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Article

Exergy Analysis in Highly Hydrogen-Enriched Methane Fueled Spark-Ignition Engine at Diverse Equivalence Ratios via Two-Zone Quasi-Dimensional Modeling

by
Dimitrios C. Rakopoulos
1,
Constantine D. Rakopoulos
2,*,
George M. Kosmadakis
2,
Evangelos G. Giakoumis
2 and
Dimitrios C. Kyritsis
3
1
Chemical Process and Energy Resources Institute, Center for Research and Technology Hellas, GR-57001 Thermi, Thessaloniki, Greece
2
Department of Thermal Engineering, School of Mechanical Engineering, National Technical University of Athens, Zografou Campus, 9 Heroon Polytechniou Street, 15780 Athens, Greece
3
NEOM Education, Research and Innovation Foundation and NEOM University, Al Khuraybah, Tabuk 49643-9136, Saudi Arabia
*
Author to whom correspondence should be addressed.
Energies 2024, 17(16), 3964; https://doi.org/10.3390/en17163964
Submission received: 21 June 2024 / Revised: 14 July 2024 / Accepted: 19 July 2024 / Published: 9 August 2024
(This article belongs to the Special Issue Internal Combustion Engine Performance 2024)

Abstract

:
In the endeavor to accomplish a fully de-carbonized globe, sparkling interest is growing towards using natural gas (NG) having as vastly major component methane (CH4). This has the lowest carbon/hydrogen atom ratio compared to other conventional fossil fuels used in engines and power-plants hence mitigating carbon dioxide (CO2) emissions. Given that using neat hydrogen (H2) containing nil carbon still possesses several issues, blending CH4 with H2 constitutes a stepping-stone towards the ultimate goal of zero producing CO2. In this context, the current work investigates the exergy terms development in high-speed spark-ignition engine (SI) fueled with various hydrogen/methane blends from neat CH4 to 50% vol. fraction H2, at equivalence ratios (EQR) from stoichiometric into the lean region. Experimental data available for that engine were used for validation from the first-law (energy) perspective plus emissions and cycle-by-cycle variations (CCV), using in-house, comprehensive, two-zone (unburned and burned), quasi-dimensional turbulent combustion model tracking tightly the flame-front pathway, developed and reported recently by authors. The latter is expanded to comprise exergy terms accompanying the energy outcomes, affording extra valuable information on judicious energy usage. The development in each zone, over the engine cycle, of various exergy terms accounting too for the reactive and diffusion components making up the chemical exergy is calculated and assessed. The correct calculation of species and temperature histories inside the burned zone subsequent to entrainment of fresh mixture from the unburned zone contributes to more exact computation, especially considering the H2 percentage in the fuel blend modifying temperature-levels, which is key factor when the irreversibility is calculated from a balance comprising all rest exergy terms. Illustrative diagrams of the exergy terms in every zone and whole charge reveal the influence of H2 and EQR values on exergy terms, furnishing thorough information. Concerning the joint content of both zones normalized exergy values over the engine cycle, the heat loss transfer exergy curves acquire higher values the higher the H2 or EQR, the work transfer exergy curves acquire slightly higher values the higher the H2 and slightly higher values the lower the EQR, and the irreversibility curves acquire lower values the higher the H2 or EQR. This exergy approach can offer new reflection for the prospective research to advancing engines performance along judicious use of fully friendly ecological fuel as H2. This extended and in-depth exergy analysis on the use of hydrogen in engines has not appeared in the literature. It can lead to undertaking corrective actions for the irreversibility, exergy losses, and chemical exergy, eventually increasing the knowledge of the SI engines science and technology for building smarter control devices when fueling the IC engines with H2 fuel, which can prove to be game changer to attaining a clean energy environment transition.

1. Introduction

Despite the realism of enormous shifts in the power generation and transportation areas, it is true that combustion research still remains very significant as ever. At least for the near- to middle-range future, combustion technologies will dominate the power generation fields. Huge reserves of fossil fuels existing in developing countries still will be used as dictated by basic economics, whereas in the developed-world countries ecological concerns are inclined to impel the technology to infrequent optional routes [1]. All over the world, internal combustion (IC) engines are still the chief enabler in society for the needed energy in the commerce, transport, and electric power production sectors [2]. Despite the related incessant debates on that matter, the IC engines have not been put out of place at all, though huge amounts of money and time of research have been devoted to the development of alternative, relatively efficient systems that are power-producing, such as fuel cells, solar, Stirling, etc. [3].
The dynamic course of green energy transition brought to the foreground technologies of zero emissions like that of hydrogen. The creation of a green hydrogen economy that is produced with energy from Renewable Sources is included in the strategic planning of the European Union (EU). The epicenter is laid on the progressive development of hydrogen production installations and associated transport networks, with priority of its use as fuel in transportation and industry as well as of its implementation for long-range energy storage in electric power generation. However, as this technology is not fully matured yet, significant state or EU subsidies are required for its support alongside a strategic and regulatory framework. Evidently this is a very welcome prospect, but it turns out to be clear that transition to a fully-sustainability state requires usage of already existing power-trains in a sustainable manner as a first step, given that transition to an energy-globe that is entirely devoid of fossil fuels appears to be a good deal slower than at first thought and enthusiastically anticipated. Contrary to prevalent misconception the two approaches can function in harmony by serving the same reason, so that clean-combustion research for presently used fuels pave the way for future synthetic fuels fully devoid of carbon (C), like hydrogen and ammonia (NH3) [4,5].
The energy necessary for commerce, transport and electricity production is hitherto vastly relied upon the well established conventional classes of internal combustion (IC) engines, i.e., SI and Diesel. The SI engines are fueled by gasoline and the diesel engines by diesel fuel in their customary version, based on the fact of energy-density superiority of these liquid fuels that are acquired from the big quantities of petroleum, which is drilled out from the huge (natural) reservoirs still existing in the planet [1]. In general, the diesel engine dominates the higher-size and the SI engine the lower-size engines that can also be fueled by gaseous fuels such as mainly natural gas (NG) found today in immense quantities and less by liquefied petroleum gas (LPG). Although challenged recently by the fast developing gasoline direct injection (GDI) engine [6], the high-speed, smaller size, traditional homogeneous charge spark-ignition engine (HCSI) is still dominating the market in the specific area, hence forming the subject matter of the current study.
In the strive to boosting the efficiency and mitigating exhaust emissions from IC engines, an incessant dynamic research is ongoing directed on two general tracks, the first one referring to engine-related and the second one to fuel-related techniques, with a view to upgrading the engine design features and determining the optimal operation conditions ultimately tailored to the particular fuel in hand [7]. The first category of the engine-related techniques is divided into internal ones such as primarily exhaust gas recirculation (EGR) [8] and to lesser extent oxygen enrichment, and the second ones into external measures such as a variety of exhaust-gas after-treatment systems [9] including traps and diesel oxidation catalysts [10]. The second category of the fuel-related techniques concerns both liquid and gaseous alternative fuels. Liquid bio-fuels that contain ad hoc molecule-contained oxygen [11] can provide improvement towards emission reduction, such as in SI engines using mainly blends of gasoline with ethanol or methanol (or even at neat form), and in diesel engines using blends of diesel fuel mainly with biodiesel, butanol or ethanol and in low proportions with pure plant oils [12]. On the other hand, the gaseous fuel used in IC engines is mainly the natural gas (NG) containing circa 90% to 98% by vol. methane (CH4) [5], which is more abundant and easily extracted than the liquid fossil-fuel counterparts.
In the endeavor to accomplish a fully de-carbonized globe, recently a sparkling interest is growing towards the use of natural gas (NG) in engines and other power producing plants as a stepping-stone towards this ultimate goal. The vastly major component of methane (CH4) in the NG contains a very favorable low carbon/hydrogen atom ratio of 1/4 compared to roughly 1/2 for the conventional liquid fossil fuels and so mitigates the carbon dioxide (CO2) emissions, which are one of the major culprits causing the Greenhouse Gases (GHG) Effect that imperils seriously life on our planet [5]. Nonetheless NG is still of fossil nature, though possessing relatively least carbon in its molecule, so that the definitive solution would be to use neat H2, which notwithstanding possesses a number of issues focusing predominantly on safety concerning applications in practice in neat mode [13], hopefully to be resolved in the near to middle future. It is certainly a strong candidate for a game changer in clean energy transition.
In the meantime, a plausible step-up solution points towards the use of progressively higher enriched methane blends with hydrogen, as investigated in the present work for a homogeneous charge SI engine. Natural gas presents better knock resistance as having a superior octane number in the region of 120 compared to usual gasoline, which empowers elevated compression ratios (CR) and advanced spark-ignition timings (SIT) [14]. However, it has a smaller laminar flame speed (LFS) with respect to the one of gasoline that leads to slower combustion speed, which eventually guides to poor lean-burn operation that is escorted by severe CCV activity mainly at the lower lean stability limit, which can become detrimental for the engine integrity as early reviewed in [15]. It is welcome and coincidental that the mixing of hydrogen with methane improves highly this inherent adverse CCV phenomenon in engines, as hydrogen possesses much higher LFS and so rate of combustion, further to being a wholy climate-friendly fuel regarding GHG Effect as containing nil carbon atoms. However, it is cautioned that the more rapid burning rate induced by the ever larger proportions of hydrogen addition in the blends results in higher temperatures of combustion and so emissions of nitric oxide (NO) [16]. Several works dealing with this adverse CCV phenomenon in SI engines have appeared for either neat methane as e.g., reviewed briefly in [17] or for its blends with hydrogen operation in [5], while a more general review for CCV investigations can be found in [18].
It is true that the soaring progress of the last decades in measuring systems and methodologies regarding IC engines performance has furnished valuable information. However, the time and cost for the previous are high so that the obvious option is to use modeling techniques that are attractive, especially in the light of the modern augmented comprehension of engine processes and the continually increasing power of computers and associated numerical techniques. As regards the numerical tools for the modeling of the closed cycle of IC engines, they are graded in descending order of complexity as [19]: computational fluid-dynamics codes (CFD, multi-dimensional), multi-zone, two-zone, and single-zone. These are principally based on the energy (1st-law) analysis while they are rarely followed by an exergy (2nd-law, earlier called availability) analysis, which yet furnishes additionally helpful information regarding the efficient exploitation of energy that the sole energy analysis cannot disclose. The 1st-law of thermodynamics analysis when it deals with processes in a system, such as in IC engine of either spark-ignition or diesel type, overlooks the ‘quality’ of its energy content, that is the potential to produce useful mechanical work at any given state, so that this shortcoming is cured by the 2nd-law of thermodynamics analysis. A key notion of the latter analysis is that all forms of energy are not to any further extent equal on an energy basis, but their supremacy is established on its capability to convert wholly into another one [20], hence bringing in appropriately the notion of ‘exergy’, which is a quantity that is not conserved [21].
Exergy analysis works started appearing in the literature more than six decades ago and have been increased in number and quality with a high rate ever since. Many of those investigations refer to the operation of SI or compression-ignition (CI) engines, which were reviewed earlier in [22] and later in a more detailed review work in [23], and very recently updated and briefly reviewed in [24]. The various appeared papers briefly reveal the engine cycle parts where thermodynamic irreversibility appears, that is the destruction of the working medium for doing useful mechanical work which is mainly attributed to the combustion process [25], and expose the undesirable heat loss exergy transfer to the various combustion chamber parts and exergy loss contained in the gases exhausting from the engine, with the latter ones possibly being exploited in appropriate heat recovery devices [26].
Briefly, the modeling techniques used in the above exergy works in IC engines started in [27] with an ideal Otto cycle exergy analysis, and continued in [28] with a single-zone model in DI (direct injection) diesel engine by separation of the in-cylinder exergy into chemical and thermomechanical components with a variant in [29] of an SI 2-zone model using a specified sinusoidal function for the mass fraction burned. In [30] a 2-zone model was used by specifying the burned mass fraction by a Wiebe function that was extended in [31] by sub-dividing the burned zone into an adiabatic core and a boundary layer. In [32] a spherically propagating flame front of in-house single-zone model for a gasoline-fueled SI engine was used, while in [33] a multi-zone in-house model consisting of one unburned and five burned zones and a quasi-dimensional model of combustion was used for a biogas-fueled SI engine.
In [34] the authors used a comprehensive single-zone simulation code in a diesel engine cylinder, showing that the combustion irreversibility induced during CH4 or methanol (CH3OH) combustion is much smaller than the one induced from the combustion of n-dodecane (C12H26) in the engine. These results were ascribed to the smaller entropy of mixing of the products of combustion for the first two fuels with lighter molecules and to the higher entropy-production decomposition reaction of the comparatively chemically complex and heavier customary hydrocarbon fuel molecule. In [35] a comprehensive single-zone exergy study on a direct injection (DI) and an indirect injection (IDI) diesel engine at diverse operating conditions was carried out, revealing the close relationship of the normalized combustion irreversibility with the fuel fraction reacted. The authors recently in [36] used an in-house, two- zone, comprehensive model for a DI diesel engine functioning at a variety of loads and EGR values, revealing the very tight likeness of the normalized combustion irreversibility rate and mass fraction burned rate ones.
From the reviewed literature on exergy analyses in IC engines, it becomes obvious that very few and sparse works, either experimental or even less theoretical, exist concerning the use of hydrogen blends despite this specifically interesting case. These works are reviewed below in short and in higher detail at Section 3, where their results are compared with the findings of the present investigation.
In [37] the authors carried out a computational exergy study on an SI engine fueled with biogas blended with low fractions of H2, by utilizing their multi-zone model of [33]. Based on their analysis simulation code in [34], the authors in [38] carried out an exergy analysis on the combustion of H2 in blends with either NG or landfill gas in an IC engine, confirming that combustion irreversibility can diminish when using H2 in blends. In [39] the author carried out a computational exergy study on an SI engine fueled with NG enriched with H2, by using a 2-zone model with a pre-specified Wiebe function of fuel combustion-law. In [40] the authors carried out a computational exergy study on an SI engine fueled with ethanol (CH3CH2OH) enriched with H2, by using a 2-zone model with a pre-specified Wiebe function of fuel combustion-law.
In [41] the authors carried exergy balance investigation by direct processing of the experimental measurements on an SI engine operated at constant EQR, two CR, two speeds, and at medium load, using various H2 contents in blend with NG. Cylinder pressure diagrams were acquired and processed. In [42] the previous research group carried out exergy balance investigation by direct processing of the experimental measurements in the same SI engine as before. The experiments were conducted at one CR, speed, EQR and load, with hydrogen NG blends fueling. Cylinder pressure diagrams were acquired and processed. A 1D GT-Power simulation model was used for computing energy and exergy balances at various hydrogen-NG blends and three EGR values.
In [43] the authors conducted exergy balance investigation by direct processing of the experimental measurements on an SI engine operated at constant speed 1500 rpm, intake port absolute pressure 54 kPa, and SIT corresponding to MBT (maximum brake-torque). The experiments were carried out at two different engine fueling modes with the one of relevance to the current study corresponding to gasoline port injection plus H2 direct injection (GPI+HDI), at five EQR values and five values of H2 injected in parallel to gasoline. Cylinder pressure diagrams were not presented. In [44] the previous research group conducted exergy balance investigation by direct processing of the experimental measurements in the same SI engine as before. The experiments were carried out at three speeds of 1200, 1500 and 1800 rpm and intake port absolute pressures 44 kPa, 54 kPa and 64 kPa, for the same as before different engine modes. Cylinder pressure diagrams were acquired and presented.
In [45] the authors conducted exergy balance investigation by direct processing of the experimental measurements on an SI engine operated at constant speed and various loads. It was fueled either with compressed natural gas (CNG) containing 89.14% methane, or HCNG (‘H’ stands for hydrogen) containing 72.5% methane and 17.8% hydrogen, or neat hydrogen. Cylinder pressure diagrams were not presented.
For evaluating the performance of engines at several operational conditions and possibly optimizing in the presence of a large number of investigated parameters as in the current study with logical accuracy and fast computing calculations, a judicious choice from the classes of engine performance numerical modeling techniques, mentioned above, is the use of a comprehensive 2-zone model. This is because the CFD codes are very computer time and cost demanding [46] while the multi-zone ones usually prerequisite a mass fraction burned rate profile. More specifically, an in-house geometric-thermodynamic (quasi-dimensional) model for an HCSI engine is adapted here and used, which predicts geometrically the real position of the flame front and the features of each zone histories in the combustion chamber [47] as well as the turbulent entrainment of the unburned zone fresh mixture mass into the burning one to be combusted, thus in effect being a quasi-three zone model. To be noted that in view of the restricted space allotted by a journal, such a relatively simpler model leaves room to depict more illuminative diagrams without any serious compromise on the analysis results.
That model has been developed and validated before extensively at various operation conditions and CR as regards energy analysis and emissions performance in a Ricardo E6, experimental, variable CR, naturally-aspirated (NA), gasoline-fueled HCSI engine set-up at the lab of the authors [47], which was afterwards adapted and expanded to comprise exergy analysis results too [24]. By utilizing the available experimental results for a 2-cylinder, Lombardini LGW 523 MPI, NA, HCSI engine [48,49] in the case of its fueling with methane (CH4) in neat form, the above mentioned in-house model lately was modified duly as concerns its combustion sub-model with a view to validate its combustion cyclic variability (CCV) behavior on top of energy analysis and emission performance [17].
A similar energy analysis and CCV investigation was performed very lately for the same engine but this time when fueled with highly hydrogen-enriched methane, by taking appropriately into account in the same model the methane-hydrogen mixture properties and their effect on combustion [5]. In view of the objective of the current study, the analysis of the previous study is extended and adapted to furnish exergy results when that engine is fueled either with neat methane (i.e., 0% hydrogen) or its methane-hydrogen blends at various hydrogen proportions up to a high of 50% value. Besides, the engine is operated simultaneously at various equivalence ratio (EQR) values from the stoichiometric one deeply into the lean region of up to a value of 0.70, at which value the engine is unable to operate smoothly with neat methane but only when mixed with hydrogen owing to the much broader flammability limits of H2 (mainly the lean limit).
The separate handling of the two zones in the simulation model and its flame front propagation and turbulent entrainment feature enable the direct prediction (not pre-definition) of the combustion rate, which empowers the accuracy of the crank angle (CA) histories in every zone distinctly (burned and unburned) of composition, temperature and pressure, and eventually of the various exergy terms. Among others, this is mainly important for determining the correct burned zone conditions where (combustion) irreversibility is produced as well as the discrete consideration of the reactive and diffusion components that make up the chemical exergy, which can be decisive when the irreversibility is calculated from a balance comprising all the rest exergy terms
Crank angle (history) diagrams of all exergy terms separately for each zone and for the sum content of both zones (whole cylinder charge) are created, which offer in-depth details regarding the work and heat loss exergy transfers, the flow exergy exchange between the two zones and the net transfer (flow) out of the cylinder loss, while it analyzes rigorously how the various processes and parameters influence the sources of the two components of chemical exergy and the irreversibility (owed to combustion). To this end, for implementing a comparison among the various cases examined, the corresponding normalized exergy values (divided by the fuel chemical exergy) are used to recognize their relative authority and the involved fundamental chemical and physical mechanisms. Construction of normalized exergy along corresponding energy balance diagrams at the EVO event under various hydrogen fractions (in its blend with methane) and mixture (air + fuel) richness conditions provide a clearer picture on the efficient energy use.
All the above can lead to undertaking corrective actions for the irreversibility, exergy losses, and chemical exergy, eventually increasing the knowledge of the SI engines science and technology community for building smarter control devices when fueling the engines with this promising hydrogen fuel, in the endeavor to achieve a clean energy environment transition.
From the previously exposed literature survey and the above clearly stated objectives, to the authors’ best knowledge it can be said that such an in-depth exergy analysis on the use of hydrogen in engines has not appeared in the open literature so far.

