Sage Journals: Discover world-class research

Abstract

This work compares the fundamental thermodynamic underpinnings (i.e. working fluid properties and heat release profile) of various combustion strategies with engine measurements. The approach employs a model that separately tracks the impacts on efficiency due to differences in rate of heat addition, volume change, mass addition, and molecular weight change for a given combination of working fluid, heat release profile, and engine geometry. Comparative analysis between the measured and modeled efficiencies illustrates fundamental sources of efficiency reductions or opportunities inherent to various combustion regimes. Engine operating regimes chosen for analysis include stoichiometric spark-ignited combustion and lean compression-ignited combustion including homogeneous charge compression ignition, spark-assisted homogeneous charge compression ignition, and conventional diesel combustion. Within each combustion regime, the effects of engine load, combustion duration, combustion phasing, compression ratio, and charge dilution are explored. Model findings illustrate that even in the absence of losses such as heat transfer or incomplete combustion, the maximum possible thermal efficiency inherent to each operating strategy varies to a significant degree. Additionally, the experimentally measured losses are observed to be unique within a given operating strategy. The findings highlight the fact that to create a roadmap for future directions in internal combustion engine technologies, it is important to not only compare the absolute real-world efficiency of a given combustion strategy but also to examine the measured efficiency in context of what is thermodynamically possible with the working fluid and boundary conditions prescribed by a strategy.

Keywords

Thermodynamics Otto cycle modeling spark ignition compression ignition efficiency cycle analysis

Introduction

The dominant prime-mover for personal mobility and freight transport is the internal combustion engine (ICE). In the United States, ICE applications are heavily dependent on market segment. For light-duty applications, spark-ignited (SI) engines dominate the segment, while compression-ignited (CI) engines, primarily based on conventional diesel combustion (CDC), dominate the heavy duty-passenger and freight transport segments.

SI engines rely on spark timing for controlling the combustion event, and therefore require fuels with high resistance to autoignition, which in the United States is specified by anti-knock index (AKI)—calculated by averaging the research octane number (RON) and motor octane number (MON). Recent evolution in the SI segment has been driven toward downsizing and downspeeding for maximum efficiency,^1,2 which has seen the increased market penetration of enabling technologies such as continually variable or 6 +speed transmissions, gasoline direct injection (GDI), and turbocharging.^3,4 At high loads, SI engines are limited by knock, and this is exacerbated by the downsizing trend. Methods of raising the knock limit include reducing compression ratio (r_c)⁵ which reduces efficiency, increasing fuel AKI,^6–8 and the use of exhaust gas recirculation (EGR), which can result in efficiency gains comparable to compression ratio increases,⁹ and also introduce problems with combustion stability.^10,11

CI engines operating with a CDC strategy rely on combustion that is mixing-controlled, where combustion control is achieved through injection timing and pressure. Because CDC is not limited by knock, it can achieve high thermal efficiency by operating at high r_c. The primary challenge with CDC is controlling NO_x and soot emissions, which presents cost and efficiency trade-offs.¹² As an alternative to CDC, several advanced low-temperature CI strategies have been proposed.^13–18 These strategies generally seek to avoid NO_x and soot formation using long ignition delay and low equivalence ratio, which reduces peak temperatures. This approach has shown order-of-magnitude reductions in both pollutants while maintaining or improving on gross efficiency. However, these advanced concepts still face technical challenges such as control, stability, combustion noise, operating range, and transient capability before they are likely to find market acceptance.

To create a roadmap for future directions in ICE technologies, it is important to not only compare the absolute real-world efficiency of a given combustion strategy but also put that number in context of what is thermodynamically possible with the conditions prescribed by a given strategy. In other words, to assess the future potential of a given strategy, there needs to be an understanding of the efficiency ceiling, how close the state of the art is to the ceiling, and how much closer we can expect to come in the future. As an idealization, ICEs are often modeled as heat engines undergoing reversible thermodynamic cycles, such as the Otto cycle. In the Otto cycle, the working fluid is air with a constant ratio of specific heat, $γ$ , and it undergoes a closed cycle with isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection.¹⁹ The efficiency of the Otto cycle can be expressed as

η_{O t t o} = 1 - \frac{1}{r_{c}^{(γ - 1)}}

(1)

For a closed cycle with constant $γ$ , the Otto cycle represents the upper bound on heat engine efficiency. Several studies have proposed thermodynamic cycle-based analysis of maximum engine efficiency. For instance, a conventional slider-crank approach by Patterson and Hampson²⁰ and non-conventional designs such as those illustrated in opposed piston engines by Herold et al.²¹ and free piston engines by Teh et al.²² However, as noted by Foster,²³ an ICE is not a closed-cycle heat engine; rather, it is an open-cycle thermochemical energy conversion device. An ICE irreversibly converts the chemical energy stored within the working fluid (i.e. the reactant mixture) into thermal energy, and then converts that thermal energy into mechanical energy via constrained expansion. Thus, the composition and thermodynamic properties of the working fluid change throughout this process, and the heat release event occurs over a finite range of time (and therefore, volume), which is not necessarily coincident with the minimum volume of the cycle at top dead center (TDC). All these considerations mean that even in an idealized case with no losses due to heat transfer, incomplete combustion, or turbulence, the maximum efficiency achievable with a given working fluid may vary considerably from the Otto cycle prediction.^23
–25 To that end, we present a model which seeks to capture these working fluid and heat release effects in an attempt to calculate a more realistic maximum efficiency, as well as a framework for interpreting and comparing experimental efficiency data from various combustion strategies.

