energies Article Efficiency at Maximum Power of the Low-Dissipation Hybrid Electrochemical–Otto Cycle David Diskin 1 and Leonid Tartakovsky 1,2,* 1 Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel; [email protected] 2 Grand Technion Energy Program, Technion—Israel Institute of Technology, Haifa 3200003, Israel * Correspondence: [email protected] Received: 24 June 2020; Accepted: 24 July 2020; Published: 1 August 2020 Abstract: A novel analytical method was developed for analysis of efficiency at maximum power of a hybrid cycle combining electrochemical and Otto engines. The analysis is based on the low-dissipation model, which relates energy dissipation with energy transfer rate. Efficiency at maximum power of a hybrid engine operating between two reservoirs of chemical potentials is evaluated. The engine is composed of an electrochemical device that transforms chemical potential to electrical work of an Otto engine that uses the heat generated in the electrochemical device and its exhaust effluent for mechanical work production. The results show that efficiency at maximum power of the hybrid cycle is identical to the efficiency at maximum power of an electrochemical engine alone; however, the power is the product of the electrochemical engine power and the compression ratio of the Otto engine. Partial mass transition by the electrochemical device from the high to the low chemical potential is also examined. In the latter case, heat is generated both in the electrochemical device and the Otto engine, and the efficiency at maximum power is a function of the compression ratio. An analysis performed using the developed method shows, for the first time, that, in terms of a maximal power, at some conditions, Otto cycle can provide better performance that the hybrid cycle. On the other hand, an efficiency comparison at maximum power with the separate Otto-cycle and chemical engine results in some advantages of the hybrid cycle. Keywords: finite time thermodynamics; efficiency at maximal power; electro-chemical reaction; low-dissipation; Otto cycle 1. Introduction According to equilibrium thermodynamics, the maximal efficiency of a cycle operating between two reservoirs at thermodynamic potential PH and PL (PH > PL) is the Carnot efficiency, η = 1 PL/PH. C − However, finite size engines that work at equilibrium conditions (i.e., undergo only reversible processes) cannot produce finite power. Therefore, non-equilibrium thermodynamics that predicts efficiency as a function of power is meaningful. The first to analyze heat engines in a finite power regime were Novikov in 1957 [1] and Curzon-Ahlborn in 1975 [2]. Their approach was to model the interactions between the engine and its reservoirs with energy transfer resistance. The engine itself was modeled as a reversible system, called lately and expended to be an endoreversible cycle [3]. An equivalent approach of engine analyses at maximum power is based on the low-dissipation assumption and was suggested by Esposito et al. [4]. They found, with this approach, the bounds of the efficiency at maximal power for heat engines. Guo et al. [5] expended those limits to chemical engines and non-Carnot heat cycles (Otto, Brayton, etc.). To the best of our knowledge, the combination of chemical engine and Otto cycle was not analyzed by the low-dissipation approach for finite power. This combination is called a “hybrid cycle” hereafter. A schematic outline of the hybrid cycle is shown Energies 2020, 13, 3961; doi:10.3390/en13153961 www.mdpi.com/journal/energies Energies 2020, 13, 3961 2 of 10 in Figure1. Electrochemical engines use the high chemical potential (µH) of a substance (for example fuel-oxygen mixture) as the high-potential reservoir to generate electrical work. Petrescu et al. [6] studied the main differences between electrochemical engines and heat engines from the viewpoint of efficiency at maximum power. Pavelka et al. [7] and Vagner et al. [8] commented on the maximum work of electrochemical engines that undergo heat interactions. They concluded that, in general, the maximum power of electrochemical engines cannot be evaluated by exergy analysis or entropy minimization. The low-dissipation assumption is consistent with this conclusion. The Otto cycle implemented in internal combustion engines (ICEs) uses the same high chemical potential µH carrier to generate mechanical work by converting the chemical potential to thermal energy with subsequent gas expansion. The conversion of chemical potential to thermal energy in ICE is a spontaneous process and is thus completely irreversible. Hybrid cycles that combine electrochemical engine (fuel cell) and a bottoming heat engine have been studied and developed since 1990s [9,10]. The combination of a high efficiency fuel