2. Methodology

2.1. Outline of the Energy Analysis Modeling

The two-zone, turbulent combustion quasi-dimensional SI engine model to be used in this paper has been developed by the present group and described in detail initially in [47] where it was validated for an SI engine run on gasoline, while later on was validated for the present SI engine fueled either with neat CH4 [17] or CH4/H2 blends [5], so that here only a brief outline is given.
It concerns the closed cycle from inlet valve closing (IVC) to exhaust valve opening (EVO) timings of an HCSI engine, so that at each time instant the gas composition and temperatures are uniform in each one of the two zones, while the two zones hold equal pressures. In the following, the unburned zone is designated by subscript ‘u’ and the burned one by subscript ‘b’. On account of its quasi-dimensional attribute, this model predicts at each instant of time the real location of the flame front and hence determines the exact wetted areas Au, Ab and volumes Vu, Vb of each zone in the cylinder.
Three ordinary differential equations are set up for the chief three dependent variables of (common) pressure p, unburned zone temperature Tu and burned zone temperature Tb, where the independent variable is the degree crank angle (CA) a or time t, where da = ω·dt with ω = 2πNs/60 the angular speed and Ns the engine rotational speed in revolutions per minute (rpm) [50]. These are based in turn on the energy conservation in the unburned zone, the conservation of energy for the sum of the two zones, and the constraint condition of the whole cylinder volume to be equal to the sum of the volumes of the two zones:
A u h t u ( T u T w ) ω =
= ( 1 x ) m d u u d a + p ( 1 x ) m d v u d a + ( 1 x ) C b l m ω ( 1 x 2 ) h u + x 2 h b
A u h t u ( T u T w ) + A b h t b ( T b T w ) ω p d V d a =
= ( 1 x ) m d u u d a m u u d x d a + x m d u b d a + m u b d x d a + C b l m ω ( 1 x 2 ) h u + x 2 h b
1 m d V d a = ( 1 x ) d v u d a v u d x d a + x d v b d a + v b d x d a V C b l m ω
In the previous three equations, m is the entire mass and x = mb/m is the burned zone mass fraction burned (MFB) so that 1 − x = mu/m is the unburned zone one. Further, vu and vb are the respective specific volumes, uu and ub the specific internal energies, and hu and hb the specific enthalpies. From knowledge of the engine geometrical data such as the cylinder bore Bc, the piston stroke Lp, the connecting rod length Zr and the compression ratio CR, standardized relations are utilized for computing the volume of the cylinder V and its derivative dV/da [51].
The well recognized formula of Annand [52] (consisting of one convection and one radiation term) is used for furnishing the corresponding heat transfer (total) coefficient htu and htb in each zone, which is then used for the calculation of the heat exchange between the gas in each zone (separately) and the cylinder walls of temperature Tw. The holding blow-by rate equation is assumed of the form dmbl/dt = Cblm with Cbl = 0.80 (in units 1/s) [50], where its effect on results is in any case minimal. The state equation of the perfect gases is applied too discretely to each one of the two zones.
The thermodynamic properties (specific) of v, u, h, and also of specific entropy s, of specific Gibbs function g and of specific heat capacity cp and their derivatives with respect to p, Tu and Tb are calculated considering the mole (vol.) fraction of each one of the species and the gas-mixture law [50]. Eleven chemical species are presumed to compose the products of combustion in the burned zone, literally N2, O2, CO2, H2O, CO, H2, H, O, OH, NO, and N. Those are presumed to exist in chemical equilibrium apart from the CO and NO species for which are used kinetics formation schemes [17,53,54].
A turbulent entrainment (or otherwise called ‘eddy-burning’) model of combustion is tailored to the present needs and used, which was firstly proposed in [55] and then supplemented in [56]. The basic entrainment and combustion ordinary differential equations with respect to time t of this model read:
d x e d t = 1 m ρ u C A A f C u u T 1 exp t C L τ L + S l
d x d t = x e x τ b
In those two equations, ρu is the unburned zone gas density, xe is the mass fraction of entrained mass me, Sl is the laminar flame speed (LFS), and Af is the front area of the un-stretched flame. The turbulence in the combustion chamber is supposed homogeneous and isotropic, having turbulence intensity uT.
Furthermore, in the above equations the term τL = L/Sl is the characteristic reaction time and the term τb = λ/Sl is the characteristic burn-up time, where symbols λ and L designate, respectively, the Taylor microscale and the integral length scale (macroscale). Quantity λ is correlated with L and uT via the next relation (μu is the unburned zone dynamic viscosity) [57]:
λ = C T L 15 ( μ u / ρ u ) u T L
The evolution of quantities L and uT at each time instant (after combustion initiation) is computed by presuming conservation of angular momentum in the macro-eddies that exist in the unburned zone. Details can be found in [5,17,47].
The values of the calibrating constants Cu, CL and CT are of the order 1, and are used for validating reasons of the present case engine model. The reason of inclusion and determination of the constant CA is that it acts as an enlarging factor of the front area Af of the un-stretched flame in Equation (4), because of the presence of H2.
Since the entrained (enflamed) volume is larger than the burned one, when the flame front arrives at the remotest edge of the cylinder walls a (small) quantity of mass still stays behind within the flame front for burning (xe > x). The burning of this remaining mixture is treated computationally using an exponential type ‘wall-law’ equation [5,17,47].
The laminar flame speed is a crucial factor in turbulent combustion engines modeling, while when H2 is blended in the fuel the flame front stretch is considerable and must be allowed for. The correlation of Ouimette and Seers [58] is used for the LFS of CH4, Sm, while the correlation of Verhelst and Sierens [59] is used for the LFS of H2, Sh. Both of these correlations refer to these fuels when they are premixed with air and include a factor to cater for the lessening effect on the LFS when the mixture is diluted with residual gas of mole fraction yr [60]. These are described plainly in previous publication by the authors [5].
By knowing the above individual speeds Sm and Sh, the CH4/H2 blend LFS Sl is calculated by making use of the fairly well acknowledged Le Chatelier rule-like formula [61], due to its relatively simple form and given the overall uncertainty, by taking into consideration the molar (vol.) proportions of the two fuels in hand, i.e., z for hydrogen and 1 − z for methane in their blend:
S l = 1 z S h + ( 1 z ) S m
The previously calculated LFS of the CH4/H2 blend Sl refers to un-stretched flame, given that the individual laminar flame speeds Sm and Sh that was calculated from referred also to un-stretched flames. Therefore, the wrinkling (owing mainly to the presence of H2 in the blend) of the initially smooth laminar-form flame front is accommodated by the constant CA discussed above with reference to Equation (4). Trailing the simplified approach followed in [62], after fitting the present experimental data on hand, the next easy to use formula for CA was determined solely as an increasing function of the hydrogen vol. fraction z [63], valid for values of z up to ~ 0.50 [61]:
C A = 1.0 + 0.38 · z
The un-stretched surface area Af of the flame front is assumed to be thin and propagating spherically from its center positioned at the spark-plug gap. Certainly, the flame wrinkles mainly due to the existence of H2 in the blend, so that the real surface area of the stretched flame front rises acquiring the value CA·Af. Given the above assumptions regarding the shape of the un-stretched flame front, when the combustion chamber is nearly disc-shaped the calculation of the surface area Af along with the contact (wetted) areas of the two zones, Au and Ab, needed in the heat exchange equations is relatively simpler, by applying the methodology of [64].
The constraint condition at each degree CA dictates that the entrained volumes Ve calculated first by Equation (4) as Ve = Vmvu(1 − xe) and then by the relationship Ve = Ve (a, rf) must be equal, where rf is the radius of the flame-front centered at the spark-plug that is fixed at distance 0.50·BcGc apart from the cylinder axis. A trial and error procedure is required to accomplish the equality of the two volumes Ve as described in [5].
The calculations of Ve, Af, Au and Ab is fairly easy when the combustion chamber is disc-shaped, although some numerical integrations are still required as reported in [17,47]. The combustion chamber of the present engine is assumed to be of that type for the simplicity of modeling, possessing a cylinder with flat head and a spark-plug that is located at distance Gc = 30 mm away from the cylinder periphery.
Finally, by carrying out some further mathematical manipulations, the main differential Equations (1)–(3) take a structure that leads to easier computations, as detailed in [5,17,47].

2.2. Outline of the Exergy Analysis Modeling

At a given thermodynamic state the exergy of a system is closely associated with the environment with which it interacts, as this is made obvious by its definition stating that this is the max useful work that can be obtained as the system is brought to equilibrium with it in a reversible way. Regarding thermal systems when this equilibrium concerns exclusively thermal and mechanical ones, that is equal temperatures and pressures respectively, the so called restricted dead state is attained by the system (thermomechanical part of exergy, Etm), whereas when it concerns thermal, mechanical, and on top chemical (i.e., the same composition) ones the so called true (or un-restricted) dead state is attained (total exergy, E, designated without superscript) [65].
Thus, the difference E − Etm forms the chemical exergy part Ech. This is separated into a diffusion Edf and a reactive component Erc. Moreover, the reactive component is subdivided into an oxidation Eox and a reduction Erd component.
Therefore, the next relations are valid:
E = E t m + E c h   with   E c h = E d f + E r c = E d f + E o x + E r d
Including applications for IC engine works, as for the study in hand, a standard reference environment is classically approved with the pressure p0, the temperature T0, and the composition on molar (or vol.) basis at the dead state (subscript 0) having the values [65] as displayed in Table 1.
As the present case deals in effect with an open system (even over the closed cycle), since the two zones (during combustion) inside the combustion chamber exchange mass (and so energy) among themselves or loose mass to the surroundings owing to blow-by, it is pertinent to introduce the concept of the flow (stream) specific exergy b that comprises the two related (as above) parts btm and bch. Concerning engine applications, it is customary to neglect the kinetic and potential energy terms in exergy or energy computations since these are indeed minute.
Following e.g., the authoritative textbooks in [66,67], the diverse exergy terms are developed for the total exergy and flow specific total exergy terms that are provided firstly (with superscript 0), while their respective thermomechanical terms are similar (but with subscript 0) and their chemical exergy terms are found as difference of the previous ones. In below relations for the flow (stream) specific exergy b and its parts, the general index z = i or e denotes, respectively, inlet or exit flow from (any) zone or the entire (cylinder) content.
E = U + p 0 V T 0 S N k = 1 ν y k μ k 0
b z = h z T 0 s z 1 M z k = 1 ν y k μ k 0 z
E t m = ( U U 0 ) + p 0 ( V V 0 ) T 0 ( S S 0 ) = U + p 0 V T 0 S G 0 =
= U + p 0 V T 0 S N k = 1 ν y k μ k 0
b z t m = ( h z h 0 z ) T 0 ( s z s 0 z ) = h z T 0 s z g 0 z =
= h z T 0 s z 1 M z k = 1 ν y k μ κ 0 z
E c h = E E t m = N k = 1 ν y k ( μ k 0 μ k 0 )
b z c h = h z h z t m = 1 M z k = 1 ν y k μ k 0 μ k 0 z
In the above relations, the various quantities are denoted by their symbol as follows: internal energy U, entropy S, specific Gibbs function g, Gibbs function G, molecular weight M, number of total moles N, and mol fraction yk of any species k.
The chemical potential μk of any species (denoted by index k) in a mixture of ideal gases that obey the ideal gases equation of state with Rmol the universal gas constant (8314.3 J/kmol/K), is equal to its molar specific Gibbs function (the ‘overbar’ denotes molar quantity) that is computed at mixture (comprising ν ideal gases) temperature T and its partial pressure p(r), so that it takes the form:
μ k = g ¯ k ( T , p k ( r ) ) = g ¯ k ( T , y k p ) = h ¯ k ( T ) T s ¯ k ( T , y k p ) =
= h ¯ k ( T ) T s ¯ k 0 ( T ) R m o l ln y k p p 0
where the first term inside the brackets is the standard state, i.e., at p0 = 0.101325 MPa, molar specific entropy of any species ‘k’ at the temperature T of the mixture
s ¯ k 0 ( T ) = s ¯ k ( T , p 0 ) = s ¯ k ( T 0 , p 0 ) + T 0 T c ¯ p k ( T ) T d T
At this point, it is appropriate to mention first the composition of each zone that pertains to the present study. The unburned zone contains the 12 species of CH4, CO2, H2O, N2, O2, CO, H2, H, O, OH, NO and N, where the presence of CH4 is justified as forming the fuel blend (with H2) while the rest CO2, H2O, CO, H2, H, O, OH, NO and N are due to the residual gas (or to EGR if existed) apart from the N2 and O2 of the pure air. The burned zone is composed of all the previously mentioned species with the exception of methane, with the rest 11 species existing in thermodynamic equilibrium with the exception of the CO and NO that are kinetically controlled, as stated in Section 2.1.
According to Equation (9), the chemical exergy part Ech consists of the diffusion Edf and the reactive component Erc. For convenience, the evaluation of these terms is given in Appendix A.
Generally speaking, for the cylinder (index ‘cyl’) of engine the differential equation of the exergy balance is written as [23]:
d E c y l d a = d E l d a d E w d a d I d a + d E i d a d E e d a
where for an open (thermodynamic) system subscripts ‘i’ and ‘e’ signify incoming and exiting flow exergy rates at the respectve cylinder manifolds, including blow-by loss exergy.
Particularly for the case of SI engine cylinder simulation utilizing two-zone combustion modeling (as in current work) that examines solely the system ‘closed’ cycle (the engine cylinder is in a strict sense ‘open’ in view of the blow-by mass consideration), apart from the work transfer and the heat (loss) transfer exergy rate terms dEw/da and dEl/da, respectively, also mass-exchange (and so energy) between the two zones takes place. The latter is realized by the entrainment of fuel-air mixture (possibly containing residual gas) from the unburned into the burned zone where it is to be combusted, so that any zone is anyway an open system.
It is mentioned that the work term herein is the ‘indicated’ one (Wind) referring to the cycle closed part as it is calculated from the simulation model cylinder pressure CA diagrams (cf. the first-law analysis results), which means that the gas exchange process and engine friction parts are not endorsed in this work term.
By considering the form of the flow exergy terms for each one of the two zone as formulated by introduction of the mass fraction burned x and the blow-by rate dmbl/da term (see Section 2.1), and the term dvu/da evaluated as in [68], the above exergy balance Equation (13) for each zone (discretely) takes a suitable form [24], as given in Appendix B for convenience together with explication of their terms.
It is mentioned that combination of the energy (1st-law) and exergy (2nd-law) equations provides one more very usually valuable equation that refers to the balance of entropies in the thermodynamic system [66,67], evidently not being an independent equation. When this is expressed for an open system in derivative form, as for example the two zones of the engine cylinder under study (j = u, b), reads:
d S c y l , j d a = 1 T j d Q l , j d a + d S i r r , j d a + d m i d a s i d m e d a s e
where the last two terms manifest in a two-zone modeling the mass (flow) exchange between the zones (apart from other mass exchanges) while Sirr,j is the entropy generation (or production) owed to irreversibility inside any zone j, where it applies
I j = T 0 · S i r r , j
Before this subsection closure, it is remarked that the dI/da term (inside the cylinder) in Equation (13) is by foremost attributed to the combustion in the cylinder, as this acquires the very major dividend (~95%) as reviewed in [23].
An estimate of the entropy generation over this combustion process is provided by the following relation [25,31]:
Δ S i r r , j ( Δ m f b , j · L H V ) / T j
where Tj is the (instantaneous) temperature prevailing in the zone while Δmfb,j is the fuel combusted over the considered time step.
In [35] by the authors another relation was presented for the combustion irreversibility concluding that this can be correlated exclusively with the mixture composition differentials.

