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Mathematical Theory of Flow of a Viscous Incompressible Fluid through a Turbine Cascade
(2023) Neustupa, Tomáš
The thesis presents a relatively complete mathematical theory of a steady flow of a viscous incompressible fluid through a 2D profile cascade. The motivation is a flow through a rotating axial turbine, which is, however, a 3D object. Thus, it is at first explained that, under reasonable assumptions, the corresponding 3D mathematical model can be reduced to a 2D model of a flow through an infinite spatially periodic profile cascade, see Section 2. Reasons why, studying this problem, one can focus just on one spatial period (denoted by ) are given in Section 4.The considered mathematical model in domain consists of the system of Navier–Stokes equations and various boundary conditions: inhomogeneous Dirichlet’s condition on the inflow, the no–slip condition on the surface of a profile, an artificial “do–nothing” (respectively modified “do–nothing”) condition on the outflow and conditions of spatial periodicity on other parts of the boundary of . This combination of boundary conditions makes the problem different from other “standard” problems of the Navier–Stokes type, often studied in literature. The corresponding linearized model (the so called Stokes problem) is in detail studied in Section 5. We prove the existence and uniqueness of a weak solution in the framework of the space L2 and then also in the framework of the space Lr for 1 < r < 1. In both cases, we also prove the so called maximum regularity property of a solution. Section 6 is devoted to the nonlinear Navier–Stokes problem. The case of the so called “small data” is studied by means of the “do–nothing” boundary condition in Subsection 6.1 and the case of arbitrarily large data is studied by means of the modified “do–nothing” condition in Subsection 6.2. We prove the existence and regularity of steady solutions. A local uniqueness is proven for small data in a neighborhood of each regular point of a certain associated nonlinear operator.
Station Passenger Information System - Best Practic
Staniční informační systém pro cestující - Best Practice
(Czech Technical University in Prague, 2025-12-01) Kulakovský, Adam; Heidu, Rudolf Franz; Michl, Zdeněk; Svozil, Radek
The subject of the thesis "Station Information System for Passengers - Best Practice" is to compare existing passenger information systems. This is followed by the creation and analysis of a questionnaire survey on the comprehensibility of information boards and monitors. Based on the questionnaire survey, a formal proposal for a new visualization of station information systems at Prague Main Station is created.
Optimization of Storing and Picking Products Involving Separate Storage
Optimalizace naskladňování a vyskladňování produktů ukládaných odděleně
(Czech Technical University in Prague, 2025-12-01) Čech, Martin; Teichmann, Dušan; Kozel, Petr
The thesis deals with the optimization of storing and picking products, especially dangerous goods substances that must be stored separately in the warehouse. The thesis first characterizes logistics and warehouse processes and summarizes the legal and safety requirements for the storage and handling of hazardous substances. The main output of the thesis is four variants of a linear mathematical model that take into account the capacity limitations of individual positions in the warehouse, the requirements for separate storage of certain commodities, and the level of danger of certain commodities. The optimization criteria are the total handling time for storing and retrieving commodities, and in some variants, the number of racks used is also taken into account. The functionality of the proposed models is tested on data from an experimental warehouse using Xpress IVE optimization software. The result of the thesis is therefore a decision support system that increases storage safety and operational efficiency.
Risk Assessment of the II/608 x III/0087 Intersection
Zhodnocení rizikových aspektů při realizaci křižovatky II/608 x III/0087
(Czech Technical University in Prague, 2025-12-01) Havránek, Petr; Dvořáčková, Alexandra; Kocourek, Josef; Kočka, Ondřej
This bachelor thesis focuses on the risk assessment of the II/608 x III/0087 intersection in the cadastral area of Odolena Voda, including the connection to the road leading to the Vodochody Airport complex. The aim of the thesis is to analyze available materials and traffic engineering data, including previously considered technical solutions, accident rates, and traffic intensities in the locality. The thesis includes a road safety inspection at the intersection in question. Based on the evaluated data, a comprehensive risk assessment of the location is carried out, including accident analysis and assessment of traffic intensities. The outcome of the thesis is a proposal of measures to improve safety and traffic flow. The final part presents a socio-economic evaluation of the proposed solution, including an indicative list of implementation costs and an assessment of the overall societal losses from traffic accidents. The thesis provides specific recommendations for enhancing safety and operational efficiency at the intersection.
Havránek, Petr