Methods

The current approach uses a first-law thermodynamic model coupled with experimental data from multiple GM 2.0L GDI SI engines (engine code LNF) and a GM 1.9L compression-ignition engine (engine code DTH). The subsequent sections will detail the specifics of the thermodynamic model and experimental platforms.

Thermodynamic model

For this work, a model was developed to track the properties of a working fluid undergoing a prescribed heat release profile. This model is based on a single-zone, first-law analysis of an ideal gas under adiabatic conditions, with all derivatives taken in the crank angle (CA) $(θ)$ space. With these assumptions, the pressure derivative, $d p / d θ$ , can be written in terms of the contributions due to heat addition, $\overset{\cdot}{Q}$ , volume change, $d V / d θ$ , mass addition, $d m / d θ$ , and molecular weight change, $d M / d θ$ , as

\frac{d p}{d θ} = {(\frac{d p}{d θ})}_{Q} + {(\frac{d p}{d θ})}_{V} + {(\frac{d p}{d θ})}_{m} + {(\frac{d p}{d θ})}_{M}

(2)

{(\frac{d p}{d θ})}_{Q} = (\frac{γ - 1}{V}) \overset{\cdot}{Q}

(3)

{(\frac{d p}{d θ})}_{V} = - \frac{γ p}{V} \frac{d V}{d θ}

(4)

{(\frac{d p}{d θ})}_{m} = [\frac{γ p}{m} - (\frac{γ - 1}{V}) (h - h_{f})] \frac{d m}{d θ}

(5)

{(\frac{dp}{d θ})}_{M} = - \frac{p}{M} \frac{d M}{d θ}

(6)

where $h$ is the specific enthalpy of the in-cylinder mixture and $h_{f}$ is the specific enthalpy (both sensible and vaporization) of the injected fuel. The derivation of equations (2)–(6) is provided in Appendix 2. By independently calculating the change in pressure from each term, the impact of the individual terms on work extraction and efficiency can be determined. If the slider-crank geometry is known, the values of $V$ and $d V / d θ$ are known a priori at all θ, and we therefore need $\overset{\cdot}{Q}$ , $M$ , and $γ$ to calculate the pressure. In other words, the pressure trace can be found for any arbitrarily prescribed heat release and composition profile. For this work, we have chosen to represent the heat release rate with a normal distribution, shown in equation (7), as it requires the specification of only two parameters (mean, $μ$ , and standard deviation, $σ$ ), is symmetric about its mean, and is equivalent to the Otto cycle in the limiting case that $μ = 0$ CA degrees (°CA) after top dead center (aTDC) and $σ = 0^{\circ} CA$ . An experimental condition can be modeled simply by setting $μ$ equal to the combustion phasing as represented by the crank angle at 50% of heat release (CA50) and by setting $σ$ such that the combustion duration, or number of crank angles between 25% and 75% of heat release (CA25-75), of the resulting normal distribution will match that of the heat release $(CA 25 - 75 ≅ 1.35 σ)$ . More information regarding the implications of using the normal distribution to represent heat release rate is provided in Appendix 2

\overset{\cdot}{Q} (θ) = \frac{1}{σ \sqrt{2 π}} \exp [- \frac{{(θ - μ)}^{2}}{2 σ^{2}}]

(7)

The model assumes that the rate of conversion from reactants to products is proportional to the rate of heat release. No kinetic models, intermediate species, or dissociation products are considered. Any injected fuel is assumed to vaporize and mix instantly, and the enthalpy difference between the fuel and air (including enthalpy of vaporization) is captured in equation (5). No other mass changes are considered. The simulation spans from −180° to +180°CA aTDC and does not consider any gas exchange process. At each step in the simulation, the thermodynamic properties of the fluid ( $γ$ and $h$ ) are calculated from NASA polynomials.²⁶ Each component of the pressure derivative is calculated and summed to find the total pressure change, which then yields the total pressure and temperature for a given step. The temperature dependence of $γ$ and $h$ drives the selection of step size and also dictates that the combustion and injection durations must be finite for their impact on the properties of the working fluid to be accurately captured. Note that this model does not attempt to accurately model or predict the actual combustion process, as done in other zero-dimensional models which quantify potential loss mechanisms.²⁷ Rather, by including the effects of temperature and compositional changes within the working fluid for an arbitrarily prescribed heat release event under adiabatic conditions with no other loss mechanisms, this model endeavors to represent a more realistic upper bound on thermodynamic efficiency than the air-standard Otto cycle, and thereby allows for the performance of a given combustion strategy to be put in context of theoretical limits.

Experimental platforms and conditions

The operating conditions from the selected experimental results were used as inputs to the model described in the previous section. The specifics of the engine design parameters are presented in Table 1. Note that the bore, rod length, and stroke are similar between the two engine platforms, representing common light-duty passenger car applications.

Table 1.

Experimental and modeled engine geometries.

