Analytical model-based energy and exergy analysis of a gas microturbine at part-load operation
Introduction
Small gas turbines whose mechanical power do not exceed several hundred kilowatts are classified as microturbines. In general gas microturbines operate according to the open Brayton cycle with or without heat regeneration. A typical microturbine is a single shaft design with the turbine, compressor and generator mounted on the same shaft. The pressure ratio is of the order 3.5 to 4.0 and the microturbine is controlled by fuel delivery alone. Usually, during load changes the rotational speed of the microturbine also changes while the temperature of the exhaust gas leaving the turbine is kept constant.
Gas microturbines are increasingly used as a primary source of electricity and heat for individual objects, such as: hotels, sports facilities, greenhouses, offices, small businesses, small houses and others. Such micro plants operate under varying demand for electricity and heat. However, running the microturbine at a reduced load results in loss of efficiency.
In the literature, some attention has been paid to the problem of modeling of gas turbines operated at part load and to the analysis of their performance based on the first and second laws of thermodynamics. Zhang et al. [1] formulated an analytical model of a constant rotating speed single shaft gas turbine operated at part load and determined basic part-load characteristics of the turbine. Wang et al. [2] extended the model presented in Reference 1 for microturbines operated with variable rotational speed. They derived the optimal rotational speed for part-load operation and analyzed the effect of pressure and temperature ratios on the off-design performance. Song et al. [3] presented an exergy-based performance analysis of a 150 MWe gas turbine based power plant for part-load operation. They investigated numerically the influence of the variable inlet guide vane and the blade cooling on exergy destruction. Kim et al. [4] investigated the performance characteristics of recuperated gas turbines operating at partial load. They examined the influence of various design and operational factors on the part load efficiency. They considered simple (fuel only control), variable speed and variable inlet guide vane operation, constant and variable area nozzles (for two-shaft turbine). Their analysis was based on the manufacturer's compressor and turbine performance maps. Aklilu et al. [5] developed a mathematical model to simulate a part-load operation of a single shaft gas turbine with variable geometry compressor. They created performance maps for the compressor and turbine based on manufacturer data and thermodynamic laws. In their model average values of the specific heat at constant pressure and isentropic exponent of the working gas were used. They tested their model with the data from a 4.2 MWe turbine. Badami et al. [6] performed an exergy analysis of a small 150 kWe combined cycle cogeneration plant with an internal combustion engine as a primary source of energy. They examined exergy and energy efficiency of the plant for part load operation. Ghaebi et al. [7] applied the first and second laws of thermodynamics as well as economic analysis to investigate a combined cooling, heating and power system with gas turbine of 19 MWe. They investigated the effect of selected parameters on the efficiency of heat, cold and power production for rated load. In their analysis, they used a constant heat capacity at constant pressure while calculating the enthalpy and exergy of the working gas. Khaliq et al. [8] studied, by the energy and exergy method, the influence of compressor intake air cooling on energy and exergy efficiency of a gas turbine cycle. They also examined exergy destruction rate in the power plant components as well as the effect of the pressure ratio and turbine inlet temperature on the energy and exergy efficiency of the cycle. They used an average value of the specific heat at constant pressure of the working gas and an average isentropic exponent in their model. Bakalis et al. [9] performed a part load exergetic analysis of a hybrid gas microturbine fuel cell system using the commercial AspenPlus software. They created the microturbine performance maps through the scaling of representative maps. Meybodi et al. [10] studied the optimum arrangement of prime movers in small scale microturbine-based CHP systems. In their analysis, they used approximate equations for the relative efficiency, fuel consumption, exhaust mass flow rate, and exhaust temperature for partial-load conditions. These equations were derived based on the manufacturers' data for five microturbines. Wei et al. [11] investigated the off-design performance of a small-sized humid air turbine. Their numerical calculation model was based on digitized performance maps. They validated the results from the model with own experimental data. Full and partial load performance tests of a small trigeneration pilot plant based on a microturbine were carried out by Rocha et al. [12]. Experimental results presented by the authors include the fuel consumption, electrical and thermal power, primary energy saving index, and energy utilization factor.
This paper deals with the development of a universal analytical model of microturbines operated with partial load, at variable rotational speed, for use in energy and exergy analysis. The model is based on the heuristic part-load performance formulas proposed in References 1 and 2. Due to commercial reasons, the manufacturers usually do not publish performance maps of turbines and compressors in the open literature, hence the large usefulness of universal performance formulas. Thanks to the availability of such formulas, the microturbine's suitability for the intended use can be thoroughly verified. To reduce calculation errors, we do not use an average isentropic coefficient in our model, but the temperature dependence of the specific heat at constant pressure of the working fluid is directly implemented into the equation of isentropic process. The condition Δs = 0 brings us to the following isentropic equation , where c0 and c1 are coefficients in the equation describing the dependence of specific heat at constant pressure on temperature. The temperature dependence of specific heat at constant pressure is also taken into account during the calculation of enthalpy and exergy. When calculating the thermodynamic cycle parameters and exergy destruction and losses in the microturbine components, a non-linear dependence of pressure drop in the components on the microturbine load is accounted for. The model also allows to include the heat absorbed by intake air from the generator in the energy and exergy analysis.
Section snippets
Basic assumption and expressions
A schematic flow diagram for the modeled microturbine is presented in Fig. 1. When formulating the mathematical model of microturbine the following assumptions are adopted:
- •
microturbine is operated as stand alone,
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turbine is controlled by fuel flow rate at constant turbine exit temperature (TET),
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compressor and turbine are of radial type,
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turbine and compressor are mounted on a common shaft,
- •
compression in the compressor and expansion in the turbine are adiabatic irreversible processes (i.e.
Analytical model for part load operation
In our model we make use of the performance formulas for compressor and turbine at part load operation, and a modified Flügel formula proposed in Refs. [1], [2]. Performance formulas for compressor arewhere
The efficiency characteristic of the turbine is
The coefficients: m, p, c4, and t4 appearing in Eqs. (14), (15), (16),
Model validation
Using the model elaborated in the paper a case study is carried out. The data for the Capstone C30 microturbine available in the open literature and some typical data for microturbines were used. Both these data are collected in Table 1. The computations of selected parameters were performed for the microturbine part load ranging from 2 to 30 kWe. Although the model allows performing calculations for various ambient conditions, the calculations were carried out for ISO ambient conditions
Exergy analysis of the power plant
Exergy rates in the characteristic points of the plant thermodynamic cycle are determined from Eq. (6). Particular rates of exergy destruction or loss are calculated as follows.
The rate of internal exergy destruction in the compressor
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from the Gouy–Stodola law
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from the exergy balance equation
The rate of exergy destruction in the compressor due to mechanical losses
The total rate of exergy destruction in the compressor
The rate of
Conclusions
Essential elements of a model for the microturbine part-load operation are the compressor and turbine performance maps. These maps are usually not disclosed by the microturbine manufacturers. This difficulty can be overcome by using universal formulas with adjustable coefficients for the part-load operation of a microturbine. In the analytical model of a microturbine presented in this paper such formulas have been successfully used for a 30 kWe commercial microturbine. A surprisingly good
Acknowledgements
This study was partly supported by the following project: the strategic program of scientific research and experimental development of the National (Polish) Centre for Research and Development: “Advances Technologies for Energy Generation”; Task 4. “Elaboration of Integrated Technologies for the Production of Fuels and Energy from Biomass as well as from Agricultural and other Waste Materials”.
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