The paper deals with the numerical modelling of the unsteady temperature fields in the elements of technological systems using data subject to errors. The multistagemultigroup approach to numerical modelling of transient temperature fields is suggested. The internal structure of the matrix of coefficients of the set of constraint equations has been analyzed and simplifications in the adjustment procedure indicated. The method is easy to use in modelling of 2D and 3D transient problems. The efficiency of the presented algorithm enables us to estimate temperature fields using data subject to errors in on-line calculations.
The progressing development of industry and the associated increasing environmental pollution create the need for the intensification of combustion processes and the implementation of increasingly stringent environmental protection standards. Therefore, an intensive progress in scientific and research work is observed, and studies with the use of numerical methods are becoming an indispensable element of experimental research, enabling the optimization of combustion processes with the simultaneous evaluation of ecologic effects and, as a result, the development of new designs of burners and special, low-emission combustion technologies. This article presents possibilities for the numerical modelling of combustion processes and gas dynamics in heating furnaces. The chemistry of the combustion process was modelled using the software CHEMKIN version 4.02, while the gas dynamics of flue gas flow in the combustion chamber was modelled with the program FLUENT. Numerical computations were performed for both the experimental chamber and real facilities, namely a pusher furnace and a sheet hardening furnace.
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Coastal upwelling often reveals itself during the thermal stratification season as an abrupt sea surface temperature (SST) drop. Its intensity depends not only on the magnitude of an upwelling-favourable wind impulse but also on the temperature stratification of the water column during the initial stage of the event. When a "chain" of upwelling events is taking place, one event may play a part in forming the initial stratification for the next one; consequently, SST may drop significantly even with a reduced wind impulse. Two upwelling events were simulated on the Polish coast in August 1996 using a three-dimensional, baroclinic prognostic model. The model results proved to be in good agreement with in situ observations and satellite data. Comparison of the simulated upwelling events show that the first one required a wind impulse of 28000 kg m-1 s-1 to reach its mature, full form, whereas an impulse of only 7500 kg m-1 s-1 was sufficient to bring about a significant drop in SST at the end of the second event. In practical applications like operational modelling, the initial stratification conditions prior to an upwelling event should be described with care in order to be able to simulate the coming event with very good accuracy.
Artykuł przedstawia przykład modelowania numerycznego prasowania obwiedniowego wyrobu typu tarcza, wykonanego ze stali gatunku C45 w warunkach kształtowania na zimno. Symulację tego procesu wykonano metodą elementów skończonych (MES) przy użyciu aplikacji DEFORM-3D. W obliczeniach przyjęto pełny model przestrzenny procesu, włącznie z uwzględnieniem zjawisk cieplnych. Uzyskane wyniki dostarczają informacji na temat wpływu charakteru ruchu narzędzia (tj. matrycy wahającej) na podstawowe parametry procesu prasowania. W obliczeniach założono, że narzędzie wykonuje dwa ruchu - tj. tradycyjny, wahający oraz wahający, gdzie wyimaginowany punkt należący do narzędzia wykreśla na płaszczyźnie czołowej tzw. "rozetę trzylistną". W artykule dyskusji poddano wyniki symulacji w postaci przebiegu siły kształtującej, rozkładu funkcji zniszczenia Cockrofta-Lathama (C-L) i intensywności naprężenia w wyprasce.
EN
In this paper the example of rotary forging a part type disc made of steel C45 formed in cold forming condition is presented. Numerical calculation were made with the application of Deform-3D software based on finite element method (FEM). The couplet three-dimension model of rotary forging taking into consideration thermal phenomena was assumed, the obtained results gave information about the tool movement influence on the basic process parameters. Moreover, in the calculations it was assumed that the tool realizes two movements eg. traditional and rocking on the three-flute wobbler trajectory. Distribution of forces and Cockroft-Latham damage criterion and stress effective those process was discussed.
