inventions

Article The Thermodynamics of Internal Combustion Engines: Examples of Insights

Jerald A. Caton Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA; [email protected]; Tel.: +1-979-845-4705



Received: 27 April 2018; Accepted: 16 May 2018; Published: 22 May 2018


Abstract: A major goal of the development of internal combustion (IC) engines continues to be higher performance and efficiencies. A major aspect of achieving higher performance and efficiencies is based on fundamental thermodynamics. Both the first and second laws of thermodynamics provide strategies for and limits to the thermal efficiencies of engines. The current work provides three examples of the insights that thermodynamics provides to the performance and efficiencies of an IC engine. The first example evaluates low heat rejection engine concepts, and, based on thermodynamics, demonstrates the difficulty of this concept for increasing efficiencies. The second example compares and contrasts the thermodynamics associated with external and internal exhaust gas dilution. Finally, the third example starts with a discussion of the Otto cycle analysis and explains why this is an incorrect model for the IC engine. An important thermodynamic property that is responsible for many of the observed effects is specific heat.

Keywords: thermodynamics; exergy; IC engines; combustion; efficiency

1. Introduction Internal combustion (IC) engines are prevalent in a wide range of applications throughout the world. Applications for IC engines include small utility (e.g., garden equipment such as edgers and trimmers), recreation, agriculture, construction, light-duty vehicles, heavy-duty vehicles, marine, and electric power generation. As one example, the number of vehicles and their associated engines in the world is estimated at 1.2 billion, and is estimated to be over 2 billion by 2035. For such a complex device, these are exceptional numbers. The reasons for the success of the IC engine are well documented (e.g., [1–3]). These reasons include relatively low initial cost, high power density, reasonable efficiencies, ability to meet emission standards, and being well matched to available fuels. This latter reason is particularly important. Since liquid hydrocarbon fuels possess high energy densities, the IC engine is able to provide a continual operation with minimum refueling needs. Typical refueling times for many vehicles are of the order of ten minutes or so. These features are particularly important in the transportation sector. Although the popular press occasionally publishes opinions on the demise of the IC engine (e.g., [4]), the IC engine remains a successful device. Alternative power plants continue to be examined, but none have managed to displace the IC engine. Future improvements to fuel cells and batteries will be required, such that these alternatives will be acceptable to the consumer. For these reasons, the IC engine is expected to be the dominant power plant for many of the above applications for many more decades. Finally, when it comes to transportation, IC engines should continue to be the dominant technology for commercial marine vessels, large trucks, and aircraft for the foreseeable future. While there are possible alternatives, none offer the same combination of low cost and high energy density found with a simple tank of fuel and an IC engine.

Inventions 2018, 3, 33; doi:10.3390/inventions3020033 www.mdpi.com/journal/inventions Inventions 2018, 3, 33 2 of 30

One of the major current goals of IC engine development is to achieve higher performance and thermal efficiencies. Perhaps the most important aspects of the performance and efficiency of engines is related to the fundamental thermodynamics. An engine’s performance and efficiency is limited by the first and second laws of thermodynamics. To provide quantitative examples of the thermodynamics of engines, a cycle simulation is used in this work. This cycle simulation incorporates all features of the first and second laws of thermodynamics. Although many examples exist of the importance of thermodynamics relative to engine efficiency and performance, this paper will select three examples to illustrate the insights available. These three examples are the thermodynamics of low heat rejection engines, the thermodynamics of exhaust gas dilution, and the thermodynamics of the ideal Otto cycle. This paper includes subsections on the laws of thermodynamics and a description of the engine cycle simulation. The paper ends with a summary, and a list of conclusions and findings.

2. Brief Review of the Laws of Thermodynamics The primary laws of thermodynamics that are relevant to this discussion are the first and second laws. These laws are well described in numerous thermodynamic (e.g., [5,6]) and engine text books [1,2,7]. The following is a brief summary. The first law of thermodynamics is often attributed to James Joule and Julius Mayer [5]. In the early 1840s, they individually recognized that heat transfer and work were different forms of the same quantity. This observation led quickly to the idea that energy remained constant, but could change form. The first law of thermodynamics is often called the conservation of energy law. Basically, energy cannot be created or destroyed. This means that for a control volume, the change of energy must be equal to the net result of all inputs and outputs of energy. The second law of thermodynamics is perhaps a much richer and more complex law than the first law. This law is often attributed to the original work of Carnot [8] in 1824. The second law is based on a number of related physical observations that have a wide range of implications with respect to engineering design and operation of thermal systems. For example, the second law can be used to determine the direction of processes, to establish the conditions of equilibrium, to specify the maximum possible performance of thermal systems, and to identify those aspects of processes that are detrimental to overall performance. Because of this large number of related observations, there is no simple, single statement that captures the full extent of the second law of thermodynamics. Although thermodynamic text books commonly use the Kelvin-Planck and Clausius observations as statements of the second law, these are but two aspects of the second law. The second law is basically a set of observations that share a common fundamental principle that relates to the quality of energy. As described below, one way to quantify this quality of energy is to introduce a property (exergy or availability) that captures this concept. This will be described in the following subsection on the second law.

3. Description of the Engine Cycle Simulation

3.1. Basics of the Simulation The engine cycle simulation used in this work is a zero-dimension formulation that includes all four strokes, uses three-zones for the combustion process, and requires a number of empirical sub-models. The details of this cycle simulation are available in a book [9] and in numerous technical articles (e.g., [10–13]). The following is a brief description of the simulation. This will be followed by subsections on the required items for solutions, descriptions of the engine and operating conditions, and strategies for the following computations. Figure1 is a schematic of the control volume for the three-zone simulation. The three-zones are the unburned zone, the adiabatic core, and the boundary layer. The latter two regions comprise the burned zone. Cylinder heat transfer is based on one of several heat transfer correlations (described Inventions 2018, 3, 33 3 of 30 below). The cylinder heat transfer is allocated to the unburned zone and the boundary layer (of the burnedInventions zone) based 2018, 3, x on FOR the PEER temperatures REVIEW and volumes of the zones [9]. 3 of 30

Figure 1. Schematic of the three-zone configuration of the cycle simulation. dashed lines represent Figure 1. Schematic of the three-zone configuration of the cycle simulation. dashed lines represent control volumes and arrows denote energy transfers and designate two of the zones. control volumes and arrows denote energy transfers and designate two of the zones. 3.2. Formulations 3.2. FormulationsThe first law of thermodynamics is used to derive expressions for the time (crank angle) derivatives of the pressure, the three temperatures, the three volumes, and the three masses in terms The first law of thermodynamics is used to derive expressions for the time (crank angle) of engine design variables, operating parameters, and sub-model constants. For this development, derivativesonly ofsteady the state pressure, operation the is three considered. temperatures, The fuel is the assumed three to volumes, be completely and vaporized the three and masses mixed in terms of enginewith design the incoming variables, air. Any operating blow-by parameters,is neglected, and and combustion sub-model is assumed constants. 100% For complete this development, (Note only steadythat due state to operationthe Wiebe function is considered. used for combustion The fuel is a assumed small amount to be (0.7%) completely of fuel is vaporizednot consumed. and). mixed with the incomingThe set of air. ordinary Any blow-bydifferential is equations neglected, is solved and combustionnumerically as is a assumedfunction of 100%crank angle. complete The (Note that dueitems to the needed Wiebe for function the solutions used include for combustion the thermodynamic a small properties, amount (0.7%) piston of-cylinder fuel is kinemat not consumed).ics, combustion process descriptions, cylinder heat transfer, mass flow rates, and algorithms for the The set of ordinary differential equations is solved numerically as a function of crank angle. mechanical friction. Each of these is briefly described next. The items needed for the solutions include the thermodynamic properties, piston-cylinder kinematics, combustion3.3. Items process Needed descriptions, for Solutions cylinder heat transfer, mass flow rates, and algorithms for the mechanical friction. Each of these is briefly described next. 3.3.1. Properties 3.3. Items NeededThe properties for Solutions of the working fluid are based on air, fuel vapor, and combustion properties. For the thermodynamic conditions of IC engines, the working fluid may be assumed to obey the ideal 3.3.1. Propertiesgas model. The concentrations of combustion products may be “frozen” for the lower temperatures, or based on instantaneous (shifting) chemical equilibrium for the higher temperatures. The unburned Themixture properties during ofthe the compression working stroke fluid prior are basedto combustion on air, consists fuel vapor, of the andinlet mixture combustion of air, fuel properties. For the thermodynamicvapor, exhaust gas conditions recirculation of (if IC specified), engines, and the theworking residua fluidl gases may (combustion be assumed products). to obey The the ideal gas model.burned The gases concentrations are determined of combustion from the stoichiometry products may and be either “frozen” the frozenfor the or lower equilibrium temperatures, or basedcomposition. on instantaneous Once the(shifting) composition chemical of the gas equilibrium mixtures is known, for the the higher thermodynamic temperatures. properties The may unburned mixturebe during determined. the Properties compression for each stroke species prior are determined to combustion from polynomial consists curve of the-fits inletto the property mixture of air, data for the species [1,9]. fuel vapor, exhaust gas recirculation (if specified), and the residual gases (combustion products). The burned3.3.2. Kinematics gases are determined from the stoichiometry and either the frozen or equilibrium composition. Once the composition of the gas mixtures is known, the thermodynamic properties may The kinematics and geometric parameters are based on standard reciprocating engines [9]. The be determined.required inputs Properties include for the each cylinder species bore, are stroke, determined connecting from rod length, polynomial and compression curve-fits ratio. to the With property data forthese the speciesinputs, the [1, 9instantaneous]. cylinder volume, the rate of change of the cylinder volume, and the instantaneous surface area may be determined. 3.3.2. Kinematics The kinematics and geometric parameters are based on standard reciprocating engines [9]. The required inputs include the cylinder bore, stroke, connecting rod length, and compression ratio. With these inputs, the instantaneous cylinder volume, the rate of change of the cylinder volume, and the instantaneous surface area may be determined. Inventions 2018, 3, 33 4 of 30

3.3.3. Combustion For the version of the cycle simulation used here, the mass fraction of the burned fuel as a function of crank angle is needed. For this work, this is supplied by a Wiebe function [14].

 m+1 xb = 1 − exp −ay (1) in which xb is the mass fraction of fuel burned, and a and m are constants that are selected to provide an appropriate burn curve. For this work, as suggested by Heywood [1], a = 5.0 and m = 2.0. In this equation, y represents the non-dimensional progress variable

θ − θ y = o (2) θb in which θ is the instantaneous crank angle, θo is the start of combustion, and θb is the combustion duration. This provides a good representation of the actual combustion process. At the start of combustion, the mass fraction burned increases slowly, which is representative of the slow ignition process. Then, the mass fraction burned increases more rapidly, representing the rapid flame propagation during the mid-parts of the combustion process. Finally, at the end of combustion, the mass fraction burned slows due to lack of reactant material and greater heat transfer as the flame nears the combustion chamber walls. The burn duration (θb) for this study is defined as the 0–100% duration. Another common interval is the 10–90% duration. These two definitions of the burn duration are related. For the Wiebe constants used in this study, the 10–90% duration is about one-half of the 0–100% duration.

3.3.4. Cylinder Heat Transfer Cylinder heat transfer is a complex phenomenon that continues to be studied. In the current work, the cylinder heat transfer is approximated by empirical expressions from the literature for the convective heat transfer, which are given by

.
Q = hA Twall − Tgas (3) in which h is the instantaneous heat transfer coefficient, A is the instantaneous cylinder surface area, Twall is the cylinder wall temperature, and Tgas is the one-zone gas temperature. Numerous correlations are available for the heat transfer coefficient (e.g., [15,16]). For the work reported here, the correlation from Hohenberg [16] is used. For convenience, the heat transfer results will be reported as positive from the gases to the walls.

3.3.5. Mass Flow Rates The mass flows are estimated from standard quasi-steady, one-dimensional flow equations [1,9]. An empirical discharge coefficient is used to account for real flow effects. At each calculation step, the flow conditions are examined to determine if the flow is sonic or sub-sonic. Sonic (also known as choked or critical) flow may exist if the upstream pressure is sufficiently high relative to the downstream pressure. In addition to the flow equations, the details of the valve operation are needed to estimate the flow open area.