Engine platform	Bore (mm)	Stroke (mm)	Rod (mm)
GM LNF	86.0	86.0	145.5
GM DTH	82.0	90.4	145.4

The experimental conditions are presented in Table 2. The engine speed for all experimental conditions was 2000 r/min. The operating conditions can be grouped into three general combustion modes: autoignition, mixing-controlled, and flame propagation. For the cases shown in Table 2, the engine was operated at conditions relevant to the given combustion strategy and with an emphasis on achieving the highest practical gross thermal efficiency (GTE) while sweeping load. For each condition, load sweeps were conducted from 200 kPa gross indicated mean effective pressure (IMEP_g) to a constraint of CA50 of 25°CA aTDC, coefficient of variation (COV) of IMEP_g of 3%, 96 dB combustion noise, or the engine peak cylinder pressure limit. Additional information on the operating conditions, engine specifics, and detailed results can be found in previous works.^6,7,28,29

Table 2.

Experimental and modeled engine operating conditions for load sweeps.

Engine platform	Combustion mode	Fuel	r_c (-)	EGR (%)	IMEP_g range (kPa)	CA50 range (°CA aTDC)
GM LNF	SI, ϕ = 1	87 AKI gasoline	11.85:1	0	200–900	8–25
GM LNF	SI, ϕ = 1	87 AKI gasoline	9.2:1	0	200–1400	8–25
GM LNF	SI, ϕ = 1	87 AKI gasoline	11.85:1	15	200–1000	8–25
GM LNF	SA-HCCI, ϕ = 1	87 AKI gasoline	11.85:1	40–48	250–600	7–18
GM LNF	HCCI, ϕ < 1	87 AKI gasoline	11.85:1	20–38	350–800	7.5–9
GM DTH	CDC, ϕ < 1	ULSD	16.5:1	0	315–1625	14–10

EGR: exhaust gas recirculation; IMEP_g: gross indicated mean effective pressure; CA50: crank angle at 50% of heat release (combustion phasing); °CA: crank angle degrees; aTDC: after top dead center; SI: spark-ignited; AKI: anti-knock index; SA-HCCI: spark-assisted homogeneous charge compression ignition; CDC: conventional diesel combustion; ULSD: ultra-low-sulfur diesel.

Results and discussions

The results are presented in three sections: combustion phasing and duration, stoichiometric operation, and lean operation.

Thermodynamic implications of combustion phasing and duration

A visualization of the impact that combustion phasing and duration have on modeled thermal efficiency is shown in Figure 1. The reactants for this example were a premixed stoichiometric mixture of iso-octane and air with no EGR and a starting temperature of 40°C at −180°CA aTDC. The modeled volume trace was prescribed from the geometry of the LNF engine in Table 1 with r_c = 11.85:1. The general trend, as expected, is that increasing combustion duration and moving combustion phasing away from TDC both contribute to decrease efficiency, because both cause a reduction in the effective expansion ratio. However, due to the temperature dependence of $γ$ , the contour is not symmetrical about TDC. The phasing at which maximum efficiency can be found is retarded with increasing combustion duration. It can also be observed that for phasing close to TDC, combustion duration is the dominant factor driving efficiency, whereas for sufficiently retarded combustion phasing, combustion duration has negligible impact on efficiency.

Figure 1.

Contour plot of model-predicted maximum thermal efficiency (no losses) as a function of combustion duration and phasing for a stoichiometric mixture of iso-octane and air in the LNF engine with r_c = 11.85:1. The heavy solid black line represents the combustion phasing resulting in maximum efficiency for a given value of combustion duration.

For each of the experimental cases in the load sweep from Table 2, CA50, CA25–75, and GTE were calculated from the measured in-cylinder pressure. The results are shown in Figure 2, where all data are plotted on a common axis in Figure 2(a) and are also delineated by combustion regime and load sweep direction in Figure 2(b)–(d). Figure 2 illustrates that a wide range of CA50, CA25–75, and GTE are encountered in the various regimes and that each moves through the CA25–75 versus CA50 space in a different way as load is increased. For the CDC load sweep, shown in Figure 2(c), the low-load condition has relatively late phasing and short duration, and the initial load increase is achieved by increasing injection duration at fixed start of injection (SOI), which causes combustion duration to increase without changing the phasing, because the rate of combustion is limited by the rate of injection due to the majority of heat release occurring within the mixing-limited regime. As illustrated in Figure 1, there is only a modest thermodynamic penalty to increasing CA25–75 in this range of CA50, and it is outweighed by other factors such as changing equivalence ratio, heat transfer, and incomplete combustion, resulting in a 2% absolute GTE improvement from 315 to 600 kPa IMEPg. At this transition point, the operating strategy transitions to 0% EGR with the EURO 4 emissions calibration used for these experiments. The CDC strategy changes such that SOI advances while increasing rail pressure, which causes combustion phasing to advance and the premixed portion of the burn to increase, essentially maintaining constant combustion duration. This coincides with a 1.7% absolute GTE improvement from 600 to 1625 kPa IMEPg.

Figure 2.

Load sweep of various combustion regimes from two engines (Table 2) illustrating combustion phasing and duration effects shaded by GTE: (a) all data, (b) autoignition regime (HCCI and SA-HCCI), (c) mixing-controlled regime (CDC), and (d) flame-propagation regime (SI).

