Technological University Dublin ARROW@TU Dublin Conference Papers Dublin Energy Lab 2010-06-01 Thermodynamic Optimisation of the Otto / Stirling Combined Cycle Barry Cullen Technological University Dublin, [email protected] Michel Feidt University “Henri Poincare” of Nancy, [email protected] Jim McGovern Technological University Dublin, [email protected] See next page for additional authors Follow this and additional works at: https://arrow.tudublin.ie/dubencon2 Part of the Energy Systems Commons Recommended Citation Cullen, B., Feidt, M., McGovern, J., Petrescu, S. Thermodynamic Optimisation of the Otto / Stirling Combined Cycle. 23rd International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems. Lausanne, Switzerland, 14-17 June. This Conference Paper is brought to you for free and open access by the Dublin Energy Lab at ARROW@TU Dublin. It has been accepted for inclusion in Conference Papers by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License Authors Barry Cullen, Michel Feidt, Jim McGovern, and Stoian Petrescu This conference paper is available at ARROW@TU Dublin: https://arrow.tudublin.ie/dubencon2/6 Thermodynamic Optimisation of the Otto / Stirling Combined Cycle Barry Cullena, Michel Feidtb, Jim McGoverna, Stoian Petrescuc a. Dublin Energy Lab, Dublin Institute of Technology, Bolton Street, Dublin 1, Ireland b. L.E.M.T.A., U.R.A.C.N.R.S.7563, University “Henri Poincare” of Nancy 1, Avenue de la Foret de Haye, 54504, Vandouevre-les-Nancy, France c. Department of Engineering Thermodynamics, University Politehnica of Bucharest, Splaiul Independentei, 313, 060042 Bucharest, Romania Abstract: Combined cycle systems are an established method for increasing primary energy efficiency of power generation systems. Some ongoing research is concerned with investigating the novel combined cycle system involving the Otto and Stirling thermodynamic cycles. The Otto cycle is to act as the topping cycle, with the Stirling cycle acting to recover heat from the exhaust for the purpose of additional power generation. The present work investigates the thermodynamic optimisation of the combined cycle system for the case of the engines operating under two imposed parametric constraints: 1) imposed heat addition to the Otto cycle, and 2) imposed maximum cycle temperature of the Otto cycle. These conditions are analogous to a specified fuel consumption of the engine and the metallurgical limit of the operating components respectively. The optimum work output for each scenario is analysed with respect to the particular physical constraints of the Stirling cycle heat exchangers – effectiveness, NTU, heat transfer coefficient and heat transfer area. Only interactions between the engine and the external source and sink are considered in this treatment. Regeneration within the cycle, as would typically be used within the practical engine, is considered as perfect. The existence of an optimum power output for the combined system is proven analytically. A numerical study is then presented to further investigate the performance for each of the parameters named above. Keywords: Combined Cycles, Otto Cycle, Stirling Cycle, Thermodynamic Optimisation 1. Introduction Arising from this is an interest in small-scale combined cycle systems involving reciprocating Combined cycle power generation systems are engines such as gas fired Otto cycle and Diesel an established method for increasing primary cycle engines. These engines traditionally generation efficiency. An established dominate this smaller scale (<5MW) power technology that have benefitted from several systems market as Combined Heat and Power decades of development, they are more typically (CHP) generators, renewable gas prime movers associated with large scale centralised and standby generators [6, 7]. Some recent generation systems, and almost exclusively work has focused on use of the Rankine cycle as involve turbine plant operating on Brayton / a heat recovery device on a reciprocating Rankine combinations. Current thinking, internal combustion engine. Gambarotta and however, favours development towards Vaja [8] investigated the Organic Rankine Distributed Generation (DG) networks in an Cycle (ORC) as a bottoming cycle on an Otto effort to increase energy efficiency for both Cycle spark ignition engine. Badami et al [9] environmental and security reasons [1-5]. investigated the standard Rankine cycle Corresponding Author: Barry Cullen, Email: [email protected] http://www.ecos2010.ch 1 14-17th june 2010, Lausanne, Switzerland Nomenclature bottoming an Otto cycle for use as a CHP Heat Capacitance Rate, = , W/K generator. Endo et al [10] have investigated the ̽ʖ ͡ʖ ̽+ exergy gains possible from utilising a Rankine Specific Heat at Constant Pressure, cycle as a bottoming cycle on an automotive ̽+ J/kgK internal combustion engine. Similar work has been conducted by Chammas and Clodic [11]. Heat loss