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Mathematical-physical analysis of dynamic pressure for the experimental differentially pumped chamber
Lepltová, Kristýna ; Bílek, Michal (referee) ; Maxa, Jiří (advisor)
This thesis is based on the series of scholarly article dedicated to the issue of pumping in the differential scanning chamber of an environmental scanning microscope. The thesis is based on Danilatos’s study where the pumping of the differential pumped chamber is solved by means of the Monte Carlo statistical method. The thesis analyzes gas flow in the experimental chamber using the Pipot tube. The analyses will be used for the design of the experimental chamber which will serve for the experimental evaluation of the flow results in the chamber using the continuum mechanics.
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Boundary conditions for stratified flows
Řezníček, Hynek ; Beneš, Luděk (advisor) ; Brechler, Josef (referee)
In this thesis is presented mathematical model of stratified 2D flow of viscous incopressible fluid and its program realization. Basic equations of fluid flow in Boussinesq approximation were solved by finite volume method on structured nonortogonal grid. Discretization was done by the principle of semi-discretisation. The space derivative was solved by AUSM me- thod with MUSCL velocity reconstruction. The viscid terms were solved through auxiliary grids. During time discretization artificial compressibility method was used in dual time. The resulting system of ODEs is integrated in time by a suitable Runge-Kutta multistage scheme. Numerical experiments were calculated for flow with Reynolds number equals 1000. Further 3 numerical experiments are presented with different boundary conditions. 1
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ADER schemes for the shallow water equations
Monhartová, Petra ; Felcman, Jiří (advisor) ; Dolejší, Vít (referee)
In the present work we study the numerical solution of shallow water equations. We introduce a vectorial notation of equations laws of conservation from which we derive the shallow water equations (SWE). There is the simplify its derivation, notation and the most important features. The original contribution is to derive equations for shallow water without the using of Leibniz's formula. There we report the finite volume method with the numerical flow of Vijayasundaram type for SWE. We present a description of the linear reconstruction, quadratic reconstruction and ENO reconstruction and their using for increasing of order accuracy. We demonstrate using of linear reconstruction in finite volume method of second order accuracy. This method is programmed in Octave language and used for solving of two problems. We apply the method of the ADER type for the shallow water equations. This method was originally designed for the Euler's equation.
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Calculation of the cooling of the asynchronous machine ANSYS CFX
Horálek, Lukáš ; Veselka, František (referee) ; Janda, Marcel (advisor)
The issue this master’s thesis discusses the cooling synchronous machines. Specifically, the calculation of cooling induction motor using the finite volume method. Using Autodesk Inventor will create a 3D model of a real electric machine, ie asynchronous motor and then ANSYS WORKBENCH perform system analysis CFX, based on the finite volume method. Furthermore, we realize the air speed measurements on a particular machine and the individual results obtained by measuring and calculating the actual compared with each other. The master’s thesis also deals marginally with closely related to it. For the same machine model, we apply the calculation of the temperature fields using the finite volume method and them perform a thermal analysis. Next, we can carry out the measurement of the temperature on the motor itself and calculate the measured values and the measured compare each other.