2.3. Test Engine, Measuring Instruments, Properties of Fuels and Available Experimental Data

The present investigation uses the experimental data from extensive investigation carried out at the University of Zaragoza [48,49] on a Lombardini LGW 523 MPI (multiple-point injection), 2-cylinder, homogeneous charge SI engine, which is naturally-aspirated (NA), 4-stroke, water-cooled, and is connected to dynamometer. Each cylinder has Bc = 72 mm, Lp = 62 mm, Zr = 107 mm, and CR = 10.7:1. At earlier stages it was run on gasoline and later was upgraded to run on methane, hydrogen, and other gaseous fuels including their blends. Complete details of the test rig pertinent control, monitoring, and measuring equipment can be found in [48,49].
A differential pressure transmitter measured the air flow rate with accuracy ±0.1%. As concerns the present investigation, two flow meters with accuracy ±0.5% measured the respective (gaseous) methane-hydrogen fuel flow rate of their various blends supplied by high-pressure bottles, where each one of those was filled with the specific blend under examination. A complete set of standardized gas-analyzer modules for IC engines measured the regulated emissions (NO, CO and HC) emissions at the engine-exhaust, which nonetheless are not directly related to the present exergy study.
A Kistler 6053CC60 piezoelectric pressure transducer was utilized for acquiring the cylinder pressure (CP) diagrams from one (of the two) cylinder with an accuracy of ±0.032 MPa in conjunction with an optical encoder pulse signal. A National Instruments DAQPad 6070E data acquisition card recorded these signals that were consequently fed into a personal computer, with a ‘Labview’ based in-house software controlling the data acquisition. Generally, more than 300 consecutive cycles were acquired for each operating case, which were used to calculate the average cylinder pressure diagram that is used in the present investigation, while on the other side the use of these multiple cycles can serve the purpose of cyclic variability investigations such as reported e.g., recently by the authors in [69].
Table 2 displays the chief properties of (gaseous) CH4 and H2 [65,70] that make up the components of the fuel blends used herein. It is appealing to watch the much broader lean and rich flammability limits of H2 as compared to CH4, with the former limit being attractive for lean-fueled engine operation, where this cannot operate e.g., with neat methane or gasoline. Also the lower quenching distance of the hydrogen points to less unburned hydrocarbons (resting) on the combustion chamber walls.
Further, it is remarkable to detect from Table 2 that despite the much higher LHV (lower heating value) or chemical exergy of H2 on a mass basis as compared to CH4, when these are reduced to the volume (e.g., per normal cubic meter, Nm3) of the total (cylinder) charge, e.g., at conditions referring to stoichiometric combustion, this difference is vastly diminished and as a matter of fact slightly reverted. This is a significant quantity in IC engine studies since it affects greatly the power output of the engine (at a certain speed), given that the latter depends directly on the fuel heat input (at IVC event) that can prospectively be released in a cylinder of certain volume (per cycle), which is (can be) filled with fuel and its attending air at inlet conditions. Therefore, for any EQR value the above fuel heat input per (certain) cylinder engine volume does not change much (less than ~ 5%) for any of H2 vol. fraction value used (see values in the last paragraph), while obviously it changes much at different EQR values.
If z is the (known) H2 molar (or volume) fraction in the blend of CH4 and H2, one kmol of blended fuel comprises (1 − z) kmol of methane and z kmol of hydrogen. Thus, the ‘equivalent’ chemical formula of (1 kmol) of fuel is C(1−z) H(4−2z) to be utilized in combustion computations, as given for convenience in Appendix C.
For all the cases treated by the present investigation the engine was operated at wide open throttle (WOT) conditions, at SIT of 33 deg. CA before top dead center (TDC), and at 4500 rpm rotational speed. The EQR possessed the values of 1.00, 0.80 and 0.70, while the various hydrogen/methane blends the values z of the H2 vol. fraction 0.00 (neat methane), 0.10, 0.30 and 0.50. All the previous combinations of equivalence ratio and H2 vol. fraction values were utilized, with the exception of the neat CH4 run at the leanest EQR = 0.7 value, since then weak combustion and extended wobbly performance were exhibited by the engine, thus rendering any of these obtained measurements untrustworthy [49].

3. Results and Discussion

3.1. Energy Analysis Results and Validation to Be Used in the Exergy Analysis

For the explication and elucidation of the corresponding exergy (second-law) analysis findings that form the subject of the current investigation, it is firstly necessary to conduct and present the respective energy (first-law) analysis results as these play a decisive role on their correct interpretation. The calibration and validation of the energy analysis model realized by the features of quasi-dimensional turbulent combustion and of two zones described in Section 2, has recently been reported in full detail by the authors whilst the engine in hand was operated either with neat CH4 [17] or with hydrogen/methane blends [5]. Therefore, for the sake of the present work to be standalone, here only an outline will be given concerning the test cases examined mentioned at the final paragraph of the preceding Section 2.
The residual gas fraction fres was estimated at a value of 0.10 [5,71]. The setting up of the calibrated constants was performed at the stoichiometric (EQR = 1.00) and highest hydrogen z = 0.50 case, and thereafter were held invariable for all the other values of z, viz. 0.00, 0.10 and 0.30. Thereafter, the same values of constants were used intact for all the other remaining combinations values of z and EQR, managing a straight comparison of the model-derived cylinder pressure (CP) diagrams against the available corresponding ones of the experimental investigation. For the engine in question the IVC timing is 59 deg. CA after BDC and the EVO timing is 57 deg. CA before BDC, hence defining the range of the degrees CA in the CP in all the associated diagrams, where BDC means bottom dead center. The ‘hot’ top dead center (TDC) in the above diagrams, i.e., when combustion is in progress, corresponds to 0 deg. CA.
The determination of the constants was a three step process. In the first step, the three correlation constants comprised in the heat transfer correlation of Annand [52] were selected so that the compression lines of the experimental and numerical CP diagrams match at best [72] while estimating a constant and uniform [73] cylinder-walls temperature of Tw = 420 K. In the second step, the effort focused on matching at best the remaining combustion and expansion lines of the CP diagrams, so that a trial and error process on the three correction factors of the turbulent combustion model (cf. Equations (4) and (6)) was applied (using ‘initial’ guesses near to unity), which resulted in values of Cu = 1.25, CL = 0.35 and CT = 0.80. In the final third step, the critical constant CA was determined in a way to match as much as possible all the hydrogen z values concerning this study, ending up to a simple linear function CA = 1.0 + 0.38·z (cf. rational reasoning related to Equation (8) in Section 2) after a trial and error process. It is mentioned that the values of constants Cu, CL and CT stated above were the same with the ones determined for the neat methane-fueling cases in Ref. [17], in appreciation of the fact to be in line with the values at z = 0.00 (the lower limit) concerning the current investigation.
Figure 1 comprising three subfigures depicts the calculated and experimental CP and calculated MFB vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c). It is pointed out that the scale and range of values in all subfigures has been kept identical to set up an easy comparison.
Figure 1a reveals a very satisfactory matching of the experimental and calculated CP curves concerning the EQR = 1.00, z = 0.50 case, which is an anticipated fact since the calibration of the constants was performed for this case, while this good matching is valid also for all the other CP curves corresponding to the rest H2 values of z. Figure 1b and c show similar sensible coincidence for the experimental and calculated CP curves as in Figure 1a, which worsens slightly when shifting towards lower values of EQR. The latter is expected given that the calibration constants were held identical throughout as for the cases referring to Figure 1a.
In [5] reported by the authors, the corresponding experimental and calculated heat release rate (HRR) curves were also compared showing a good to moderate coincidence. The latter was mainly attributed to the quasi-dimensional model and the cylinder chamber geometry simplifying assumptions, which nonetheless was judged reasonable for energy and CCV evaluations and the same is logical to hold true for the present exergy analysis. This support to credible modeling was additionally based on the one hand to the very adequate comparison of experimental and calculated CP rise rate vs. CA diagrams related to Figure 1, and on the other hand to the very reasonable comparison of the corresponding experimental and calculated nitric oxide (NO) exhaust emission values for all combinations of EQR and H2 value cases [5], given that these form very rigorous testing criteria as concerns engines research. It is remarked that the calculated nitric oxide emissions vs. CA diagrams were based on the extended Zeldovich chemical reaction scheme [53] incorporating also an intermediate nitrous oxide (N2O) path [54]. These are not displayed in the current paper as they are not directly relevant to the present exergy analysis.
Examining now the three subfigures of Figure 1, it can be seen that the cylinder pressures, including their peak pressures, elevate and their CA diagram advances with increasing hydrogen addition (in the blended fuel) for any EQR value, and the same is true with increasing EQR values for any hydrogen addition value z. This is explained by examining the corresponding calculated mass fraction burned (MFB) vs. crank angle diagrams depicted also in the same Figure 1, which acquire the usual S-shaped form [51] and follow the same logic of advancement and burn rate (revealed by their inclination at around their mid-range values), either with increasing hydrogen z value for any EQR value or increasing EQR value for any hydrogen addition value z. This is attributed to the correspondingly quicker and more intense combustion with increasing hydrogen addition because of the higher laminar flame speeds prevailing then, and to the higher amount of fuel burned with increasing EQR (mixture richness). All these contribute to correspondingly more elevated temperatures existing then as will be displayed and explained in the next figure. It is mentioned that the corresponding mass fraction enflamed (MFE) curves (not shown as the figures are already overpopulated) are almost similar in shape but a little advanced with respect to the burned ones (as explained in Section 2) since they possess a relatively bigger (entrained) volume at any time instant.
Figure 2 comprising three subfigures depicts the unburned zone, burned zone and mean-state temperatures and LFS vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c). It is mentioned again that the scale and range of values in all subfigures has been kept identical to set up an easy comparison. It is remarked from the outset that the articulation of each zone temperature discretely is a strong asset, as this is a critical feature for the interpretation not only of the engine performance indices (including emissions) from the energy perspective but from the exergy analysis viewpoint too (concerning the present study), influencing the calculation of the diverse exergy losses and (combustion) irreversibility.
By examining in conjunction the three subfigures of Figure 2, it is clear that all burned zone temperatures elevate and their CA diagram advances with increasing hydrogen addition for any EQR value, and the same holds true with increasing EQR values for any hydrogen addition value z. The explanation for this behavior was provided at the end of discussion for the previous Figure 1 related to the influence of the combustion process. The peak burned zone temperature relative positioning follows the same logic as that of the peak CP shown in Figure 1. The burned zone temperatures increase during combustion and then decrease during the expansion phase, actually on a comparative basis in reverse order with respect to the ones during combustion, owing to the more effective expansion process the higher the initial temperatures in this zone [74].
Besides the temperatures of the unburned zone, which exists alone over the period of the engine compression phase, rise exclusively by the compression process and then also by the expanding burned zone when this is created. As shown plainly in the three subfigures of Figure 2, the unburned zone temperatures during the compression stage are almost identical for all cases examined given that the engine compression ratio remains constant, with any minimal differences due to slightly different specific heat capacities of the various mixtures at IVC event. However, when combustion initiates they deviate acquiring higher values the higher the (combustion) burned zone temperatures, i.e., according to the above explanations the higher the H2 content in the fuel blend or the EQR (mixture richness) value. Figure 2 portrays also the mean-state temperatures obtaining values in-between the unburned and burned zone ones, by performing isenthalpic mixing of the two zones when they co-exist [47]. They follow the same trend as before among themselves as far as the various hydrogen content and EQR combination values are concerned.
The same Figure 2 shows also the corresponding (un-stretched) LFS vs. CA diagrams using Equation (7) and the specifics for the calculation of its component H2 and CH4 laminar flame speeds (LFS) stated in Section 2. The LFS values seem relatively unvarying over the combustion stage. On a comparative basis, it is seen that these increase with hydrogen addition for any EQR value as well as with increasing EQR values for any hydrogen addition value z. The explanation for this behavior lies in that the laminar flame speed increases with temperature (cf. influence on temperatures stated above), and further it achieves highest values in the neighborhood of stoichiometric combustion conditions having a bell-shaped like variation with EQR (with increasing values the richer the mixture in the lean region) [5]. The value of LFS has a crucial impact on combustion. The higher its value the more intense the combustion intensity becomes. For example, in the EQR = 1.00, z = 0.00 (neat CH4) case its value is seen to be in the vicinity of 0.40 m/s, whereas it increases by nearly 100% for the current highest hydrogen addition z = 0.50 value.

3.2. Exergy Assumptions and Methodology Adaptation to the Engine Operation

In the present and the following subsections, the results of the exergy study are concentrated on all combinations of EQR = 1.00, 0.80 and 0.70 values with the hydrogen-methane blends having values of H2 vol. fractions z = 0.00 (neat methane), 0.10, 0.30 and 0.50, with the exception of the EQR = 0.70, z = 0.00 case (cf. remark at the end of Section 2). All these cases have been validated and discussed from the energy perspective (first-law) in Section 3.1, thus forming a rigid ground on which to base a rigorous highlighting and explanation of the exergy analysis findings. For all exergy analysis results the exergy terms values are ‘cumulative’, i.e., up to a certain degree crank angle, for any zone or then for their sum content. The use of two zones instead of one zone alleviates the disadvantage of the latter as this under-predicts the combustion temperatures that lead eventually to erroneous evaluation of the irreversibility and exergy losses [36].
Since in the present study the closed cycle of the engine is addressed, the work transfer is the ‘indicated’ one and the irreversibility is owed only to the combustion process that takes place solely in the burned zone. Since in IC engines operation the ‘net’ heat transfer is a loss from the gases to the engine combustion chamber parts, it is customary to use its (negative-signed) term ‘heat transfer loss’. This is supposed to occur at the bulk-gas temperature, which is interpreted into that the relevant exergy heat loss is charged to the surroundings by not including the associated irreversibility in the system.
The following subsections related to the engine exergy analysis are articulated as below. The just next subsection studies the diverse exergy and entropy absolute values separately for each zone and then for their sum content, assessing their relative impact as being of unswerving practical significance to engines technology. However, from the fundamental science perspective, it is logical and fair to compare the various exergy terms for all the cases examined by using their normalized values (otherwise named ‘reduced’), that is their absolute values divided by the inducted (at IVC event) in the cylinder (absolute) fuel chemical exergy (cf. discussion in Section 2). This facilitates the identification of the influencing factors and the main physical and chemical mechanisms involved. The (absolute) fuel chemical exergy differs in value because of a possible slight difference of pressure at IVC event or/and any difference in the fuel specific chemical exergy owing to the different proportions of the two components composing any fuel blend. Therefore all the following subsections deal with the normalized exergy values, with specific subsections devoted to the factors influencing the irreversibility and chemical exergy terms. Lastly, normalized vis-à-vis exergy and energy balance diagrams (at EVO timing) for the various tested cases disclose diversities and highlight exergy analysis benefits concerning IC engines operation.
In all figures to follow, where cited, abbreviations ‘TM’ and ‘CH’ mean thermomechanical and chemical exergies, respectively. Moreover, the Abbreviation ‘norm.’ is used instead of ‘normalized’ at some places in the text for brevity.

