Original article
Analytical design and optimization of a new hybrid solar-driven micro gas turbine/stirling engine, based on exergo-enviro-economic concept

https://doi.org/10.1016/j.seta.2020.100845Get rights and content

Highlights

  • A new solar-driven power system based on Capstone micro gas turbine and Stirling engine is proposed.

  • Exergo-Enviro-Economic analysis of cycle and thermohydraulic design of equipment is performed.

  • The analytical model for objective functions is provided based on the presented numerical model.

  • The artificial intelligence tool (Genetic Programming) is used for multivariate fitting.

  • Various optimizations (using the PSO tool) have been made to find the final optimal design.

  • The final optimum design shows an increase of 6.525 and 8.842 percent for energy and exergy efficiency.

Abstract

One of the crucial problems in the power systems is the selection of energy-efficient systems with suitable efficiency, cost, and environmental performance. Accordingly, this paper introduces a new power generation system that supplies a significant part of the required energy from solar energy and uses liquefied natural gas (LNG) fuel as an auxiliary source. To evaluation of the system, exergo-enviro-economic analysis and thermohydraulic design of are performed using Matlab code. A comparison of the governed results with the base cycle (ThermoFlex simulation) shows good improvement in exergy efficiency fuel consumption. Since the preparation of an analytical model has a practical effect on the selection of optimum configuration, an analytical model for objective functions is provided based on the exergoeconomic and environmental numerical model. For this analytical model, A large data bank from the numerical simulation results is obtained, and the artificial intelligence tool known as Genetic Programming is used for multivariate fitting. Finally, to find the optimal configuration, various optimizations (using the particle swarm optimization) have been made, and the final optimal design has been selected. The results indicated that the thermal and exergetic efficiencies in the ultimate optimum point increased about 6.252 and 8.842 percent, respectively.

Introduction

Microturbines are gas turbines with a power generation between 25 and 600 kW that recently are widely used to power generation. Previously, the diesel engines were the primary choice for distributed power generation, but micro gas turbines are more reliable than diesel engines [1], [2], [3]. These turbines have a simple structure and can be used easily to generate power using a variety of fuels (natural gas, propane, or other fuel). Labinov et al. Proposed a quasi-empirical model based on the experimental data of a commercial microturbine [4]. This study was conducted based on the constant efficiency in the turbine, compressor, and recuperator. Song et al. [5] performed the exergy analysis of gas turbine cycles in different loads. They concluded that the chemical reactions in the combustion chamber, as well as the high-temperature difference between the flame and the operating fluid, caused significant losses in the gas turbine cycle. In another study, Kesseli et al. [6] showed that the compression ratio for the maximum thermal efficiency depends on the inlet turbine temperature. In micro gas turbines, this optimum compression ratio is about 4 for turbine input temperatures between 800 and 900 °C. The limitation of fossil fuel resources, environmental pollution, and the increase in electric energy demand has increased the use of renewable energy for electricity production [7]. One of the capabilities of the gas micro-turbine is its ability to hybridize with solar energy as clean energy. Sheu and Mitsos analyzed the combined solar cycle, and the results showed that the thermal efficiency is improved using the solar system [8]. Freire et al. [9] designed and installed a hybrid solar turbine system in France. In this research, the authors increased the combustor's inlet air temperature using a recuperator. In this study, they performed thermodynamic analyzes for three solar radiation intensities. They showed that for radiation intensity higher than 700 (W/m ^ 2), they would provide 16.3% of the total electricity demand in the considered area. Grange et al. [10] simulate and analyze a solar-powered hybrid turbine system with a storage tank. They also used this method to increase the output power of the power plant. They used the storage tank to keep the combustor's inlet air temperature in the design condition. Hybrid solar flameless combustion system: Modeling and thermodynamic analysis was studied by Hosseini et al. [11]. Their research showed considerable environmental advantages, and according to the existing technologies, it was appropriate for high-temperature solar towers. Experimental and numerical study of a hybrid solar-combustor system for energy efficiency increasing was performed by Sirignano et al. [12]. They used a detailed model of grime organization and oxidation to simulate the conduct of a coflowing propagation ethylene flare with and without the disposal to focused solar radiation.

