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.
The study concerns modeling and simulation of the growth of biofilms with heterogeneous structures with a discrete mathematical model based on theory of cellular automata. The article presents two-dimensional density distributions of biofilms for microbial processes: oxidation of ammonium by Nitrosomonas europaea bacteria and glucose utilization by Pseudomonas aeruginosa bacteria. The influence of limiting substrate concentration in the liquid phase on biofilm structure was determined. It has been shown that the value of death rate coefficient of microorganisms has the qualitative and quantitative influence on the density and porosity of the biofilm.
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 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.
In the paper, verification of welding process parameters of overlap joints of aluminium alloys EN AW-6082 and EN AW-7075, determined on the grounds of a numerical FEM model and a mathematical model, is presented. A model was prepared in order to determine the range of process parameters, for that the risk of hot crack occurrence during welding the material with limited weldability (EN AW-7075) would be minimum and the joints will meet the quality criteria. Results of metallographic and mechanical examinations of overlap welded joints are presented. Indicated are different destruction mechanisms of overlap and butt joints, as well as significant differences in their tensile strength: 110 to 135 MPa for overlap joints and 258 MPa on average for butt joints.
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.
Two formal types of models of living processes, especially evolutionary ones, may be distinguished: the well-known mathematical type and the less-known logical one. The latter applies the terms “class” or “set”; both the terms are understood either in a collective sense (in mereology) or in a distributive sense (in set theory). These formal terms may be used among others to such organic multiplicities as populations or species of organisms, and to organic constituents (molecules, cells, organs) of living organism. Collective concepts refer to objects existing in nature, whereas distributive concepts refer to the linguistic and research constructions of models of natural objects, developed to cognitively grasp natural regularities.
The article presents the procedure for how to establish a mathematical model of nitrogen oxides formation based on the theory of dimensional analysis. The model is based on selected physical quantities (parameters) measurable during regular operation of a heat generation plant. The objective of using dimensional analysis to describe nitrogen oxides formation is to show that between operating parameters of the combustion equipment and the NOx formation there is a significant correlation. The obtained results, which are further described in this article, have proved this fact. The obtained formula expressing nitrogen oxides formation, based on dimensional analysis, applies universally to any boiler fuelled by coal, gas or biomass. However, it is necessary to find C, m, n constants for the formula by experiment, individually for each type of boiler and used fuel. The experiment is based on on-line measurements of selected operational parameters for a given boiler, combusting a certain type of fuel with its actual moisture content and calorific value. The methodology, described in this article, helps to find relationships between the operational parameters and the formation of NOx emissions for a particular furnace. The developed mathematical model has been validated with boilers fuelled by black coal and biomass. Both the results obtained from direct measurements of NOx in both types of boilers, and the results obtained by calculation using equation based on the dimensional analysis, are in a very good accord. When burning coal, the variation between NOx expression from the model and the on-line measurements ranges between -12.23 % and + 9.92 %, and for burning biomass between -0.54 % and 0.48 %. The intention of the authors is to inform the professional community about the suitability of the dimensional analysis to describe any phenomena for which there is currently no exact mathematical formulation based on differential equations or empirical formulas. Many other examples of dimensional analysis applications in practice may be found in the work of Čarnogurská and Příhoda (2011).
In generalized method of data reconciliation as equations of conditions beside substance and energy balances can be used equations which don’t have precisely the status of conservation lows. Empirical coefficients in these equations are traded as unknowns’ values. To this kind of equations, in application of the generalized method of data reconciliation in supercritical power unit, can be classified: steam flow capacity of a turbine for a group of stages, adiabatic internal efficiency of group of stages, equations for pressure drop in pipelines and equations for heat transfer in regeneration heat exchangers. Mathematical model of a power unit was developed in the code Thermoflex. Using this model the off-design calculation has been made in several points of loads for the power unit. Using these calculations identification of unknown values and empirical coefficients for generalized method of data reconciliation used in power unit has been made. Additional equations of conditions will be used in the generalized method of data reconciliation which will be used in optimization of measurement placement in redundant measurement system in power unit for new control systems
In this study, batch fermentation of glucose to ethanol by Saccharomyces cerevisiae (ATCC 7754) was carried out using 2.5 dm3 BioFlo®115 bioreactor. The main objective of this study was to investigate the kinetics of ethanol fermentation by means of the non-structured model. The fermentation process was carried out for 72 h. Samples were collected every 4 h and then yeast growth concentration of ethanol and glucose were measured. The mathematical model was composed of three equations, which represented the changes of biomass, substrate and ethanol concentrations. The mathematical model of bioprocess was solved by means of Matlab/SimulinkTM environment. The obtained results from the proposed model showed good agreement with the experimental data, thus it was concluded that this model can be used for the mathematical modeling of ethanol production.
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.
This paper aims at providing a framework for comprehensive steady-state time-domain analysis of rotating machines considering motion. The steady-state waveforms of electromagnetic and circuit quantities are computed via iterative solution of the nonlinear field-circuit-and-motion problem with constraints of time periodicity. The cases with forced speed and forced load torque are considered. A comparison of execution times with a conventional time-stepping transient model is carried out for two different machines. The numerical stability of a time-periodic model with forced speed is shown to be worse than that of traditional transient time-stepping one, although the model converges within a reasonable number of iterations. This is not the case if forced load via equation of mechanical balance is accounted for. To ensure convergence of the iterative process the physical equation of motion is replaced by the fixed-point equation. In this way the model delivers time-periodic solutions regarding not only the electromagnetic quantities but also the rotational speed.
Based on mathematical modeling and numerical simulations, applicativity of various biofuels on high temperature fuel cell performance are presented. Governing equations of high temperature fuel cell modeling are given. Adequate simulators of both solid oxide fuel cell (SOFC) and molten carbonate fuel cell (MCFC) have been done and described. Performance of these fuel cells with different biofuels is shown. Some characteristics are given and described. Advantages and disadvantages of various biofuels from the system performance point of view are pointed out. An analysis of various biofuels as potential fuels for SOFC and MCFC is presented. The results are compared with both methane and hydrogen as the reference fuels. The biofuels are characterized by both lower efficiency and lower fuel utilization factors compared with methane. The presented results are based on a 0D mathematical model in the design point calculation. The governing equations of the model are also presented. Technical and financial analysis of high temperature fuel cells (SOFC and MCFC) are shown. High temperature fuel cells can be fed by biofuels like: biogas, bioethanol, and biomethanol. Operational costs and possible incomes of those installation types were estimated and analyzed. A comparison against classic power generation units is shown. A basic indicator net present value (NPV) for projects was estimated and commented.
An innovative method for determining the structural zones in the large static steel ingots has been described. It is based on the mathematical interpretation of some functions obtained due to simulation of temperature field and thermal gradient field for solidifying massive ingot. The method is associated with the extrema of an analyzed function and with its points of inflection. Particularly, the CET transformation is predicted as a time-consuming transition from the columnar- into equiaxed structure. The equations dealing with heat transfer balance for the continuous casting are presented and used for the simulation of temperature field in the solidifying virtual static brass ingot. The developed method for the prediction of structural zones formation is applied to determine these zones in the solidifying brass static ingot. Some differences / similarities between structure formation during solidification of the steel static ingot and virtual brass static ingot are studied. The developed method allows to predict the following structural zones: fine columnar grains zone, (FC), columnar grains zone, (C), equiaxed grains zone, (E). The FCCT-transformation and CET-transformation are forecast as sharp transitions of the analyzed structures. Similarities between steel static ingot morphology and that predicted for the virtual brass static ingot are described.
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.