3.3. Absolute Exergy and Entropy Terms Crank Angle Diagrams for Each Zone Discretely and for the Sum Content of Both Zones

Figure 3 comprising two subfigures displays the absolute exergy terms vs. crank angle diagrams of the heat loss transfer, work transfer, cylinder thermomechanical, cylinder chemical, cylinder total, irreversibility, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.70 as a sample example. More specifically, Figure 3a displays the above terms for each zone discretely, while Figure 3b for the sum content of both zones. The lower part of Figure 3a displays in a narrower scale the heat loss transfer exergy in the unburned zone and the blow-by loss exergy only for the sum content of both zones, since their depiction in the master diagram would obscure their variation owing to their considerably lower values than the rest of terms.
Owing to brevity of space, the corresponding diagrams for all the other H2 vol. fraction and EQR values tested are not shown as they demonstrate a similar qualitative ‘picture’ as far as the role and influence of each of the two zones and their sum content is concerned. It is also remarked that the respective exergy terms for the sum content of the two zones referring to the entire cylinder charge will be displayed in normalized form in the figures of Section 3.4, where they will be discussed on a comparative basis for the various cases tested. Before proceeding, for being consistent with the presented diagrams, it is reminded that from the Thermodynamics point of view the work transfer is considered positive when transferred-out of the system, whereas the opposite holds true (transferred-in from outside the system) for the heat transfer. However, if the heat loss transfer (i.e., having the same absolute value but with different sign) is used instead as it happens with the present analysis, this is likewise positive when it is transferred-out of the system.
At the lower part of Figure 3a the history of the exergy loss due to blow-by mass is shown for the sum content of both zones, which constantly flows out of the system increasing steadily but in any case as seen it is very little as compared to the rest of exergy terms. For the same reason, the unburned zone heat loss transfer exergy term is depicted on this lower part.
Firstly, Figure 3a is examined regarding the separate two zones. As seen for the compression period until before the starting of combustion (creation of burned zone) in the singly present then unburned zone, the heat loss transfer exergy in its first (history) part decreases (from the IVC event point when it is zero) to negative values and then reverts increasing to positive values. This is because the cylinder walls possess a (constant) temperature value Tw in-between the gas mixture temperature at the IVC event and at the end of its compression (before combustion) as gas temperatures increase due to the compression process [51]. In any case, as seen both these negative or positive values are relatively small. Besides, as seen in (main part) Figure 3a for the same above period in the only existing unburned zone, the work transfer exergy (starting from zero at IVC timing) drops to negative values due to the input of work by the piston of the engine as the compression process proceeds. Therefore, given the very small heat loss (and blow-by) transfer exergy term values and that irreversibility is absent here, the (cylinder charge) thermomechanical exergy acquires virtually equal (absolute) values (with different sign) to the work transfer exergy, as revealed by applying the exergy balance Equation (13). Furthermore, the corresponding total exergy (chemical plus thermomechanical) of the cylinder gas content consists of the sum of the thermomechanical exergy (as determined previously) and the fuel chemical exergy that possesses a (large) value that remains constant as combustion has not started yet.
After combustion commencement when the burned zone is created too, the above picture of exergy events changes drastically as displayed in (main part) Figure 3 due to the large rise of temperatures and pressures induced by the combusting fuel in the burned zone. Besides, inside the unburned zone the work transfer exergy continues to decrease with its negative values and the heat loss transfer exergy to augment as this zone is compressed by the expanding burned zone, until its disappearance when all its mixture is expended.
Besides, as seen in Figure 3a in the burned zone at the beginning of combustion a big thermomechanical exergy boost is created due to combustion, which however in later stages begins to decrease because of the associated increase of heat loss and work exergy transfers (out) in parallel to the increase of the (combustion) irreversibility, as application of the exergy balance Equation (13) orders. The irreversibility (in the burned zone) begins with the start of combustion and increases continuously lasting until its conclusion. Figure 3a also depicts the flow exergy resulting from the entrained fresh-gas mass originating from the unburned zone that enters (entrains) the unburned zone for burning there. This exergy term is essential as two zones are considered and examined by the present model, appearing in the respective exergy balance equations exposed in Section 2. This term has the same absolute value but with different sign for the two zones that are then in effect open systems, while when the sum content of the two zones is considered (thus this is a closed system during the ‘closed’ cycle of the engine) the two terms offset each other, noting that for a single-zone model this term is not present at all. It is apparent that the related to the cylinder-gas content exergy term is shifted as being influenced by the flow exergy curve. Furthermore, the shape of the flow (between the zones) exergy term shows a very similar form to the irreversibility one owing to their intimate link, as will be discussed in a following dedicated to it subsection. As regards the unburned zone, the reactive and diffusion components of chemical exergy are negligible, whereas for the burned zone receive small but perceptible values as will also be discussed in a following related to them subsection.
Now one can turn the attention to examining Figure 3b that depicts the corresponding exergy terms for the sum content of both zones, by noting that the flow exergy term between the two zones (same as before) is again depicted only for reference purposes (cf. discussion in the previous paragraph). The irreversibility term is again the same as in the previous Figure 3a by referring only to combustion (in the burned zone). The cylinder-gas content thermomechanical exergy curve is seen to shift smoothly as the flow exergy exchange between the two zones (shown in the previous Figure 3a) takes place, with its shape following fairly closely the in-cylinder mean-temperatures curve (see Figure 2) as it mainly depends on temperature (a monotonic increasing function). The cylinder-content chemical exergy term follows a smooth pattern from its maximum value at the IVC event (unburned zone), then falls down sharply during combustion as the fuel is exhausted in the unburned zone, and lastly attains the lowest (remaining) values at the late expansion stage in the only then existing burned zone. The shape of the cylinder-content total exergy (chemical plus thermomechanical) curve is then obvious. The work transfer exergy curve (starting from zero) alters from negative to positive values at a point of some deg. CA after TDC, rising then continuously. The heat loss transfer exergy curve is positive, augmenting much during the combustion and expansion phases since then the gas temperatures are a great deal above the cylinder walls temperature Tw.
Figure 4 displays for each zone discretely and for the sum content of both zones, the entropy terms vs. crank angle diagrams of the heat loss transfer, cylinder content, generation, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.80 as a sample example. This provides the respective (cumulative) entropy terms as founded on the entropy related balance Equation (14) stated in Section 2. As discussed accordingly in Figure 3a before, the lower part of this figure displays in a narrower scale the blow-by loss entropy for the sum content of both zones because of the significantly smaller values with respect to the other entropy terms. In the same lower part subfigure the heat loss transfer entropy for each zone discretely and for the sum content of both zones are also depicted here, for the same reason.
The history of the blow-by (mass) loss entropy that is shown for the sum content of both zones flows constantly out of the system increasing steadily, but in any case as seen it is indeed negligible. Further, as seen for the compression period until before the beginning of combustion, in the singly present at that time unburned zone the heat loss transfer entropy in its first (history) part decreases (from the IVC event point) to negative values and then reverts increasing to positive values, for the reasons exposed in detail for the relevant exergy term of Figure 3a. In any case, as seen both these negative or positive entropy values are relatively very little compared to the rest of entropy terms. Thus, given the very small heat loss (and blow-by) transfer exergy term values and that entropy generation is absent here, as dictated by the entropy balance Equation (14) the mixture gas entropy acquires in essence a constant value all over this period, equal to the one at the IVC event.
After combustion initiation when the burned zone is also created, the above picture of entropy events changes drastically as displayed in the (main part) Figure 4, owing to the large rise of temperatures and pressures caused by the combusting fuel in the burned zone. Thus, big entropy increase is incurred in the burned zone as it adds up generation of entropy due to the combustion (irreversibility) and receives (from the unburned zone) flow entropy, while the heat loss entropy continues to increase nonetheless still possessing relatively low values. The entropy generation (in the burned zone) begins with the start of combustion and rises continually lasting until its conclusion. It is obvious that the related to the cylinder-gas content entropy term is shifted as being influenced by the flow entropy curve. Furthermore, the shape of the flow (between the zones) entropy term shows a very alike form to the entropy generation one, as was also discussed for the analogous exergy terms of the previous Figure 3, where the virtues of the flow exergy term manifested by the two zone model considered here was stressed. The cylinder-gas content entropy after the combustion finishes obtains an essentially constant value, which actually drops very little due to the (small) heat loss transfer entropy term. Figure 4 depicts also the curve of the respective entropy term for the sum content of both zones, which acquires an obvious shape by linking the respective curves of the two zones. It is understood that all the above stated entropy values comply with the limitations integrated in the entropy balance Equation (14).

3.4. Normalized Exergy Terms Crank Angle Diagrams for the Sum Content of Both Zones

Figure 5 comprising two subfigures shows for the sum content of both zones, the norm. exergy terms vs. crank angle diagrams for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00. In particular, Figure 5a depicts the cylinder-content thermomechanical, chemical and total exergies, while Figure 5b depicts the heat loss transfer, work transfer, irreversibility and flow (between the two zones) exergies.
As mentioned before this is a useful diagram for the direct comparison of various exergy terms as concerns the influence of the hydrogen addition value (in blending with methane), in this case at an EQR value equal to 1.00. For extending the above comparison also to examine the influence of the EQR value (mixture richness), the following analogous Figure 6a,b and Figure 7a,b for the same exergy terms are presented next referring to EQR values of 0.80 and 0.70, respectively. As mentioned in Section 2 the case of H2 vol. fraction z = 0.70 at EQR = 1.00 is not examined. It is stressed that in all subfigures ‘(a)’ the range of values and scale has been kept identical to set up an easy comparison and the same applies too for all subfigures ‘(b)’.
Examining first any of the Figure 5a, Figure 6a and Figure 7a concerning the cylinder-content thermomechanical exergy curves, it can be observed that they trail an alike pattern to that of the mean-temperature ones as this exergy term mainly depends on temperature, actually increasing monotonically, as also stated and discussed with reference to Figure 3b (sum of zones). This explains the observed fact in these figures that the thermomechanical exergy curves in their (rapid) ascending limb possess a higher inclination the higher the z value of H2, following the same ordering as that of the corresponding mean-temperature curves as depicted in Figure 2. It is interesting to observe that the distance among the different H2 vol. fraction value curves decreases as moving into their descending limb at the expansion phase, following again the corresponding relative (narrowing) positioning of the gas temperature curves as depicted clearly in Figure 2. Therefore, their values at the EVO event that are of practical interest in engines work are pretty the same, with their numerical values presented in the last Section 3.8 dealing with the energy and exergy balances of the engine closed cycle. On the other side, when comparing the variation and relative positioning of the previous curves with reference to the different EQR values, one can observe that the corresponding curves present no appreciable differences in their shape, but they are advancing the higher the EQR value as then combustion starts earlier with higher intensity and temperatures. However, it is reminded that these are normalized values so that the respective absolute exergy values are higher the higher the EQR value.
Examining now any of the same as above Figure 5a, Figure 6a and Figure 7a concerning the cylinder-gas content chemical exergy curves, it can be observed that they follow a pattern from a constant maximum value (possessed at the IVC event) when only the unburned zone exists, then fall rapidly during combustion as the fuel is exhausted (transferred to the burning zone) in the unburned zone, and lastly reach least values at the late expansion stage in the solely then existent burned zone (cf. relevant discussion in Figure 3b). It can be observed that the chemical exergy curves in their rapidly falling part, corresponding to the combustion process when the two zones co-exist, are steeper and start earlier the higher the z value of H2 since then the combustion process is more intense with higher attained temperatures, as discussed and explained with reference to Figure 1 and Figure 2. On the other hand, when comparing the variation and relative positioning of the previous curves with reference to the different EQR values, it is observed that they are steeper and start earlier the higher the EQR value, since in that case the combustion process starts earlier and is further intense. However, it is reminded again that these are normalized values with the chemical exergy curves starting always from unity, so that the respective absolute exergy values are higher the higher the EQR value. The low values of the chemical exergy components (reactive and diffusion) remaining in the (only) burned zone over the last (nearly horizontal) part of the curves will be presented and discussed in next Section 3.5.
From the above presented and explained behavior of the thermomechanical and chemical exergies, the shape and relative positioning of the cylinder-gas content total exergy (chemical plus thermomechanical) curves at various H2 vol. fraction z and EQR combination values is obvious.
Now attention is turned to examining any of the Figure 5b, Figure 6b and Figure 7b concerning the irreversibility and flow (between the zones) exergy curves. As seen both curves start from zero with the combustion advent and increase continuously till the ending of combustion (in the burned zone) while the unburned zone is vanished. The flow exergy emanates from the entrained fresh-mixture mass, which originating from the unburned zone enters (entrains) into the burned zone to be burned. It can be seen the very close shape (qualitatively) of those exergy curves as was also discussed with reference to Figure 3. This mass entrainment rate influences the combustion process that in turn influences the irreversibility incurred, with the latter (close) connection to be further analyzed and discussed in a following subsection dedicated to irreversibility.
For any of the above figures it can be observed that the irreversibility curves acquire a final value (at the end of combustion) that is lower the higher the z value of H2, whereas the corresponding flow exergy curves acquire a final value that follows an exactly reverse order of dependence on the H2 vol. fraction values. The explanation lies in that higher z values of H2 lead to further intense combustion and so higher final flow exergy values, while the higher occurring (burned zone) temperatures lead to lower irreversibility. On the other hand, when comparing the relative positioning of the previous curves with reference to the different EQR values, one can observe that both the corresponding final values of the flow exergy and irreversibility curves slightly increase with decreasing EQR values, which can be credited to the longer then duration of combustion and the lower temperatures.
Revisiting now any of the same as above Figure 5b, Figure 6b and Figure 7b for examining the heat loss transfer exergy curves, it can be observed that they are positive increasing over the combustion and expansion phases, since then the gas temperatures are much above the cylinder walls temperature. As observed these curves acquire higher values the higher the z value of H2 because of the higher then existing gas temperatures (cf. Figure 2). On the other hand, when comparing the relative positioning of these curves with reference to the different EQR values, it can be observed that they acquire higher values the higher the EQR value owing to the same reason as just before. Concerning now the work transfer exergy curves that starting from zero revert later from negative to positive values (cf. discussion of Figure 3b), it can be seen that for any EQR value they acquire slightly higher values the higher the z value of H2 because of the higher then temperatures. On the other hand, when comparing the relative positioning of these curves with reference to the different EQR values, it can be seen that they acquire slightly higher values the lower the EQR value since then the expansion process is more complete [74]. They follow then the same trend as the respective energy values as will also be exposed in the last Section 3.8 that presents vis-à-vis the energy and exergy balances of the engine cycle at the EVO event (containing numbers for clarity).
To further highlight the above discussed behavior of the norm. heat loss and work transfer exergies for the sum content of both zones, Figure 8 provides as a sample example for each zone discretely and the sum content of both zones the norm. exergy terms vs. crank angle diagrams of the heat loss and work transfers, for the case of the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 0.70. Regarding the heat loss transfer exergy, it can be seen that this always increases with positive values (with the exception of the very first part of compression phase) in both zones due to the increasing gas temperatures, so that obviously the same applies for their sum. On the contrary concerning the work transfer exergy, it can be seen that in the unburned zone this always decreases to negative values (due to the compressive effect from the creating burned zone), whereas in the burned zone it increases having positive values due to the high pressures resulting from the combustion process. Thus, the corresponding exergy values for the sum of the two zones is a delicate difference of the corresponding values in the two zones, which for the present conditions ends up to slightly higher work transfer exergies for the higher z value of H2 case.

