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Development of real gas model operating in gas turbine system in Python programming environment

100%

Trawiński P.

Archives of Thermodynamics

2020

tom Vol. 41, no 4

23--61

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.

Turbine stage expansion model including internal air film cooling and novel method of calculating theoretical power of a cooled stage

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Trawiński P.

Archives of Thermodynamics

2022

tom Vol. 43, no 3

3--27

Systematic attempts to maximise the efficiency of gas turbine units are achieved, among other possibilities, by increasing the temperature at the inlet to the expansion section. This requires additional technological solutions in advanced systems for cooling the blade rows with air extracted from the compressor section. This paper introduces a new mathematical model describing the expansion process of the working medium in the turbine stage with air film cooling. The model includes temperature and pressure losses caused by the mixing of cooling air in the path of hot exhaust gases. The improvement of the accuracy of the expansion process mathematical description, compared with the currently used models, is achieved by introducing an additional empirical coefficient estimating the distribution of the cooling air along the profile of the turbine blade. The new approach to determine the theoretical power of a cooled turbine stage is also presented. The model is based on the application of three conservation laws: mass, energy and momentum. The advantage of the proposed approach is the inclusion of variable thermodynamic parameters of the cooling medium. The results were compared with the simplified models used in the literature: separate Hartsel expansion, mainstream pressure, weighted-average pressure and fully reversible. The proposed model for expansion and the determination of theoretical power allows for accurate modelling of the performance of a cooled turbine stage under varying conditions.

Development of flow and efficiency characteristics of an axial compressor with an analytical method including cooling air extraction and variable inlet guide vane angle

100%

Trawiński P.

Archives of Thermodynamics

2021

tom Vol. 42, no 4

17--46

The development of a reliable mathematical model of an axial compressor requires applying flow and efficiency characteristics. This approach provides performance parameters of a machine depending on varying conditions. In this paper, a method for developing characteristics of an axial compressor is presented, based on general compressor maps available in the literature or measurement data from industrial facilities. The novelty that constitutes the core of this article is introducing an improved method describing the performance lines of an axial compressor with the modified ellipse equation. The proposed model is extended with bleed air extraction for the purposes of cooling the blades in the expander part of the gas turbine. The variable inlet guide vanes angle is also considered using the vane angle correction factor. All developed dependencies are fully analytical. The presented approach does not require knowledge of machine geometry. The set of input parameters is based on reference data. The presented approach makes it possible to determine the allowed operating area and study the machine’s performance in variable conditions. The introduced mathematical correlations provide a fully analytical study of optimum operating points concerning the chosen criterion. The final section presents a mathematical model of an axial compressor built using the developed method. A detailed study of the exemplary flow and efficiency characteristics of an axial compressor operating with a gas turbine is also provided.