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Paper summarizes the first results of two-dimensional (2D) numerically modelled expansion and flow of compressible and non-viscous gas in typical parts of air jet weaving system ; namely in main nozzle designed as an ejector with various shapes of the mixing zone, in relay (auxiliary) nozzle with substantial flow separation in the rash flow bend directly before the nozzle outlet, and the influence of the reed dent edges shape on the free stream reflection and penetration through reed gaps along a real 'porous' wall. The used Euler's equations are solved by a Finite Volumes Method (FVM) with automatic mesh generation and optimization of unstructured triangle mesh. Graphical results show 2D isolinies of all gas state values, further Mach number, entropy and velocity vectors. 1D profiles of all quantities along chosen cross-section or surfaces can be obtained, too. They give to the designer a large and quick review about the problem. The condicience with experiment, measuring and weaving tests is very good. The advantage of numerical modelling consists in the very quick, simple and user-friendly operation.
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A simple probabilistic numerical model was used to construct synthetic De distributions by combining the simulated OSL from grains of different sensitivities and with various simulated De values. This is useful for exploring the complex patterns generated by summing the signals from many grains in real, multiple grain OSL dating scenarios, and demonstrates that the form of the sensitivity distribution has a significant effect on the identification of mixed dose populations in multiple grain single aliquot methods. I describe the simple numerical model and its implementation. I present measured quartz single grain OSL sensitivity distributions for an aeolian dune sample from the Simpson Desert, Northern Territory, Australia, and from a suite of 9 fluvial sediments from Namadgi National Park, Australian Capital Territory, Australia, to illustrate effects that result from natural differences. Minimum age model determinations of synthetic De values are used to assess the validity of dose values estimated from multiple grain single aliquot measurements.
In the paper, the mathematical model, numerical algorithm and examples of computations concerning thermal processes proceeding in a multi-layered thin film subjected to an ultrafast laser pulse are discussed. The equations describing a course of the analysed process correspond to the dual-phase-lag model and contain both the relaxation time tau q and additionally the thermalization time tau T. At the stage of numerical simulation, the finite difference method has been used. The algorithm is based on an artificial decomposition of the domain considered, while common thermal interactions between successive layers are taken into account using conditions of heat flux and temperature continuity at points corresponding to internal boundaries (1D task has been considered).
PL
W pracy przedstawiono model matematyczny, algorytm numeryczny i przykłady symulacji dotyczących przebiegu procesów cieplnych w wielowarstwowym mikroobszarze nagrzewanym ultraszybkim impulsem generowanym przez laser. Równanie opisujące przebieg procesu odpowiada modelowi z dwoma opóźnieniami wynikającymi z czasu relaksacji i czasu termalizacji. Na etapie obliczeń numerycznych wykorzystano metodę różnic skończonych. Algorytm bazuje na sztucznej dekompozycji obszaru wielowarstwowego, przy czym wzajemne oddziaływania między warstwami uwzględniono poprzez założenie ciągłości strumienia ciepła i pola temperatury na powierzchniach kontaktu. Biorąc pod uwagę geometrię obszaru, rozpatrywano zadanie jednowymiarowe.
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A simple model of behaviour of a single particle on the bulging membrane was presented. As a result of numerical solution of a motion equation the influence of the amplitude and frequency of bulging as well as the particle size on particle behaviour, especially its downstream velocity was investigated. It was found that the bulging of a membrane may increase the mean velocity of a particle or reinforce its diffusive behaviour, dependeing on the permeation velocity. The obtained results may help to design new production methods of highly fouling-resistant membranes.
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A numerical algorithm is presented for the filling process of a cylindrical column with equilateral cylinders. The process is based on simplified mechanics - the elements are added one by one until the mechanical equilibrium is reached. The final structure is examined with respect to the global and local porosity distribution. Oscillating radial porosity profile is obtained in accordance with experimental data.