3.5. Normalized Chemical Exergy Components Crank Angle Diagrams in the Burned Zone

It is stated from the outset that apart from the significance of the analysis of the diffusion and reactive exergy term of oxidation (chemical exergy components) by themselves, their right computation is very important as it directly affects the exact determination of the irreversibility term if this is calculated by applying the exergy balance equation. Only the results for the burned zone are shown and analyzed here, since both these components assume values in the unburned zone that are two orders of magnitude less. Furthermore as stated in Section 2, only the oxidation term of the reactive component is considered as the other term of reduction is by some orders of magnitude less.
Figure 9 comprising three subfigures depicts the burned zone norm. chemical exergy terms vs. crank angle diagrams of diffusion, reactive, and diffusion plus reactive, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
From all the subfigures of Figure 9, it can be observed that the diffusion component increases during combustion because then complete combustion products, like carbon dioxide and water vapor, begin to be produced at much higher levels than the ones existing in the reference environment (see Table 1), obtaining an effectively stable value during the follow-up expansion stage after combustion ends. On the other side, the oxidation component assumes large values during combustion since then the elevated existing combustion temperatures provoke dissociation reactions of the complete products of combustion into incomplete ones, such as primarily CO and H2, which are missing from the reference environment as Table 1 shows. However, during the follow-up expansion stage the oxidation component decreases greatly since then the falling temperatures provoke recombination reactions of the incomplete combustion products back into complete ones. The finally acquired value (e.g., at EVO event) of the oxidation component is indeed very small for the stoichiometric and leaner cases as concerns the current study, unlike the case of rich mixtures where it stabilizes at high values [24].
The above explanations regarding the assumed shapes of the diffusion and oxidation components assist to the proper explanation of their comparative behavior either with H2 vol. fraction or EQR values variation. This is done in the next paragraphs.
Examining firstly any of the subfigures of Figure 9 concerning the diffusion component of chemical exergy curves, it can be seen that they acquire lower values the higher the H2 vol. fraction in the blend, which is attributed to the higher then attained combustion temperatures (see Figure 2) that promote stronger dissociation. On the other hand, when comparing the relative positioning of the previous curves with reference to the different EQR values, it is observed that they acquire lower values the lower the EQR value, which is due to that the lean mixtures generate less concentration of complete products of combustion owing to the presence of surplus oxygen in the gases.
Examining now any of the same above subfigures of Figure 9 concerning the oxidation component of chemical exergy curves, it can be observed that they acquire higher values the higher the H2 vol. fraction in the blend, which is due to the higher then attained combustion temperatures (see Figure 2) that promote stronger dissociation. On the other hand, when comparing the relative positioning of the previous curves with reference to the different EQR values, it is observed that they acquire lower values the lower the EQR value, which is due to that lean mixtures generate less concentration of incomplete combustion products due to the presence of the surplus oxygen in the gases. Actually at the low EQR values of 0.80 and more so of 0.70, these exergy oxidation values are indeed minimal.
After the above presentation and discussion of the diffusion and reactive (only oxidation here) components of chemical exergy, the shape of the curves referring to their sum is obvious disclosing decreasing values the higher the H2 vol. fraction and increasing values the higher the EQR. Because at the lower EQR = 0.80 or 0.70 cases the exergy oxidation values are indeed very small, the corresponding diffusion and sum of diffusion plus reactive curves virtually coincide.
Insisting a bit more on the behavior of the reactive (oxidation) component, companion Figure 10 is presented that portrays the carbon monoxide (CO) concentration (a) and hydrogen (H2) concentration (b) vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70. The CO concentration is determined by considering its chemical kinetics controlled formation scheme (cf. Section 2) [17], by which it is ‘frozen’ at near its maximum value, while the molecular H2 is determined from chemical-equilibrium considerations. As discussed above, these are the chief oxidation species of the reactive component of chemical exergy. The exergy curves of the oxidation component shown before in Figure 9 follow rather closely the shape of the CO and H2 concentration ones, while their respective relative positioning is the same with either H2 vol. fraction or EQR variations.
It is customary in engines work dealing with exergy analysis to appraise the comparative share of the chemical exergy, thereby evaluating the ratio of its value by the total exergy value of the whole cylinder charge at the EVO timing that could be of practical interest [29]. For this purpose Figure 11 displays this ratio values against equivalence ratio (EQR) diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50. It can be observed that this ratio acquires values in a very narrow window of values between 0.07 and 0.08, which is considered a normal range [24]. This ratio of values drops with either H2 vol. fraction increase or EQR decrease, showing a similar behavior to that of the chemical exergy as was discussed before with reference to Figure 9.

3.6. Analysis of the Combustion Irreversibility Term

Figure 12 displays for the burned zone the mass fraction burned (MFB) rate and norm. irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 0.80. It is to bear in mind that the mass fraction burned (MFB) rate quantity is effectively normalized too as referring to mass fraction, so that its comparison with the norm. irreversibility rate becomes fair. It is interesting to detect the striking similarity of the corresponding curves, thus disclosing the dominant authority of the combustion process on the irreversibility produced. Actually, the norm. irreversibility rate curves are ordered among themselves as their corresponding MFB-rate curves with respect to the variation of the z values of hydrogen.
In order to demonstrate the ordering of the corresponding curves with respect to the EQR values variation, Figure 13 is provided that displays for the burned zone the mass fraction burned (MFB) rate and norm. irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 1.00 or 0.70. Yet again, it is seen that the norm. irreversibility rate curves are ordered among themselves as their corresponding MFB-rate curves with respect to the EQR values variation. The same behavior happens also for all the rest conditions of H2 vol. fraction and EQR values combinations, which are not shown here due to brevity of space. It is reminded that the form of the combustion rate curve and its dependence on either H2 vol. fraction or EQR values variation has been outlined in Section 3.1, while full details have been reported in [5] by the authors.
Given that the present work uses a comprehensive, two-zone, quasi-dimensional model that caters for following up the flame front movement in the course of time, it is motivating to provide pertinent Figure 14 that illustrates for the burned zone the norm. irreversibility and flame front radius vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10, 0.30 and 0.50 and functioning at EQR = 0.80 or 0.70 as sample examples. The shape of the norm. irreversibility curves and their relative positioning shown here with respect to the z values of hydrogen and EQR different values has been explained in Section 3.4. On the other side, the flame front propagation as realized by the radius of the flame front initiating from the spark-plug fixing point and expanding outwards until meeting the remotest edge of the combustion chamber walls, it is seen to follow a nearly straight line pattern. The relative positioning (inclination) of these lines follows closely the relative positioning of the respective norm. irreversibility curves with respect to the various hydrogen vol. fraction and EQR values combinations. Thus, once more it is revealed the tight linking of the irreversibility and the combustion process, with the latter depending on the flame front propagation that dictates at each instant of time the quantity of entrained mixture to enter the burned zone for eventual combustion (cf. equations in Section 2).
Since the combustion temperatures are linked to the combustion process and so to the irreversibility production and the nitric oxide (NO) formation, it is motivating to construct the compound Figure 15 comprising two subfigures that connects the (representative) peak burned zone temperatures, the norm. irreversibility and the (exhaust) NO quantities, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70. More specifically, Figure 15a illustrates the norm. irreversibility against peak burned zone temperature diagrams where it can be seen that, at least for the operating conditions of the present engine, at any EQR value the norm. irreversibility varies almost linearly with peak combustion temperature (solid lines), decreasing with increasing values of either H2 vol. fraction or EQR. It is interesting to connect also the corresponding equal H2 vol. fraction values (with dashed lines) and see that these follow again an almost straight line pattern. On the same subfigure are also illustrated the NO concentration at the EVO event against peak burned zone temperature diagrams (dotted lines), which demonstrate that the NO concentration elevates with elevating values of either hydrogen vol. fraction or EQR.
From the above it becomes evident that the norm. irreversibility and the NO concentration exhibit a completely inverse behavior with respect to changes of either hydrogen vol. fraction or EQR. This is attributed to that increasing values of either H2 vol. fraction or EQR give rise to higher combustion temperatures, which in turn lead to lower irreversibility values (cf. Equation (16)) but simultaneously to higher NO production ones [75]. To illustrate this better, Figure 15b is called for that depicts the norm. irreversibility against nitric oxide concentration at EVO event diagram, for all the EQR and hydrogen vol. fraction values as before. It can be seen that all the points concerned are well fitted by a 2nd order polynomial curve (coefficient of determination R2 = 0.9233), which unfortunately discloses an adverse trade-off between these two quantities, i.e., for any pair of values for EQR and hydrogen vol. fraction decreasing the norm. irreversibility leads to NO increase and vice versa. A usual technique to decrease the NO emissions is to use EGR (exhaust gas recirculation) as reported e.g., in [76] for a hydrogen-fueled SI engine using experiments and CFD simulation or for small size passenger-car engine using 0D/1D computations [77], or to use water injection [78] or improve the piston-bowl design [79] for emissions mitigation.

3.7. Normalized Energy and Exergy Balances for the Closed Cycle of the Engine at EVO

Figure 16 comprising three subfigures illustrates at line-diagrammatic form for comparison purposes, the distribution balances of the (cumulative) norm. exergy and energy terms (sum content of both zones) for the closed cycle of the engine (from IVC up to EVO timings) against the engine fueling hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, functioned at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c). The values for each test-case point are shown by a small number near the respective symbol, so that when their differences are small can be more easily discerned. The corresponding blow-by loss terms are omitted in the diagrams as having tiny values less than 0.01. For the energy balances, the combustion (efficiency) loss is charged to the exhaust loss for the convenience of figures, given that the combustion efficiency is ~0.985% for the EQR = 1.00 case and ~0.995% for the other two (lean) cases. This is ascertained by detecting in Figure 10 the minute values at the EVO event of the main combustion inefficiency species of CO and (unburned) molecular H2 especially at lean conditions.
The trend variation shown in Figure 16 for the norm. exergy terms of the heat loss transfer, work transfer, cylinder-content thermomechanical, and irreversibility have already been explained in Section 3.4 as well as for the (burned zone) chemical exergy in Section 3.5 as far the influence of the hydrogen vol. fraction and EQR values is concerned, so they will not be repeated here. It can be noticed from Figure 16 that the corresponding (only existing) norm. energy terms of the heat loss transfer, work transfer and cylinder-content exhibit the same trend variation with hydrogen vol. fraction and EQR values, with the explanations being similar as those for their exergy counterparts.
It is proper to clear out from the outset the difference of the respective fuel LHV and fuel specific chemical exergy for assisting the explanations when comparing the corresponding values of the various energy and exergy terms since these are normalized, i.e., the first ones with respect to the fuel chemical energy at IVC event and the second ones with respect to the fuel chemical exergy at IVC. From Table 2 it can be witnessed that the fuel specific (chemical) exergy is a little elevated (~4%) than the fuel LHV for the neat methane case (z = 0), which drops slightly with increasing hydrogen enrichment in the blend (still acquiring higher values) at a value of around 2.5% for the (highest here) H2 vol. fraction case of z = 0.50.
It can be seen that the norm. heat loss exergy transfer values are lower than the corresponding energy ones, which is attributed on the one hand to the reducing effect of the factor (1 − T0/Tcyl) that is less than unity (see relevant Equations in Appendix B), and on the other to the fuel specific (chemical) exergy that is somehow larger than the fuel LHV as stated in just previous paragraph.
Likewise, it can be seen that the norm. work exergy transfer values are lower than the corresponding energy ones, which is attributed to that the fuel specific (chemical) exergy is a little bigger than the fuel LHV as stated in the paragraph before the previous one, while there is also influence from the negative-signed term p0(dV/da) that appears in the work transfer exergy term (cf. relevant Equations in Appendix B). To be noted that the above energy term is the commonly used 1st-law efficiency, whilst the exergy term is the simplest form of the 2nd-law efficiency. It is repeated that the above work terms are ‘indicated’ as referring to the engine closed cycle.
The work and heat loss transfer energy terms establish the net exhaust (flow-out) transfer energy term, because the sum of the three should add up to unity as the equation of energy balance constrains. On the other hand, the equation of exergy balance apart from the above three (exergy) terms contains also a sizable irreversibility term and a rather small chemical exergy term, so that the net exhaust (flow-out) transfer exergy term ends up to be markedly lower than the corresponding energy one as indeed Figure 16 depicts.
From Figure 16 the relationship between the norm. irreversibility and the norm. (indicated) work transfer exergy (simplest form of 2nd-law efficiency) can be seen (shown with values). Nonetheless, to make more emphatic the relation for these important quantities, Figure 17 displays the norm. irreversibility against the norm. work transfer exergy for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70. It can be observed that at any EQR value the norm. irreversibility drops and at the same time the norm. work transfer exergy increases with increasing H2 vol. fraction values, which is a very favorable outcome indicating the beneficial effect of hydrogen enrichment. However, at any H2 vol. fraction value, with increasing EQR values the norm. irreversibility drops but this is escorted by a decrease of the norm. (indicated) work transfer exergy.

