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 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.
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.
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 paper is a presentation of an analysis concerning performance of a 12/8 dual-channel switched reluctance motor (DCSRM). Formulas constituting a base for a non-linear mathematical model of DCSRM are presented. Simulation and laboratory tests were carried out for the motor operating in the dual-channel and single-channel mode. The results of the field theory-based calculations are presented in the form of fluxes in individual phases expressed as functions of currents and a rotor position angle. The results of the computer simulations are shown as the static characteristics of fluxes and the torque as well as voltage, current, and torque waveforms. The results of the laboratory tests are also presented.
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 paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental verification of the method is a second part of the study and is not presented in this paper. In order to perform this verification, the mathematical model would be completed with additional energy conservation equations. The experimental verification will be carry out in the close future.
In this paper a mathematical model enabling the analysis of the heat-flow phenomena occurring in the waterwalls of the combustion chambers of the boilers for supercritical parameters is proposed. It is a one-dimensional model with distributed parameters based on the solution of equations describing the conservation laws of mass, momentum, and energy. The purpose of the numerical calculations is to determine the distributions of the fluid enthalpy and the temperature of the waterwall pipes. This temperature should not exceed the calculation temperature for particular category of steel. The derived differential equations are solved using two methods: with the use of the implicit difference scheme, in which the mesh with regular nodes was applied, and using the Runge-Kutta method. The temperature distribution of the waterwall pipes is determined using the CFD. All thermophysical properties of the fluid and waterwall pipes are computed in real-time. The time-spatial heat transfer coefficient distribution is also computed in the on-line mode. The heat calculations for the combustion chamber are carried out with the use of the zone method, thus the thermal load distribution of the waterwalls is known. The time needed for the computations is of great importance when taking into consideration calculations carried out in the on-line mode. A correctly solved one-dimensional model ensures the appropriately short computational time.
A steam generator in a nuclear power plant with a light water reactor is a heat exchanger, in which the heat is being transferred from the primary to the secondary loop (it links the primary and secondary loops). When the power plant is running, the inlet parameters (temperatures and mass flow rates) on both sides of the steam generator can change. It is important to know how the changes of these parameters affect the steam generator performance. The complexity of the processes taking place in the steam generator makes it difficult to create a simulator reflecting its performance under changed conditions. In order to simplify the task, the steam generator was considered as a ‘black box’ with the aim of examining how the changes of the inlet parameters affect the changes of the outlet ones. On the basis of the system (steam generator) response, a simple mathematical model of the steam generator under variable load conditions was proposed. In the proposed model, there are two dimensionless parameters and three constant coefficients. A linear relation between these dimensionless parameters was obtained. The correctness of the model was verified against the data obtained with a steam generator simulator for European Pressured Reactor and AP-600 reactors. A good agreement between the proposed model and the simulator data was achieved.
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.
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.