual fuels separately, which expands the knowledge obtained from experimental tests on the engine.
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.
The paper presents the results of numerical computations performed for the furnace chamber waterwalls of a supercritical boiler with a steam output of 2400 × 103 kg/h. A model of distributed parameters is proposed for the waterwall operation simulation. It is based on the solution of equations describing the mass, momentum and energy conservation laws. The aim of the calculations was to determine the distribution of enthalpy, mass flow and fluid pressure in tubes. The balance equations can be brought to a form where on the left-hand side space derivatives, and on the right-hand side – time derivatives are obtained. The time derivatives on the right-hand side were replaced with backward difference quotients. This system of ordinary differential equations was solved using the Runge-Kutta method. The calculation also takes account of the variable thermal load of the chamber along its height. This thermal load distribution is known from the calculations of the heat exchange in the combustion chamber. The calculations were carried out with the zone method.
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.