3.8. Review by Comparison vs. Reported Data and Trends for SI Engines with Hydrogen Blends

A concise comparison is carried out in the present section against pertinent data and trends reported in the open literature, regarding exergy studies for spark-ignition (SI) engines fueled with blends of hydrogen with gaseous fuels such as NG or methane (as in the present study), or other less utilized bio-fuels like landfill gas or bio-gas. Moreover, exergy investigations of SI engines fueled with gasoline or ethanol will be used too for qualitative comparison, on the understanding that these liquid (volatile) fuels do not differentiate exergy analysis fundamentals. Generally, there is nearly a two handful of exergy analysis studies dealing with SI engines fueled by hydrogen enriched blends, which can be categorized in two broad classes as regards the general methodology followed.
The first ones are founded on theoretical exergy analysis of the engine closed cycle using energy analysis models of diverse level of involvedness hence presenting exergy history (CA diagrams) of various terms, after performing validation of calculated against experimental cylinder pressure (CP) CA diagrams or/and of other parameters. Obviously, their results can be directly compared with the ones of the current study as far as trends of the various exergy terms with changing H2 fraction or EQR values is concerned.
The second ones conduct a direct processing of the experimental measurements and so establish energy and exergy balances (global character) for the whole engine system, which can then be used to expose trends of the respective terms with respect to changes of certain engine attributes or different fuel blends used. However, in this case their results cannot be directly compared with the ones of the current study, mainly because the work transfer obtained is the brake (shaft) one as measured by a dynamometer (brake) coupled to the engine (W = Wbr + Wfr). Nevertheless, Wfr is a very strong function of speed and a very weak function of load, so that for a constant engine speed (as in present study) it is virtually constant. Besides, the fuel heat input (used in the normalization) for a (certain) cylinder engine volume (fuel-air mixture) is sensibly the same at a certain EQR value for different H2 fractions (cf. discussion for Table 2 in Section 2). Therefore, at a certain EQR value comparison is vindicated between the absolute work transfer terms of W and Wbr as far as their trends with changing H2 fraction is concerned. Consequently, the total irreversibility (found by the experimental exergy balance) from which the constant Wfr term should be subtracted to produce the irreversibility due to combustion, can be compared with the corresponding (theoretical) combustion irreversibility as far as their trends with changing H2 fraction is concerned. Comparison for the corresponding trends of changing the EQR at a certain H2 fraction is uncertain, since now the respective fuel heat inputs are different. Sometimes, in these investigations the indicated power is (additionally) computed from the processing of acquired (experimental) CP diagrams (if available), making easier the above comparisons.
In [37] the authors carried out a theoretical exergy analysis concerning the closed cycle of an SI engine fueled with biogas enriched with hydrogen of low vol. fraction values 0%, 5%, 10% and 15%. They used their in-house quasi-dimensional multi-zone model to fit the available experimental cylinder pressure diagrams [33]. This is a mono-cylinder, 4-stroke, air-cooled, NA, homogeneous charge SI engine that has Bc = 87.5 mm, Lp = 110 mm, Zr = 231 mm and CR = 13:1, and operates at wide open throttle (WOT), speed Ns = 1500 rpm, EQR = 0.9 and SIT of 20 deg. CA before TDC. The form of the diverse norm. exergy terms for the entire cylinder charge vs. CA diagrams are in agreement with the corresponding ones of the current study, while their ordering with respect to the effect of the hydrogen content is identical. Similarly, the same agreement holds true for the form and ordering of the corresponding norm. chemical exergy components of reactive and diffusion and their add-up content vs. CA diagrams.
In [38] the authors carried out a theoretical exergy (second-law) analysis concerning the closed cycle of a DI (direct injection) diesel engine fueled with natural gas or landfill gas enriched with hydrogen of low vol. fraction values 0%, 5% and 10%. They based the analysis on their simulation code as presented earlier in [34], where they demonstrated that combustion irreversibility can diminish when using lighter type molecules like hydrogen. Although it concerns a diesel engine, the conclusions derived are very useful for comparison against the respective ones of the current study. The engine is mono-cylinder, 4-stroke, air-cooled and NA that has Bc = 85.73 mm, Lp = 82.55 mm, Zr 148.60 mm and CR = 18:1, and operates at speed Ns = 1500 rpm, EQR = 0.5 and static injection-timing of 22 deg. CA before TDC. For either the H2 enriched natural gas or landfill gas cases, the shape of the (absolute) heat loss and work transfers and the irreversibility exergy terms for the entire cylinder charge vs. CA diagrams are in accord with the corresponding ones of the present study. At the EVO event the norm. (indicated) work transfer exergy increases slightly and the norm. irreversibility decreases with H2 vol. fraction increase, which accords with the current study findings.
In [39] the author conducted a theoretical exergy (second-law) analysis concerning the closed cycle of an SI engine fueled with NG (assumed as neat methane) enriched with hydrogen. He used a 2-zone model with a pre-specified Wiebe combustion pattern so that to fit the available experimental engine cylinder pressure diagrams of other investigators. This is an in-line, 6-cylinder, 4-stroke, SI engine that has Bc = 105 mm, Lp = 120 mm, Zr = 192 mm and CR = 10.5:1. The computations were carried out at fixed SIT of 30 deg. CA before TDC and speed 1200 rpm. He considered for the computations H2 vol. fraction values equal to 0%, 10%, 30% and 50% (in its blends with methane), combined with several excess air ratio (λα) values (λα is the reciprocal of EQR) spanning the stoichiometric λα = 1.0 condition deep into the lean region. The form of the diverse absolute exergy terms for the entire cylinder charge vs. CA diagrams are in agreement with the corresponding ones of the current study, while their ordering with respect to the effect of the hydrogen content is identical. That investigation concerning the cumulative norm. exergy values (at EVO) showed the following trends. The (indicated) work transfer exergy slightly increases with increasing H2 content and decreases with increasing EQR (reciprocal of λα) value, the heat loss transfer exergy increases either with increasing H2 content or EQR value (up to λα = ~1.15), and the irreversibility decreases either with increasing H2 content or EQR value. Therefore, all the previous exhibit analogous trends to the respective ones of the current study.
In [40] the authors conducted a theoretical exergy and exergoeconomic (not relevant to the present study) analysis concerning the closed cycle of an SI engine fueled with ethanol enriched with hydrogen. They used a two-zone model of the commercially available software AVL Boost with a pre-specified Wiebe (or fractal geometry) combustion pattern so that to fit the available experimental engine cylinder pressure diagrams. This is a 4-cylinder, 4-stroke, turbocharged SI (squared) engine that has Bc = 86 mm, Lp = 86 mm and CR = 10:1. They considered for the computations hydrogen fraction values of 0%, 3% and 6% on an energy basis in its blends with ethanol, combined with EQR values of 1.0, 0.85 and 0.70. That investigation concerning the cumulative norm. exergy values (at EVO) showed the following trends. The (indicated) work transfer exergy slightly increases with increasing H2 content and decreases with increasing EQR value, the heat loss transfer exergy increases with increasing H2 content value, and the irreversibility decreases with increasing H2. Therefore, all the previous exhibit analogous trends to the corresponding ones of the current study.
In [41] the authors conducted a direct processing of the experimental measurements. They used an in-line, 6-cylinder, 4-stroke, water-cooled, heavy-duty, turbocharged and intercooled, port-injected SI engine having Bc = 126 mm, Lp = 130 mm, Zr = 219 mm and operated at constant λα = 1.07. The experiments were performed at two engine compression ratios CR = 13.6:1 and 14.5:1, and at two speeds Ns = 1000 rpm and 1800 rpm, at a medium load of brake mean effective pressure, bmep = 6.0 bar, while the hydrogen content in its blends with NG (containing 99% methane) was varied from 0% to 16% on an energy basis. Indicated power was also computed from processing of 200 acquired cylinder pressure diagrams. The cumulative norm. friction energy was found virtually constant for any H2 content used. The ordering with respect to the influence of the hydrogen content of the experimental cylinder pressure and mass fraction burned vs. CA diagrams is identical to the one of the present study. The investigation reveals that with increasing H2 proportion in the blend the cumulative normalized values of the (indicated) work transfer exergy slightly increase, of the heat loss transfer exergy increase, and of the irreversibility decrease, hence exhibiting analogous trends to the corresponding ones of the current study.
In [42] the previous research group conducted a direct processing of the experimental measurements in the same SI engine as before. The experiments were carried out at compression ratio CR = 13.6:1, speed Ns = 1400 rpm, λα = 1.18 and load of bmep = 6.05 bar, with hydrogen-NG blends fueling. Indicated power was also computed from processing of 200 acquired cylinder pressure diagrams. A relevant 1D GT-Power commercially available simulation code was set-up and validated to accord with the experimental data, which was used for computing the energy and exergy balances for hydrogen content in its blends with NG (containing 99% methane) values of 0%, 2%, 5%, 8% and 10% on a mass basis, at three different values of the exhaust gas recirculation EGR = 0%, 10% and 20% to study the effect of EGR (not relevant to the present study). The cumulative norm. friction energy was found virtually constant for any H2 content used. The ordering with respect to the effect of the hydrogen content of the experimental cylinder pressure and mass fraction burned vs. CA diagrams is identical to the one of the present study. The investigation reveals that with increasing H2 content in the blend the cumulative normalized values of the heat loss transfer exergy increase and of the irreversibility decrease, hence exhibiting analogous trends to the corresponding ones of the current study.
In [43] the authors conducted a direct processing of the experimental measurements. They used a 4-cylinder, 4-stroke, water-cooled, naturally-aspirated SI engine that has Bc = 82.5 mm, Lp = 92.8 mm and CR = 9.6:1. The engine was run at Ns = 1500 rpm, (absolute) pressure at intake port of 54 kPa, and SIT corresponding to MBT. The experiments were carried out at two dissimilar engine fueling modes with the one of relevance to the current study corresponding to gasoline port injection plus H2 direct injection (GPI+HDI), at five values of λα = 1.0, 1.1, 1.2, 1.3 and 1.4, and at five values of hydrogen injected in parallel to gasoline of 0%, 5%, 10%, 15% and 20% on an energy basis. Cylinder pressure diagrams were not presented and so their indicated power computed there of. For the (GPI+HDI) fueling mode of interest to the present study, the investigation shows that with increasing EQR the heat loss transfer and the exhaust loss transfer exergies increase while the irreversibility decreases with either EQR increase or with H2 content injected increase, hence exhibiting analogous trends to the corresponding ones of the current study.
In [44] the previous research group conducted a direct processing of the experimental measurements in the same SI engine as before. The experiments were carried at three speeds of Ns = 1200, 1500 and 1800 rpm and intake port absolute pressures of 44 kPa, 54 kPa and 64 kPa for the purpose of examining the effects of speed and load (not relevant to the present study), at the two previous engine fueling modes. Cylinder pressure diagrams were acquired and presented. For the (GPI+HDI) fueling mode of interest to the present study, the investigation shows that the ordering with respect to the effect of the hydrogen content on the experimental cylinder pressure and mass fraction burned vs. CA diagrams is identical to the one of the present study. It also shows that with increasing H2 content injected the norm. work transfer and heat loss transfer exergies increase while the norm. irreversibility decreases, hence exhibiting analogous trends to the corresponding ones of the current study.
In [45] the authors conducted a direct processing of the experimental measurements. They used a 4-cylinder, 4-stroke, NA SI engine that has Bc = 105 mm, Lp = 120 mm and CR = 12:1. The engine was run at constant speed Ns = 1500 rpm and various loads. It was fueled either with CNG (compressed natural gas) containing 89.14% methane, or HCNG (‘H’ stands for hydrogen) containing 72.5% methane and 17.8% hydrogen with the rest being higher gaseous hydrocarbons, or neat hydrogen (not relevant to the present study). Cylinder pressure diagrams were not presented. The norm. combustion irreversibility calculated from processing of acquired cylinder pressure diagrams was found lower for the HCNG against the corresponding CNG fueling case, while the cumulative norm. friction energy was found virtually the same for the above two fuels. The irreversibility decrease with hydrogen use in the NG accords with the corresponding findings of the current study.

4. Conclusions

In very recent works, an in-house, comprehensive, 2-zone, quasi-dimensional, turbulent combustion model is utilized, that was further adapted to handle energy- and emission-wise including CCV the validation on a homogeneous charge, NA, spark-ignition engine run either with neat methane or its blends with highly enriched hydrogen (up to 50% vol.), which in the present work is further extended to provide its exergy analysis results. The influence of the H2 vol. fraction (in the blended fuel) and the equivalence ratio (EQR) values on the diverse exergy terms of that engine is analyzed.
The fueling strategy comprised hydrogen-methane blends containing H2 vol. fractions z = 0.00 (neat methane), 0.10, 0.30 and 0.50, while the (fuel) equivalence ratio was taking values EQR = 1.00 (stoichiometric), 0.80 and 0.70.
The main conclusions drawn from the present study, as mainly derived from the curves of the computed CA diagrams, are stated below.
The blow-by loss exergy at any conditions is really minimal.
In the unburned zone, the heat loss transfer exergy decreases initially to negative values and then reverts increasing to positive values that are in any case small, and the work transfer exergy decreases continuously with negative values. The thermomechanical exergy of the charge obtains sensibly equal values (with different sign) to the work transfer exergy.
In the burned zone, the heat loss transfer and the work transfer exergies increase continuously with positive values. The thermomechanical exergy initially shows a considerable boost due to combustion that nonetheless later on begins to decrease.
The irreversibility bgins with the combustion starting (inside the burned zone only) and increases continuously lasting until its ending, and the flow exergy due to the mass of entrained fresh-mixture originating from the unburned zone follows exactly the same shape, hence revealing an intimate link with the irreversibility.
The cylinder-content chemical exergy possesses a (large) value in the unburned zone that remains constant before combustion, then it drops rapidly with the course of combustion as its fuel is exhausted in the burned zone, and lastly it obtains the lowest (remaining) values at the late expansion stage.
For the sum content of both zones, the cylinder-content thermomechanical exergy curve shifts smoothly as the flow exergy exchange between the two zones takes place with its shape following fairly closely the in-cylinder mean-temperatures curve. Further, the work transfer exergy curve alters from negative to positive values a little after the TDC position increasing then continuously, and the heat loss transfer exergy curve is positive increasing much over the combustion and expansion phases.
In the unburned zone, the heat loss transfer entropy decreases initially to negative values and then reverts increasing to positive values that are in any case small, and the mixture charge entropy acquires in essence a constant value all over this period equal to the one at the IVC event.
In the burned zone, the heat loss transfer entropy increases continuously with positive (but still small) values, and the zone-content acquires high entropy values as it gains generation (production) of entropy due to (combustion) irreversibility and receives flow entropy (from the unburned zone). The related to the zone-content entropy term is shifted as influenced by the curve associated with the flow entropy.
For the sum content of both zones norm. exergy values, the cylinder-content thermomechanical exergy curves trail an analogous pattern to that of the mean-temperature curves with their ascending limb possessing a higher inclination the higher the hydrogen value in the blended fuel, hence following the same ordering as that of the respective mean-temperature curves. When comparing the variation and relative positioning of the previous curves with reference to the different EQR values, the corresponding curves present no appreciable differences in shape but are advancing the higher the EQR value.
For the sum content of both zones norm. exergy values, the irreversibility curves acquire a final value (at the end of combustion) that is lower the higher the H2 value in the blended fuel, whereas the corresponding flow exergy curves acquire a final value that follows an exactly reverse order of dependence on the H2 values. When comparing the relative positioning of these curves with reference to the different EQR values, the corresponding final values of the flow exergy and irreversibility curves slightly increase with decreasing EQR values.
For the sum content of both zones norm. exergy values, the heat loss transfer exergy curves acquire higher (positive) values the higher the H2 or EQR values.
For the sum content of both zones norm. exergy values, the work transfer exergy curves acquire slightly higher values the higher the H2, while they acquire slightly higher values the lower the EQR value.
The norm. (in the burned zone) diffusion component of the chemical exergy term increases and thereafter obtains a stable value in the expansion stage, while the corresponding reactive component increases and then falls close to zero at the ending of the expansion, thus following rather closely the pattern of the incomplete combustion products of CO and H2 concentration curves. The diffusion component acquires lower values the higher the H2 and lower values the lower the EQR. The oxidation component acquires higher values the higher the H2 or EQR values.
The shape of the norm. irreversibility rate curve trails very tightly the respective mass fraction burned (MFB) rate curve for all cases examined, thus disclosing the dominant authority of the combustion process on the irreversibility produced.
The CA diagrams of the flame front radius that manifests the flame front propagation assume a nearly straight line pattern, with their relative positioning (inclination) following closely the relative positioning of the respective norm. irreversibility curves with respect to the various H2 and EQR values combinations.
Unfortunately, an adverse trade-off between the norm. irreversibility and NO concentration (at EVO) values exists.
At the EVO timing, the values of the norm. exergy work and heat loss transfers are smaller than their norm. energy counterparts, exhibiting a similar trend with the variation of either the H2 or EQR values.
A succinct comparison was performed against reported pertinent data and trends. In analogy to the results reported by each study, the comparison showed a reasonable agreement with the shape of the various exergy terms histories or of their values at the EVO event for the various H2 content in the fuel blends and engine operating EQR values. This adds to the confidence of the present exergy assessment merits, which can contribute to a new thought for the prospective research to improving engines performance along the judicious use of a friendly environmental fuel such as hydrogen in engines. Such an extended and in-depth exergy analysis on the use of hydrogen in engines has not appeared in the open literature. It can lead to undertaking corrective actions for the irreversibility, exergy losses, and chemical exergy, eventually increasing the knowledge of the SI engines science and technology community for building smarter control devices when fueling the IC engines with this very promising H2 fuel, in the endeavor to achieving a clean energy environment transition.

Author Contributions

D.C.R.: Software, Writing-Reviewing and Editing; C.D.R.: Conceptualization, Supervision, Project administration; G.M.K.: Methodology, Writing-Original draft preparation; E.G.G.: Investigation, Formal analysis; D.C.K.: Validation, Data curation. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data is contained within the article.

Acknowledgments

The authors express their appreciation to Prof. F. Moreno and Dr. J. Arroyo (University of Zaragoza, Spain) for providing kindly the experimental data.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Evaluation of the Chemical Exergy Diffusion and Reactive Components

The evaluation of the Edf diffusion component concerns exclusively the species N2, O2, H2O and CO2 that exist also in the environment (cf. composition of reference environment in Table 1). Thus, Edf can be calculated from Equation (10b) after applying first Equation (12) at the restricted and afterwards at the true dead state [24], taking the following form:
E d f = N R m o l T 0 k N 2 , H 2 O O 2 , C O 2 y k ln y k y k 0
with the respective mole fractions y0k of the species N2, O2, H2O and CO2 (existing in the environment) taken from the composition of the reference environment (cf. values in Table 1).
Regarding the reactive Erc = Eox + Erd component, its oxidation component Eox refers to the species existing in the system CO, H2, H and CH4 that can be completely oxidized, whereas its reduction component Erd refers to the species O, OH, NO and N that are able to be reduced to species existing in the environment.
The oxidation and reduction exergy components Eox and Erd are calculated as follows:
E o x = N k C O , H 2 H , C H 4 y k ( μ k 0 μ k 0 )
E r d = N k O , O H N O , N y k ( μ k 0 μ k 0 )
The above two components can be calculated as before from Equation (10b) after applying first Equation (12) at the restricted and afterwards at the true dead state, but a problem arises here because the species to be oxidized CO, H2, H and CH4 as well as the ones to be reduced O, OH, NO and N are not existent in the (reference) environment. That problem for these non-environmental species is circumvented by defining at the true dead state effective chemical potentials, founded on chemical reactions that can result in their transformation into environmental species as described in detail in [28,65].
For the sake of easiness of the current modeling, the reduction exergy component is neglected since it is quite a lot orders (~5) of magnitude less than the Edf or Eox ones [33] and for the same reason the minute adding up of the atomic hydrogen (H) is omitted from the calculation of the oxidation exergy component, which is valid at least as far as applications in engines is concerned. Actually, a more convenient equivalent [65] form of Equation (A.2a) is used here:
E o x = N k C O , H 2 C H 4 y k [ ε ¯ k c h ( T 0 , p 0 ) + R m o l T 0 ln y k ]
where for a combustible substance (symbolized here by subscript f instead of k) that is existent solely at the restricted dead state, its molar chemical exergy is defined as below (and utilized herein):
ε ¯ f c h ( T 0 ,   p 0 ) = g ¯ f ( T 0 ,   p 0 ) μ f 0
The values of the specific chemical exergies to be used in Equation (A.3a) are for the methane (CH4) 52 MJ/kg, the molecular hydrogen (H2) 117 MJ/kg, and the carbon monoxide (CO) 9.83 MJ/kg [65].

