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 mathematical model of postproduction suspension concentration by microfiltration has been developed. This model describes a process conducted in a batch system with membrane washing by reverse flow of permeate. The model considerations concern filtration pseudocycles consisting of the filtration period and the membrane washing period. The balances of continuous phase volume, dispersed phase mass and energy, for each period of pseudocycle respectively, have been presented.
This paper presents a method of describing an airlift bioreactor, in which biodegradation of a carbonaceous substrate described by single-substrate kinetics takes place. Eight mathematical models based on the assumption of liquid plug flow and axial dispersion flow through the riser and the downcomer in the reactor were proposed. Additionally, the impact of degassing zone with assumed complete mixing on the obtained results was analyzed. Calculations were performed for two representative hydrodynamic regimes of reactor operation, i.e. with the presence of gas bubbles only within the riser and for complete gas circulation. The conclusions related to the apparatus design and process performance under sufficient aeration of the reaction mixture were drawn on the basis of the obtained results.
The paper presents results of research focused on modelling heat storage tank operation used for forecasting purposes. It presents selected issues related to mathematical modelling of heat storage tanks and related equipment and discusses solution process of the optimisation task. Presented detailed results were obtained during real-life industrial implementation of the optimisation process at the Siekierki combined heat and power (CHP) plant in Warsaw owned by Vattenfall Heat Poland S.A. (currently by Polish Oil & Gas Company - PGNiG SA) carried out by the Academic Research Centre of Power Industry and Environment Protection, Warsaw University of Technology in collaboration with Transition Technologies S.A. company.
The situation when groundwater considerably rises above the “normal” level, water intake, lowering of groundwater levels and other relevant practical tasks require the drainage facilities. The most effective techniques of numerical studies of the corresponding boundary problems at present time are methods of dealing with inverse boundary value problems (conformal and quasi-conformal mappings). As basis of this research we used the case of combining the fictitious domain methods with quasi-conformal mappings of the solution of nonlinear boundary value problems for the calculation of filtra-tion regimes in environments with free boundary areas (depression curves) and zones of “mountainous” areas. This paper reviews the stationary issue of flat-vertical stationary non-pressure liquid filtration to horizontal symmetric drainage. In the paper a practical methodology for solving boundary value problems on conformal mappings is suggested for the calculation of the filtration process in the horizontal symmetrical drainage. The idea of block iterative methods was used during the creation of the corresponding algorithm which is based on the alternating “freeze” of the anticipated conformance parameter, the internal and boundary connections of the curvilinear area. The results of the conducted numerical calculations confirmed the effectiveness of the suggested problem formulations and algorithms of their numerical solution and the possibility of their use in the modelling of nonlinear filtration processesoccurring in horizontal drainage systems, as well as in the design of drainage facilities and optimizing other hydrosystems. Therefore these results are of great importance.
Energy based approach was used in the study to formulate a set of functions approximating the magnetic flux linkages versus independent currents. The simplest power series that approximates field co-energy and linked fluxes for a two winding core of an induction machine are described by a set of common unknown coefficients. The authors tested three algorithms for the coefficient estimation using Weighted Least-Squared Method for two different positions of the coils. The comparison of the approximation accuracy was accomplished in the specified area of the currents. All proposed algorithms of the coefficient estimation have been found to be effective. The algorithm based solely on the magnetic field co-energy values is significantly simpler than the method based on the magnetic flux linkages estimation concept. The algorithm based on the field co-energy and linked fluxes seems to be the most suitable for determining simultaneously the coefficients of power series approximating linked fluxes and field co-energy.
Results of mathematical modelling and computer simulation of transient processes in the turbine jet engine SO-3 have been presented. The transient processes result from two different fault conditions. In the first case, the transient process has been induced with a rapid fuel shut-off. In the second case, the transient process follows some failure to the shaft that connects the turbine rotor to that of the compressor. The failure occurred in the area of the middle engine bearing support.
In this paper, a new simple method for determination of flow parameters, axial dispersion coefficients DL and Péclet numbers Pe was presented. This method is based on an accurate measurement model considering pulse tracer response. Our method makes it possible to test the character of gas flow motion and precisely measure flow parameters for different pressures and temperatures. The idea of combining the transfer function, numerical inversion of the Laplace transform and optimisation method gives many benefits like a simple and effective way of finding solution of inverse problem and model coefficients. The calculated values of flow parameters (DL and/or Pe) suggest that in the considered case the gas flow is neither plug flow nor perfect mixing under operation condition. The obtained outcomes agree with the gas flow theory. Calculations were performed using the CAS program type, Maple®.
