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EN
Jump-diffusion models of financial market described by stochastic differential equations (SDEs) driven by a Brownian motion and Poisson processes are incomplete. Prices for contingent claims can not be determined in a unique way. For different equivalent martingale measures different values for options can be obtained. In the paper the theorems on the range of European options prices corresponding to the class of all such measures for jump-diffusion models of financiel market are presented. Equivalent martingale measures are explicitly described by appropriate linear stochastic differential equations, which can be solved with the use of general semimartingale Ito formula. In comparison with a content of the basic paper of N. Bellamy and M. Jeanblanc [1], the results are slightly more general (see Lemma 1) and proofs (presented in [4]) corrected and improved at some points. The price corresponding to the Schweizer minimal martingale measure is derived for a more general market model driven by Poisson random measures defined by Poisson processes with jumps of random size. The Schweizer price is located and compared with the Merton price in the range of prices corresponding to the class of all possible equivalent martingale measures for jump-diffusion models described by stochastic differential equations driven by a Brownian motion and a nnite number of Poisson processes. Results of computer experiments based on approximate construction of equivalent martingale measures provide a quantitative illustration of obtained results.
EN
A detonation is the strongest form of all gas explosions. The ease with which a flammable mixture can be detonated (detonability) commonly and traditionally is classified by a detonation cell width λ and an ignition delay time behind the detonation leading shock τ. Additionally, two more parameters were proposed 3 years ago – χ and RSB, which inform about regularity of a detonation structure. The problem of a detonation is significant in industry, in particular in power engineering, where restricted emission standard impose to introduce hydrogen-rich fuels, such as syngas. The most possible initiation of a detonation in industrial conditions is deflagration to detonation transition (DDT), where a deflagration under some conditions (obstacles, confinement, etc.) accelerates and a transition to a detonation takes places. In industry, this acceleration of a flame may progress in initially smoke-filled space. The goal of this paper is to analyse influence of exhaust gas on detonation propensity of a mixture of carbon monoxide and hydrogen. The analysis concerns the detonation cell width λ, ignition delay time τ, RSB and χ parameters. The composition of exhaust gas is calculated by setting it to a state of chemical equilibrium. Combustion temperature influence on exhaust gas composition is assessed. Species, which have the strongest influence on detonability, are assessed. Computations are performed with the use of Cantera tool.
PL
W pracy przedstawiono wyniki analizy numerycznej powstawania lokalnych koncentracji naprężeń elementów tocznych w warunkach pracy. Obliczenia przeprowadzono dla elementów wykonanych z materiału idealnie sprężystego oraz z materiału sprężysto plastycznego z kinematycznym wzmocnieniem liniowym. W pracy zaprezentowano modelowanie strefy styku. Obliczenia wykonano, stosując MES, profesjonalny pakiet ANSYS.
EN
The paper presents the results of the numerical analysis of the local concentrations of stresses of rolling elements in working condition and process of modelling of the contact zone. Calculations were done for the elements made of the elastic-ideally plastic material and the elastic-plastic material with kinematic linear reinforcement using MES, professional package ANSYS.
EN
The detonation propensity of hydrogen-air mixtures with addition of methane, ethane or propane in wide range of compositions is analyzed. The analysis concerned the detonation cell width, ignition delay time, RSB and χ parameters. Results are presented as a function of hydrogen molar fraction. Computations were performed with the use of three Cantera 2.1.1. scripts in the Matlab R2010b environment. The validated mechanisms of chemical reactions based on data available in the literature were used. Six mechanisms were assessed: GRI-Mech 3.0, LLNL, SanDiego, Wang, POLIMI and AramcoMech. In conclusion, the relation between detonation propensity parameters is discussed.
EN
The influence of the crystallization conditions on microstructure of Inconel 713 C superalloy was presented in the paper. Turbine blades with airfoil section width of 22 and 30 mm and length of 50 mm were casted in investment molds in a vacuum furnace. The secondary dendrite arm spacing was determined through microscopic examinations. On the basis of obtained results it was established that prolonged process of crystallization results in an increase of microstructure constituents dispersion.
PL
W pracy przedstawiono wyniki badań wpływu warunków krystalizacji na mikrostrukturę odlewniczego stopu Inconel 713 C. Łopatki turbin o szerokości pióra 22 i 30 mm i długości pióra 50 mm wykonano metodą wytapianych modeli w piecu próżniowym. Dyspersję składników mikrostruktury określono poprzez pomiar odległości ramion dendrytów wtórnych.
8
Content available remote Wpływ FKN w analizie naprężeń w strefie kontaktu w łożyskach tocznych
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PL
W pracy przedstawiono wpływ współczynnika sztywności kontaktowej FKN na wyniki obliczeń naprężeń w strefie kontaktu w łożyskach tocznych. Obliczenia analityczne wg wzorów zalecanych w literaturze zakładają daleko idące uproszczenia – między innymi nie uwzględniają wpływu chropowatości współpracujących powierzchni. Zastosowanie MES pozwala uwzględnić sztywność chropowatych powierzchni.