For the SI load sweeps, shown in Figure 2(d), the path through the combustion phasing and duration space is essentially opposite to the CDC strategy in Figure 2(c). For SI combustion, idle occurs at relatively advanced phasing and long duration, and the initial load increase occurs with a maximum brake torque (MBT) strategy at fixed phasing and coincides with a decrease in duration and an increase in GTE. Once the knock limit is reached, the spark timing is retarded with further load increase, a region commonly referred to as knock-limited spark advance (KLSA). Increased load in the KLSA region coincides with a moderate increase in duration and a 1.4% absolute decrease in GTE from KLSA onset at 500–900 kPa IMEP_g for the 0% EGR case shown in Figure 2(d). The addition of 15% EGR shifts the entire SI load sweep to longer combustion duration, but has several benefits that will be discussed in the following sections. Note that the GTE trends for SI follow Figure 1 more closely than those for CDC because SI employs fixed equivalence ratio $(ϕ = 1)$ , whereas for CDC $ϕ$ starts lean and increases with load (from ϕ = 0.23 to ϕ = 0.6).

Two distinct combustion strategies are included in the autoignition regime presented in Figure 2(b). Homogeneous charge compression ignition (HCCI) operates at lean conditions throughout its load sweep and is contained to a small region at early combustion phasing and short combustion duration, all of which are beneficial to GTE. However, the lack of control over the heat release profile for HCCI relative to the other strategies is evident in Figure 2(a). Spark-assisted (SA) HCCI operates at $ϕ = 1$ and follows a trajectory through the combustion duration versus phasing space that is similar in shape to SI, but which spans a much larger range of duration, and is essentially between SI and HCCI in this space, as seen in Figure 2(a). For the presented experimental results, SA-HCCI tends not to exhibit significant advantages as it combines the small load range of HCCI (Figure 4) with the low GTE of SI, where the GTE and maximum load of SA-HCCI were less than HCCI (Table 2).

To directly compare the measured efficiency to the model-predicted efficiency, the measurement conditions were provided as inputs to the model. In this approach, the measured CA50, CA25–75, initial conditions (i.e. intake temperature, EGR, $ϕ$ ), and engine geometry were supplied to the model, thereby generating a prediction of maximum possible efficiency for each experimental case. The model-predicted GTE was then compared to the measured GTE for each condition in Table 2 using equation (8)

Relative efficiency loss (%) = \frac{100 \times (Model GTE - Measured GTE)}{Model GTE}

(8)

Using this approach, the trends of Figure 2 were analyzed in terms of the relative efficiency loss as a function of combustion phasing and presented in Figure 3. Data in Figure 3 show that as the load increases, the relative efficiency loss decreases. Interestingly, for combustion modes that are knock-limited, that is, SA-HCCI in Figure 3(b) and SI in Figure 3(d), the relative efficiency loss decreases with increasing load even when combustion phasing is retarded. On the contrary, Figure 3(c) shows that CDC actually advances combustion phasing with load and continues to reduce relative efficiency loss with increasing load. Finally, unlike the SI and CI strategies that illustrate reduction in relative efficiency loss that are functions of combustion phasing, the HCCI data in Figure 3(b) were contained to a narrow range of CA50, and the SA-HCCI data show little to no dependency of relative efficiency loss on combustion phasing. The data for all three regimes are shown together in Figure 3(a), where trends in relative efficiency loss seem to be non-universal as a function of combustion phasing. This finding illustrates that there are complex aspects and relations present in trends of engine efficiency which could be regime dependent and may not be uniquely aspects of combustion phasing. What is suggested by the trends in Figure 3 is that relative efficiency loss may be better correlated to load than combustion phasing. To explore this possibility, the data in Figure 3 were plotted as a function of IMEP_g in Figure 4.

Figure 3.

Relative efficiency loss as a function of combustion phasing for various combustion regimes from two engines (Table 2) illustrating reduction in losses with increasing load: (a) all data, (b) autoignition regime (HCCI and SA-HCCI), (c) mixing-controlled regime (CDC), and (d) flame-propagation regime (SI).

Figure 4.

Load sweep of various combustion regimes from two engines (Table 2) illustrating reduction in losses with increasing load: (a) all data, (b) autoignition regime (HCCI and SA-HCCI), (c) mixing-controlled regime (CDC), and (d) flame-propagation regime (SI).

While Figure 4(a) shows that all combustion strategies except CDC tend to operate with a similar relative efficiency loss for a given load, it should be noted that the absolute GTE values are widely divergent, with a nearly 10% GTE difference between modes. The CDC trend in Figure 4(a) does show that relative efficiency loss is inversely proportional to load; however, the trend is not as steep as with the other combustion strategies. Again, unlike the other combustion strategies, as load increased with CDC, combustion phasing was advanced, causing an increase in heat transfer. CDC is the only combustion regime not knock-limited (HCCI has a knock-induced noise limit), suggesting that if knock is not encountered, there could be dependency of relative efficiency loss on combustion phasing. Another factor illustrated in Figure 4 is that dilution could also offer reduced relative efficiency loss. For example, Figure 4(d) shows that the addition of 15% EGR with SI combustion reduced losses for a given load, and comparing directly to lean operation with HCCI in Figure 4(a) shows similar or slightly greater reductions. Whether accomplished by adding EGR or air, dilution tends to reduce heat transfer by decreasing the temperature of the charge. The effects of EGR on SI combustion will be studied in greater detail in the following section, but the trends observed in Figure 4 suggest that the complex relations previously shown in Figure 3 could be functions of heat transfer and incomplete combustion, which both tend to decrease on a relative basis as load increases.