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The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To describe the latter the Derjaguin-Landau- Vervey-Overbeek (DLVO) model has been employed. We have investigated the influence of various parameters of the process like flow rate, mean particle diameter, amplitude and frequency of the oscillations, and others, on the efficiency of the defouling process. The investigated parameters is close to that of a silica suspension in , a typical system modelling used to investigate membrane separation. On the basis of numerical simulation results e have defined an optimal set of parameters preventing membrane fouling.
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The main aims of the work were to determine material characteristics of cold work tool steel, grade 21 OCR 12 in semisolid forming conditions, as well as developing of numerical model of this steel. Moreover, possibilities of application of Computational Fluid Dynamic methods and solid mechanics modelling techniques were tested. Methodology and results of experimental investigation is described. The results of experiments were then utilized for developing series of numerical simulations. Two sets of simulations are presented, based on the Computational Fluid Dynamics or solid mechanic modelling methods. Comparison of experimental and numerical results is presented, as well as comparison of CFD and structural mechanics based numerical models.
PL
Zasadniczym celem pracy było wyznaczenie charakterystyk stali narzędziowej 21 OCR 12, formowanej w warunkach stałociekłych, a także opracowanie modeli numerycznych dla tej stali. Ponadto, zweryfikowane zostały możliwości stosowania metod dynamiki płynów (Computational Fluid Dynamics, CFD) oraz metod modelowania odkształcania ciał stałych do modelowania procesów formowania w stanie stałociekłym. Opisane zostały metodologia oraz wyniki prac doświadczalnych. Wyniki te zostały wykorzystane do opracowania symulacji numerycznych. Przedstawiono symulacje oparte na metodach CFD oraz oparte na modelach ciał stałych. W pracy porównano wyniki osiągnięte za pomocą metod doświadczalnych i symulacyjnych, jak również porównano wyniki uzyskane z metod CFD i strukturalnych.
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This paper presents possibilities for of numerical modelling of biomass combustion in a commercially available boiler. A sample of biomass was tested with respect to its physical and chemical properties. Thermogravimetry studies of biomass were carried out. Computer simulation makes it possible to analyse complex phenomena which are otherwise difficult to observe. The aim of this work was to model biomass combustion to predict the amount of pollutants generated (NOx, CO, SO2) in the exhaust gases coming out from boilers The calculations were made using the CHEMKIN program. Results of calculations were performed taking into account the influence of temperature, pressure and residence time.
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In the paper the problems connected with numerical modelling of bio-heat transfer processes are discussed. The mathematical model of phenomena discussed bases on the Pennes equation, at the same time the steady and transient tasks are considered. The basic equation is supplemented by the adequate geometrical, physical, boundary and (in the case of transient heat transfer) initial conditions. In the first part of the paper the examples of direct solutions are discussed. Next the possibilities of sensitivity analysis applications in the domain of bio-heat transfer are presented. In the final part the selected solutions of inverse problems are shown. On the stage of numerical simulations both in the case of direct and inverse problems, as a rule, the different variants of the boundary element method have been used.
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Critical analysis and classification of rheological models of a human blood is the objective of the paper. In the first part of the paper main features of a blood and their influence on modelling blood flow are discussed. Various models available in the scientific literature have been analysed and classified on the basis of a mathematical form of equations. Capabilities of the models to account for certain physical features of blood were evaluated. Power laws, commonly used in basic simplified simulations, have simple mathematical form and are not analysed. Among the remaining models, three groups were distinguished and selected for further analysis: Casson type models, be-exponential law and Quemada model. Sensitivity analysis was performed for these models using Morris OAT Design method. Sensitivity of the viscosity predicted by various models, with respect to the coefficients in these models and with respect to the external variable (shear rate), was determined. Importance of the investigated coefficients and their influence on models’ predictions was evaluated. Suggestions concerning identification of coefficients in the models are given in conclusions.