3.3.6. Mechanical Friction To determine brake values for the performance and efficiency determinations, values for the mechanical friction are needed. Mechanical friction is estimated using a series of algorithms that has been developed for automotive engines [17]. These algorithms provide friction values for groups of Inventions 2018, 3, 33 5 of 30 components: rubbing (crankshaft, bearings, pistons, valve train, etc.), pumping, and auxiliaries (oil and water pumps and alternators).

3.4. Description of the Engine All the results reported below are for the same engine: a 5.7 L, V-8 configuration with a bore and stroke of 101.6 and 88.4 mm, respectively. Most of the following results, however, are not too sensitive to the actual engine. Table1 lists some of the engine specifications, and Table2 lists some of the parameters (and “how obtained”) that are needed to complete the computations. Note that the open and close crank angles for the valve events represent a valve lift of zero.

Table 1. Engine Specifications.

Item Value Engine Speed (rpm) 2000 Bore (mm) 101.6 Stroke (mm) 88.4 Crank Rad/Con Rod Ratio 0.3 Inlet Valves Diameter (mm) 50.8 Max Lift (mm) 10.0 Open (◦CA aTDC) 357 Close (◦CA aTDC) −136 Exhaust Valves Diameter (mm) 39.6 Max Lift (mm) 10.0 Open (◦CA aTDC) 116 Close (◦CA aTDC) 371 Valve Overlap (degrees) 14◦ A/V (m−1) at TDC 469

As noted in Table2, the exhaust pressure is set as 10 kPa greater than the inlet pressure. This is an approximation, since this difference is a function of the exhaust system and whether superchargers or turbochargers are used.

Table 2. Common Engine and Fuel Input Parameters.

Item Value Used How Obtained Fuel Isooctane input AFstoich 15.13 for isooctane [1] Inlet (air-fuel) Temperature 319.3 K Input Compression Ratio varies input Equivalence Ratio varies Input Inlet pressure (kPa) varies Input Exhaust Pressure (kPa) pin + 10 computed Fuel LHV (kJ/kg) 44,400 for isooctane [1] Fuel Exergy (kJ/kg) 45,670 for isooctane [1] Wiebe constant “m” 2.0 [1] Wiebe constant “a” 5.0 [1] Heat Transfer correlation Hohenberg Input [16]

A base case operating condition has been selected for the following study. This will be called case 1, and consists of a bmep of 900 kPa, and an engine speed of 2000 rpm. Other parameters for case 1 are a compression ratio of 10, stoichiometric mixtures, and a burn duration of 50 ◦CA. The fuel is isooctane, but again, the results are fairly independent of the actual fuel. Table3 lists some of major items that define case 1. Inventions 2018, 3, 33 6 of 30

Table 3. Description of Case 1.

Item Value bmep 900 rpm 2000 CR 10.0 ϕ 1.0 ◦ θb ( CA) 50 Twall (K) 450

In general, the following results are based on a similar methodology and are subject to a similar set of constraints. First, combustion is considered successful and proceeds according to the Wiebe function. The advantage of this approach is that the role of the thermodynamics is clear. The disadvantage is that items such as combustion stability, cycle-to-cycle variations, and knock or other combustion issues are not considered. Second, the general methodology of the following studies is to vary one parameter at a time. This provides a consistent and unambiguous examination of the various effects. Third, the combustion timing is adjusted to provide the maximum brake torque (MBT). Consistent with the above, combustion timing was adjusted for MBT with no concern for knock or other abnormal combustion behavior.

3.5. Second Law Results from the second law of thermodynamics provide additional insights on engine performance that are not available from the first law. The second law leads to the property entropy that is central to using the second law to evaluate engine operation. As mentioned above, an important thermodynamic property related to the second law is exergy. Exergy is also known as availability, available energy, and essergy (essence of energy). Exergy, a property of the system and the environment, is a measure of the maximum useful work that a given system may produce, as the system is allowed to reversibly transition to a state that is in equilibrium with the environment. The energy of a system may be divided into a part that is available to produce work (the exergy) and a part that is not able to produce work (the unavailable energy). In addition, unlike energy, exergy may be destroyed by irreversible processes. One of the key parts of the second law analyses for engines is to determine this exergy destruction. Once the thermodynamic properties (including entropy) are known for a given cycle, the exergy may be computed. The system specific exergy is given by

b = (u − uo) + (po(v − vo)) − To(s − so) (4) in which b is the specific exergy, and u, v, and s are the specific internal energy, specific volume, and specific entropy, respectively. uo, vo, and so are the specific values at the dead state. The dead state is defined as the condition of the environment at po and To. Once the system is in equilibrium with the dead state, there is no further opportunity of it to produce useful work. Exergy may be destroyed by irreversible processes such as combustion, heat transfer through a finite temperature difference, friction, or mixing. For completing the exergy analyses, the exergy of the fuel is needed

B = −( G) f uel ∆ To,po (5) in which ∆GTo,po is the change of the Gibbs free energy for reactants to products. For many hydrocarbon fuels, the fuel exergy is not much different than the lower heating value (LHV). For isooctane, the fuel exergy is 1.0286 greater than the LHV. Inventions 2018, 3, 33 7 of 30

The destroyed exergy (Bdest) during combustion (CD) will be expressed as a percentage of the fuel exergy,Inventions 2018, 3, x FOR PEER REVIEW 7 of 30 B CD = dest × 100% (6) BBf uel CD dest 100% B (6) Complete details of the exergy analyses mayfuel be found elsewhere (e.g., [9,12]). Figure2 shows the partition of the fuel energy (left bar) and exergy (right bar) for case 1. From the Complete details of the exergy analyses may be found elsewhere (e.g., [9,12]). bottom, theFigure first 2 item shows is thethe partition indicated of work. the fuel This energy is the (left same bar) valueand exergy on a “kJ”(right basis bar) forfor case both 1. energy From and exergy,the but bottom, the percentagesthe first item is are the slightly indicated different, work. This since is the the same LHV value and on fuel a “kJ” exergy basis for values both areenergy slightly different.and exergy,Mechanical but the friction percentages is noted are in slightlythe figure different and represents, since the the LHV difference and fuel between exergy values the brake are and net indicatedslightly different. work. The Mechanical next item friction is the is heat noted transfer. in the figure The energyand represents percentage the difference is 16.4%, between and the the exergy percentagebrake and is 13.5%. net indicated This recognizes work. The that next not item all is the the energy heat transfer. associated The withenergy the percentage heat transfer is 16.4% is available, and to producethe work. exergy Similarly percentage for is the 13.5%. net transfer This recognizes due to the that flows, not all the the energy energy percentage associated is with 43.2% the and heat exergy percentagetransfer is is26.2%. available A large to produce fraction work. of the Similarly exhaust gas for theenergy net istransfer not available due to the to produce flows, the work. energy percentage is 43.2% and exergy percentage is 26.2%. A large fraction of the exhaust gas energy is not On the right bar for exergy, additional items are shown that represent the destruction of available to produce work. exergy. The largest of these is the 20.1% of the fuel exergy destroyed during the combustion process. On the right bar for exergy, additional items are shown that represent the destruction of exergy. CombustionThe largest is highly of these irreversible is the 20.1% due of to the the fuel chemical exergy reactions, destroyed heat during transfer, the combustion and mixing process. associated withCombustion the combustion is highly process. irreversible The nextdue to item the chemical is the exergy reactions, destruction heat transfer due, and to themixing fresh associated inlet charge mixingwith with the thecombustion residual process. gases. ForThe thisnext case,item is this the is exergy 0.8% ofdestruction the fuel exergy.due to the The fresh final inlet item charg (fore both energymixing and exergy)with the isresidual the unburned gases. For fuel this (0.7%). case, this is 0.8% of the fuel exergy. The final item (for both Asenergy described and exergy) above, is the one unburned of the unique fuel (0.7%). results from the second law of thermodynamics is the quantificationAs described of the exergy above, destructionone of the unique during results the combustionfrom the second process. law of Extensive thermodynamics work has is the shown that, inquantifica general,tion this of destructionthe exergy destruction correlates during with the the combustion combustion temperaturesprocess. Extensive [18]. work For conditionshas shown that that, in general, this destruction correlates with the combustion temperatures [18]. For conditions that result in higher combustion temperatures, more of the fuel exergy is preserved. Conversely, lower result in higher combustion temperatures, more of the fuel exergy is preserved. Conversely, lower combustioncombustion temperatures temperatures result result in in less less fuel fuel exergy exergy being preserved. preserved. This This is an is animportant important insight insight not not availableavailable from from the firstthe first law law of thermodynamics.of thermodynamics. ThisThis aspect is is highlighted highlighted in inthe the following following results. results.

2000 rpm Unused Destruction bmep = 900 kPa Fuel due to CR = 10, =1.0 (0.7%) Inlet Mixing 100 Unused (0.8%) Fuel Destruction (0.7%) Burned 80 (20.1%) Net Transfer (43.2%) Out Due (26.2%) to Flows 60

(16.4%) Heat Transfer (13.5%) 40 Friction Energy or Exergy (%) EnergyExergy or Indicated Indicated 20 Work Brake Work Work (39.7%) (38.8%)

0 1 2 Energy Exergy Figure 2. Partition of energy and exergy for case 1. Figure 2. Partition of energy and exergy for case 1. 4. Example One: Thermodynamics of Low Heat Rejection Engines 4. Example One: Thermodynamics of Low Heat Rejection Engines 4.1. Introduction 4.1. Introduction Cylinder heat transfer is an important aspect of IC engines. Since the metal components (cylinder Cylinderhead, cylinder heat transferwalls, and is piston an important crown) aspectand lubricating of IC engines. oil in the Since cylinder the metal mustcomponents be maintained (cylinder at head,temperatures cylinder walls, less thanand pistonthose of crown) the combustion and lubricating gases, the oil cylinder in the cylinder components must arebe cooled maintained to at temperaturestemperatures lesssignificantly than those below of the the gas combustion temperatures. gases, This results the cylinder in heat transfer components from the are gases cooled to to temperaturesthe components significantly during the below high the temperature gas temperatures. portions of This the cycle. results In terms in heat of transferthe efficiency, from the the heat gases to the componentstransfer is moving during thermal the high energy temperature out of the cylinder portions, and of thethen cycle. this energy In terms is not of available the efficiency, to produce the heat work. As shown below, however, even if the heat transfer energy could be retained in the cylinder, transfer is moving thermal energy out of the cylinder, and then this energy is not available to produce not much of this energy can be converted to work. Inventions 2018, 3, 33 8 of 30 work. As shown below, however, even if the heat transfer energy could be retained in the cylinder, not much of this energy can be converted to work. In general, engines designed for lower heat losses are often called low heat rejection (LHR) engines. Some of the past work has referred to this technology as adiabatic engines, but this description is not preferred, since no engine can be 100% adiabatic. Much literature (e.g., [19–22]) is available that Inventions 2018, 3, x FOR PEER REVIEW 8 of 30 describes previous attempts at achieving LHR engines. Since LHR engines would be expected to possess higherIn general, gas temperatures, engines designed these for concepts lower heat have losses not been are often applied called to low spark-ignition heat rejection engines, (LHR) since spark knockengines. would Some be of more the past likely. work has referred to this technology as adiabatic engines, but this Manydescription concepts is not have preferred been, examined since no engine to achieve can be 100% LHR adiabatic. engines. Much These literature concepts (e.g., have [19– included22]) is the available that describes previous attempts at achieving LHR engines. Since LHR engines would be use of ceramic and other low-conducting materials to minimize the cylinder heat losses. Most of expected to possess higher gas temperatures, these concepts have not been applied to spark-ignition these materialsengines, since are less spark ductile knock would than the be more cast ironlikely. and steel components that they replace. Due to this characteristic,Many these concepts materials have been suffer examined low durability to achieve and LHR often engines. have These not concepts been able have to included sustain the the harsh environmentuse of ceramic of the engineand other combustion low-conducting chamber materials [19 to– 22minimize]. the cylinder heat losses. Most of these In additionmaterials are to the less potential ductile than of the higher cast ironefficiencies, and steel other components advantages that they of replace. the LHR Due engine to this concept includecharacteristic, the possible these minimization materials suffer or eliminationlow durability of and the often cooling have not system. been able This to sustain may result the harsh in weight environment of the engine combustion chamber [19–22]. decreases andIn addition reduction to the of potential a maintenance of higher item. efficiencies, Removing other advantages cooling water of thepumps LHR engine would concept reduce the mechanicalinclude friction. the possible In addition, minimization higher or exhaust elimination gas of temperatures the cooling system. may beThis beneficial may result for inturbocharging weight and somedecreases emission and aftertreatmentreduction of a maintenance devices. item. Removing cooling water pumps would reduce the Thismechanical subsection friction. will In examineaddition, higher reductions exhaust ofgas cylinder temperatures heat may transfer be beneficial by increasing for turbocharging the cylinder wall temperatures.and some emission To decrease aftertreatment cylinder devices. heat losses, most of these previous attempts employed high This subsection will examine reductions of cylinder heat transfer by increasing the cylinder wall temperature materials (e.g., ceramics) and high temperature lubricants. These approaches effectively temperatures. To decrease cylinder heat losses, most of these previous attempts employed high increasetemperature the component materials temperatures. (e.g., ceramics) and high temperature lubricants. These approaches effectively In termsincrease of the increasing component thermal temperatures. efficiencies, most of the previous work has not been successful. The results fromIn terms thermodynamics of increasing thermal in this efficiencies, subsection most help of explainthe previous why work these has previous not been attempts successful. were not successful,The andresults the from difficulty thermodynamics of significantly in this subsection increasing help thermal explain efficiencywhy these previous by reducing attempts the were heat losses. not successful, and the difficulty of significantly increasing thermal efficiency by reducing the heat 4.2. Resultslosses. for Increases of the Wall Temperature