EN
The paper shows the influence of Normal Penalty Stiffness Factor FKN on the results of the numerical analysis of contact pressures in rolling bearings. Analytical calculations, when performed according to the formulas recommended in the literature, assume far going simplifications which do not take into account influence of surface roughness. Usage of Finite Element Method FEM allowed to take it into consideration.
EN
This text covers application of Largest Lapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a simulated control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [3] is compared to classical CPA criteria used in control engineering [1]. Introduction contains references to previous publications on Lyapunov stability. Later on, description of classical criteria for CPA along with formulae is presented. Significance of LLE in control systems is explained. Moreover, new efficient formula for calculation of LLE [3] is shown. In the second part simulation of the control system used for experiment is described. The next part contains results of the simulation in which typical criteria for CPA are compared with criterion based on value of LLE. In the last part results of the experiment are summed up and conclusions are drawn.
EN
The numerical modelling of combustion phenomena is an important task due to safety issues and development and optimization of engines. Laminar burning velocity (LBV) is one of the most important physical properties of a flammable mixture. Knowing its exact value if crucial for assessment of flame stabilization, turbulent flame structure. It influences strongly safety, probability of knocking combustion and it is one of parameters used for assessment and development of detailed chemical kinetic mechanisms. Hence, the goal of this work is to develop models by means of Machine Learning algorithms for predicting laminar burning velocities of single-fuel C1-C7 normal hydrocarbon and air mixtures. Development of the models is based on a large experimental data set collected from literature. In total more than 1000, LBVs were accumulated for hydrocarbons from methane up to n-heptane. The models are developed in MATLAB 2018a with use of Machine Learning toolbox. Algorithms taken into account are multivariate regression, support vector machine, and artificial neural network. Performance of the models is compared with most widely used detailed chemical kinetics mechanisms’ predictions obtained with use of LOFEsoft. These kind of models might be efficiently used in CFD combustion models based on flamelet approach. The main advantage in comparison to chemical kinetics calculation is much shorter computational time needed for computations of a single value and comparable performance in terms of R2 (coefficient of determination), RMSE (root-mean-square error) and MAE (mean absolute error).
EN
The aim of this study was to investigate a possibility of using gaseous fuels of a low calorific value as a fuel for internal combustion engines. Such fuels can come from organic matter decomposition (biogas), oil production (flare gas) or gasification of materials containing carbon (syngas). The utilization of syngas in the barrel type Opposed-Piston (OP) engine arrangement is of particular interest for the authors. A robust design, high mechanical efficiency and relatively easy incorporation of Variable Compression Ratio (VCR) makes the OP engine an ideal candidate for running on a low calorific fuel of various composition. Furthermore, the possibility of online compression ratio adjustment allows for engine the operation in Controlled Auto-Ignition (CAI) mode for high efficiency and low emission. In order to investigate engine operation on low calorific gaseous fuel authors performed 3D CFD numerical simulations of scavenging and combustion processes in the 2-stroke barrel type Opposed-Piston engine with use of the AVL Fire solver. Firstly, engine operation on natural gas with ignition from diesel pilot was analysed as a reference. Then, combustion of syngas in two different modes was investigated – with ignition from diesel pilot and with Controlled Auto-Ignition. Final engine operating points were specified and corresponding emissions were calculated and compared. Results suggest that engine operation on syngas might be limited due to misfire of diesel pilot or excessive heat releas which might lead to knock. A solution proposed by authors for syngas is CAI combustion which can be controlled with application of VCR and with adjustment of air excess ratio. Based on preformed simulations it was shown that low calorific syngas can be used as a fuel for power generation in the Opposed-Piston engine which is currently under development at Warsaw University of Technology.
EN
The influence of mould insulation on the microstructure of the nickel-based superalloy - Inconel 713 C, used in gas turbinę blades, was investigated. Turbinę blade castings were madę in industrial conditions. Three varieties of moulds insulation were used. Based on macroscope, fluorescence (surface defects) and radiographic investigations (internal defects) the quality of the castings was estimated. For selected castings light microscopy observations of cross sections of blades were carried out, as well. The average size and morphology of grains were estimated. It has been found, that the kind of the mould insulation influences the ąuality of castings and should be adjusted to the type of blade.