Thermodynamic implications of stoichiometric operation

To understand how the working fluid impacts efficiency, we first look at the ratio of specific heat, $γ$ . To illustrate the degree to which $γ$ can vary with both composition and temperature, Figure 5(a) shows the $γ$ versus temperature profiles for air, a stoichiometric air and iso-octane reactant mixture, the products corresponding to that reactant mixture, and the same reactant mixture with EGR added. Not only does the reactant mixture have a significantly lower $γ$ than air at 300 K, but the difference in $γ$ between the two fluids increases with temperature, which is a function of CA. As with most hydrocarbons, the product mixture for complete combustion of iso-octane has higher $γ$ than the reactants, and for that reason, adding EGR in stoichiometric engines can be an effective means of increasing the $γ$ of the reactant mixture. The CA evolution of $γ$ can be seen in Figure 5(b), which shows simulations of $γ$ assuming a prescribed heat release with CA50 = 10°CA aTDC and CA25–75 = 10°CA for working fluids consisting of air and stoichiometric mixtures of air and iso-octane at various EGR levels on the LNF engine geometry with r_c = 11.85:1.

Figure 5.

(a) Ratio of specific heat as a function of temperature for air, a stoichiometric reactant mixture of iso-octane and air, a product mixture resulting from combustion of the reactants, and the reactant mixture with 50% EGR and (b) ratio of specific heat as a function of crank angle for air and stoichiometric mixtures of iso-octane and air with various levels of EGR, both reacting and non-reacting.

As noted in Figure 5(b), the iso-octane cases were simulated as both “reacting” and “non-reacting,” with an assumption of transition from reactants to products and fixed composition, respectively. Note that the rate of heat release was imposed identically for all cases regardless of the working fluid or transition to products, which is simply modeled as being coincidental with heat release in the reacting cases. Comparing the reacting and non-reacting cases therefore illustrates the effect of compositional changes and molar conversion and expansion on $γ$ . The addition of EGR to the non-reacting cases creates an initial increase in $γ$ due to the reactants’ compositional difference and an even larger increase in $γ$ during the expansion stroke as a result of decreased combustion temperature caused by dilution. The reacting cases are identical to the non-reacting cases during the compression stroke, but the conversion of reactants to products results in the formation of species with higher $γ$ , increasing the improvement seen from EGR during combustion and the expansion stroke. Because combustion of iso-octane results in molar expansion,³⁰ there is an additional efficiency benefit in the reacting cases. The breakdown of the efficiency impacts of $γ$ and molar expansion are analyzed in Figure 6.

Figure 6.

(a) Individual contributions to efficiency from the heat addition, volume, and molecular weight terms for the 0% EGR cases from Figure 5(b), (b) same plot with the contributions from heat addition and volume combined, and (c) change in absolute efficiency of each term with addition of EGR, relative to the 0% EGR case.

Figure 6(a) illustrates the individual contributions to overall efficiency for each term in equations (3)–(6) using the 0% EGR cases from Figure 5(b). Equations (3)–(5) are dependent on $γ$ , while equations (4)–(6) are dependent on pressure, convolving pressure and $γ$ dependency. As expected from equation (3), in the reacting case, increased $γ$ increases the work output due to heat addition. However, the increase in $γ$ also increases the negative work done by the volume change, as indicated in equation (4). The cases in Figure 5(a) and (b) are fully premixed, so there is no mass change due to injection, leading equation (5) to have no contribution. The fact that the reacting case has an increase in the number of moles from products to reactants means that the molecular weight decreases, which results in positive work from equation (6). If we combine the influences of the $γ$ -dependent heat and volume terms into a single bar (Q + V), as in Figure 6(b), we observe that there is actually a net decrease in efficiency when reactions occur, although it is more than offset by the efficiency gain due to the decrease in molecular weight (M). As shown in Figure 6(c), the addition of EGR further shifts the relative contributions by bringing the composition of the reactants closer to that of the products, which has two main effects: increase in $γ$ , which improves the net effect of the heat and volume terms, and a decrease in the difference between the initial and the final molecular weights, which reduces the work output from mole creation. The sum of these effects is an increase in total efficiency with the addition of EGR.

To explore the model-predicted effects in Figures 5 and 6, measurements and the model predictions were compared. The measurements were conducted for premixed SI engine operation on a common GM LNF platform with 9.2:1 or 11.85:1 r_c and 87AKI fuel (90 RON). The specifics of the conditions are provided in Table 2 for the three experiments to be discussed here: 0% EGR at 9.2:1 r_c and both 0% and 15% EGR at 11.85:1 r_c. Load was swept from 200 kPa to knock at MBT CA50 (8°CA aTDC) for all configurations. Once knock-limited, CA50 was retarded from 8° to 25°CA aTDC while maintaining constant combustion noise and visual inspection of end gas knock. Further details on the specific results and approach are found in Splitter and Szybist.^6,7,28 The general operating conditions for the experiments, that is, engine geometry, r_c, intake temperature, and EGR rate, were used as inputs to the model to generate efficiency contours as a function of combustion phasing and duration, such as the one presented in Figure 1. The model used a toluene reference fuel (TRF) with a molar blend of 50% iso-octane, 20% n-heptane, and 30% toluene, which was determined using the method described by Morgan et al.,³¹ resulting in an octane rating and H/C ratio equivalent to the 87AKI gasoline used in the measured conditions from Table 2. This blend is referred to as TRF87.