Figure4.2. Results3 shows for theIncreases relative of the heat Wall transfer Temperature as a function of the cylinder wall temperature. The relative heat transferFigure is the 3 ratio shows of the the relative actual heat transfer transfer as and a function fuel energy. of the Thecylinder high wall wall temperature. temperatures The are not realistic,relative but the heat attempt transfer was is to the capture ratio of the the trends. actual heat The heattransfer transfer and fuel decreases energy. in The a linear high wall fashion as the walltemperatures temperature are increases. not realistic, For but a the cylinder attempt wall was temperatureto capture the oftrends. about The 1500 heat K,transfer the net decreases cylinder heat transferin is a near linear zero. fashion For as this the highwall temperature wall temperature, increases. heat For transfera cylinder is wall first temperature from the cylinder of about walls1500 to the K, the net cylinder heat transfer is near zero. For this high wall temperature, heat transfer is first from gases, and then later in the cycle, the heat transfer is from the gases to the walls. The heat transfer into the cylinder walls to the gases, and then later in the cycle, the heat transfer is from the gases to the the cylinderwalls. and The out heat of transfer the cylinder into the is cylinder equal, and such out that of the cylinder net heat is transfer equal, such is near that zero the net for heat a cylinder wall temperaturetransfer is near of 1500 zero for K. a cylinder wall temperature of 1500 K.

20 bmep = 900 kPa 2000 rpm, Hohenberg MBT Timing, CR = 10 Case 1 o  = 1.0, b = 50 CA

15

10 Relative Heat TransferHeat (%) Relative 5

0 500 1000 1500 T (K) wall

FigureFigure 3. Relative 3. Relative heat heat transfer transfer as as a a function function of of cylinder cylinder wall wall temperature temperature for case for 1. case 1. Inventions 2018, 3, x FOR PEER REVIEW 9 of 30

InventionsDetails2018, 3from, 33 the cases with wall temperatures of 450 K (case 1) and 1500 K (case 1a) will now9 of 30be presented to better illustrate the nature of the LHR engine concept. Table 4 lists some of the inputs and outputs for these two cases. Note that to maintain the constant bmep of 900 kPa, the inlet pressure Details from the cases with wall temperatures of 450 K (case 1) and 1500 K (case 1a) will now be needed to increase for the high wall temperature case. Also, for the high wall temperature case, the presented to better illustrate the nature of the LHR engine concept. Table4 lists some of the inputs heat transfer is near zero. Figure 4 shows the instantaneous heat transfer as functions of crank angle and outputs for these two cases. Note that to maintain the constant bmep of 900 kPa, the inlet pressure for the two cases. The higher heat transfer for the lower wall temperature is obvious. The heat transfer needed to increase for the high wall temperature case. Also, for the high wall temperature case, the heat is identified as either from the gases to the walls or from the walls to the gases. For the higher wall transfer is near zero. Figure4 shows the instantaneous heat transfer as functions of crank angle for temperature, heat transfer from the walls to the gases is significant. For the higher wall temperature, the two cases. The higher heat transfer for the lower wall temperature is obvious. The heat transfer the heat transfer from the walls to the gases is equal to the heat transfer from the gases to the walls. is identified as either from the gases to the walls or from the walls to the gases. For the higher wall temperature, heat transfer from the walls to the gases is significant. For the higher wall temperature, Table 4. Some of the Inputs and Outputs for Two Wall Temperatures. the heat transfer from the walls to the gases is equal to the heat transfer from the gases to the walls. Item/Case 1 1a Table 4. Some of theTwall Inputs (K) and Outputs450 for Two Wall1500 Temperatures. bmep (kPa) 900.9 899.7 ηindicatedItem/Case 39.73 1 1a 41.23

ηbrakeTwall (K)36.35 450 150037.62 θo (bmep°aTDC(kPa)) 900.9–21.0 899.7–21.5 ηindicated 39.73 41.23 pin (kPa) 86.6 100.7 ηbrake 36.35 37.62 pmax (MPa)◦ θo ( aTDC) –21.05.21 –21.55.51 MPRR * p(MPa/CA)in (kPa) 0.211 86.6 100.70.208 RHTpmax (%)(MPa) 16.36 5.21 5.510.29 MPRRQ (kJ) * (MPa/CA) 0.2110.291 0.2080.005 RHT (%) 16.36 0.29 2 havg (J/sQ·m (kJ)·K) 0.291351 0.005363 comb 2 hγavg (J/s(---)·m ·K) 1.2252351 3631.2056 CDγ **comb (%)(—) 1.225220.06 1.205617.57 TcombCD (K)** (%) 20.061929 17.572171 Tcomb (K) 1929 2171 Texh (K) 1310 1597 Texh (K) 1310 1597 FuelingFueling (kJ) (kJ) 1.7761.776 1.7141.714 * MPRR* MPRR is the is maximum the maximum pressure pressure rise rise rate rate;; ** CD isis thethe percentage percentage of theof the fuel fuel exergy exergy destroyed destroyed during during the combustionthe combustion process. process.

1.0

bmep = 900 kPa T = 450 K wall 2000 rpm, = 1.0 o 0.8 CR = 10, b = 50 CA MBT Timing

0.6

0.4

Twall = 1500 K Heat Transfer from 0.2 gases to walls Instantaneous Heat (J) InstantaneousHeat Transfer

0.0 Heat Transfer from walls to gases

-0.2 -180 0 180 360 540

o Crank Angle ( aTDC)

FigureFigure 4.4. Instantaneous heat heat transfer transfer as as functions functions of of crank crank angle angle for for cylinder cylinder wall wall temperatures temperatures of 450 of 450and and 1500 1500 K. K. Inventions 2018, 3, 33 10 of 30 Inventions 2018, 3, x FOR PEER REVIEW 10 of 30 Inventions 2018, 3, x FOR PEER REVIEW 10 of 30

FigureFigure5 5 shows shows the the instantaneous instantaneous average, average, one-zone one-zone gas gas temperature temperature as as functions functions of of crank crank angle angle forfor thethe twotwo wall wall temperature temperature cases. cases. For For the the case case of of the the high high wall wall temperature, temperature, the the gas gas temperatures temperatu areres higherare higher throughout throughout the completethe complete cycle. cycle. These These higher higher temperatures temperatures are discussedare discussed below below as part as part of the of reasonthe reason for thefor difficultythe difficulty of achieving of achieving higher higher thermal thermal efficiencies efficiencies with with LHR LHR engine engine concepts. concepts. FigureFigure6 6 shows shows the the instantaneous instantaneous cylinder cylinder pressure pressure as as functions functions of of crank crank angle angle forfor thethe twotwo cases.cases. TheThe cylindercylinder pressurespressures areare higherhigher forfor thethe highhigh wallwall temperaturetemperature case.case. ForFor the compression process, thesethese higherhigher pressurespressures contributecontribute toto higherhigher compressioncompression work,work, whichwhich detractsdetracts fromfrom increasingincreasing thethe efficiencies.efficiencies. ForFor thetheexpansion expansion process, process, these these higher higher pressures pressures increase increase the the efficiencies. efficiencies. The The net net result result is reflectedis reflected in thein the thermal thermal efficiencies—which efficiencies—which are are described described next. next.

3000 3000 bmep = 900 kPa bmep = 900 kPa 2000 rpm,  = 1.0 Twall = 1500 K 2000 rpm,  = 1.0 Twall = 1500 K CR = 10, MBT timing 2500 CR = 10, MBT timing 2500

2000 2000

1500 1500

1000 T = 450 K 1000 wall Twall = 450 K Average, One-Zone Temperature (K) Temperature One-Zone Average,

Average, One-Zone Temperature (K) Temperature One-Zone Average, 500 500

0 0-180 -90 0 90 180 270 360 450 540 -180 -90 0 90 180 270 360 450 540 o Crank Angle (oaTDC) Crank Angle ( aTDC) FigureFigure 5.5. Average, one-zoneone-zone cylindercylinder gasgas temperaturestemperatures asas functionsfunctions ofof crankcrank angleangle withwith cylindercylinder wallwall temperaturestemperatures ofof 450450 andand 15001500 K.K.

6000 6000

T = 1500 K bmep = 900 kPa Twall = 1500 K bmep = 900 kPa wall 2000 rpm,  = 1.0 2000 rpm,  = 1.0o CR = 10,  = 50oCA 5000 CR = 10, b = 50 CA 5000 MBT timingb MBT timing

4000 4000

3000 3000

2000 2000 Cylinder Pressure Pressure (kPa) Cylinder Cylinder Pressure Pressure (kPa) Cylinder

1000 1000

Twall = 450 K Twall = 450 K

0 0-180 -90 0 90 180 -180 -90 0 90 180 o Crank Angle (oaTDC) Crank Angle ( aTDC) Figure 6. Cylinder pressures as functions of crank angle with cylinder wall temperatures of 450 and FigureFigure 6.6. CylinderCylinder pressurespressures asas functionsfunctions ofof crankcrank angleangle withwith cylindercylinder wallwall temperaturestemperatures ofof 450450 andand 1500 K. 15001500 K.K.