PL
W pracy ustalono wpływ ocieplenia formy na mikrostrukturę odlewów łopatek turbiny ze stopu Inconel 713C. Wykonano w warunkach przemysłowych odlewy łopatek o szerokości pióra 22 i 30 mm oraz jego długości 50 mm. Stosowano trzy rodzaje ocieplenia form ceramicznych. Jakość odlewów określono na podstawie badań makroskopowych, fluorescencyjnych (wady powierzchniowe) i rentgenowskich (wady wewnętrzne). Dla wybranego odlewu łopatki wykonano badania mikroskopowe. Określono średnią średnicę ziaren i ich rozmieszczenie na przekroju odlewu łopatki. Stwierdzono wpływ sposobu ocieplenia formy na mikrostrukturę pióra łopatek wykonanych ze stopu Inconel 713C. Wyniki badań stanowią podstawę dla dalszych prac dotyczących wpływu ocieplenia form na jakość odlewów łopatek turbin.
EN
Glycerol is a major by-product of biodiesel production. Per one tone of produced biodiesel, one hundred kilograms of glycerol is produced. Production of glycerol is increasing due to increase of demand for biodiesel. One of methods of glycerol utilization is combustion. Recent experimental studies with use of a diesel engine and a constant volume combustion chamber show that utilization of glycerol as a fuel results in lower NOx emissions in exhaust gases. It combusts slower than light fuel oil, what is explained by higher viscosity and density of glycerol. Glycerol has low cetane number, so to make combustion in a diesel engine possible at least one of the following conditions need to be fulfilled: a pilot injection, high temperature or high compression ratio. The aim of the paper is to compare glycerol to diesel and to assess influence of glycerol doping on gasoline and diesel fuel in dependence of pressure, temperature and equivalence ratio. The subject of this study is analysis of basic properties of flammable mixtures, such as ignition delay times and laminar burning velocities of primary reference fuels (diesel: n-heptane and gasoline: iso-octane). Calculations are performed with use of Cantera tool in Matlab and Python environments. Analyses of influence of glycerol on ignition delay times of n-heptane/air and iso-octane/air mixtures covered wide range of conditions: temperatures from 600 to 1600 K, pressure 10-200 bar, equivalence ratio 0.3 to 14, molar fraction of glycerol in fuel 0-1 in air. Simulations of LBV in air cover temperatures: 300 K and 500 K, pressures: 10, 40, 100, 200 bar and equivalence ratio from 0.3 to 1.9. Physicochemical properties of gasoline, diesel and glycerol are compared.
EN
Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.
PL
Dynamika układów nieliniowych jest bardzo komplikowanymzagadnieniem z wieloma aspektami wciąż pozostającymi bez rozwiązania. Do badań takich układów stosuje się wiele różnych metod. Wnikliwa analiza związana jest najczęściej z bardzo czasochłonnymi symulacjami numerycznymi. Istnieje w związku z tym duże zapotrzebowanie na opracowanie metod upraszczających ten proces. W artykule pokazano zastosowanie sztucznych sieci neuronowych (ANN) wspomagających badania przepływu i synchronizacji energii. W badaniach zastosowano Mapy Uderzeń, będące efektem przedstawienia dynamiki układu z uderzeniami w przestrzeni energetyczno-wektorowej. Pokazano zmiany przepływu energii z przejściowym stanem synchronizacji. Wprowadzono nowy rodzaj parametru pozwalającego na określanie stanu dynamicznego układu z uderzeniami. Wyniki przeprowadzonych symulacji numerycznych zostały wykorzystane w procesie uczenia sztucznej sieci neuronowej. Przedstawiono następnie porównanie wyników symulacji i rozwiązania uzyskanego z sieci neuronowej oraz przewidywania parametrów układu, dla których występuje synchronizacja przepływu energii.
EN
The main aim of this study to reproduce methane combustion experiment conducted in a rapid compressionexpansion machine using AVL FIRETM software in order to shed more light on the in-cylinder processes. The piston movement profile, initial and boundary conditions as well as the geometry of the combustion chamber with a prechamber were the same as in the experiment. Authors by means of numerical simulations attempted to reproduce pressure profile from the experiment. As the first step, dead volume was tuned to match pressures for a non-combustion (air-only) case. Obtained pressure profile in air compression simulations was slightly wider (prolonged occurrence of high pressure) than in the experiment, what at this stage was assumed to have negligible significance. The next step after adjusting dead volume included combustion simulations. In the real test facility, the process of filling the combustion chamber with air-fuel mixture takes 15 s. In order to shorten computational time first combustion simulations were started after the chamber is already filled assuming uniform mixture. These simulations resulted in more than two times higher maximum pressure than recorded in experiments. It was concluded that turbulence decays quickly after filling process, what was also confirmed by next combustion simulations preceded by the filling process. Then the maximum pressure was significantly decreased but still it was higher than in the experiments. Based on the obtained results it was assumed that the discrepancy noticed in air cases is further increased when combustion is included. Moreover, the obtained results indicated that pre-combustion turbulence level is very low and suggested that either piston profile movement is not correct or there is high-pressure leak in the test facility.
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