The experimental values and model contours of GTE as a function of CA50 and CA25–75 are compared in Figure 7, which reveals several interesting trends in combustion phasing and duration space, as well as the effects of relative efficiency loss as a function of load. First, in Figure 7(a), for a given combustion phasing and duration, the model-predicted efficiency contour lines illustrate that the efficiency of the 11.85:1 r_c is higher than the 9.2:1 r_c. This is not unexpected, as the Otto cycle efficiency given in equation (1) is a function of compression ratio. However, what is illustrated in Figure 7(a) is that the compression ratio could not be increased without affecting combustion phasing or duration. Increasing r_c required both a reduction in load and an increase in combustion duration to maintain a given phasing, and maintaining a given load required both a retard in phasing and increase in duration. While the impact of duration was minimal due to the nearly vertical slope of the efficiency contours in this region, being forced to retard combustion phasing moved the 900-kPa IMEP_g point from just above the 44% model GTE contour for 9.2:1 r_c to below the 42% model GTE contour for 11.85:1 r_c. This resulted in a decrease in measured GTE for the 900-kPa load condition, even with the reduction in relative efficiency loss shown in Figure 7(b). This reduction in relative efficiency loss with increased compression ratio can be attributed to heat transfer reduction due to retarded combustion phasing, which reduces peak temperatures, in-cylinder turbulence intensities, and the amount of time available for heat transfer. However, these reductions in relative efficiency loss are not enough to overcome the direct GTE loss due to retarded combustion phasing. In addition to the decrease in GTE for a given load, operating with 11.85:1 r_c also restricts the maximum load due to combustion instability and increased exhaust gas temperatures encountered at very retarded combustion phasing.

Figure 7.

Measured KLSA conditions of 87 AKI fueled data from (Table 2): (a) model-predicted contours overlaid with measured data and measured GTE in CA25–75 versus CA50 space and (b) the same measured data plotted in relative efficiency loss versus IMEP_g space.

One method for recovering the lost GTE and load at increased compression ratio is the use of EGR, which reduces the bulk gas temperature by diluting the charge, and therefore reduces knocking propensity. As Figure 7(a) shows, the addition of 15% EGR allowed the 900-kPa IMEP_g point to advance in phasing while increasing in duration. The increase in duration has a negligible impact on model GTE, while the advance in phasing moves the operating point up the efficiency gradient. Simultaneously, the use of EGR inherently increases the efficiency for a given phasing and duration by increasing $γ$ during combustion, as shown previously in Figure 6. This gives a double benefit, as not only does the point move to the left in Figure 7(a) with EGR but also the contour moves to the right, moving the 900-kPa load point from below the 42% GTE contour for 11.85:1 r_c with 0% EGR to the 44% GTE contour for 11.85:1 r_c with 15% EGR. A third benefit is that peak temperature reduction with EGR reduces heat transfer, resulting in further decrease in relative efficiency loss, as shown in Figure 7(b). The horizontal line in Figure 7(b) illustrates that a given relative efficiency loss can be achieved at significantly lower load when using increased compression ratio with EGR. These three benefits to efficiency are complimented by an increased load limit for a given compression ratio, making EGR a very attractive addition to SI combustion.

The trends in Figure 7 illustrate that relative efficiency losses can be reduced through increasing load or r_c, albeit with tradeoffs between load range and absolute efficiency. However, EGR was found to reduce the tradeoff magnitude by increasing load range, but more importantly, the combination of increasing r_c with EGR offered multiple benefits in both relative efficiency loss and absolute GTE through $γ$ improvement and combustion phasing improvement with EGR knock suppression. The combined trends and tradeoffs in Figure 7 suggest that in SI engines, EGR, heat transfer, fuel octane number, load, and combustion chamber design could affect how far the relative efficiency loss can be minimized.

Thermodynamic implications of lean operation

CDC and other compression-ignition strategies typically involve direct injection under lean conditions. The model presented here allows us to examine the losses inherent to direct injection as described in equation (5), as opposed to the previous analysis in which the charge was assumed to be completely premixed before the start of simulation. For the purpose of illustration, simulations were performed with n-heptane at ϕ = 0.3, a starting temperature of 100°C, CA50 = 10°CA aTDC, and CA25–75 = 10°CA using the geometry of the LNF engine with r_c = 11.85. The evolution of $γ$ is shown for air, a premixed case, and several injection timings in Figure 8(a).

Figure 8.

(a) Ratio of specific heat as a function of crank angle for air and lean mixtures of n-heptane and air at the premixed condition and with various injection timings and (b) change in absolute efficiency of the heat addition, volume, and molecular weight terms as a function of injection timing, relative to the premixed case.

