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 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).
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.
Skin dynamic termography supplemented by a mathematical model is presented as an objective and sensitive indicator of the skin prick test result. Termographic measurements were performed simultaneously with routine skin prick tests. The IR images were acquired every 70 s up to 910 s after skin prick. In the model histamine is treated as the principal mediator of the allergic reaction. Histamine produces vasolidation and the engorged vessels are responsible for an increase in skin temperature. The model parameters were determined by fitting the analytical solutions to the spatio-temporal distributions of the differences between measured and baseline temperatures. The model reproduces experimental data very well (coefficient of determination = 0.805÷0.995). The method offers a set of parameters to describe separately skin allergic reaction and skin reactivity. The release of histamine after allergen injection is the best indicator of allergic response. The diagnostic parameter better correlates with the standard evaluation of a skin prick test (correlation coefficient = 0.98) than the result of the thermographic planimetric method based on temperature and heated area determination (0.81). The high sensitivity of the method allows for determination of the allergic response in patients with the reduced skin reactivity.
In the projects of protection of soil-water environment there is a need to combine and process large amount of information from various disciplines to estimate parameters of phenomena and to determine the range and time table of necessary undertakings.
Due to complex assessment of processes taking place in aquifers, mathematical modeling is the best tool supporting evaluation off pollution in the ground water environment. It is also an effective method of forecasting the risk associated with the harmful impact of objects polluting grounds and grounds waters.
Significant application of mathematical modeling is the use for the enlargement of information gathered in the process of recognition and assessment of condition that prevail in soil-water environment. Results of modeling, if appropriately presented, could be an important element of decision support system in environmental management.
This paper describes procedures for developing an environmental remediation decision support system by linking CADD and GIS software with the hydro geological flow and transport models.
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.
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 lumbosacral region of the spine is the most susceptible to pathology in large breed dogs. The most common pathologies of this segment include intervertebral disc disease, distortion of vertebrae, narrowing of the lumbosacral canal and congenital defects of the spine. The aim of this study is to develop a mathematical model describing the height of each lumbosacral vertebra in the dog in relation to the position of the vertebra. For the mathematical analysis we used the results of two measurements for each lumbar vertebra. The first measurement was made from the top of the spinous process to the center of the spinal cord. The second measurement was made from the center of the body of one vertebra to the center of the body of the next one. It is possible to determine an approximate mathematical model that would be uniform for the entire species and would connect the height of the lumbar vertebrae with their location for every breed of the domestic dog. Despite the considerable differences in the constitutional type (small, medium and large breeds), the morphology of the lumbosacral region of the spine exhibits similar proportions. Therefore, it is possible to assess an anomaly of this spinal region objectively. These findings suggest that it is possible to determine an approximate mathematical model that would be uniform for the entire species. The present study was carried out as part of a larger project. This particular work is a pilot study.
The problems of mathematical modelling of vibration signal for bearings with specific geometrical structure or defect is important insofar as there are no model bearings (to facilitate carrying out a calibration procedure for industrial measurement systems). It is even more so that there are no precise reference systems to which we would compare the results. This article presents a general outline of the most important studies on modelling of vibrations in rolling bearings. Papers constituting the basis for the most recent studies and a review of articles from the past few years have been considered here. Five different models have been analyzed in detail in order to show the directions of the latest studies. Completed analysis presents different viewpoints on the issue of modelling a rolling bearing operation. This overview article makes it possible to derive the final conclusion that in order to include all factors affecting bearing vibrations, even those ignored in the most recent models, it is necessary to carry out practical statistical research including the principles of multicriteria statistics. This approach will facilitate developing a versatile model, also applicable to predicting vibrations of a new bearing just manufactured in a factory.
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 agrarian process includes many industrial phenomena and events. The goal of economics as a science is to precisely detect and describe the relationships between various market mechanisms. These phenomena can be presented as the desire “to describe reality in terms of systems, their components and relationships, both between components of the system and between different systems” (Jankowski 1997). The energy sector is a special field among many areas of the national economy, and the products of this sector have a major impact on the branches of the economy and the mechanisms of action occurring in them. The publication is devoted to the construction of a mathematical model used to support the energy policy of local government units. The aim of the study is to build a mathematical model of energy production, taking the development potential of renewable energy into account, as well as to propose the desired direction of energy policy development in the analyzed periods to the regional authorities and to offer a model for creating an energy policy in other local government units: poviats, communes. Until now, few authors have comprehensively dealt with this issue. To date, no detailed research has been published on issues related to renewable energy development and the use of mathematical methods in the construction of the energy production model in local government units. The undertaken research is a contribution to the development of knowledge about alternative energy sources in the energy margin.
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