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EN
Choosing the right pipeline diameter is essential for both newly designed district heating (DH) networks and existing ones undergoing upgrades. A multi-stage optimization algorithm was developed for the purpose of selecting optimal diameters of pipelines in a DH network that has a complex layout including branches and rings. The DH network was represented as a set of graphs and then as matrices, which made hydraulic and heat-and-flow calculations possible for any network layout. The optimization algorithm was developed as a Visual Basic program consisting of 37 macros. The program considers hydraulic resistances, heat-balance equations, capital expenditure for DH pipelines of 32 to 1,100 mm in diameter, and the operating cost, including the costs of heat transmission losses and DH water pumping. Microsoft Excel’s Solver tool was used to solve the non-linear optimization algorithm with constraints. To provide an example of the program’s application, the paper includes calculations used to verify the correctness of selected diameters for part of an existing DH network in a large DH system in Poland.
2
Content available remote Modeling of warm-keeping process with hot air in steam turbines
EN
Steam turbines in conventional power plants have to deal with an increasing number of start-ups due to the high share of fluctuating power input in renewable power generation. As a result, the development of new methods for flexibility improvements - such as reductions in start-up time and the effects these start-ups have on turbine lifetime - have become increasingly important. In pursuit of this objective, General Electric has developed a concept for both the pre-warming and warm-keeping of a high-pressure (HP) / intermediate-pressure (IP) steam turbine with hot air: hot air is passed through the turbine while the turbine is rotated by the turning engine. Due to the high impact of transient flow phenomena on heat transfer during turbine warm-keeping operations, the reliable modeling of the time-dependent temperature distribution within thick-walled components is required as a tool for the optimization of these operations. Due to the extremely high computational effort required for conventional transient Conjugate Heat Transfer (CHT) simulations, alternative fast calculation approaches must be developed. The applied methodology for modeling warm-keeping turbine operations with hot air is presented in this paper. Furthermore, the key modeling steps have been analyzed. A fast transient CHT simulation approach called the Equalized Timescales (ET) method was developed to investigate heat transfer in the fluid and blades. Moreover, the setup of ET simulations was optimized with regard to accuracy and computing time. As a result, several operating points characterizing the turbine warm-keeping operational range were calculated for a single stage model. A sensitivity analysis regarding the heat transfer between fluids and solids was conducted to identify the most relevant surfaces. The ET method was then expanded to a numerical 3-stage turbine model in order to determine a HTC characteristic map for heat transfer in warm-keeping operations. This enables fast calculation of heat transfer rates and, consequently, computationally efficient determination of temperature distribution in warm-kept steam turbines. For comparison, the distribution of HTC was additionally calculated for one operating point of a 5-stage turbine model. Finally, the contact heat transfer in blade roots, which is believed to have a high impact on the temperature distribution of the rotor, was experimentally assessed in a test rig. The description of the test rig and the methodology of determination of the thermal contact resistance (TCR), as well as the impact of TCR on the temperature distribution in the rotor are presented.
PL
W artykule dokonano analizy generacji entropii dla wymiennika typu rura w rurze, w którym czynnikami przekazującymi ciepło była woda. Rozważono cztery konfiguracje wymiennika z czynnikiem grzejnym w rurze wewnętrznej i zewnętrznej oraz przy przepływie współ i przeciwprądowym. Celem analiz było znalezienie średnicy wewnętrznej rury dla minimalnej generacji entropii. Uwzględniono generację entropii na skutek przepływu ciepła i wynikającą z oporów przepływu (spadków ciśnień) czynników przekazujących ciepło. Minimalną generację entropii w funkcji średnicy wewnętrznej rury uzyskano dla dwóch przypadków dla przepływu przeciwprądowego i współprądowego kiedy czynnik chłodniejszy przepływa przez wewnętrzną rurę a cieplejszy przepływa przez przestrzeń pomiędzy rurami. Dla dwóch pozostałych przypadków dla przepływu przeciwprądowego i współprądowego kiedy czynnik cieplejszy przepływa przez wewnętrzną rurę a chłodniejszy przepływa przez przestrzeń pomiędzy rurami generacja entropii maleje w przybliżeniu liniowo wraz ze wzrostem średnicy wewnętrznej rury i nie występuje ekstremum generacji entropii (minimum).
EN
The paper presents analysis of entropy generation for a double-tube heat exchanger with water as heat transferring fluids. Four heat exchanger configurations were considered: with the heating fluid in the inner and outer tubes, and with the parallel and counter flows. The aim of the analyses was to determine the tube inner [inner tube] diameter for which entropy generation is minimum. The entropy generation resulting from heat flow and from resistance to flow (pressure losses) of hest transferring fluids were taken into account. The minimum entropy generation as a function of the inner tube diameter was found for two cases: for the counter and parallel flows when the cold fluid flow through the inner tube and the hot fluid passed through the space between the tubes. For two other cases of the counter and parallel flows when the hot fluid flows through the inner tube and the cold fluid passes through the space between the tube, entropy generation is approximately linearly decreasing with the increase in the inner tube diameter, and there is no entropy generation extremum (minimum) in the range of dimensions analysed in the study.
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