Figure 7 shows the net indicated and brake thermal efficiencies as functions of the wall temperature. The efficiencies increase nearly linearly as the wall temperature increases. As the wall temperature increased from 450 to 1500 K, the relative heat transfer decreased about 16% (absolute). Inventions 2018, 3, 33 11 of 30

Figure7 shows the net indicated and brake thermal efficiencies as functions of the wall temperature. The efficiencies increase nearly linearly as the wall temperature increases. As the wall temperatureInventions increased 2018, 3, x FOR from PEER 450 REVIEW to1500 K, the relative heat transfer decreased about 16%11 of (absolute). 30 For this change in the wall temperature, however, the net indicated and brake efficiencies increased only aboutInventionsFor 1.5%this 2018change and, 3, x 1.3% FORin the PEER (absolute), wall REVIEW temperature, respectively. however, This the net small indicated increase and ofbrak thee efficiencies efficiencies increased relative11 of 30 to the only about 1.5% and 1.3% (absolute), respectively. This small increase of the efficiencies relative to greater decrease of the heat loss is consistent with the cited literature above that demonstrated similar Forthe thisgreater change decrease in the of wall the temperature,heat loss is consistent however, withthe net the indicated cited literature and brak abovee efficiencies that demonstrated increased results inonlysimilar numerous about results 1.5% experiments.in andnumerou 1.3% s(absolute), experiments. The thermodynamic respectively. The thermodynamic This reasons small increasereasons for this forof arethethis efficiencies explainedare explained relative below. below. to the greater decrease of the heat loss is consistent with the cited literature above that demonstrated similar results in numerous experiments.44 The thermodynamic reasons for this are explained below. bmep = 900 kPa 2000 rpm, Hohenberg 44 MBT Timing, CR = 10  = 1.0,  = 50oCA bmep = 900b kPa 2000 rpm, Hohenberg 42 MBT Timing, CR = 10  = 1.0,  = 50oCA Net Indicated Efficiencyb 42

Net Indicated Efficiency Case 1 40

Case 1 40 Thermal Efficiencies (%) Efficiencies Thermal 38 Brake Efficiency Thermal Efficiencies (%) Efficiencies Thermal 38 Case 1 Brake Efficiency

36 Case500 1 1000 1500 T (K) 36 wall 500 1000 1500 Figure 7. Brake and net indicated thermal efficiencies as functions of cylinder wall temperature. Figure 7. Brake and net indicated thermal efficienciesT (K) as functions of cylinder wall temperature. wall FigureFigure 8 7.shows Brake theand averagenet indicated of gamma thermal (the efficiencies ratio of as specific functions heats) of cylinder as a functionwall temperature. of the cylinder Figurewall8 temperature. shows the Due average to the ofincreasing gamma temperatures, (the ratio of gamma specific decreases heats) from as aabout function 1.225 to of 1.206 the cylinderas wall temperature.the cylinderFigure 8 Duewall shows temperature to the average increasing increases. of gamma temperatures, Although (the ratio a small of gamma specific change decreasesheats) of gamma, as a function from this contributes about of the 1.225 cylinder to tothe 1.206 as the cylinderwalldifficulty temperature. wall of temperature converting Due to the increases. increasing thermal energy Althoughtemperatures, to work. a small gamma In other change decreases words, of from gamma, low about heat this rejection1.225 contributes to 1.206 engine as to the theconcepts cylinder have wall the temperature disadvantage increases. of decreasing Although gamma a small values, change which of causes gamma, less this thermal contributes energy to to the be difficulty of converting the thermal energy to work. In other words, low heat rejection engine concepts difficultyconverted ofto convertingwork. In the the subsection thermal concerning energy to thework. ideal In Otto other cycle, words, this aspect low heat of the rejection importance engine of have theconceptsgamma disadvantage i shave illustrated. the ofdisadvantage decreasing of gamma decreasing values, gamma which values, causes which lesscauses thermal less thermal energy energy to be to convertedbe to work.converted In the subsection to work. In the concerning subsection concerning the ideal Ottothe ideal cycle, Otto this cycle, aspect this aspect of the of importancethe importance of of gamma is illustrated.gamma is illustrated. 1.23 bmep = 900 kPa 2000 rpm, Hohenberg 1.23 Case 1 MBT Timing, CR = 10  = 1.0,  = 50oCA bmep = 900b kPa 2000 rpm, Hohenberg Case 1 MBT Timing, CR = 10 o  = 1.0, b = 50 CA 1.22

1.22 (---) comb  (---) 1.21 comb 

1.21

1.20 500 1000 1500 T (K) 1.20 wall 500 1000 1500 Figure 8. Average gamma during combustion as functions of cylinder wall temperature. T (K) wall Figure 8. Average gamma during combustion as functions of cylinder wall temperature. Figure 8. Average gamma during combustion as functions of cylinder wall temperature. Inventions 2018, 3, 33 12 of 30 InventionsInventions 20182018,, 33,, xx FORFOR PEERPEER REVIEWREVIEW 1212 ofof 3030

ForFor completeness, completeness, Figures Figures9 and 9 10 and show 10 theshow partition the partition of the fuel of energy the fuel and energy exergy, respectively,and exergy, forrespectively,respectively, three cylinder forfor threethree wall cylindercylinder temperatures. wallwall temperatures.temperatures. As the wall AsAs temperature thethe wallwall tempetempe increases,raturerature increases,increases, the energy thethe and energyenergy exergy andand ofexergy the heat of the transfer heat transfer decreases, decreases, the indicated the indicated work increases work increases slightly, slightly, and the and energy the of energy the exhaust of the increases.exhaust increases. As mentioned As mentioned above, the exergy above, destroyed the exergy during destroyed the combustion during the process combustion decreases process as the gasdecreases temperatures as the gas increase. temperatures increase.increase.

20002000 rpmrpm Unused bmepbmep == 900900 kPakPa FuelFuel  == 1.0,1.0, CRCR == 1010 (0.7%)(0.7%) 100100

Net Transfer 80 Net Transfer 80 Out Due (43.2%) toto FlowsFlows (43.2%) (47.9%)(47.9%) (57.8%)(57.8%)

6060

Heat Energy (%) Energy Energy (%) Energy (16.4%)(16.4%) (11.2%) TransferTransfer (11.2%) (0.3%) 4040 (0.3%)

TotalTotal 20 Indicated 20 Indicated (39.7%)(39.7%) (40.3%)(40.3%) (41.2%)(41.2%) Work

00 T = 45011 K 22 150033 K Twallwall = 450 K 800 K 1500 K

FigureFigure 9.9. TheThe fuel energyenergy distributiondistribution forfor threethree cylindercylinder wallwall temperatures.temperatures.

20002000 rpmrpm UnusedUnused FuelFuel bmepbmep == 900900 kPakPa && MixMix DestDest  == 1.0,1.0, CRCR == 1010 100100

Dest (20.1%)(20.1%) (19.1%) (17.6%) Comb (19.1%) (17.6%) 8080

NetNet TransferTransfer OutOut DueDue (26.2%) to Flows (26.2%) (29.7%)(29.7%) (37.4%)(37.4%) 6060 to Flows

Heat Exergy (%) Exergy Heat Exergy (%) Exergy (13.5%)(13.5%) TransferTransfer (9.8%)(9.8%) 4040 (0.8%)(0.8%)

TotalTotal IndicatedIndicated 2020 (38.8%)(38.8%) (39.4%)(39.4%) (40.5%) Work (40.5%)

00 T = 45011 K 22 33 Twallwall = 450 K 800 K 1500 K

FigureFigure 10.10. The fuel exergy distributiondistribution forfor threethree cylindercylinder wallwall temperatures.temperatures.

4.3.4.3. ReasonsReasons forfor NegligibleNegligible EfficiencyEfficiency IncreasesIncreases ForFor anan explanationexplanation ofof thethe efficiencyefficiency resultsresultsresults (Figure((Figure7 7),),), this thisthis discussion discussiondiscussion will willwill consider considerconsider the thethe two twotwo cases casescases withwith wallwall temperaturestemperatures ofof 450450 KK (case(case 1)1) andand 15001500 KK (case(case 1a).1a). TheThe following itemsitems areare responsibleresponsible forfor limitinglimitinglimiting thethethe increaseincreaseincrease ofofof thethethe thermalthermalthermal efficienciesefficienciesefficiencies when whenwhen the thethe net netnet heat heatheat transfer transfertransfer is isis reduced reducedreduced to tto near near zero. zero.  • NotNot allall thethe heatheat energyenergy isis availableavailable toto dodo work.work. TheThe totaltotal exergyexergy ofof thethe heatheat transfertransfer isis aboutabout 13%13% (as(as(as opposedopposedopposed tototo the thethe 16% 16%16% based basedbased on onon energy). energy).energy).  Some of the preserved heat transfer is during compression. This increases compression pressures • SomeSome ofof thethe preserved heatheat transfertransfer isis during compression. This increases compression pressures and causes additional compression work, which negates some of the gains during the expansion. andand causescauses additionaladditional compressioncompression work,work, whichwhich negatesnegates somesome ofof the gains during the expansion.  The volumetric efficiency decreases slightly for the high cylinder wall temperature case due to thethe higherhigher gasgas temperatures.temperatures.  Only the heat transfer preserved near TDC willill contributecontribute toto additionaladditional expansionexpansion work.work. Inventions 2018, 3, 33 13 of 30

• The volumetric efficiency decreases slightly for the high cylinder wall temperature case due to the higher gas temperatures. • Only the heat transfer preserved near TDC will contribute to additional expansion work. • Only a fraction of the preserved thermal energy near TDC can be converted to work. • As shown above, gamma decreases due to the higher temperatures for the high cylinder wall temperature case. This decreases the conversion of thermal energy to work. • For this case, the exhaust gas temperature increases from about 1310 K for the 450 K case to about 1600 K for the 1500 K case (Table4). This is evidence that a considerable amount of the energy preserved remains in the gases. • Due to the higher gas temperatures, the exergy destroyed during the combustion process is reduced from 20.1% to 17.6% (Table4). This improvement is offset by the items mentioned above.

The following is a quantitative estimate of how the preserved thermal energy contributes to additional work. First, only the 13% of the heat transfer energy is available (exergy) for work production (Figure2). As mentioned above, only a portion of this is available near TDC. If 30% of this exergy is available near TDC, this means about 4% of the exergy could be converted to work. The efficiency is a measure of thermal energy conversion to work—say this is about 40%. This results in about 1.6% (absolute) thermal efficiency gain due to the reduction of the heat transfer, which is in rough agreement with the results presented above. Finally, the above discussion considered the unrealistic cylinder wall temperature of 1500 K. Any actual implementation of a LHR engine design will operate at lower wall temperatures. This means any actual gains will be near zero and essentially impossible to separate from experimental uncertainties. This then, explains the thermodynamics related to trying to improve engine efficiency by reducing the cylinder heat transfer. Although the LHR engine concept is not particularly effective for increasing thermal efficiencies, this concept does convert energy that originally would be part of the heat loss to energy in the exhaust. The energy in the exhaust may be useful for items such as turbocharging or aiding in heating exhaust system emission control devices. In addition, energy in the exhaust may justify exhaust gas energy recovery devices such as those related to turbo-compounding. The results presented above are not unique to case 1 engine operating conditions. Similar analyses were completed for other conditions, and the results were comparable.