cell and the recovery of the waste heat and fuel by the bottoming heat cycle is a promising path towards clean and efficient energy use. Most of the combinations include a solid oxide fuel cell (SOFC) and a Rankine [11] or a Brayton cycle [12,13]. Lately, research on an ICE in combination with a SOFC was initiated as well [14,15]. In these studies, integration of engine experiment results with a basic fuel cell model were performed. Exergy analysis showed efficiency dependence on basic parameters such as compression ratio and anode off-gas temperature. Thermo-economic analysis for this configuration was also performed [16]. An efficient onboard storage and utilization of fuel as the high chemical potential carrier is another important aspect to be addressed when fuel cell usage is considered. Fuel cells are known to be fuel sensitive, and fuel reforming processes are implemented frequently in fuel cell power pack designs [17]. When a hybrid cycle involving a fuel cell and an ICE is considered, usage of fuel reforming in combination with waste heat recovery known as Thermochemical Recuperation (TCR) could be beneficial. Recently, utilization of fuel reforming through TCR in ICEs was proven to be energetically efficient [18–20]. Hence, a potential of its implementation in a hybrid Fuel-Cell-ICE cycle should be evaluated. Chuahy and Kokjohn [21] analyzed a hybrid powertrain including a diesel engine and a fuel cell with diesel fuel reforming to produce hydrogen and reported on the high thermal efficiency (above 70%) of the system. The main goal of the previously published studies investigating the hybrid fuel cell–ICE cycle was an achievable efficiency gain. However, as stated earlier, approaching Carnot efficiency will result in the loss of power. Hence, a question arises of whether the combination of electrochemical engine and ICE can provide power gain in addition to efficiency improvement. Considering this, the reported study aims at the analysis of the power–efficiency relation of the hybrid cycle combining chemical and Otto engines and a comparison with the pure Otto cycle and chemical engine operation alone. For this purpose, a novel analytical method of analysis of the power–efficiency tradeoff for this hybrid cycle was suggested for the first time. This method enables better understanding of the advantages and drawbacks of the hybrid cycle compared to the other cycles in terms of the power–efficiency relationship. Energies 2020 13 Energies 2020,, 13,, 3961 x FOR PEER REVIEW 33 ofof 1011 Figure 1. Schematic outline of a fuel cell–internal combustion engine (ICE) hybrid cycle. Air is Figure 1. Schematic outline of a fuel cell–internal combustion engine (ICE) hybrid cycle. Air is compressed in the ICE and then reacts in the electrochemical device (fuel cell) to produce electrical power. compressed in the ICE and then reacts in the electrochemical device (fuel cell) to produce electrical Hydrogen-rich fuel cell exhaust gases combust and expand in the ICE to produce mechanical work. power. Hydrogen-rich fuel cell exhaust gases combust and expand in the ICE to produce mechanical 2. Low-Dissipationwork. Model of the Hybrid Cycle 2. Low-DissipationIn this analysis, Model we assume of the that Hybrid the only Cycle irreversible processes take place in the electrochemical engine, and the bottoming Otto cycle is reversible. This assumption means that the mechanical processesIn this are analysis, reversible, wei.e., assume the compression that the only and irreve expansionrsible processes are isentropic. take place Moreover, in the theelectrochemical processes in theengine, Otto and cycle the are bottoming assumed toOtto be relativelycycle is reversib fast comparedle. This toassumption the chemical means energy that transfer, the mechanical thus the highprocesses and low are chemicalreversible, potential i.e., the compression reservoirs could and beexpansion considered are asisentropic. the isothermal Moreover, boundaries the processes of the chemicalin the Otto engine. cycle are The assumed low-dissipation to be relatively model assumesfast compared that the toirreversibility the chemical energy in the process transfer, of thus energy the conversionhigh and low between chemical the potential reservoirs reservoirs and the hybridcould be engine considered is proportional as the isothermal to 1/t, where boundariest is the of time the ofchemical the energy engine. conversion The low-dissipation process. The model meaning assumes of this that assumption the irreversibility is that the in relaxationthe process time of energy in the hybridconversion engine between is relatively the reservoirs short compared and the hybrid to the energy engine transmissionis proportional time. to 1/ Accordingt , where tot thisis the model, time