A complex model of mechanically ventilated ARDS lungs is proposed in the paper. This analogue is based on a combination of four components that describe breathing mechanics: morphology, mechanical properties of surfactant, tissue and chest wall characteristics. Physical-mathematical formulas attained from experimental data have been translated into their electrical equivalents and implemented in MultiSim software. To examine the adequacy of the forward model to the properties and behaviour of mechanically ventilated lungs in patients with ARDS symptoms, several computer simulations have been performed and reported in the paper. Inhomogeneous characteristics observed in the physical properties of ARDS lungs were mapped in a multi-lobe model and the measured outputs were compared with the data from physiological reports. In this way clinicians and scientists can obtain the knowledge on the moment of airway zone reopening/closure expressed as a function of pressure, volume or even time. In the paper, these trends were assessed for inhomogeneous distributions (proper for ARDS) of surfactant properties and airway geometry in consecutive lung lobes. The proposed model enables monitoring of temporal alveolar dynamics in successive lobes as well as those occurring at a higher level of lung structure organization, i.e. in a point P0 which can be used for collection of respiratory data during indirect management of recruitment/de-recruitment processes in ARDS lungs. The complex model and synthetic data generated for various parametrization scenarios make possible prospective studies on designing an indirect mode of alveolar zone management, i.e. with
The paper presents major issues associated with the problem of modelling change output accelerometers. The presented solutions are based on the weighted least squares (WLS) method using transformation of the complex frequency response of the sensors. The main assumptions of the WLS method and a mathematical model of charge output accelerometers are presented in first two sections of this paper. In the next sections applying the WLS method to estimation of the accelerometer model parameters is discussed and the associated uncertainties are determined. Finally, the results of modelling a PCB357B73 charge output accelerometer are analysed in the last section of this paper. All calculations were executed using the MathCad software program. The main stages of these calculations are presented in Appendices A−E.
In the paper, a solution to the problem of elastic deformation of thin-walled shell structures with complex shapes within the theory of geometrically non-linear shells has been presented. It is a modification of the Newton-Raphson method. In a variational formulation, the problem is based on a Lagrange’s functional for increments of displacements. The method has been applied to investigations of a harmonic drive, in particular to analysis of the stress state in the flexspline with a variable curvature as well as bearings of the generator. For verification of the obtained results, a more adequate FEM model calculated by ANSYS has been used.
A mathematical model of a hybrid culture system supported with a stationary layer of liquid perfluorochemical (PFC) as a source of O2 for cells which grow in the aqueous phase of culture medium has been developed and discussed. The two-substrate Monod kinetics without inhibition effects, i.e. the Tsao-Hanson equation, has been assumed to characterise the biomass growth. The Damköhler number which relates the growth rate to the mass transfer effects has been used to appraise the regime (i.e. diffusion-limited or kinetics) of the whole process. The proposed model predicted accurately previously published data on the submerged batch cultures of Nicotiana tabacum BY-2 heterotrophic cells performed in a culture system supported with a stationary layer of hydrophobic perfluorodecalin as a liquid O2 carrier. Estimated values of the parameters of the model showed that the process proceeded in the kinetics regime and the growth kinetics, not the effects of the mass transfer between aqueous phase and liquid PFC, had essential influence on the growth of biomass.
The paper examines from the thermodynamic point of view operation of coal fired power unit cooperating with the cryogenic oxygen unit, with a particular emphasis on the characteristic performance parameters of the oxygen unit. The relatively high purity technical oxygen produced in the oxygen unit is then used as the oxidant in the fluidized bed boiler of the modern coal fired power unit with electric power output of approximately 460 MW. The analyzed oxygen unit has a classical two-column structure with an expansion turbine (turboexpander), which allows the use of relatively low pressure initially compressed air. Multivariant calculations were performed, the main result being the loss of power and efficiency of the unit due to the need to ensure adequate driving power to the compressor system of the oxygen generating plant.
This work presents the co-simulation approach to the analysis of control systems containing detailed models of electromagnetic and electromechanical converters. In this method of analysis the attention is paid to the whole system and not only to its electromagnetic part. The latter is described by equations resulted from the two-dimensional finite element discretisation of the Maxwell equations, and is coupled weakly with the remaining part of the system. The simulation is carried out in Matlab/Simulink environment wherein the coupling is realised through the S-function. Example results regarding simulation of the operation of the control system of an electrical machine and the operation of a power electronic converter are presented and compared with available reference data.
In this work, a design equation was presented for a batch-recirculated photoreactor composed of a packed bed reactor (PBR) with immobilised TiO2-P25 nanoparticle thin films on glass beads, and a continuous-flow stirred tank (CFST). The photoreactor was studied in order to remove C.I. Acid Orange 7 (AO7), a monoazo anionic dye from textile industry, by means of UV/TiO2 process. The effect of different operational parameters such as the initial concentration of contaminant, the volume of solution in CFST, the volumetric flow rate of liquid, and the power of light source in the removal efficiency were examined. A rate equation for the removal of AO7 is obtained by mathematical kinetic modelling. The results of reaction kinetic analysis indicate the conformity of removal kinetics with Langmuir-Hinshelwood model (kL-H = 0.74 mg L-1 min-1, Kads = 0.081 mg-1 L). The represented design equation obtained from mathematical kinetic modelling can properly predict the removal rate constant of the contaminant under different operational conditions (R2 = 0.963). Thus the calculated and experimental results are in good agreement with each other.