5. Example Two: Thermodynamics of Exhaust Gas Dilution

5.1. Introduction Investigations of exhaust gases as diluent for IC engines have a long history. For example, Berger et al. [23] reported on engine operation in mines in which the inlet mixture was contaminated with exhaust gases. Miller et al. [24] reported on the use of exhaust gases as part of the inlet mixture to minimize knock. Perhaps the most widely known use of exhaust gas dilution is to suppress nitric oxide formation. Some of the first work on this topic was reported by Kopa and Kimura [25] and by Kopa et al. [26]. This work and work that has followed have shown the dramatic effectiveness of exhaust gas dilution to reduce nitric oxides. This subsection will examine the thermodynamics associated with the use of exhaust gas dilution. Exhaust gas dilution may be accomplished by mixing a portion of the exhaust gases with the entering fuel–air mixture via external piping, or the exhaust gases may be retained in the cylinder via the selection of certain valve timings. The use of the external approach is known as exhaust gas recirculation (EGR). Both of these approaches supply a level of dilution, but the processes are different. Each of these approaches is discussed in the following. Inventions 2018, 3, 33 14 of 30

5.2. External Exhaust Gas Dilution The use of exhaust gas dilution alters the thermodynamic properties of the working fluid. First, theInventions concentrations 2018, 3, x FOR of PEER the species REVIEW of the inlet charge change. In particular, the concentrations of nitrogen,14 of 30 carbon dioxide, water, and other combustion products increase in the inlet charge. Also, the exhaust gasexhaust dilution gas dilution causes decreases causes decreases of the combustion of the combustion temperatures. temperatures. These changes These tendchanges to increase tend to theincrease ratio ofthe the ratio specific of the heats, specific which heats may, which have may a significant have a significant effect on thermaleffect on efficiencies. thermal efficiencies. The use of external external piping piping to to redirect redirect exhaust exhaust gases gases into into the the inlet inlet stream stream provides provides the the option option of ofcooling cooling the the recirculated recirculated exhaust exhaust gases. gases. Two Two configurat configurationsions are are examined examined here here,, which which bracket bracket the thevarious various cooling cooling designs. designs. An An adiabatic adiabatic configuration configuration assumes assumes that that the the exhaust exhaust gases gases retain their cylinder exit temperaturetemperature andand nono cooling occurs.occurs. The cooled configurationconfiguration assumes that the exhaust ◦ gases are cooled cooled to to the the inlet inlet temperature temperature of the of the air- air-fuelfuel mixture mixture (319.3 (319.3 K (115 K °F) (115 for F)this for study). this study). These Thesetwo configurations two configurations result result in final in finalinlet inlettemperatures temperatures that thatrange range between between the thepossible possible temperatures temperatures in inpractice. practice. Figure 11 11 shows shows the inlet inlet temperature as a function function of thethe EGR EGR percentage percentage for for the the two two configurations.configurations. ForFor thethe cooledcooled EGREGR configuration, configuration, the the inlet inlet temperature temperature remains remains at at a constanta constant 319.3 319.3 K. ForK. For the adiabatic the adiabatic EGR EGRconfiguration, configuration, the inlet the temperature inlet temperature increases increases as the EGR as thepercentage EGR percentage increases. Asincreases. the EGR As percentage the EGR percentag increases,e theincreases, exhaust the gas exhaust temperature gas temperature decreases, anddecreases, therefore, and thetherefore, rate of increasethe rate of of increase the inlet of mixture the inlet temperature mixture temperature decreases for decreases the higher for EGRthe higher levels. EGR levels. Although the main focus of this discussion is on the thermodynamics thermodynamics related to the use of exhaust gas dilution, for completeness, a brief illustration of the nitric oxide reduction is presented. Figure 12 showsshows the nitric oxide concentrations as functions of the EGR percentage for the two EGR configurations.configurations. For For case case 1, 1, with no EGR, the nitric nitric oxide oxide concentration concentration is is 4070 4070 ppm. ppm. Both EGR configurationsconfigurations resultresult inin decreasesdecreases ofof thethe nitricnitric oxides,oxides, but the cooled EGR configurationconfiguration isis much more effective. For 20% EGR, the cooled EGR configurationconfiguration results in 1284 ppm or about a 68% reduction of nitric oxide. oxide. For For 20% 20% EGR EGR for for the the adiabatic adiabatic EGR EGR configuration, configuration, the nitric the nitric oxide oxide is 3161 is ppm 3161 or ppm about or abouta 22% a reduction. 22% reduction. These These are significant are significant reductions reductions,, especially especially for for this this relatively relatively high high load load engine condition. More information on thethe nitricnitric oxideoxide computationscomputations isis availableavailable elsewhereelsewhere [[9].9].

650

2000 rpm bmep = 900 kPa 600 CR = 10,  = 1.0 Adiabatic EGR o b = 50 CA

550

500

450 Inlet Temperature (K) TemperatureInlet

(for EGR, air & fuel vapor mixture) &vapor fuel air EGR, (for 400

Case 1 350

Cooled EGR

300 0 5 10 15 20 25 30 EGR (%)

FigureFigure 11.11. The inlet mixture temperature as functions of the EGR level for the two EGR configurations.configurations. Inventions 2018, 3, 33 15 of 30 Inventions 2018, 3, x FOR PEER REVIEW 15 of 30

5000

Case 1 4000

"Adiabatic" EGR 3000 NO (ppm) NO NO (ppm) NO 2000

1000 2000 rpm Cooled EGR bmep = 900 kPa CR = 10,  = 1.0  = 50oCA b = 50 CA

0 0 5 10 15 20 25 30 EGR (%) FigureFigure 12. 12.Nitric Nitric oxide oxide concentrations concentrations asas functionsfunctions of the EGR percentage percentage for for the the two two EGR EGR configurations. configurations.

Figure 13 shows the net indicated and brake efficiencies as functions of the EGR percentage for Figure 13 shows the net indicated and brake efficiencies as functions of the EGR percentage for the the two EGR configurations. For the cooled EGR configuration, the efficiencies increase, whereas for twothe EGR adiabatic configurations. EGR configuration, For the cooled the efficiencies EGR configuration, decrease with the efficienciesincreasing EGR increase, percent whereasages. These for the adiabaticresults EGR can configuration, be understoodthe by efficiencies examining decrease some of with the increasing thermodynamics EGR percentages. associated Thesewith these results canconditions. be understood Figures by 14 examining–19 show, as some functions of the of thermodynamics the EGR percentage, associated the relative with heat these transfer, conditions. the Figuresaverage, 14– one19 show,-zone gas as functions temperature of during the EGR combustion, percentage, the theheat relative transfer heat coefficients, transfer, the the average average, one-zoneratio of gas the temperature specific heats during during combustion, combustion, the and heat the transfer exergy coefficients, destroyed during the average the combustion ratio of the specificprocess. heats during combustion, and the exergy destroyed during the combustion process.

43

Cooled EGR Net Indicated Efficiency 41

Case 1

Adiabatic EGR 39 Adiabatic EGR

Cooled EGR Brake Efficiency

37 Case 1 Thermal Efficiency (%) Thermal Efficiency Thermal Efficiency (%) Thermal Efficiency

Adiabatic EGR 35 2000 rpm bmep = 900 kPa CR = 10,  = 1.0  = 50oCA b = 50 CA

33 0 5 10 15 20 25 30 EGR (%) Figure 13. Net indicated and brake efficiencies as functions of the EGR percentage for the two EGR FigureFigure 13. 13.Net Net indicatedindicated and and brake brake efficiencies efficiencies as asfunctions functions of the of EGR the EGRpercentage percentage for the for two the EGR two configurations. EGRconfigurati configurations.ons.

The efficiencies increase for the cooled EGR configuration largely because the heat transfer decreasesThe efficiencies (Figure 1 increase4) and the for ratio the ofcooled the specific EGR configuration heats (Figurelargely 17) increases. because The the heatratio transferof specific decreases heats (Figure 14) and the ratio of the specific heats (Figure 17) increases. The ratio of specific heats increases Inventions 2018, 3, 33 16 of 30

Inventions 2018, 3, x FOR PEER REVIEW 16 of 30 due to the composition change and the lower temperatures. The heat transfer decreases, since the increases due to the composition change and the lower temperatures. The heat transfer decreases, gas temperatures decrease (Figure 15) even though the heat transfer coefficient increases (Figure 16). since the gas temperatures decrease (Figure 15) even though the heat transfer coefficient increases The heat transfer coefficient increases for both configurations, since the temperatures decrease and the (Figure 16). The heat transfer coefficient increases for both configurations, since the temperatures pressures increase. The pressures increase as the EGR percentage increases, since to maintain the same decrease and the pressures increase. The pressures increase as the EGR percentage increases, since to load (bmep = 900 kPa), the inlet pressure increases. The heat transfer coefficient for the Hohenberg maintain the same load (bmep = 900 kPa), the inlet pressure increases. The heat transfer coefficient for correlation [16] depends on the pressures and temperatures as follows the Hohenberg correlation [16] depends on the pressures and temperatures as follows 0.8 −0.4 h h∼~p p0.8T T  0.4 (7) (7) TheThe efficiencies efficiencies decrease decrease for for the the adiabaticadiabatic EGR EGR configuration configuration due todue increased to increased heat transfer heat transfer (Figure (Figure14) in spite 14) inof spitea modest of a modestincrease increaseof the ratio of theof specific ratio of heats specific (Figure heats 1 (Figure7). The heat17). Thetransfer heat increases transfer increaseseven though even the though gas temperatures the gas temperatures decrease decrease as the EGR as the percentage EGR percentage increases. increases. This is This due is to due the toincrease the increase of the of heat the heat transfer transfer coefficient coefficient (Figure (Figure 16) 16, which), which,, as as mentioned mentioned above above,, increases with with increasesincreases ofof cylindercylinder pressurepressure andand decreasesdecreases ofof thethe gasgas temperatures.temperatures. FigureFigure 1818 showsshows thethe exergyexergy destructiondestruction duringduring thethe combustioncombustion processprocess asas functionsfunctions ofof thethe EGREGR percentagepercentage for for the the two two EGR EGR configurations. configurations. The exergy destruction increases increases for for the the cooled cooled EGR EGR configurationconfiguration largely largely duedue to to the the significantsignificant temperaturetemperature decrease decrease associatedassociated with with increasing increasing EGREGR percentage.percentage. In spite of thethe increaseincrease ofof thethe exergyexergy destruction,destruction, thethe thermalthermal efficienciesefficiencies increaseincrease withwith increasingincreasing EGREGR percentagepercentage duedue toto thethe itemsitems mentionedmentioned above.above. TheThe exergy exergy destruction destruction decreasesdecreases for for the the adiabaticadiabatic EGREGR configurationconfiguration in in spite spite of of thethe modestmodest decreasedecrease of of the the temperatures temperatures (Figure (Figure 15 15).). This is due to the the combined combined effects effects of of increasing increasing inlet inlet temperatures,temperatures, lowerlower combustioncombustion temperatures,temperatures, higher heat transfer,transfer, andand increasingincreasing dilutiondilution asas thethe EGREGR percentagepercentage increases.increases. Finally,Finally, Figure 19 showsshows the the partition partition of of the the fuel fuel exergy exergy among among work, work, heat heat transfer, transfer, exhaust, exhaust, and anddestruction destruction for thefor the 0% 0% EGR EGR case case and and the the two two 30% 30% EGR EGR cases. cases. The The indicated indicated work work is is less for the the adiabaticadiabatic EGREGR configurationconfiguration andand isis higherhigher forfor thethe cooledcooled EGREGR configurationconfiguration comparedcompared toto thethe 0%0% EGREGR case.case. The exergyexergy associatedassociated withwith thethe heatheat transfertransfer isis highesthighest forfor thethe adiabaticadiabatic EGREGR configurationconfiguration andand lowestlowest forfor the cooled cooled EGR EGR configuration. configuration. The The exergy exergy associated associated with with the the net net flo floww out out is lowest is lowest for forthe thecooled cooled EGR EGR configuration. configuration. Additionally, Additionally, the the exergy exergy destruction destruction is is lowest lowest for for the the adiabatic EGR EGR configuration,configuration, asas discusseddiscussed above.above.

24

2000 rpm Adiabatic EGR bmep = 900 kPa CR = 10,  = 1.0  = 50oCA 22 b

20

18 Case 1 Relative Heat Transfer (%) Heat Transfer Relative

16 Cooled EGR

14 0 5 10 15 20 25 30 EGR (%)

Figure 14.14. Relative heat transfer as functions ofof the EGREGR percentagepercentage forfor thethe twotwo EGREGR configurations.configurations. Inventions 2018, 3, 33 17 of 30 InventionsInventions 2018,, 3,, xx FORFOR PEERPEER REVIEWREVIEW 17 of 30

2000 2000

Case 1 Case 1

1900 1900 Adiabatic EGR Adiabatic EGR

1800 1800

1700 1700 Cooled EGR Cooled EGR

1600 2000 rpm 1600 2000 rpm bmep = 900 kPa bmep = 900 kPa CR = 10,  = 1.0 CR = 10, o = 1.0 Average, One-Zone DuringTemperature Combustion (K) One-Zone Average, o Average, One-Zone DuringTemperature Combustion (K) One-Zone Average, b = 50 CA b = 50 CA 1500 1500 0 5 10 15 20 25 30 0 5 10 15 20 25 30 EGR (%) EGR (%) FigureFigure 15. 15. The average, oneone-zone--zone gas temperature during combustion as functions functions of of the the EGR EGR percentagepercentage forfor thethe twotwo EGREGR configurations.configurations.