The Stirling engine is one of the efficient devices that has attracted a lot of attention in recent years. Robert Stirling first invented this engine in 1816 [13]. The Stirling engine is a thermal engine with an external heat source, and its thermal efficiency is close to the Carnot efficiency [14]. Also, these low noise engines have the potential to use fossil, biomass, nuclear, and solar sources [15]. Considering the importance of Stirling engine modeling, a lot of research has been done on the modeling and optimization of this engine. In the analysis and modeling of the Stirling engine, the firs thermodynamic analysis was performed by Schmidt [16]. In this model, the temperature of the compression space with the cold heat exchanger and the temperature of the expansion space with the hot heat exchanger was considered equal, and isothermal analysis was presented. Finkelstein [17] considered adiabatic compression and expansion spaces. In this analysis, the temperature of the working fluid changes during the compression and expansion process, and the heaters and coolers are considered isothermal. Timoumi et al. [18] presented a semi-stable adiabatic model that considered the effects of pressure drop and heat losses in different parts of the engine. Andersen et al. [19] presented mass and energy balance differential equations with a thirteen control volume for analyzing the Stirling engine. To validation of the presented model, the experimental results (9-kilowatt engine) were used, which showed an acceptable agreement between the governed and the experimental results. Martaj et al. [20] studied the thermodynamics of the Stirling engine using energy, entropy, and exergy analysis. This analysis is performed by dividing the engine into three isothermal chambers. And the effect of regenerator's dead volume on energy and exergy efficiencies has been evaluated. The results showed that the exergetic and thermal efficiencies are increased with decreasing in the dead volume. Babaelahi et al. [21] presented a new thermal model based on the polytropic numerical simulation of Stirling engines. In this study, the polytropic compression and expansion are considered in working spaces. In another work, Babaelahi et al. [22] present a new polytropic model, so-called PSVL (polytropic analysis of Stirling engine with various losses), for the analysis of the Stirling engine. In this model, various loss calculation is performed, and the previous model is corrected. For a better analysis of the Stirling engine, Babaelahi et al. [23] present an analytical tool for the prediction of Stirling engine behavior.

In this research, the Capstone C200 micro gas turbine has been selected as a base case, and some significant changes have been made. In the new proposed system, the LNG fuel and solar Heliostat are added to the base case as the heat source. Also, the output heat of the micro gas turbine has been used as a hot source for the Stirling engine. In fact, in the new proposed system, the required output power is produced using the Stirling engine and micro gas turbine. For the evaluation of this power system, the combined energy/exergy/economic/environmental analysis is used. In the analysis procedure, in the first step, the energy and exergy balance equations for different equipment are written. In the second step, the exergoeconomic balance equation for various equipment is presented. To accurately estimate the purchase cost of equipment, the detailed design of the equipment is performed, and appropriate relationships are presented to calculate the purchase cost. All steps of analysis have been performed with the help of coding in MATLAB software. To evaluate the accuracy of the coding, the proposed cycle is simulated in ThermoFlex software, and a comparison is made between the code results and the simulation. To evaluate and optimization of the proposed system, a multivariate fitting tool based on artificial intelligence called genetic programming has been used, and the analytical correlations for the objective function are provided. Based on these analytic correlations, various multi-objective optimizations are performed using the particle swarm optimization method with different objective functions. Finally, based on the decision-making strategy, the optimal final point has been chosen from different optimization results. Therefore the novelty of this research can be expressed as below:

  • -

    The new renewable power system, including gas microturbine and Stirling engine, was introduced.

  • -

    The energy-exergy-economic-environmental concepts were used for the evaluation of the proposed power plant.

  • -

    The analytical correlation for the efficiencies and cost are presented based on operational variables using genetic programming.

  • -

    The multi-objective optimizations for improvement inefficiencies, cost and environmental are performed using particle swarm optimization method

  • -

    reduction of fuel consumption and increase of the thermal and exergetic efficiencies were considered using a genetic algorithm.

In this paper, the proposed power generation system is a hybrid cycle that consists of a gas microturbine, heliostat solar field, Stirling engine, and phase-change material reservoir. In this system, LNG fuel is also used as a fuel. Initially, the ambient air (stream 1) enters the compressor, and after compression comes the recuperator (for heat recovery from exhaust gases) and solar Heliostat. The heated air mixed with LNG in the combustion chamber and the desired combustion gases are generated. The combustion gas enters the turbine, and shaft work is produced. The exhaust gas from the recuperator (flow 7) enters the phase change material (PCM) tank and transferring the heat to phases exchange material. The phase change material (PCM) in the packing type is used for this purpose. For the reaction between air and LNG, LNG should be turned into vapor.

For this reason, an LNG evaporator (VAP) has been used. The required heat to vaporization of LNG in the evaporator is provided by the rejected heat from the Stirling engine's cooler using the nitrogen as a working fluid. The required temperature for the hot section of the Stirling engine is provided PCM storage using XCELTHERM MK1 working fluid [24]. In this cycle, the heliostat solar field has been used for fuel consumption reduction. Also, the Stirling engine has been coupled with the proposed cycle to use the waste heat from the micro gas turbine. For the cold section of the Stirling engine, the cold exergy of LNG evaporation in VAP is used. The schematic of the proposed cycle is shown in Fig. 1.

The proposed cycle consists of a gas microturbine, Stirling engine, solar field, and recuperator. The detailed analysis of the Stirling engine, solar field, and recuperator is necessary to accurately thermodynamic evaluation of the current system. The energy and exergy analysis of the proposed cycle is presented in Appendix A, and the precise design of the components is discussed in the following sections.

