Effect of ideal gas model with temperature-independent heat capacities on thermodynamic and performance analysis of open-cycle gas turbines

Abstract

The ideal gas model with temperature-independent heat capacities is the most widely used thermodynamic model in gas turbine cycle simulations. This model is sometimes known as the “perfect gas model”. Closed analytical expressions for specific works and temperatures of the cycle are obtained in this way. If the results are accurate enough then the perfect gas model becomes a powerful analysis tool because its simplicity. For this reason it is the usually chosen option when energy, exergy or thermoeconomic assessments and optimizations of gas turbine cycles are carried out. However, there is a shortage of research works about the analysis of the uncertainty in the calculation of the performance parameters of open-cycle gas turbines with respect to the ideal gas model-based approach (ideal gas with temperature-dependent heat capacities). This analysis is presented in this paper for the simple cycle taking the net specific work output or specific power of the cycle and its Specific Fuel Consumption (SFC) as the performance parameters to be analyzed. First, to gain in internal coherence, an accurate thermodynamic model of the simple cycle based on the ideal gas assumption with temperature-dependent heat capacities is presented. For the sake of accuracy the isobaric heat capacity functions used in this model for every gaseous component present in the cycle are the employed in developing its actual multiparameter equations of state as real fluids. Once this model is established the perfect gas simplification is applied which requires a procedure or rule to evaluate the constant heat capacity values needed. In many cases this rule is not always given or is not clearly specified in the specific literature. In this paper four different evaluation methods (named as A, B, C and D) are considered. These methods are designed to be directly run from known input fixed parameters of the cycle model. The analysis of the absolute and relative errors in computations with the perfect gas approach with the four heat capacity evaluation methods is then carried out. The main result from the analysis is that the own configuration of the open-cycle can lead to an increase (amplification) of the uncertainty in the values of the performance parameters. It is also observed that: (1) this amplification also depends on the method used to evaluate the heat capacities and (2) for a given evaluation method the amplification of the deviations may affect the performance parameters differently. As an example, maximum relative errors of 4.4% and −19.2% are observed in the net specific work output with methods C and D respectively for compressor pressure ratios from 5:1 to 40:1 and turbine inlet temperatures from 1200 K to 1800 K. For the SFC maximum values are −19.51% with method C and 3.95% with method D.