1.5 2000 rpm Adiabatic EGR 2000 rpm Adiabatic EGR bmep = 900 kPa CR = 10,  = 1.0 CR = 10, o = 1.0 1.4 o 1.4 b = 50 CA b = 50 CA

1.3 (---) (---) 1.2 Cooled EGR 1.2 Cooled EGR avg,base avg,base /h /h avg avg h h

1.1

1.0 Case 1 Case 1

0.9 0 5 10 15 20 25 30 EGR (%) EGR (%) Figure 16. The ratio of the average heat transfer coefficient and the average heat transfer coefficient FigureFigure 16.16. TheThe ratioratio ofof the the average average heat heat transfer transfer coefficient coefficient and and the the average average heat heat transfer transfer coefficient coefficient for for case 1 as functions of the EGR percentage for the two EGR configurations. casefor case 1 as 1 functions as functions of the of EGRthe EGR percentage percentage for thefor twothe two EGR EGR configurations. configurations. Inventions 2018, 3, 33 18 of 30 InventionsInventions 20182018,, 33,, xx FORFOR PEERPEER REVIEWREVIEW 1818 ofof 3030

1.261.26 Cooled EGR 20002000 rpmrpm Cooled EGR bmepbmep == 900900 kPakPa CRCR == 10,10,  == 1.01.0  = 50ooCA bb = 50 CA 1.251.25 (---) (---) comb comb 1.241.24 gamma gamma

AdiabaticAdiabatic EGR EGR 1.231.23

CaseCase 1 1

1.221.22 00 55 1010 1515 2020 2525 3030 EGREGR (%)(%) FigureFigure 17.17. The The averageaverage ratioratio ofof specificspecificspecific heatsheatsheats duringduring combustioncombustion asas functionsfunctions ofof thethe EGREGR percentagepercentage forfor thethe twotwotwo EGREGREGR configurations.configurations.configurations.

2323 20002000 rpmrpm bmepbmep == 900900 kPakPa CR = 10,  = 1.0 CR = 10,  = 1.0 Cooled EGR 2222  = 50ooCA Cooled EGR bb = 50 CA

2121

CaseCase 1 1 2020

1919

AdiabaticAdiabatic EGR EGR Exergy Destruction During Combustion (%) During Combustion Destruction Exergy Exergy Destruction During Combustion (%) During Combustion Destruction Exergy 1818

1717 00 55 1010 1515 2020 2525 3030 EGREGR (%)(%) Figure 18. The exergy destruction during combustion as functions of the EGR percentage for the two FigureFigure 18.18. TheThe exergyexergy destructiondestruction duringduring combustioncombustion asas functionsfunctions ofof thethe EGREGR percentagepercentage forfor thethe twotwo EGR configurations. EGREGR configurations.configurations. Inventions 2018, 3, 33 19 of 30 Inventions 2018, 3, x FOR PEER REVIEW 19 of 30

2000 rpm Unused Fuel bmep = 900 kPa & Mix Dest  = 1.0, CR = 10 100

Dest (20.1%) Comb (17.8%) (22.7%) 80

Net Transfer Out Due (26.2%) (25.0%) (23.7%) 60 to Flows

Heat Exergy (%) Exergy (13.5%) (18.6%) (11.9%) Transfer 40

Total Indicated 20 (38.8%) (37.5%) Work (40.9%)

0 EGR1 EGR2 3 ad EGRcool 0% 30% 30% FigureFigure 19.19. TheThe partition partition of of the the fuel fuel exergy exergy for for three three cases: cases: 0% 0%EGR, EGR, 30% 30% EGR EGR adiabatic, adiabatic, and 30% and EGR 30% EGRcooled. cooled.

5.3.5.3. InternalInternal ExhaustExhaust GasGas DilutionDilution AsAs anan alternativealternative toto externalexternal exhaustexhaust gasgas recirculation,recirculation, thethe retentionretention ofof combustioncombustion gasesgases fromfrom thethe previousprevious cyclecycle maymay bebe accomplishedaccomplished usingusing certaincertain valvevalve timingtiming strategies.strategies. ThisThis approachapproach maymay havehave firstfirst beenbeen reportedreported byby OnishiOnishi etet al.al. [[27]27] andand NoguschiNoguschi etet al.al. [[28].28]. A major fundamental difference betweenbetween thethe externalexternal andand internalinternal exhaustexhaust gasgas dilutiondilution approachesapproaches isis thatthat thethe retentionretention ofof combustioncombustion gasesgases providesprovides higherhigher temperaturestemperatures andand perhapsperhaps aa moremore reactivereactive mixture.mixture. ThisThis maymay havehave advantagesadvantages forfor certaincertain combustion systems systems in in which which ignition ignition aid aid is isuseful. useful. This This may may be betrue true for fora number a number of low of lowtemperature temperature combustion combustion systems systems such such as as homogeneous homogeneous charge charge compression compression ignition ignition (HCCI), (HCCI), controlledcontrolled autoignitionautoignition (CAI),(CAI), andand partiallypartially premixedpremixed combustioncombustion (PPC).(PPC). AA wide variety variety of of valve valve strategies strategies have have been been used used to accompl to accomplishish the internal the internal exhaust exhaust gas dilution gas dilution[29]. These [29 ].strategies These strategies include negative include negative valve overlap valve overlap(NVO), delayed (NVO), delayedexhaust exhaustvalve closing valve (dEVC), closing (dEVC),and the anduse of the a usesecond of a exhaust second exhaustevent during event the during intake the process. intake process. ThisThis brief brief evaluation evaluation will will consider consider the the negative negative valve valve overlapoverlap strategy. strategy. Table5 5shows shows the the conventionalconventional (positive (positive valve valve overlap) overlap) valve valve timing timing and the the negativenegative valve valve overlap overlap valve timings. TheseThese schematicsschematics showshow thethe qualitativequalitative valvevalve liftlift asas aa functionfunction ofof crankcrank angle.angle. AsAs shown,shown, forfor thethe NVONVO strategy,strategy, thethe exhaustexhaust valvevalve closescloses beforebefore thethe intakeintake valvevalve opens.opens. ThisThis providesprovides aa periodperiod nearnear TDCTDC inin whichwhich nono valvesvalves areare open,open, andand thereforetherefore thethe pistonpiston compressescompresses thethe cylindercylinder gases.gases. ThisThis isis oneone reasonreason thatthat the the NVO NVO strategy strategy is sometimes is sometimes referred referred to as to “recompression.” as “recompression.” In any In case, any the case, strategy the isstrategy effective is foreffective increasing for increasing the retention the retention of combustion of combustion gases and gases providing and providing internal exhaustinternal gasexhaust dilution. gas dilution. TheThe uniqueunique characteristicscharacteristics ofof NVONVO strategiesstrategies areare illustratedillustrated inin thethe nextnext twotwo figures.figures. FigureFigure 2020 showsshows thethe exhaustexhaust andand intakeintake massmass flowflow ratesrates asas functionsfunctions ofof crankcrank angleangle forfor thethe casecase ofof aa NVONVO ofof 120120 ◦°CA.CA. ToTo achieveachieve thethe samesame load,load, thethe flowflow ratesrates forfor NVONVO strategiesstrategies areare higherhigher thanthan forfor thethe originaloriginal valvevalve timings.timings. InIn addition,addition, the the period period near near TDC TDC has has no no flows. flows. Figure Figure 21 21 shows shows the the cylinder cylinder pressure pressure as aas function a function of crankof crank angle angle for for the the case case of a of NVO a NVO of 120 of 120◦CA. °CA. The The peak peak cylinder cylinder pressure pressure is higher is higher for thefor NVO the NVO case compared case compared to the to conventional the conventional valve timing. valve timing. In addition, In addition, the “recompression” the “recompression” around 360around◦TDC 360 is °TDC illustrated. is illustrated.

Inventions 2018, 3, 33 20 of 30

InventionsInventions 2018,, 3,, xx FORFOR PEERPEER REVIEWREVIEW 20 of 30 Table 5. Alternative Valve Timings for Internal Exhaust Gas Dilution. Table 5.5. Alternative Valve Timings for Internal Exhaust Gas Dilution.

Exhaust IntakeIntake ConventionalConventional Valve Valve Timings—PositiveTimingsTimings—Positive—Positive Valve Overlap (PVO) Overlap (PVO) Expansion Exhaust IntakeIntake Compression BC TCBCTC BC

NVO Exhaust IntakeIntake

“Recompression”—Negative“Recompression”“Recompression”—Negative—Negative ValveValve Overlap Overlap (NVO) Expansion Exhaust IntakeIntake Compression BC TCBCTC BC

FigureFigure 22 22shows shows the the net net indicatedindicated and and brake brake thermal thermal efficiencies efficiencies as functions as functions of the of negative the negative valvevalve overlap. overlap. The The efficiencies efficiencies decrease decrease as as the the NVO NVO increases increases due due to the to the following. following. As the As NVO the NVO increases,increases, thethe burnedburned gasgas percentagepercentage increasesincreases fromfrom aboutabout 4%4% toto 21%21% forfor thesethese conditionsconditions andand rangerange increases, the burned gas percentage increases from about 4% to 21% for these conditions and range of of NVO. Due to the conflicting effects of retaining high temperaturetemperature gases and the dilution, the NVO. Due to the conflicting effects of retaining high temperature gases and the dilution, the average average combustion temperatures (the average combustion temperature represents the average of combustionthe one-zoneone-zone temperatures gas temperature (the average during combustionthe combustion temperature event) decreased represents from the 1932 average to 1814 of K the as the one-zone gasNVO temperature increased. during The heat the transfer combustion increasesincreases event) as the decreased NVO increases from due 1932 to increases to 1814 K of as the the heat NVO transfer increased. Thecoefficient. heat transfer The effects increases of increasing as the NVO heat transfer increases on duethe thermal to increases efficiency of theare heatsomewhat transfer offset coefficient. by Thethe effects increase of increasing of the ratio heat of specific transfer heats on as the the thermal NVO increases. efficiency are somewhat offset by the increase of the ratioOf of interest specific is heatsa comparisoncompar as theison NVO of the increases. external and internal exhaust gas dilution approaches relative toOf the interest thermal is efficiencies. a comparison Since of the the internally external retained and internal gases maintain exhaust gastheir dilution high temperatures, approaches the relative to thecomparison thermal is efficiencies. with the adiabatic Since EGR the configuration, internally retained which would gases be maintain expected their to be highsimilar temperatures, to the internalinternal exhaust exhaust gas gas dilution dilution approach. approach. To To compare compare the the two two approaches, approaches, the the total total burned burned gas gas the comparison is with the adiabatic EGR configuration, which would be expected to be similar to percentage is used. For the internal exhaust gas dilution, the burned gas percentage is identical to the the internal exhaust gas dilution approach. To compare the two approaches, the total burned gas residual gas percentage. For the externalexternal exhaust gas dilution, the burned gas percentage is a percentagecombination is used. of the residual For the gases internal and exhaustthe recirculated gas dilution, exhaust gases. the burned gas percentage is identical to the residualFigure 23 gas shows percentage. the net indicated For the and external brake thermal exhaust efficiencies gas dilution, as functions the burned of the gas burned percentage gas is a combinationpercentage for of the the residual NVO approach gases and and the the recirculated adiabatic EGR exhaust approach. gases. For both approaches, the efficienciesFigure 23 decrease shows with the netincreasing indicated burned and gas brake percentage thermal for these efficiencies conditions. as functionsThe two approaches of the burned gasresult percentage in about for the thesame NVO thermal approach efficiencies. and The the use adiabatic of the adiabatic EGR approach.EGR configuration For both provides approaches, a theslight efficiencies advantage decrease for the lower with burned increasing gas percentages. burned gas This percentage appears to be for due these to a conditions.slight decrease The of two approachesthe exergy result destruction in about during the same combustion thermal and efficiencies. a slight decrease The use of the the adiabatic pumping EGR work configuration for the adiabatic EGR approach compared to the NVO approach. provides a slight advantage for the lower burned gas percentages. This appears to be due to a slight decrease of the exergy destruction during combustion and a slight decrease of the pumping work for the adiabatic EGR approach compared to the NVO approach. Inventions 2018, 3, 33 21 of 30 InventionsInventions 2018 2018, ,3 3, ,x x FOR FOR PEER PEER REVIEW REVIEW 2121 of of 30 30

180180 2000 rpm, bmep = 900 kPa 2000 rpm, bmep = 900 kPa 160  = 1.0, CR = 10 160  = 1.0, CR =o 10 NVO = 120o CA Exhaust NVO = 120 CA Exhaust Flow 140 Flow 140 Intake Intake Flow Flow 120120

100100

80 80 NVO NVO

6060 Flow Rates (g/s) Flow Rates (g/s)

4040

2020 IVO IVC IVO IVC 00 EVO EVC EVO EVC -20-20 100100 200200 300300 400400 500500 600600 o Crank Angle o( aTDC) Crank Angle ( aTDC) Figure 20. Exhaust and intake mass flow rates as functions of crank angle for a NVO of 120 °CA for Figure 20.20. ExhaustExhaust andand intakeintake mass flowflow ratesrates as functionsfunctions of crankcrank angle for aa NVONVO ofof 120120 ◦°CCAA for case 1. case 1.1.