Appendix B

Differential Equations of Exergy Balance for Each Zone Discretely and Explication of Terms

  • − Unburned zone
    d E c y l , u d a = d E l , u d a d E w , u d a d I u d a d m b d a b u ( 1 x ) d m b l d a b u =
    = d E l , u d a d E w , u d a d I u d a m d x d a b u ( 1 x ) C b l m ω b u
  • − Burned zone
    d E c y l , b d a = d E l , b d a d E w , b d a d I b d a + d m b d a b u x d m b l d a b b =
    = d E l , b d a d E w , b d a d I b d a + m d x d a b u x C b l m ω b b
The work transfer exergy rate terms in Equations (B.1) and (B.2) take the form:
  • − For the unburned zone
d E w , u d a = ( p p 0 ) d V u d a = ( p p 0 ) d ( m u v u ) d a =
= ( p p 0 ) m ( 1 x ) d v u d a v u d x d a ( 1 x ) v u C b l ω
where the term dvu/da being a function of p and Tu is evaluated as [68]
d v u d a = d v u d T u d T u d a + d v u d p d p d a = v u T u ln v u ln T u d T u d a + v u p ln v u ln p d p d a
  • − For the burned zone
    d E w , b d a = ( p p 0 ) d V d a d E w , u d a
The same way, the heat transfer (loss) exergy rate terms (to the combustion chamber walls) in Equations (B.1) and (B.2) take the form:
  • − For the unburned zone
    d E l , u d a = 1 T 0 T u d Q l u d a = 1 T 0 T u A u h t u ( T u T w ) ω  
  • − For the burned zone
    d E l , b d a = 1 T 0 T b d Q l b d a = 1 T 0 T b A b h t b ( T b T w ) ω  
If all the rest terms are determined plainly in the exergy rate balance Equations (B.1) and (B.2), these can be solved for the irreversibility term dI/da in the corresponding zone. Then, the still missing term to be calculated is the rate of change in the total exergy of the unburned and burned zones content, dEcyl,u/da and dEcyl,b/da respectively (the lhs term of Equations (B.1) and (B.2)), which comprises the Etm and the Ech exergy parts. The incorporation of the chemical term is significant when the irreversibility is computed from the equation expressing the exergy balance, especially when it concerns elevated fuel/air ratios either globally or at some periods in the engine cycle [24].
Thus, either the term dEcyl,u/da or the term dEcyl,b/da on the lhs of Equations (B.1) and (B.2), respectively, is computed by differentiating Equation (10) with respect to CA degree a, yielding the total exergy (rate) part as:
d E c y l d a = d U d a + p 0 d V d a T 0 d S d a d N d a k = 1 ν y k μ k 0 N k = 1 ν d y k d a μ k 0
Similarly, differentiation of Equation (10a) yields the thermomechanical exergy (rate) part. This is virtually the same as Equation (B.7) but with μ0k replaced by μk0. The chemical exergy part (with its diffusion and reactive components) is calculated by using Equations (A.1) and (A.3a).
The expressions of the derivatives of U, V, and S with respect to CA degree a in the above Equation (B.7) in the respective zone, as well as the last two terms comprising the derivatives (having rather involved form) of the mole fractions yk and the total number of moles N are provided in detail in [24].

Appendix C

Combustion Stoichiometry for Hydrogen-Methane Blends and Related Quantities

The stoichiometric (by mass) fuel/air ratio is [50]:
F s = ζ   [ M c ( 1 z ) + ( M h / 2 ) ( 4 2 z ) ] / 28.85 = ζ   [ 12.01 ( 1 z ) + 1.008 ( 4 2 z ) ] / 28.85
where ζ = 0.210/[(1 − z) + 0.25 (4 − 2z)].
The molecular weight of the fuel blend is Mhm = Mh z + Mm (1 − z) where subscripts h, m and hm denote hydrogen, methane and their blend, respectively, so that the LHV denoted here by hflv of the CH4 and H2 blend is (index f denotes fuel):
( h f l v ) h m = [ ( h f l v ) h M h z + ( h f l v ) m M m ( 1 z ) ] / M h m
Besides, if m0 is the cylinder charge trapped mass (index 0 refers to IVC event value), the fuel mass at IVC timing is [50]:
m f 0 = m 0 [ Φ F s ( 1 f r e s ) ] / [ 1 + Φ F s ( 1 f r e s ) ]  
where Φ stands for the EQR and fres for the residual gas mass fraction.
Therefore, the (absolute) chemical energy of fuel at the IVC timing is equal to mf0 · (hflv)hm and the corresponding chemical exergy of fuel equal to mf0 · εfch, where εfch is the specific chemical exergy of the fuel. These two quantities are used for the normalization of the various (absolute) energy or exergy quantities, respectively, as will be discussed in Results and Discussion Section 3.

