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EN
Identification of working fluids and development of their mathematical models should always precede construction of a proper model of the analysed thermodynamic system. This paper presents method of development of a mathematical model of working fluids in a gas turbine system and its implementation in Python programming environment. Among the thermodynamic parameters of the quantitative analysis of systems, the following were selected: specific volume, specific isobaric and isochoric heat capacity and their ratio, specific enthalpy and specific entropy. The development of the model began with implementation of dependencies describing the semi-ideal gas. The model was then extended to the real gas model using correction factors reflecting the impact of pressure. The real gas equations of state were chosen, namely due to Redlich–Kwong, Peng–Robinson, Soave– Redlich–Kwong, and Lee–Kesler. All the correction functions were derived analytically from the mentioned equations of real gas behaviour. The philosophy of construction of computational algorithms was presented and relevant calculation and numerical algorithms were discussed. Created software allowed to obtain results which were analysed and partially validated.
PL
W artykule przedstawiono metodę modelowania akumulatora hydropneumatycznego na przykładzie akumulatora tłokowego stosowanego w układach hydraulicznych m.in. jako wtórne źródło energii. Opracowany został model matematyczny akumulatora ze szczególnym uwzględnieniem równań opisujących zachowanie się gazu w akumulatorze (między innymi równanie Van der Waalsa i Benedicta-Webba-Rubina). Otrzymane wyniki z badań symulacyjnych dla różnych modeli gazu porównano z badaniami uzyskanymi podczas testów doświadczalnych i dokonano oceny, który z przyjętych modeli najlepiej odzwierciedla przebiegi parametrów rzeczywistego akumulatora.
EN
The paper deals with the simulation model of hydro-pneumatic accumulator. Mathematical model of the system uses the motion and flow continuity equations, as well as, formulas determining hydro-pneumatic piston accumulator behavior. A few models of real gas were used to calculate gas parameters in accumulator (eg Van der Waals and Benedict-Webb-Rubin eguations) and numerical model of the accumulator was elaborated. Simulation tests were performed for different work cycles and compared with experimental tests to determine which models accurately reflects the behavior of the real hydro-pneumatic accumulator.
EN
This paper includes the purposefulness of using real gas model in thermodynamic analysis of combustion process parameters. Conversion energy optimization in internal combustion engine is possible through well understanding phenomena occurring in combustion chamber. Nowadays the main investigation method of combustion engines is pressure indication. Measurement of pressure in cylinder gives some information about possibility of improving parameters of internal combustion engines work. On the basis of obtained experimental data, applying suitable mathematical model, values of thermodynamic parameters, difficult or impossible to measure, are determined, for example: - course of temperature change in combustion chamber, - rate and course of heat release versus crank angle, - rate and course of fuel charge burning. Calculation results are strongly depended on accepted simplifications in mathematical model. Wide range of temperature and pressure change of working medium within single cycle can require application of real gas state equation. In this situation, determination of compressibility factor of working medium is of primary importance.
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