6000 6000 bmep = 900 kPa bmep = 900 kPa 2000 rpm, CR = 10 2000 rpm, CR = 10o  = 1.0,  = 50o 5000  = 1.0,  b= 50 5000 b o NVO = 120o CA NVO = 120 CA

4000 4000

3000 3000 Pressure (kPa) Pressure Pressure (kPa) Pressure 2000 2000

1000 1000

0 0 -180 -90 0 90 180 270 360 450 540 -180 -90 0 90 180 270 360 450 540 o Crank Angle o( aTDC) Crank Angle ( aTDC) FigureFigure 21. 21. Cylinder Cylinder pressurepressure as as aa a functionfunction function of of crankcrank crank angleangle angle forfor for aa a NVONVO NVO ofof of 120120 120 ◦°C CA°CAA for for case case 1.1. 1. Inventions 2018, 3, 33 22 of 30 Inventions 2018,, 3,, xx FORFOR PEERPEER REVIEWREVIEW 22 of 30

41

bmep = 900 kPa 2000 rpm CR = 10,  == 1.01.0 40 MBT Timing Net Indicated Efficiency MBT Timing

39

38 Base

37 Thermal Efficiencies Thermal (%) Thermal Efficiencies Thermal (%) Brake Efficiency

36

35 -20-20 0 20 40 60 80 100 120 140 NVO (---) NVO (---) FigureFigure 22.22. Net indicatedindicated andand brakebrake thermalthermal efficienciesefficiencies asas functionsfunctions ofof thethe negativenegative valvevalve overlap.overlap.

41 bmep = 900 kPa 2000 rpm Net Indicated Efficiency 2000 rpm CR = 10,  == 1.01.0 EGR increasing MBT Timing 40 EGRadad increasing MBT Timing Base

NVO increasing 39

38

37 Thermal Efficiency (%) ThermalEfficiency Thermal Efficiency (%) ThermalEfficiency Brake Efficiency Base Base EGR increasing EGRadad increasing 36 NVO increasing

35 0 5 10 15 20 25 Burned Gas Percentage (%) Figure 23. Net indicated and brake thermal efficiencies as functions of the burned gas percentage for FigureFigure 23.23. NetNet indicatedindicated andand brakebrake thermalthermal efficienciesefficiencies asas functionsfunctions ofof thethe burnedburned gasgas percentagepercentage forfor both the NVO and the adiabatic EGR strategies. bothboth thethe NVONVO andand thethe adiabaticadiabatic EGREGR strategies.strategies.

6. Example Three: Thermodynamics of the Otto Cycle 6.6. ExampleExample Three:Three: Thermodynamics ofof thethe OttoOtto CycleCycle

6.1.6.1. BasicsBasics ofof thethe IdealIdeal OttoOtto CycleCycle InIn this this subsection, subsection, the the Otto Otto cycle cycle and its and applicability its applicability to IC engines to IC engines will be described. will be described. In particular, In theparticular, features the of thefeatures Otto of cycle the thatOtto are cycle consistent that are andconsistent not consistent and not withconsistent IC engines with IC will engines be identified. will be Theidentified. Otto cycle The is Otto one cycle of several is one ideal of several (air standard) ideal (air models standard) that have models been that used have since been atleast used the since early at 1900s.least the The early Otto 1900s. cycle is The based Otto on cycle constant is based volume on (typicallyconstant volume at TDC) heat(typically addition. at TDC) These heat ideal addition. models These ideal models consist of a number of simplifying assumptions and approximations. One of the most common sets of these assumptions and approximations is

Inventions 2018, 3, 33 23 of 30 consist of a number of simplifying assumptions and approximations. One of the most common sets of these assumptions and approximations is Inventions 2018, 3, x FOR PEER REVIEW 23 of 30 • The working fluid is air; • TheThe compressionworking fluid and is air expansion; processes are adiabatic and reversible (isentropic); • TheThe combustioncompression process and expansion is replaced processes with a heatare adiabatic addition processand reversible under prescribed(isentropic) conditions;; • TheThe exhaustcombustion blow-down process processis replaced is replaced with a heat by a addition constant process volume under heat rejection prescribe atd BDC; conditions; • InletThe exhaust and exhaust blow strokes-down process are not included.is replaced by a constant volume heat rejection at BDC;  Inlet and exhaust strokes are not included. These assumptions and approximations allow a solution for the thermal efficiency to be These assumptions and approximations allow a solution for the thermal efficiency to be obtained obtained [1]. For constant volume heat addition and constant properties, [1]. For constant volume heat addition and constant properties, − η  =1 −CRCR11 γ (8) OttoOtto (8) inin whichwhich CRCRis is the the compression compression ratio ratio and andγ γis is the the ratio ratio of of the the specific specific heats. heats. The The resulting resulting values values of the of thermalthe thermal efficiency efficiency are not are in not agreement in agreement with actual with actual IC engines IC engines for a number for a number of reasons. of reasons. These reasons These arereasons explained are explained in this subsection. in this subsection. FigureFigure 2424 showsshows the thermal efficiencyefficiency forfor the Otto cyclecycle using constant properties (Equation(Equation (8))(8)) asas functionsfunctions ofof thethe ratioratio ofof specificspecific heatsheats forfor compressioncompression ratiosratios ofof 88 andand 16.16. TheThe thermalthermal efficiencyefficiency increasesincreases withwith increasesincreases ofof compressioncompression ratioratio andand increasesincreases ofof thethe ratioratio ofof specificspecific heats.heats. OfOf particular importanceimportance is the high sensitivity of the thermal efficiency efficiency on the value of the ratio of specific specific heats. ForFor aa changechange ofof the the ratio ratio of of specific specific heats heats from from 1.2 1.2 to 1.3,to 1.3, the the thermal thermal efficiency efficiency increases increases by about by about 13% (absolute).13% (absolute). The importanceThe importance of the of ratio the ratio of the of specific the specific heats heats is described is described in the in following. the following.

70

Otto Cycle CR = 16

60

CR = 8

50

40 Otto Cycle Efficiency (%) Efficiency Cycle Otto

30

20 1.1 1.2 1.3 1.4 Gamma ()

FigureFigure 24.24. TheThe thermal efficiencyefficiency forfor thethe OttoOtto cyclecycle asas aa functionfunction ofof gammagamma forfor compressioncompression ratiosratios ofof 88 andand 16.16.

Traditionally, the Otto cycle analysis has been used to model IC engines. This is inappropriate Traditionally, the Otto cycle analysis has been used to model IC engines. This is inappropriate for for a number of reasons. The fact that several features of the Otto cycle are consistent with IC engines a number of reasons. The fact that several features of the Otto cycle are consistent with IC engines has obscured the fact that the Otto cycle is fundamentally incorrect as a model of the IC engine. First, has obscured the fact that the Otto cycle is fundamentally incorrect as a model of the IC engine. those features of the Otto cycle that are consistent with the IC engine are described. This is followed First, those features of the Otto cycle that are consistent with the IC engine are described. This is by a discussion of those features of the Otto cycle that are not consistent with IC engines. This followed by a discussion of those features of the Otto cycle that are not consistent with IC engines. subsection ends with a quantitative description of the importance of the ratio of specific heats relative to thermal efficiencies.

6.2. Features Consistent with IC Engines At least some of the appropriate thermodynamics (relative to IC engines) are included in the following portions of the Otto cycle: Inventions 2018, 3, 33 24 of 30

This subsection ends with a quantitative description of the importance of the ratio of specific heats relative to thermal efficiencies.

6.2. Features Consistent with IC Engines At least some of the appropriate thermodynamics (relative to IC engines) are included in the following portions of the Otto cycle:

• The compression and expansion processes. • Temperature (and pressure) increases due to thermal energy addition • The mechanical conversion of pressure increases to work.

As described below, certain characteristics of IC engines can be explored using the Otto cycle based on these features that are consistent with IC engines. Basically, due to these features, the two items that are often considered are the effects of the ratio of specific heats and compression ratio on the thermal efficiencies. These are examined below.

6.3. Features Inconsistent with IC Engines The major weakness of the Otto cycle as a model for IC engines is that it represents a heat engine and not a chemical conversion device. The fact that the Otto cycle uses heat addition to simulate combustion is fundamentally incorrect. This means that the Otto cycle does not include the combustion irreversibilities that are a significant reason for the less than 100% thermal efficiencies. In fact, the Otto cycle is based completely on ideal processes and has no irreversibilities. AppendixA is a description of the combustion irreversibilities and their impact on efficiency. Other deficiencies of the Otto cycle are well known (e.g., [1]) and are summarized next:

• Heat transfer in actual engines is significant, particularly during combustion and expansion. • Actual combustion processes require a finite time (of order 50 ◦CA), and do not occur instantaneously at TDC. • Flow processes in actual engines may limit the charge mass, and may compromise the network of the cycle due to valve timings (e.g., exhaust valve opening before BDC). • Other real effects that are not part of the Otto cycle include blow-by, incomplete combustion, chemical dissociation, and mechanical and fluid friction.

6.4. Thermodynamics of the Otto Cycle As mentioned above, two items of the Otto cycle that are relevant to actual IC engines are the ratio of specific heats and compression ratio. The following is a brief summary of the role of the ratio of specific heats on engine performance and thermal efficiency. Complete details may be found elsewhere [9,10]. The ratio of specific heats is often given the symbol gamma (γ). For simplicity, the expression “ratio of specific heats” will be replaced with “gamma” in the following. Although gamma is the property used throughout this discussion, the specific heats are the primary properties of importance. Gamma and the specific heats are related:

Cp R gamma = γ = Cp = Cv + R γ = 1 + (9) Cv Cv

Note that gamma increases when the specific heats decrease. Figure 25 shows the cylinder pressure as a function of the cylinder volume for the Otto cycle. Isentropic compression is from 1 to 2; constant volume heat addition is from 2 to 3; isentropic expansion is from 3 to 4; and constant volume heat rejection is from 4 to 1. In the following discussion, the state points (1, 2, 3, and 4), as denoted in the figure, will be used. Inventions 2018, 3, 33 25 of 30 Inventions 2018, 3, x FOR PEER REVIEW 25 of 30

Inventions 2018, 3, x FOR PEER REVIEW250 25 of 30 3 Otto Cycle 250 3 200 Otto Cycle