References

  1. Rakopoulos, C.D.; Giakoumis, E.G. Diesel Engine Transient Operation—Principles of Operation and Simulation Analysis; Springer: London, UK, 2009. [Google Scholar]
  2. Liu, H.; Wen, M.; Yang, H.; Yue, Z.; Yao, M. A review of thermal management system and control strategy for automotive engines. ASCE J. Energy Eng. 2021, 147, 03121001. [Google Scholar] [CrossRef]
  3. Reitz, R.D. Directions in internal combustion engine research. Combust. Flame 2013, 160, 1–8. [Google Scholar] [CrossRef]
  4. Rakopoulos, C.D.; Kyritsis, D.C.; Nikolopoulos, N.P.; Rakopoulos, D.C. Frontiers in engine and power plant combustion technologies: Innovation for a sustainable future. ASCE J. Energy Eng. 2023, 149, 01023001. [Google Scholar] [CrossRef]
  5. Rakopoulos, D.C.; Rakopoulos, C.D.; Kosmadakis, G.M.; Mavropoulos, G.C. Assessing the cyclic variability of combustion and NO emissions in hydrogen-methane fueled HSSI engine via quasi-dimensional modeling under the influence of flame-kernel turbulence and equivalence ratio variation mechanisms. Energy 2024, 288, 129813. [Google Scholar] [CrossRef]
  6. Alkidas, A.C. Combustion advancements in gasoline engines. Energy Convers. Manag. 2007, 48, 2751–2761. [Google Scholar] [CrossRef]
  7. Giakoumis, E.G.; Rakopoulos, C.D.; Dimaratos, A.M.; Rakopoulos, D.C. Exhaust emissions of diesel engines operating under transient conditions with biodiesel fuel blends. Prog. Energy Combust. Sci. 2012, 38, 691–715. [Google Scholar] [CrossRef]
  8. D’Ambrosio, S.; Mancarella, A.; Andrea Manelli, A. Utilization of hydrotreated vegetable oil (HVO) in a Euro 6 dual-loop EGR diesel engine: Behavior as a drop-in fuel and potentialities along calibration parameter sweeps. Energies 2022, 15, 7202. [Google Scholar] [CrossRef]
  9. Sterlepper, S.; Fischer, M.; Classen, J.; Huth, V.; Pischinger, S. Concepts for hydrogen internal combustion engines and their implications on the exhaust gas aftertreatment system. Energies 2021, 14, 8166. [Google Scholar] [CrossRef]
  10. Carlucci, A.P.; Ficarella, A.; Strafella, L.; Trullo, G. Comprehensive characterization of the behavior of a diesel oxidation catalyst used on a dual-fuel engine. ASCE J. Energy Eng. 2020, 146, 04020055. [Google Scholar] [CrossRef]
  11. Rakopoulos, D.C.; Rakopoulos, C.D.; Giakoumis, E.G.; Papagiannakis, R.G. Evaluating oxygenated fuel’s influence on combustion and emissions in diesel engines using a two-zone combustion model. ASCE J. Energy Eng. 2018, 144, 04018046. [Google Scholar] [CrossRef]
  12. Rakopoulos, C.D.; Rakopoulos, D.C.; Kosmadakis, G.M.; Papagiannakis, R.G. Experimental comparative assessment of butanol or ethanol diesel-fuel extenders impact on combustion features, cyclic irregularity, and regulated emissions balance in heavy-duty diesel engine. Energy 2019, 174, 1145–1157. [Google Scholar] [CrossRef]
  13. Rakopoulos, C.D.; Kosmadakis, G.M.; Pariotis, E.G. Evaluation of a combustion model for the simulation of hydrogen spark-ignition engines using a CFD code. Int. J. Hydrogen Energy 2010, 35, 12545–12560. [Google Scholar] [CrossRef]
  14. Verhelst, S.; Wallner, T. Hydrogen-fueled internal combustion engines. Prog. Energy Combust. Sci. 2009, 35, 490–527. [Google Scholar] [CrossRef]
  15. Young, M.B. Cyclic Dispersion in the Homogeneous-Charge Spark-Ignition Engine—A Literature Survey; SAE Paper No. 810020; Society of Automotive Engineers International: Warrendale, PA, USA, 1981. [Google Scholar]
  16. Kosmadakis, G.M.; Rakopoulos, D.C.; Rakopoulos, C.D. Effect of two mechanisms contributing to the cyclic-variability of a methane-hydrogen fueled spark-ignition engine by using a fast CFD methodology. ASCE J. Energy Eng. 2023, 149, 04022058. [Google Scholar] [CrossRef]
  17. Rakopoulos, C.D.; Rakopoulos, D.C.; Kosmadakis, G.M.; Zannis, T.C.; Kyritsis, D.C. Studying the cyclic variability (CCV) of performance and NO and CO emissions in a methane-run high-speed SI engine via quasi-dimensional turbulent combustion modeling and two CCV influencing mechanisms. Energy 2023, 272, 127042. [Google Scholar] [CrossRef]
  18. Ozdor, N.; Dulger, M.; Sher, E. Cyclic Variability in Spark-Ignition Engines A Literature Survey; SAE Paper No. 940987; Society of Automotive Engineers International: Warrendale, PA, USA, 1994. [Google Scholar]
  19. Verhelst, S.; Sheppard, C.G.W. Multi-zone thermodynamic modeling of spark-ignition engine combustion—An overview. Energy Convers. Manag. 2009, 50, 1326–1335. [Google Scholar] [CrossRef]
  20. Gaggioli, R.A.; Paulus, D.M., Jr. Available energy-Part II: Gibbs extended. Trans. ASME J. Energy Resour. Technol. 2002, 124, 110–115. [Google Scholar] [CrossRef]
  21. Dunbar, W.R.; Lior, N.; Gaggioli, R.A. The component equations of energy and exergy. Trans. ASME J. Energy Resour. Technol. 1992, 114, 75–83. [Google Scholar] [CrossRef]
  22. Caton, J.A. A Review of Investigations Using the Second Law of Thermodynamics to Study Internal-Combustion Engines; SAE Paper No. 2000-01-1081; Society of Automotive Engineers International: Warrendale, PA, USA, 2000. [Google Scholar]
  23. Rakopoulos, C.D.; Giakoumis, E.G. Second-law analyses applied to internal combustion engines operation. Prog. Energy Combust. Sci. 2006, 32, 2–47. [Google Scholar] [CrossRef]
  24. Rakopoulos, C.D.; Rakopoulos, D.C.; Kyritsis, D.C.; Andritsakis, E.C.; Mavropoulos, G.C. Exergy evaluation of equivalence ratio, compression ratio and residual gas effects in variable compression ratio spark-ignition engine using quasi-dimensional combustion modeling. Energy 2022, 244, 123080. [Google Scholar] [CrossRef]
  25. Dunbar, W.R.; Lior, N. Sources of combustion irreversibility. Combust. Sci. Technol. 1994, 103, 41–61. [Google Scholar] [CrossRef]
  26. Zhang, W.; Wang, E.; Meng, F.; Zhang, F.; Zhao, C. Closed-loop PI control of an Organic Rankine Cycle for engine exhaust heat recovery. Energies 2020, 13, 3817. [Google Scholar] [CrossRef]
  27. Lior, N.; Rudy, G.L. Second-law analysis of an ideal Otto cycle. Energy Convers. Manag. 1988, 28, 327–334. [Google Scholar] [CrossRef]
  28. Van Gerpen, J.H.; Shapiro, H.N. Second-law analysis of diesel engine combustion. Trans ASME J. Eng. Gas Turbines Power 1990, 112, 129–137. [Google Scholar] [CrossRef]
  29. Shapiro, H.N.; Van Gerpen, J.H. Two Zone Combustion Models for Second Law Analysis of Internal Combustion Engines; SAE Paper No. 890823; Society of Automotive Engineers International: Warrendale, PA, USA, 1989. [Google Scholar]
  30. Caton, J.A. Operating Characteristics of a Spark-Ignition Engine Using the Second Law of Thermodynamics: Effects of Speed and Load; SAE Paper No. 2000-01-0952; Society of Automotive Engineers International: Warrendale, PA, USA, 2000. [Google Scholar]
  31. Caton, J.A. A Cycle Simulation Including the Second Law of Thermodynamics for a Spark-Ignition Engine: Implications of the Use of Multiple-Zones for Combustion; SAE Paper No. 2002-01-0007; Society of Automotive Engineers International: Warrendale, PA, USA, 2002. [Google Scholar]
  32. Rakopoulos, C.D. Evaluation of a spark ignition engine cycle using first and second law analysis techniques. Energy Convers. Manage 1993, 34, 1299–1314. [Google Scholar] [CrossRef]
  33. Rakopoulos, C.D.; Michos, C.N.; Giakoumis, E.G. Studying the effects of hydrogen addition on the second-law balance of a biogas-fuelled spark-ignition engine by use of a quasi-dimensional multi-zone combustion model. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 2008, 222, 2249–2268. [Google Scholar] [CrossRef]
  34. Rakopoulos, C.D.; Kyritsis, D.C. Comparative second-law analysis of internal combustion engine operation for methane, methanol and dodecane fuels. Energy 2001, 26, 705–722. [Google Scholar] [CrossRef]
  35. Rakopoulos, C.D.; Andritsakis, E.C. DI and IDI diesel engines combustion irreversibility analysis. In Proceedings of the ASME-WA Meeting, New Orleans, LA, USA, 28 November–3 December 1993; Volume 30, pp. 17–32. [Google Scholar]
  36. Rakopoulos, D.C.; Rakopoulos, C.D.; Kosmadakis, G.M.; Giakoumis, E.G. Exergy assessment of combustion and EGR and load effects in DI diesel engine using comprehensive two-zone modeling. Energy 2020, 202, 117685. [Google Scholar] [CrossRef]
  37. Rakopoulos, C.D.; Michos, C.N. Generation of combustion irreversibilities in a spark ignition engine under biogas–hydrogen mixtures fueling. Int. J. Hydrogen Energy 2009, 34, 4422–4437. [Google Scholar] [CrossRef]
  38. Rakopoulos, C.D.; Kyritsis, D.C. Hydrogen enrichment effects on the second-law analysis of natural and landfill gas combustion in engine cylinders. Int. J. Hydrogen Energy 2006, 31, 1384–1393. [Google Scholar] [CrossRef]
  39. Ozcan, H. Hydrogen enrichment effects on the second-law analysis of a lean burn natural gas engine. Int. J. Hydrogen Energy 2010, 35, 1443–1452. [Google Scholar] [CrossRef]
  40. Ayad, S.M.M.E.; Belchior, C.R.P.; Sodre, J.R. Exergoeconomic analysis of a lean burn engine operating with ethanol and hydrogen addition. Int. J. Hydrogen Energy 2024, 61, 387–394. [Google Scholar] [CrossRef]
  41. Wang, P.; Li, Y.; Duan, X.; Liu, J.; Wang, S.; Zou, P.; Fang, Y. Experimental investigation of the effects of CR, hydrogen addition strategies on performance, energy and exergy characteristics of a heavy-duty NGSI engine fueled with 99% methane content. Fuel 2020, 259, 116212. [Google Scholar] [CrossRef]
  42. Qiao, J.; Li, Y.; Wang, S.; Wang, P.; Liu, J. Experimental investigation and numerical assessment the effects of EGR and hydrogen addition strategies on performance, energy and exergy characteristics of a heavy-duty lean-burn NGSI engine. Fuel 2020, 279, 117824. [Google Scholar] [CrossRef]
  43. Yu, X.; Li, D.; Sun, P.; Li, G.; Yang, S.; Yao, C. Energy and exergy analysis of a combined injection engine using gasoline port injection coupled with gasoline or hydrogen direct injection under lean-burn conditions. Int. J. Hydrogen Energy 2021, 46, 8253–8268. [Google Scholar] [CrossRef]
  44. Sun, P.; Liu, Z.; Yu, X.; Yao, C.; Guo, Z.; Yang, S. Experimental study on heat and exergy balance of dual-fuel combined injection engine with hydrogen and gasoline. Int. J. Hydrogen Energy 2019, 44, 22301–22315. [Google Scholar] [CrossRef]
  45. Dhyani, V.; Subramanian, K.A. Experimental based comparative exergy analysis of a multi-cylinder spark ignition engine fuelled with different gaseous (CNG, HCNG, and hydrogen) fuels. Int. J. Hydrogen Energy 2019, 44, 20440–20451. [Google Scholar] [CrossRef]
  46. Kosmadakis, G.M.; Rakopoulos, D.C.; Arroyo, J.; Moreno, F.; Munoz, M.; Rakopoulos, C.D. CFD-based method with an improved ignition model for estimating cyclic variability in a spark-ignition engine fueled with methane. Energy Convers. Manag. 2018, 174, 769–778. [Google Scholar] [CrossRef]
  47. Rakopoulos, D.C.; Rakopoulos, C.D.; Giakoumis, E.G.; Kosmadakis, G.M. Numerical and experimental study by quasi-dimensional modeling of combustion and emissions in variable compression ratio high-speed spark-ignition engine. ASCE J. Energy Eng. 2021, 147, 04021032. [Google Scholar] [CrossRef]
  48. Moreno, F.; Arroyo, J.; Munoz, M.; Monne, C. Combustion analysis of a spark ignition engine fueled with gaseous blends containing hydrogen. Int. J. Hydrogen Energy 2012, 37, 13564–13573. [Google Scholar] [CrossRef]
  49. Moreno, F.; Munoz, M.; Arroyo, J.; Magen, O.; Monne, C.; Suelves, I. Efficiency and emissions in a vehicle spark ignition engine fueled with hydrogen and methane blends. Int. J. Hydrogen Energy 2012, 37, 11495–11503. [Google Scholar] [CrossRef]
  50. Ferguson, C.R. Internal Combustion Engines; Wiley: New York, NY, USA, 1986. [Google Scholar]
  51. Heywood, J.B. Internal Combustion Engine Fundamentals; McGraw-Hill: New York, NY, USA, 1988. [Google Scholar]
  52. Annand, W.J.D. Heat transfer in the cylinders of reciprocating internal combustion engines. Proc. Inst. Mech. Eng. 1963, 177, 973–990. [Google Scholar]
  53. Lavoie, G.A.; Heywood, J.B.; Keck, J.C. Experimental and theoretical study of nitric oxide formation in internal combustion engines. Combust. Sci. Technol. 1970, 1, 313–326. [Google Scholar] [CrossRef]
  54. Kosmadakis, G.M.; Rakopoulos, D.C.; Rakopoulos, C.D. Investigation of nitric oxide emission mechanisms in a SI engine fueled with methane/hydrogen blends using a research CFD code. Int. J. Hydrogen Energy 2015, 40, 15088–15104. [Google Scholar] [CrossRef]
  55. Blizard, N.C.; Keck, J.C. Experimental and Theoretical Investigation of Turbulent Burning Model for Internal Combustion Engines; SAE Paper No. 740191; Society of Automotive Engineers International: Warrendale, PA, USA, 1974. [Google Scholar]
  56. Tabaczynski, R.J.; Trinker, F.H.; Shannon, B.A.S. Further refinement and validation of a turbulent flame propagation model for spark-ignition engines. Combust. Flame 1980, 39, 111–121. [Google Scholar] [CrossRef]
  57. Beretta, G.P.; Rashidi, M.; Keck, J.C. Turbulent flame propagation and combustion in spark ignition engines. Comb. Flame 1983, 52, 217–245. [Google Scholar] [CrossRef]
  58. Ouimette, P.; Seers, P. Numerical comparison of premixed laminar flame velocity of methane and wood syngas. Fuel 2009, 88, 528–533. [Google Scholar] [CrossRef]
  59. Verhelst, S.; Sierens, R. A quasi-dimensional model for the power cycle of a hydrogen-fuelled ICE. Int. J. Hydrogen Energy 2007, 32, 3545–3554. [Google Scholar] [CrossRef]
  60. Rhodes, D.B.; Keck, J.C. Laminar Burning Speeds Measurements of Indolene-Air Diluent Mixtures at High Pressures and Temperatures; SAE Paper No. 850047; Society of Automotive Engineers International: Warrendale, PA, USA, 1985. [Google Scholar]
  61. Di Sarli, V.; Di Benedetto, A. Laminar burning velocity of hydrogen-methane/premixed flames. Int. J. Hydrogen Energy 2007, 32, 637–646. [Google Scholar] [CrossRef]
  62. Ji, C.; Liu, X.; Wang, S.; Gao, B.; Yang, J. Development and validation of a laminar flame speed correlation for the CFD simulation of hydrogen-enriched gasoline engines. Int. J. Hydrogen Energy 2013, 38, 1997–2006. [Google Scholar] [CrossRef]
  63. El-Sherif, S.A. Control of emissions by gaseous additives in methane–air and carbon monoxide–air flames. Fuel 2000, 79, 567–575. [Google Scholar] [CrossRef]
  64. Annand, W.J.D. Geometry of spherical flame propagation in a disc-shaped combustion chamber. J. Mech. Eng. Sci. 1970, 12, 146–149. [Google Scholar] [CrossRef]
  65. Moran, M.J. Availability Analysis: A Guide to Efficient Energy Use; Prentice-Hall: Upper Saddle River, NJ, USA, 1982. [Google Scholar]
  66. Bejan, A.; Tsatsaronis, G.; Moran, M. Thermal Design and Optimization; Wiley: New York, NY, USA, 1996. [Google Scholar]
  67. Moran, M.J.; Shapiro, H.N. Fundamentals of Engineering Thermodynamics; Wiley: New York, NY, USA, 2000. [Google Scholar]
  68. Lewis, G.N.; Randall, M. Thermodynamics; McGraw-Hill: New York, NY, USA, 1961. [Google Scholar]
  69. Kosmadakis, G.M.; Rakopoulos, D.C.; Rakopoulos, C.D. Assessing the cyclic-variability of spark-ignition engine running on methane-hydrogen blends with high hydrogen content of up to 50%. Int. J. Hydrogen Energy 2021, 46, 17955–17968. [Google Scholar] [CrossRef]
  70. Turns, S.R. An Introduction to Combustion—Concepts and Applications; McGraw-Hill: New York, NY, USA, 1996. [Google Scholar]
  71. Fox, J.W.; Cheng, W.K.; Heywood, J.B. A Model for Predicting Residual Gas Fraction in Spark-Ignition Engines; SAE Paper No. 931025; Society of Automotive Engineers International: Warrendale, PA, USA, 1993. [Google Scholar]
  72. Rakopoulos, C.D.; Mavropoulos, G.C. Experimental instantaneous heat fluxes in the cylinder head and exhaust manifold of an air-cooled diesel engine. Energy Convers. Manag. 2000, 41, 1265–1281. [Google Scholar] [CrossRef]
  73. Rakopoulos, C.D.; Giakoumis, E.G.; Rakopoulos, D.C. Study of the short-term cylinder wall temperature oscillations during transient operation of a turbocharged diesel engine with various insulation schemes. Int. J. Engine Res. 2008, 9, 177–193. [Google Scholar] [CrossRef]
  74. Taylor, C.F. The Internal-Combustion Engine in Theory and Practice; MIT Press: Cambridge, MA, USA, 1985; Volume II. [Google Scholar]
  75. Stone, R. Introduction to Internal Combustion Engines, 2nd ed.; MacMillan: London, UK, 1992. [Google Scholar]
  76. Kosmadakis, G.M.; Rakopoulos, C.D.; Demuynck, J.; De Paepe, M.; Verhelst, S. CFD modeling and experimental study of combustion and nitric oxide emissions in hydrogen-fueled spark-ignition engine operating in a very wide range of EGR rates. Int. J. Hydrogen Energy 2012, 37, 10917–10934. [Google Scholar] [CrossRef]
  77. Irimescu, A.; Vaglieco, B.M.; Merola, S.S.; Zollo, V.; De Marinis, R. Conversion of a small-size passenger car to hydrogen fueling: 0D/1D simulation of EGR and related flow limitations. Appl. Sci. 2024, 14, 844. [Google Scholar] [CrossRef]
  78. Shi, C.; Chai, S.; Wang, H.; Ji, C.; Ge, Y.; Di, L. An insight into direct water injection applied on the hydrogen-enriched rotary engine. Fuel 2023, 339, 127352. [Google Scholar] [CrossRef]
  79. Bao, J.; Qu, P.; Wang, H.; Zhou, C.; Zhang, L.; Shi, C. Implementation of various bowl designs in an HPDI natural gas engine focused on performance and pollutant emissions. Chemosphere 2022, 303, 135275. [Google Scholar] [CrossRef]
Figure 1. Calculated and experimental CP and calculated MFB vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
Figure 1. Calculated and experimental CP and calculated MFB vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
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Figure 2. Unburned zone, burned zone and mean-state temperatures and LFS vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
Figure 2. Unburned zone, burned zone and mean-state temperatures and LFS vs. CA diagrams, for the engine fueling with all hydrogen z values, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
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Figure 3. Absolute exergy terms vs. crank angle diagrams of the heat loss transfer, work transfer, cylinder thermomechanical, cylinder chemical, cylinder total, irreversibility, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.70, for each zone discretely (a), and for the sum content of both zones (b).
Figure 3. Absolute exergy terms vs. crank angle diagrams of the heat loss transfer, work transfer, cylinder thermomechanical, cylinder chemical, cylinder total, irreversibility, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.70, for each zone discretely (a), and for the sum content of both zones (b).
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Figure 4. For each zone discretely and for the sum content of both zones, entropy terms vs. crank angle diagrams of the heat loss transfer, cylinder content, generation, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.80.
Figure 4. For each zone discretely and for the sum content of both zones, entropy terms vs. crank angle diagrams of the heat loss transfer, cylinder content, generation, blow-by loss (only for the sum content of both zones) and flow between the zones, for the engine fueling with hydrogen vol. fraction 0.50 and functioning at EQR = 0.80.
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Figure 5. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of the heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00.
Figure 5. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of the heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00.
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Figure 6. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of the heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 0.80.
Figure 6. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of the heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 0.80.
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Figure 7. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.10, 0.30 and 0.50, and functioning at EQR = 0.70.
Figure 7. For the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the cylinder thermomechanical, cylinder chemical and cylinder total (a), and of heat loss transfer, work transfer, irreversibility and flow between the two zones (b), for the engine fueling with hydrogen vol. fractions 0.10, 0.30 and 0.50, and functioning at EQR = 0.70.
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Figure 8. For each zone discretely and for the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the heat loss and work transfers, for the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 0.70.
Figure 8. For each zone discretely and for the sum content of both zones, normalized exergy terms vs. crank angle diagrams of the heat loss and work transfers, for the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 0.70.
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Figure 9. Burned zone normalized chemical exergy terms vs. crank angle diagrams of diffusion, reactive, and diffusion plus reactive, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
Figure 9. Burned zone normalized chemical exergy terms vs. crank angle diagrams of diffusion, reactive, and diffusion plus reactive, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
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Figure 10. Carbon monoxide concentration (a) and hydrogen concentration (b) vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70.
Figure 10. Carbon monoxide concentration (a) and hydrogen concentration (b) vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70.
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Figure 11. Ratio of the chemical exergy to the total exergy at EVO timing against EQR diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50.
Figure 11. Ratio of the chemical exergy to the total exergy at EVO timing against EQR diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50.
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Figure 12. Burned zone mass fraction burned rate and normalized irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 0.80.
Figure 12. Burned zone mass fraction burned rate and normalized irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 0.80.
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Figure 13. Burned zone mass fraction burned rate and normalized irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 1.00 or 0.70.
Figure 13. Burned zone mass fraction burned rate and normalized irreversibility rate vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10 and 0.50, and functioning at EQR = 1.00 or 0.70.
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Figure 14. Burned zone normalized irreversibility and flame front radius vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10, 0.30 and 0.50, and functioning at EQR = 0.80 or 0.70.
Figure 14. Burned zone normalized irreversibility and flame front radius vs. crank angle diagrams, for the engine fueling with hydrogen vol. fractions 0.10, 0.30 and 0.50, and functioning at EQR = 0.80 or 0.70.
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Figure 15. Normalized irreversibility and nitric oxide concentration at EVO event against peak burned zone temperature diagrams (a), and normalized irreversibility against nitric oxide concentration at EVO event diagram (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70. In subfigure (a), equal hydrogen vol. fraction values are connected by (light blue) dashed lines.
Figure 15. Normalized irreversibility and nitric oxide concentration at EVO event against peak burned zone temperature diagrams (a), and normalized irreversibility against nitric oxide concentration at EVO event diagram (b), for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70. In subfigure (a), equal hydrogen vol. fraction values are connected by (light blue) dashed lines.
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Figure 16. Distribution balance diagrams of the normalized energy or exergy terms for the closed cycle of the engine against the engine fueling hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, functioned at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
Figure 16. Distribution balance diagrams of the normalized energy or exergy terms for the closed cycle of the engine against the engine fueling hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, functioned at EQR values of either 1.00 (a), or 0.80 (b), or 0.70 (c).
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Figure 17. Norm. irreversibility against norm. work transfer exergy for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70.
Figure 17. Norm. irreversibility against norm. work transfer exergy for the engine fueling with hydrogen vol. fractions 0.00, 0.10, 0.30 and 0.50, and functioning at EQR = 1.00, 0.80 and 0.70.
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Table 1. Pressure, temperature, and composition of standard reference environment.
Table 1. Pressure, temperature, and composition of standard reference environment.
Pressure p0 = 0.101325 MPaTemperature T0 = 298.15 K
SpeciesMolar (vol.) Composition
N2 Molecular Nitrogen0.7567
O2 Molecular Oxygen0.2035
H2O Water (vapor)0.0303
CO2 Carbon Dioxide0.0003
Rest trace gases, as e.g., Argon0.0092
Table 2. Chief properties of the methane and hydrogen.
Table 2. Chief properties of the methane and hydrogen.
Properties of Fuels for Combustion in AirMethaneHydrogen
Molecular weight (kg/kmol)16.0432.015
Density at 25 °C and 1 atm (kg/m3)0.6560.082
Octane number120130
Stoichiometric air-fuel ratio by vol.9.522.38
Stoichiometric air-fuel ratio by mass34.5017.25
Lower heating value per unit mass of fuel (MJ/kg)50.00120.00
Fuel specific chemical exergy (MJ/kg)52.00117.00
Lower heating value per Nm3 of fuel (kJ/Nm3)35,71410,713
Lower heating value per Nm3 of stoich. fuel-air mixture (kJ/Nm3)33843173
EQR Lean flammability limit0.460.14
EQR Rich flammability limit 1.642.54
Laminar flame speed (LFS) at 25 °C and 1 atm (m/s)0.402.10
Mass diffusivity in air at 0 °C and 1 atm (cm2/s)0.160.61
Minimum ignition energy at EQR = 1.0 (10−5 J)33.02.0
Quenching distance at EQR = 1.0 (mm)2.500.64
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Rakopoulos, D.C.; Rakopoulos, C.D.; Kosmadakis, G.M.; Giakoumis, E.G.; Kyritsis, D.C. Exergy Analysis in Highly Hydrogen-Enriched Methane Fueled Spark-Ignition Engine at Diverse Equivalence Ratios via Two-Zone Quasi-Dimensional Modeling. Energies 2024, 17, 3964. https://doi.org/10.3390/en17163964

AMA Style

Rakopoulos DC, Rakopoulos CD, Kosmadakis GM, Giakoumis EG, Kyritsis DC. Exergy Analysis in Highly Hydrogen-Enriched Methane Fueled Spark-Ignition Engine at Diverse Equivalence Ratios via Two-Zone Quasi-Dimensional Modeling. Energies. 2024; 17(16):3964. https://doi.org/10.3390/en17163964

Chicago/Turabian Style

Rakopoulos, Dimitrios C., Constantine D. Rakopoulos, George M. Kosmadakis, Evangelos G. Giakoumis, and Dimitrios C. Kyritsis. 2024. "Exergy Analysis in Highly Hydrogen-Enriched Methane Fueled Spark-Ignition Engine at Diverse Equivalence Ratios via Two-Zone Quasi-Dimensional Modeling" Energies 17, no. 16: 3964. https://doi.org/10.3390/en17163964

APA Style

Rakopoulos, D. C., Rakopoulos, C. D., Kosmadakis, G. M., Giakoumis, E. G., & Kyritsis, D. C. (2024). Exergy Analysis in Highly Hydrogen-Enriched Methane Fueled Spark-Ignition Engine at Diverse Equivalence Ratios via Two-Zone Quasi-Dimensional Modeling. Energies, 17(16), 3964. https://doi.org/10.3390/en17163964

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