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Computer simulation and numerical analysis of compressible flow problems
Kubera, Petr
The thesis deals with the construction of an adaptive 1D and 2D mesh in the framework of the cell- centered finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by the Euler equations, which is a hyperbolic system of PDE's. The used algorithm is applicable to non-stationary problems and consists of three independent parts, which are cyclically repeated. These steps are PDE evolution, mesh adaptation and interpolation of numerical solution from the old mesh to the newly adapted mesh. Owing to this the algorithm can be used also for other hyperbolic systems. The thesis is focused on the development of our mesh adaptation strategy, based on the anisotropic mesh adaptation, which preserves the geometric mass conservation law in each computational step. Several test problems with moving discontinuity are computed to compare our algorithm with Moving Mesh algorithms. Keywords: finite volume method, adaptive methods, geometric mass conservation law
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Numerical Solution of the Three-dimensional Compressible Flow
Kyncl, Martin ; Felcman, Jiří (advisor) ; Dolejší, Vít (referee) ; Brandner, Marek (referee)
Title: Numerical Solution of the Three-dimensional Compressible Flow Author: Martin Kyncl Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Jiří Felcman, CSc. Abstract: This thesis deals with a fluid flow in 3D in general. The system of the equations, describing the compressible gas flow, is solved numerically, with the aid of the finite volume method. The main purpose is to describe particular boundary conditions, based on the analysis of the incomplete Riemann problem. The analysis of the original initial-value problem shows, that the right hand-side initial condition, forming the Riemann problem, can be partially replaced by the suitable complementary condition. Several modifications of the Riemann problem are introduced and analyzed, as an original result of this work. Algorithms to solve such problems were implemented and used in code for the solution of the compressible gas flow. Numerical experiments documenting the suggested methods are performed. Keywords: compressible fluid flow, the Navier-Stokes equations, the Euler equations, boundary conditions, finite volume method, the Riemann problem, numerical flux, tur- bulent flow
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Computer simulation and numerical analysis of compressible flow problems
Kubera, Petr ; Felcman, Jiří (advisor) ; Knobloch, Petr (referee) ; Fürst, Jiří (referee)
The thesis deals with the construction of an adaptive 1D and 2D mesh in the framework of the cell- centered finite volume scheme. The adaptive strategy is applied to the numerical solution of problems governed by the Euler equations, which is a hyperbolic system of PDE's. The used algorithm is applicable to nonstationary problems and consists of three independent parts, which are cyclically repeated. These steps are PDE evolution, then mesh adaptation and recovery of numerical solution from the old mesh to the newly adapted mesh. Owing to this the algorithm can be used also for other hyperbolic systems. The thesis is focused on the development of our mesh adaptation strategy, based on the anisotropic mesh adaptation, which preserves the geometric mass conservation law in each computational step. The proposed method is suitable to solve problems with moving discontinuities. Several test problems with moving discontinuity are computed to compare our algorithm with Moving Mesh algorithms.
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Analysis of the fluid mixing in the circulation reactor
Mačák, Martin ; Vyroubal, Petr (referee) ; Maxa, Jiří (advisor)
This work deals with an analysis of the fluid mixing in pilot plant loop reactor. Multiphase flow was simulated with calculation of velocity of flow and volume fraction of individual immiscible phases in hydrogenation reactor for aniline production. Parameters of flow were reviewed in individual parts of the device. Separate attention was paid to heat transfer through wall of the device with usage of external cooling. Designed model is applicable for optimalization and design of bubble loop reactors.
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Analysis of the dimensions of pumping channels in a new design of a scintillation detector
Kryll, Josef ; Bílek, Michal (referee) ; Maxa, Jiří (advisor)
The aim of this thesis is to study the issue of eniveromental scanning electron microscopy and pumping gas to create a vacuum in the newly designed scintillation detector. Further, creating a model of recently proposed scintillation detector and simulating and analyzing pumping gas in differentially pumped chamber of detector and the results compare with the previous model. The theoretical part deals with electron microscopy, electron sources, electron optics and secondary electrons detectors. It is also presented which signals are generated by the electron beam on the surface of a solid. Further fluid flow issues and equations describing the flow in the solved chamber are dismantled. Furthermore, the impact of gaseous environment on the trajectory of primary electrons, because there are collisions of primary beam with atoms and molecules of gas. The following section discusses creating, quality and importance of the network in mathematical modelling. A method of a final volume used to calculate the differential equations describing the flow of gas at the premises of the microscope is described . The practical part consists in creating a model of scintillation detector and analyzing the gas flow in drawing a vacuum in the newly designed scintillation detector. Furthermore, the simulation results are compared with the results of simulations on the older type of scintillation detector. The output of this thesis is model of recently proposed scintillation detector with visualized simulation results.
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