200

150

1 150 p/p 100 1 p/p 100

50 2

50 2 4 0 1 4 0 0 2 4 6 8 10 12 14 16 18 1

V/Vmin 0 2 4 6 8 10 12 14 16 18 FigureFigure 25. The 25. cylinderThe cylinder pressure pressure (relative (relative to to the the initialinitialV/V pressure) as as a afunction function of ofthe the cylinder cylinder volume volume min (relative(relative to the to minimum the minimum volume) volume) for for the the Otto Otto cycle. cycle. Figure 25. The cylinder pressure (relative to the initial pressure) as a function of the cylinder volume (relativeUsing the to simplethe minimum Otto c volume)ycle, the for effects the Otto of gamma cycle. can be demonstrated for the compression, heat Usingaddition the, and simple expansion Otto cycle,processes. the effectsThe isentropic of gamma compression can be demonstrated work is given forby the compression, heat addition, andUsing expansion the simple processes.Otto cycle, the The effects isentropic of gamma compression can be demonstrated work is given for the by compression, heat CR 1 1 addition, and expansion processes. The isentropicWcomp  compression work is given by  (10) mRT  γ−11
Wcomp 1 CR 1 − 1 Wcomp= CR 1 (10) mRT  γ − 1 (10) This result means that the compressionmRT1 work increases1 as gamma increases. This is a slight 1 negative effect regarding the thermal efficiency. Figure 26 shows the increase of this non-dimensional This result means that the compression work increases as gamma increases. This is a slight workThis as a resultfunction means of gamma that the for compressiona compression w ratioork increasesof 16. as gamma increases. This is a slight negativenegative effect effect regarding regarding the the thermal thermal efficiency. efficiency. FigureFigure 26 showsshows the the increase increase of ofthis this non non-dimensional-dimensional workwork as a functionas a function of gamma of gamma for 6for a compressiona compression ratio ratio ofof 16. "Otto" Cycle 6 CR = 16 "Otto" Cycle Compression Work 5 CR = 16

Compression Work 5

4

4

3

Non-Dimensional Work Non-Dimensional 3

Non-Dimensional Work Non-Dimensional 2 Expansion Work

2 Expansion Work

1 1.2 1.3 1.4

1 Gamma 1.2 1.3 1.4 Figure 26. The non-dimensional work for the compression and expansion strokes as functions of Gamma gamma for a compression ratio of 16 for the Otto cycle. FigureFigure 26. The 26. The non-dimensional non-dimensional work work for for the the compression compression and and expansion expansion strokes strokes as functions as functions of of gammagamma for a for compression a compression ratio ratio of of 16 16 for for the the Otto Otto cycle.cycle. Inventions 2018, 3, 33 26 of 30

The heat addition results in temperature and pressure increases, and these are given by

Qin mR mR Qin ∆T = (∆p)v = ∆T = (11) Cv V V Cv

As the specific heats decrease (gamma increases), the temperature and pressures after the heat addition increase. These higher pressures are the source of the increased expansion work for increases of gamma. This is the major effect of gamma on engine thermal efficiency, and is representative of actual engines [10]. For the isentropic expansion process,   − 1 Wexp 1 CRγ−1 = (12) mRT3 γ − 1

As gamma increases, the expansion work decreases. This is a slight negative effect regarding the thermal efficiency. Figure 26 shows the decrease of this non-dimensional work as a function of gamma for a compression ratio of 16. In summary, for increases of gamma, the compression work increases, the expansion work decreases, and the heat addition results in increases of cylinder pressure. The net effect of increases of gamma is increases of the thermal efficiency (Figure 24). For a paper on the thermodynamics of IC engines, a discussion of the Otto cycle is needed, since the Otto cycle is often cited as a model of IC engines. As pointed out here, the Otto cycle is an incorrect model, since it represents a heat engine and not a chemical conversion device. This means that the Otto cycle contains no information on the combustion process, and in particular, on the irreversibilities of the combustion process. In spite of this major weakness, the Otto cycle does represent the effects of specific heats and compression ratio in an approximately correct fashion. In fact, the Otto cycle allows the effects of the specific heats on thermal efficiency to be demonstrated. The full simulation of IC engines includes these same effects, but it is much more difficult to separate the individual effects of specific heats [9,10].

7. Summary and Conclusions

7.1. Summary This paper provided examples that demonstrate the importance of thermodynamics relative to internal combustion engines. An engine cycle simulation was used for the majority of the work, and employed both the first and second laws of thermodynamics. The major focus of this work was related to increasing the thermal efficiencies. Some of the results reinforced well known ideas about achieving higher efficiencies. Other portions of this work revealed deeper insights about the important approaches for attaining higher efficiencies. Some of the major conclusions and findings are summarized next. Throughout these examples, the importance of the ratio of specific heats (gamma) was demonstrated. In particular, for engine operation or designs that result in lower combustion temperatures, gamma increases, and this results in higher levels of conversion of thermal energy to work. More details on the importance of gamma may be found elsewhere [10].

7.2. Thermodynamics of LHR Engines • A low heat rejection engine concept was examined by increasing the cylinder wall temperatures. As the cylinder wall temperature increased, the heat losses decreased, and the thermal energy of the cylinder gases increased. Inventions 2018, 3, 33 27 of 30

• Even for the extreme conditions examined (a cylinder wall temperature of 1500 K), very little of the retained thermal energy could be realized as addition work. This is consistent with the majority of the experimental results. • The paper outlined a series of reasons for the difficulty of converting the reduction of heat losses into work. • The retention of thermal energy (even if no addition work is produced) could be advantageous, since the exhaust gas energy may be useful for turbo-charging or other applications.

7.3. Thermodynamics of Exhaust Gas Dilution • Both external and internal exhaust gas dilution were examined. • External exhaust gas dilution can use some level of cooling. This work examined an adiabatic EGR configuration and a cooled EGR configuration. • The cooled EGR configuration provides significant efficiency benefits due to decreased heat losses and increases of the ratio of specific heats in spite of modest increases of exergy destruction during combustion. • The adiabatic EGR configuration resulted in lower efficiencies due to increases of the heat losses in spite of modest reductions of exergy destruction during combustion. • The use of negative valve overlap results in increased retention of combustion gases. This approach provided results that were similar to the use of the adiabatic EGR configuration.

7.4. Concerning the Otto Cycle • The classical Otto cycle was reviewed, and identified as an analysis for heat engines and not chemical conversion devices such as IC engines. • The Otto cycle does, however, possess three thermodynamic characteristics that are consistent with IC engines. These are (1) the mechanical advantage of increasing compression ratio, (2) the conversion of thermal energy to work, and (3) the compression and expansion processes. • The Otto cycle, however, is inconsistent with IC engines for several reasons. Perhaps the most important of these is that the Otto cycle does not include a combustion process, and therefore completely neglects the combustion irreversibilities. • The Otto cycle does, however, allow the importance of the ratio of specific heats and compression ratio to be demonstrated.

Acknowledgments: No funding was received related to this work, and no funding was available for publication costs. Conflicts of Interest: The author declares no conflict of interest.

Appendix A. Brief Review of Combustion Irreversibilities for IC Engines In this appendix, the combustion irreversibilities associated with IC engines are briefly reviewed. In particular, the results presented here are designed to be contrasted with results from the Otto cycle. These results are intended to emphasize the fact that since the Otto cycle does not include combustion, these irreversibilities are absent. The engine cycle simulation described in the main part of this paper was used to obtain the following results. The same engine operating at 2000 rpm with a bmep of 900 kPa was used for this evaluation. The conditions for these computations were selected to approach an ideal cycle: no heat transfer ◦ (htm = 0), no friction (fm = 0), short burn duration θb = 10 CA), and lean mixture (ϕ = 0.2). In this way, these results represent the maximum possible efficiencies for an essentially ideal engine. Figure A1 shows the partition of the fuel energy among work, exhaust, and unburned fuel as a function of compression ratio. This curve represents the thermal efficiency. Since the IC engine is a chemical conversion device, for these ideal conditions, the thermal efficiency could be close to 100%. Inventions 2018, 3, 33 28 of 30

These results (largely from the first law of thermodynamics) do not provide insight about the real limitations. This is shown next. Figure A2 shows the partitions of the fuel exergy among work, destruction during combustion, exhaust, and other items. These other items include a small exergy destruction due to the mixing of theInventionsInventions incoming 20182018,, 33 charge,, xx FORFOR PEERPEER with REVIEWREVIEW the residual gases (~1%) and unburned fuel (0.7%). The percentage28 of28 ofof the 3030 fuel exergy (Figure A2) and the percentage of the fuel energy (Figure A1) assigned to work are almost identical.identical.identical. TheThe workwork valuevalue inin “kJ”“kJ” isis thethe same,same, butbut becausebecabecauseuse thethe fuelfuel energyenergy (LHV)(LHV) andand thethe fuelfuel exergyexergy areare aboutaboutabout 3%3%3% differentdifferentdifferent (for (for(for isooctane), isooctane),isooctane), the thethe percentages percentagespercentages are areare slightly slightlyslightly different. different.different.

100100

9090 ExhaustExhaust ++ UnburnedUnburned 8080

7070

6060

5050

4040 Fuel Energy (%) Fuel Energy Fuel Energy (%) Fuel Energy WorkWork 3030

2020 bmepbmep == 900900 kPa,kPa, 20002000 rpmrpm htmhtm == 0,0, fmfm == 00  = 0.2,  = 10ooCA 1010  = 0.2, bb = 10 CA MBTMBT TimingTiming 00 55 1010 1515 2020 2525 3030 3535 CompressionCompression RatioRatio FigureFigure A1.A1.A1. PartitionPartition of of thethe fuelfuel energyenergy amongamong work,work, exhaust,exhaustexhaust,, andand unburnedunburned fuelfuel asas aaa functionfunctionfunction ofof compressioncompressioncompression ratioratioratio forforfor the thethe ideal idealideal conditions. conditions.conditions.

100100

ExhaustExhaust ++ otherother 9090

8080 DestructionDestruction DuringDuring CombustionCombustion 7070

6060

5050

4040 Fuel Exergy (%) Fuel Exergy Fuel Exergy (%) Fuel Exergy

WorkWork 3030

2020 bmepbmep == 900900 kPa,kPa, 20002000 rpmrpm htmhtm == 0,0, fmfm == 00 10  = 0.2,  = 10ooCA 10  = 0.2, bb = 10 CA MBTMBT TimingTiming 00 55 1010 1515 2020 2525 3030 3535 Compression Ratio Compression Ratio Figure A2. Partition of the fuel exergy among work, destruction, exhaust, and other items as a FigureFigure A2. A2.Partition Partition of of the the fuel fuel exergy exergy among among work, work, destruction, destruction, exhaust, exhaust and other, and items other as items a function as a function of compression ratio for the ideal conditions. offunction compression of compression ratio for the ratio ideal for conditions.the ideal conditions.

TheThe nextnext itemitem inin FigureFigure A2A2 isis thethe percentagepercentage ofof thethe fuelfuel exergyexergy destroyeddestroyed duringduring combustioncombustion.. ForFor thesethese conditions,conditions, thisthis rangesranges fromfrom 26%26% toto 32%.32%. This,This, then,then, isis thethe importantimportant insightinsight fromfrom thethe secondsecond lawlaw ofof thermodynamicsthermodynamics (and(and isis notnot partpart ofof thethe resultsresults usingusing onlyonly thethe firstfirst law).law). TheThe importanceimportance ofof thisthis informationinformation isis thatthat thethe exergyexergy destroyeddestroyed durinduringg combustioncombustion isis significant,significant, andand isis aa largelarge partpart ofof thethe reasonreason forfor thethe lessless thanthan 100%100% efficiencyefficiency eveneven forfor thesethese idealideal conditions.conditions. TheThe remainingremaining fuelfuel exergyexergy isis containedcontained inin thethe exhaustexhaust andand thethe unburnedunburned fuelfuel component.component. TheThe exergyexergy inin thethe exhaustexhaust isis duedue toto thethe Inventions 2018, 3, 33 29 of 30

The next item in Figure A2 is the percentage of the fuel exergy destroyed during combustion. For these conditions, this ranges from 26% to 32%. This, then, is the important insight from the second law of thermodynamics (and is not part of the results using only the first law). The importance of this information is that the exergy destroyed during combustion is significant, and is a large part of the reason for the less than 100% efficiency even for these ideal conditions. The remaining fuel exergy is contained in the exhaust and the unburned fuel component. The exergy in the exhaust is due to the less-than-perfect conversion of thermal energy to work. In theory, as the compression ratio increases, this percentage approaches zero. Since the Otto cycle is a model of a heat engine (and has no combustion process), the irreversibility of combustion is absent. So, in general, the Otto cycle is an incorrect model of the IC engine and does not include the important aspect of combustion.

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