PL
Celem pracy jest krytyczna analiza oraz klasyfikacja reologicznych modeli krwi. W pierwszej części artykułu omówiono główne cechy i właściwości krwi w aspekcie ich wpływu na modelowanie przepływu krwi. Analizie poddano różne modele krwi dostępne w literaturze, które sklasyfikowano w oparciu o matematyczną postać zastosowanych równań. Oceniono możliwości poszczególnych modeli w zakresie uwzględnienia wpływu fizycznych cech krwi. Prawa potęgowe, powszechnie stosowane w symulacjach przepływu krwi, maj ą prosty matematyczny zapis i nie były szczegółowo analizowane. Do dalszej analizy modele podzielono na trzy grupy: modele typu Cassona, prawo Bi-ekspotencjalne i model Quemady. Dla wybranych modeli przeprowadzono analizę wrażliwości stosując metodę opartą o algorytm Morrisa. Określono współczynniki wrażliwości lepkości krwi względem współczynników modeli oraz względem zmiennej zewnętrznej prędkości ścinania. Wyznaczono wskaźniki istotności poszczególnych współczynników oraz ich wpływ na wyniki modelu. We wnioskach z pracy zawarto wskazówki dla identyfikacji współczynników analizowanych modeli.
Main advantages and disadvantages of thixoforming are presented in the paper. Materials, which are presently used for thixoforming are described, as well. A short review of numerical methods dedicated recently to thixoforming modelling, is also included, dividing them into two groups – structural and Computational Fluid Dynamic methods. Internal Variable Convection method, which combines main advantages of both groups, is introduced IVC. Numerical models of two tests, as well as results of computations are shown. The first it the test designed to determine a semi-solid metal viscosity with a rotational viscometer. The second one is a filling of a T-shape mould. Main disadvantages, as well as expected improvements of the presented software are described in the paper.
PL
W artykule opisano wady i zalety technologii tiksoformingu, a także materiały stosowane w tej technologii. Omówiono obecnie stosowane techniki modelowania komputerowego procesów tiksoformingu, uwzględniając ich podział na metody wywodzące się z modelowania odkształcenia ciał stałych i z dynamiki płynów. Zaproponowano metodę Konwekcji Zmiennej Wewnętrznej, łączącą zalety obu tych metodologii. Przedstawiono wyniki numerycznych symulacji doświadczeń wykonywanych w celu wyznaczenia lepkości metalu w stanie stało-ciekłym oraz symulacji wypełniania formy T-kształtnej. Omówiono najistotniejsze wady obecnego rozwiązania oraz możliwości ich wyeliminowania.
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The purpose of the presented paper is the identification and assessment of causes of intensive abrasion in the open coastline of the Hel Peninsula and the effect of countermeasures. Numerical modeling of nearshore hydrodynamics, topographic analysis and field measurements were carried out. The Baltic Sea hydrodynamic model, a model of wave-induced nearshore circulation and the wave model SWAN were employed. 3D hydrodynamic modeling resulted in the become visible that fields of shear bottom stresses as well as bottom currents depended on atmospheric forcing and depth. A correlation between bottom stresses and topography was obtained. The results of modeling of the nearshore hydrodynamics demonstrated a dominant role for alongshore sediment transport. The magnitude of both cross- and alongshore wave-induced currents strongly depended on wave height gradient, which was significantly greater in storm periods. During storms, sediment transport occurs also in the cross-shore direction.
In this day and age of computers and advanced computational techniques the analyzed process can be studied not only experimentally on material model in laboratory or exploitation process but also analytically on a mathematical model. In an analytic way we can study the influence of different parameters e.g. the temperature on the considered process for many different combinations of values. The computer simulations help and make it possible to carry out complex experiments and the scientific research, the analysis of phenomena difficult to observe or impossible to realize in normal conditions. This article presents possibilities for the numerical modelling of combustion processes and gas dynamics in heating furnaces. The chemistry of the combustion process was modelled using the software the newest version of CHEMKIN program, namely CHEMKIN-PRO CHEMKIN, while the flue gas flow dynamics in the combustion chamber was modelled with the COMSOL MULTHIPHISIC software.