conductance, W/K Use of the Stirling cycle as a bottoming cycle ͅ Otto cycle entropy constraint parameter has been studied also by several different ͅ* parties, for example [12-15]. Use of the Stirling Stirling cycle entropy constraint cycle as a bottoming cycle is of interest due to ͅ. parameter the high theoretical output and efficiency that could be attained, in addition to potentially Mass flowrate, kg/s smaller plant footprint and quiet operation. ͡ʖ Some ongoing work [16-18] has been Heat, W investigating this alternative combined cycle ͋ʖ Otto cycle compression ratio utilising a Stirling cycle engine as a bottoming ͌1 cycle on an Otto cycle engine. Whereas these Entropy, J/K previous works have dealt with the modelling ͍ and simulation of the combined cycle for use in Temperature, K instances such as stationary and vehicular power ͎ generation, the present work seeks to contribute Heat exchanger effectiveness to the general model by developing an optimised Subscripts thermodynamic model of the system considering parameters concerning the Stirling engine source 1,2,3,4 Otto cycle state points and sink heat exchangers: effectiveness ( ) and NTU. This further implies the opportunity to H Stirling Source temperature study the optimal heat exchanger area (A) and overall heat transfer coefficient (U). The C Stirling Sink temperature optimisation procedure can be considered as amb Ambient being in terms of Finite Dimension Thermodynamics (FDT) [19], as the o Otto Cycle performance of the cycles is considered with regard to the physical characteristics of the heat s Stirling Cycle exchangers. Vmin T 3 2. The Combined Cycle In the combined cycle analysis, the Vmax thermodynamic cycles are considered with the Stirling cycle as the bottoming cycle on the Otto 4 cycle. The combined system is depicted on the 2 5 T-S plane in Fig. 1. Of interest is the X Perfect optimisation of the combined power output and TH Regeneration efficiency under two operating conditions: 1) V Vmin max fixed heat input to the Otto cycle and 2) fixed TC 6 1 1 maximum cycle temperature in the Otto engine. These conditions are analogous to specified S fixed fuel consumption of the engine and a Figure 1: The Combined Cycle represented on the T- metallurgical limit on the system components S plane respectively. The coupling of the two relies on http://www.ecos2010.ch 2 14-17th june 2010, Lausanne, Switzerland correct specification of the heat exchanger This entropy constraint would permit analysis inventory between both the Stirling cycle source with inclusion for internal irreversibilities, with – the Otto cycle exhaust stream, and sink – a . Under the endoreversible water cooling circuit. conditions,0 Ɨ ͅ* ƙ 1 . A similar condition exists The following section details the basic for the endoreversibleͅ* Ɣ 1 Stirling cycle: relationships of the mathematical model. (9) Section 4.0 analyses the optima in terms of a ĔĠĕ TāĢʖ x Ɣ ͅ Ǝ ʖ fixed heat addition. Section 5.0 provides a ü TüĦā Where similar analysis for the case of imposed maximum cycle temperature in the Otto cycle. TāĢʖ ʖĂ,Ħ (10) ͅ Ɣ 1 ƍ ʖ Ǝ ʖ TüĦĖ TüĦĖ 3. Basic Mathematical Model It can be seen from equation (10) that for the Depicted in Fig. 1 is the air standard endoreversible case, . Study of the cycles Otto/Stirling combined cycle. The power output in the present workͅ. Ƙ 1is limited to the of the air standard Otto cycle is readily endoreversible case; however the inclusion of expressed as: both and in the analysis permits investigationͅ* withͅ inclusion for irreversibilities. (1) Ǝ͑ʖ *//* Ɣ ɳ͋ʖ$) ƍ ͋ʖ*0/ɳ 3.1 Case of Imposed Heat Addition Ǝ͑ʖ *//* Ɣ ̽*ʖ ʞʚ͎ͧ Ǝ ͎ͦʛ Ǝ ʚ ͎ ͨ Ǝ ͎ͥʛʟ(2)Ǝ The objective function of the combined cycle is ͅ ʚ͎ͧ Ǝ ͎(ʛ Where is a generalised heat conductance term ultimately the work output. We can achieve an optimum scenario by considering cycle to accountͅ for global losses from the cycle that can not otherwise be accomodated in the temperatures. The optimum combined work analysis. Similarly, the power output of the output may most simply be expressed as: Stirling cycle can be expressed as: (11) Ǝ͑ʖ Ɣ Ǝ͑ʖ *//*Ǝ͑ʖ ./$-'$)" In order to complete the optimisation, we must ʖ ./$-'$)" *ʖ ͨ .ʖ ͥ Ǝ͑ Ɣ ̽ ʚ͎ Ǝ ͎ ʛ ƍ ̽ ʚ͎ Ǝ ͎(3)ʛ specify the constraints to be imposed. In this first scenario, the heat addition to the Otto cycle Where and are the minimum heat – and therefore the combined cycle as a whole, capacitance̽*ʖ rates of̽ .ʖthe Stirling cycle source and is to be fixed. The heat added to the Otto cycle sink heat exchangers respectively: is: (4) (12) ̽*ʖ Ɣ ͡ʖ *̽1,* (5) ͥʖ* Ɣ ̽*ʖ ʚ͎ͧƎ͎ͦʛ Ǝ ͅ ʚ͎ͧ Ǝ ͎(ʛ The entropy ̽balance.ʖ Ɣ ͡ʖ . ̽of+,. the Otto engine, with This serves as the first constraint. This equation inclusion for the heat transfer to the Stirling expresses the cycle heat addition as that cycle, can be expressed as: admitted to the engine less a cooling loss term between the engine and the surroundings.