Figure 8(a) shows that before the fuel is injected, the mixture is composed only of air, and therefore has a higher $γ$ during compression than it would if the fuel were premixed. During fuel injection, $γ$ decreases rapidly, but due to the difference in specific enthalpy between the charge and the fuel, cases with injected fuel do not decrease $γ$ as much as initially premixed fuel does. This $γ$ difference depends on the enthalpy of vaporization of the fuel, the temperature of the fuel (presently assumed 50°C), and the enthalpy of the charge, which increases with temperature during compression. As the cylinder approaches TDC, the relative impact of the injection on the total pressure is reduced due to the significant increase in total cylinder pressure, meaning that the temperature difference due to fuel vaporization is minimized, and $γ$ for late injection cases approaches that of the premixed case. Injection timing effects on the heat addition, volume, mass addition, and molecular weight terms are shown in Figure 8(b). The combined trends in Figure 8 illustrate that increased $γ$ during compression is beneficial to the sum of the heat and volume terms (equations (3) and (4)), especially as injection timing approaches TDC. However, at injection timings near TDC, the compression heating increases the difference between the enthalpy of the charge and the injected fuel, subsequently decreasing in-cylinder pressure upon injection. Viewed on its own, the integrated pressure due to the mass term (equation (5)) can be interpreted as negative work, which increases in magnitude as injections occur closer to TDC. Additionally, direct fuel injection also causes an increase in molecular weight, which reduces the work that would have been generated due to molar expansion (equation (6)). The combined increase in negative work from the mass term and the decrease in positive work from the molecular weight term outweigh the increase from the heat and volume terms as injection is retarded, causing a decrease in total efficiency for injections later than −100°CA aTDC (at the simulated condition).

The addition of EGR to lean combustion has several complications when compared to stoichiometric combustion, one of which is the selection of equivalence ratio and the subsequent impact on $γ$ and losses from the mass term. For the fully premixed cases shown in Figures 5 and 6, the equivalence ratio was held at unity. However, for lean CI combustion, equivalence ratio of unity is not present, and EGR can be added at constant intake pressure, at constant equivalence ratio, or anywhere in between. Maintaining constant intake pressure is roughly equivalent to holding constant charge-mass equivalence ratio, as defined in equation (9)

ϕ^{'} = ϕ \times (1 - \frac{EGR%}{100})

(9)

In other words, the two bounding cases for CI engine operation are that charge mass increases by adding EGR to a conserved mass of air ( $ϕ$ constant) or that charge mass is conserved by replacing air with EGR ( $ϕ'$ constant). The results for these two cases are shown in Figure 9 for n-heptane injection at −20°CA aTDC with an initial $ϕ = 0.3$ , 0% EGR, a starting temperature of 40°C, and combustion profile of CA50 = 10°CA aTDC, and CA25–75 = 10°CA with the geometry of the LNF engine at r_c = 11.85:1. Figure 9(a) shows the efficiency trends for an EGR sweep with constant $ϕ = 0.3$ , which causes a reduction in $ϕ'$ , or an overall increase in dilution.

Figure 9.

(a) Individual contributions to efficiency from the heat addition + volume, mass, and molecular weight terms for an EGR sweep under diesel-like combustion at $ϕ = 0.3$ , relative to the 0% EGR case; (b) individual contributions to efficiency from each term for an EGR sweep under diesel-like combustion at $ϕ' = 0.3$ , relative to the 0% EGR case; and (c) individual contributions to efficiency from each term for an equivalence ratio sweep spanning the same range as (a) and (b) with 0% EGR, relative to $ϕ' = ϕ = 0.3$ .

Conserving air with increasing EGR in Figure 9(a) illustrates that the total efficiency increases with EGR. Interestingly, since near-TDC injections were assumed (i.e. diesel combustion), the dilution from EGR actually decreases $γ$ during compression by diluting high-γ air with exhaust products while at the same time increasing $γ$ during expansion by lowering combustion temperature. These effects essentially cancel each other out from the perspective of the sum of the heat and volume terms (Q + V). The addition of EGR also reduces the enthalpy of the mixture, which decreases the enthalpy difference driving the losses due to mass injection, reducing the effect of near-TDC direct injection on decreasing total efficiency. As in the premixed case, we also find that EGR reduces the difference in molecular weight between the products and reactants, which diminishes the positive work from mole creation (M). The decrease in the negative work done by mass injection (m) is the dominant effect, leading to an overall improvement in efficiency with EGR.

Unlike the trends observed in Figure 9(a) with conserved air, if the total mass is conserved with increasing EGR, the trends in efficiency change significantly. Figure 9(b) shows the case of constant charge mass at $ϕ' = 0.3$ , in which EGR is replacing air. This causes a significant decrease in $γ$ , which reduces the sum of heat and volume terms (Q + V) and also causes a larger reduction in enthalpy than the constant $ϕ$ case, resulting in even less negative work from the mass term (m) than when diluting with conserved air. Note that the molecular weight term (M) has almost no change, and there is an essentially negligible decrease in overall efficiency. The comparison of Figure 9(a) and (b) illustrates the spectrum possible with increasing EGR in CI combustion strategies; total efficiency either increases (mass of air conserved) or has a negligible change (total mass conserved).