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W pracy rozważa się problematykę modelowania podłoża gruntowego z elementem wzmacniajacym. Przedstawiono w niej schemat numerycznej procedury modelowania ośrodka gruntowego z palami wielkośrednicowymi, żelbetowymi i betonowymi, wchodzącymi w skład palisady - muru oporowego, pełniącego funkcję zabezpieczenia terenu osuwiskowego w celu zrealizowania projektowanego odcinka drogi będącej wschodnią obwodnicą Bielska-Białej. Niniejsze rozważania są kontynuacją wcześniejszych prac [2], [3], [4], [5], [6], które również wykorzystywały procedury symulacji numerycznych przy użyciu MES i programu Z_Soil oraz zakładały wykorzystanie sprężysto-plastycznego modelu Druckera-Pragera, dla opisu materiałów wchodzących w skład modelowanego ośrodka gruntowego.
EN
The paper considers the issue of ground-medium with stokade construction. Based on generally accepted principles the author presents numerical modelling patterns and compares the outcome of the numerical simulations with the measured settlement and load capacity of these subsoil with palisade located along the hidhroad in Bielsko-Biała, Poland. The paper constitutes an attempt to summarise and generalise earlier research which involved FEM numeric procedures and the Z_Soil package and utilised an elastic-plastic model of a ground medium with the Drucker-Prager criterion which is very convenient from the point of view of numerical efficiency.
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The relative roles of nitrogen and phosphorus in the limitation of phytoplankton growth in Narva Bay, south-eastern Gulf of Finland, were studied by combining the results of numerical modelling and nutrient enrichment experiments. Modelled biomass-based intracellular nutrient concentrations (nutrient functions) were used to estimate the limiting nutrient in Narva Bay. Nutrient functions - NF ? [0; 1] for nitrogen and PF ? [0; 1] for phosphorus - define the dependence of the phytoplankton growth rate on nutrients: NF = PF = 1 corresponds to non-limitation of phytoplankton growth by nutrients, whereas NF = 0 or PF = 0 to zero growth. The biotests indicated the response of phytoplankton growth to an increase in nutrient concentration in the surrounding water. Three locations were selected for detailed analyses of temporal variations in the nutrient functions: the offshore station N12, station N8 at the mouth of the River Narva, and coastal station 38. The biotests were performed at the same stations. NF and PF reached values of 0.9 prior to the spring bloom. With the onset of the spring bloom, NF decreased rapidly and remained below 0.1 in the open part of Narva Bay for the rest of that period. In the coastal zone, NF was in excess of 0.1, with a local maximum in the river mouth area. PF decreased to 0.3-0.4 in the open bay after the spring bloom. In the coastal zone PF remained above 0.4, with a certain increase from the midsummer minimum towards the end of summer. The numerical modelling results clearly show that nitrogen limits phytoplankton growth in Narva Bay. Phosphorus limitation may occur only for a limited period and over a limited area at the Narva River mouth and other coastal locations. In general, the biotests backed up the modelling results, the main exception being in the open bay during summer. The model does not account for nitrogen fixation, however. Since N-fixing cyanobacteria were prevalent in the offshore area, the addition of phosphorus led to enhanced phytoplankton growth at station N12.
Przedstawiono sposób wyznaczania stref zagrożenia powodziowego przy zastosowaniu numerycznego modelu terenu. Określono źródła danych do budowy lego modelu z podaniem ich parametrów dokładnościowych. Przedstawiono technologię tworzenia modelu terenu z uwzględnieniem przekrojów dolinowych rzeki oraz zasady numerycznego wyznaczania zasięgów zalewu. Omówiono korzyści jakie wynikają z zastosowania narzędzi GIS do wyznaczania stref zagrożenia powodziowego.
EN
The paper presents a method for delimitation o( flood danger zones by applying the numerical model of the area. There have been defined the sources of data utilized in creation of that model and parameters describing their accuracy. There has been also presented the technology of creation of the model taking into consideration the cross-sections of the river valley and the principles of determination of the extend of the inundation. The benefits derived from application of the GIS fools to delimitation of the zones of flood danger have been discussed.
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