In the proposed system, the required heat for LNG vaporization in the LNG evaporator Q̇LNGvap is equal to the heat transferred from the cold Heat Exchanger of the Stirling Engine (Q̇k). Also, the required heat for the hot section of the Stirling engine Q̇h is equal to heat stored in the PCM storage (Q̇PCM). The following heat balance equation can be presented as below considering the above considerations:Q̇LNGvap=Q̇k=Ḣ11-Ḣ10=Ḣ12-Ḣ13Q̇PCM=Q̇h=Ḣ7-Ḣ8

To precise modeling of the Stirling engine, the effects of gas leakage, the temperature distribution in the heat exchangers, longitudinal heat loss, polytropic heat transfer in cylinders, heat dissipation in the regenerator, and pressure drop are applied to the primary energy equation for the Stirling engine (Modified Polytropic analysis of Stirling engine with Various Losses: Modified PSVL) [25]. The energy balance equation for the Stirling engine considering all of the above effects, can be presented with the set of ordinary differential equations (Table 1).

Recently, new types of recuperators are used in smaller sizes, lower cost, and higher efficiency. In this study, the plate-fin recuperator is selected. And the ε-NTU method is considered for the design of the recuperator [26]. The schematic view of the chosen recuperator is shown in Fig. 2.

The heat transfer areas for the hot and cold side are calculated as follows [26]:Ah=LhLcNh1+2nhHh-thAc=LcLhNc1+2ncHc-tc

The heat exchanger's effectiveness (ε) is calculated as follows:=1-exp1CrNTU0.22exp-Cr.NTU0.78-11NTU=Cmin1jh.Cph.Prh-23.ṁh×Aff,hAh+1jc.Cpc.Prc-23.ṁc×Aff,cAc

The pressure drop in the hot and cold side in the recuperator is calculated as follows [26]:ΔPh=4fhLhG2h2ρhDh,h=2fhm2hρc×LhDh,hL2cN2hHh-th21-nhth2ΔPc=4fcLcG2c2ρcDh,c=2fcm2cρc×LcDh,cL2hN2c(Hc-tc)2(1-nctc)2

The heliostat solar field is selected and modeled for preheating the inlet air before the combustion process, considering the temperature range in the proposed cycle. The input parameters considered for modeling the heliostat solar field are shown in Table 2 [27].

The following relationships are used to calculate the altitude, area of the solar field, and the area of the mirrors [27]:Ps,d=Pcap,d×106ηreceiver×ηhe×ηpb;wPD=0forrh<rhminPD=0.492-0.0939rh;forrhminrh2.8PD=0.6rh2-1forrh>2.8rh=xh2+yh2

The amount of power received from all mirrors in one hour, taking into account the value of 1 for the attenuation efficiencyηatt, is calculated as follows:Pi,a=dxh×dyh×ηhe×j=1NfDNIi×cosθi,j×PD×1

Considering the location of the power plant (Qom city) using the METEONORM and ELEMENT software, the direct normal irradiation (DNI) and azimuth angle are calculated, and the initial height of the tower used in the heliostat system is calculated as below:hprev=Ps,dPamax

The height of the tower, the area of the solar field, and the mirrors are calculated using the algorithm shown in Fig. 3 [28].

An exergoeconomic analysis is required to find the electricity cost. Before exergoeconomic analysis, exergy and energy analysis should be performed, that described in Appendix A. Based on exergoeconomic principles, the exergoeconomic balance equation can be presented as below:ĊP,tot=ĊF,tot+ŻCItot+ŻOMtotŻcomponent=ŻCItot+ŻOMtotŻcomponent=Zcomponent.CRF.φN.3600CRF=i1+in1+in-1

The assumptions used to calculate the cost of equipment are given in Table 3 [24].

Main and auxiliary cost balance equations [24] and equipment purchase cost equations for different equipment are shown in Table 4 and Table 5.

The amount of emission in the proposed system can be calculated based on the amount of carbon dioxide emissions as below [24]:ς=xCO2pṅpMCO2ẆgenẆgen=Ẇtur-Ẇcom-Ẇpump+ẆST

Section snippets

Genetic programing

The genetic programming, GP, the method was used for multivariable regression. Genetic programming is a biologically inspired machine learning method that was used for multivariable regression. It does this by randomly generating a population of computer programs and then mutating and crossing over the best performing trees to create a new population. This process is iterated until the population contains programs that (hopefully) solve the task well. GP consists of several computer program

Results and discussion

To investigation and validation of the thermodynamic modeling of the proposed cycle, the cycle is simulated in ThermoFlex software, and the results from the computer code are compared with the results of ThermoFlex (see Table 7). The comparison shows that the computer code is in good agreement with the ThermoFlex software. The values of temperature, pressure, and mass flow rate of cycle currents are shown in Table 8. Exergy destruction rates and exergetic efficiencies of various equipment are

Conclusion

Concerning the critical issues associated with power generation, this paper proposes a new power generation cycle based on combining micro turbine gas and a sterling engine using solar energy as the primary source of heat. The energy and exergoeconomics analysis has been carried out to analyze the system, and the precise design of all components has been carried out. A comparison of the results of the proposed cycle modeling with the base cycle (Capstone micro gas turbine) shows an increase of

CRediT authorship contribution statement

Mojtaba. Babaelahi: Supervision, Conceptualization, Methodology, Writing - review & editing. Hamed. Jafari: Software, Data curation, Validation, Writing - original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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