To put these results in context, a third case with no EGR was performed, in which the equivalence ratio was swept across the same values as the previous two cases. These results, in which $ϕ' = ϕ$ , are shown in Figure 9(c). Decreasing $ϕ$ (or increasing dilution with air) is seen to achieve almost identical increase in total efficiency as increasing dilution with EGR (Figure 9(a)), although the relative contributions of the various efficiency terms are different. The primary benefit for dilution with air is an improvement in $γ$ , whereas the primary benefit from dilution with EGR was a decrease in the losses from mass injection (m). The same efficiency trends continue with increasing $ϕ$ resulting in a loss in total efficiency, which illustrates that the substitution of EGR for air is far preferable to the removal of air with no substitute. In other words, in lean compression-ignition engines, dilution with either EGR or air is beneficial to efficiency by an almost identical amount, though the benefit is achieved by different mechanisms.

Conclusion

This analysis has described and coupled a first-principles zero-dimensional thermodynamic engine model with measured engine data. The results showed that combustion phasing and duration are important factors that contribute to engine efficiency, but several other factors are equally if not more important to realizing high engine efficiency:

Combustion phasing and duration space

•With all other variables constant, efficiency improves with decreased combustion duration and combustion phasing closer to TDC, though the temperature dependence of $γ$ for a given working fluid can alter the location of maximum efficiency.

•The various combustion strategies occupy different areas of the space, and their approach to traversing it with increasing load varies dramatically. Efficiency tends to maximize as load increases, provided that load can be increased without excessive CA50 retard.

Stoichiometric premixed charge SI engine operation

•The addition of EGR reduces the efficiency benefit due to molar expansion, but still provides an overall increase in efficiency due to increase in $γ$ .

•EGR reduces heat transfer losses, resulting in measured GTE closer to the model-predicted GTE.

•Efficiency is reduced during KLSA operation due to retarded combustion phasing, although not to the extent predicted by the model due to reduced heat transfer.

•Increased compression ratio can cause a reduction in efficiency for a given load by forcing the combustion phasing to retard to avoid knock (entering KLSA sooner) and by increasing heat transfer during MBT operation.

In lean CI engine operation

•Direct injection of fuel close to TDC creates a significant efficiency penalty due to pressure reduction and the impact on the molecular weight of the working fluid. This suggests that advanced CI strategies which take advantage of premixing or early direct injection may have implicit efficiency advantages that are not easily seen in the experimental results.

•Maintaining charge mass (constant $ϕ'$ ) with the addition of EGR offers little to no efficiency benefit in either the thermodynamic model or the experimental data.

•Charge dilution (constant $ϕ$ ) with the addition of EGR can increase efficiency primarily by reducing the penalty of direct injection.

•Charge dilution with the addition of air can increase efficiency primarily by increasing $γ$ . This point and the previous both suggest that strategies which operate under highly dilute conditions across the entire load range will have the highest indicated thermal efficiency. However, this would likely require further improvements to the efficiency of turbomachinery or the use of supplemental supercharging, and achieving maximum brake efficiency requires a system-wide optimization.

The presented findings illustrate that maximizing engine efficiency employs factors beyond those expressed in the Otto cycle. Most importantly, efficiency is affected not only by working fluid properties but also reductions in heat transfer, combustion phasing, fuel delivery strategies, fuel properties, and engine combustion chamber design. This analysis provides a guide as to methods and fundamentals for increasing engine efficiency, but is by no means an exhaustive analysis. Regardless, the findings and approach provide pathways for improving engine efficiency, demonstrating opportunities and challenges based on thermodynamic principles.

Footnotes

Appendix 1

Appendix 2 Acknowledgements

This research used resources at the National Transportation Research Center, a DOE Office of Energy Efficiency and Renewable Energy User Facility operated by the Oak Ridge National Laboratory.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This material is based on the work supported by the US Department of Energy, Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Office via the Advanced Combustion Engine manager Gurpreet Singh.

References

Lecointe

Monnier

. Downsizing a gasoline engine using turbocharging with direct injection. SAE technical paper 2003-01-0542, 2003.

Bandel

Fraidl

Kapus

Sikinger

Cowland

. The turbocharged GDI engine: boosted synergies for high fuel economy plus ultra-low emission. SAE technical paper 2006-01-1266, 2006.

Hula

Bunker

Alson

. Light-duty automotive technology, carbon dioxide emissions and fuel economy trends: 1975 through 2013, Appendix F. Report, US Environmental Protection Agency, Ann Arbor, MI, 2013, http://www.epa.gov/oms/fetrends.htm#report

Pawlowski

Splitter

. SI engine trends: a historical analysis with future projections. SAE technical paper 2015-01-0972, 2015.

Smith

Cheng

. Assessing the loss mechanisms associated with engine downsizing, boosting and compression ratio change. SAE technical paper 2013-01-0929, 2013.

Splitter

Szybist

. Intermediate alcohol-gasoline blends, fuels for enabling increased engine efficiency and powertrain possibilities. SAE Int J Fuels Lubr2014; 27(1): 29–47.

Splitter

Szybist

. Experimental investigation of spark-ignited combustion with high-octane biofuels and EGR. 1. Engine load range and downsize downspeed opportunity. Energ Fuel2014; 28(2): 1418–1431.

Leone

Anderson

Davis

Iqbal

ReeseII

Shelby

Studzinski

. The effect of compression ratio, fuel octane rating, and ethanol content on spark-ignition engine efficiency. Environ Sci Technol2015; 49(18): 10778–10789.

Alger

Mangold

Roberts

Gingrich

. The interaction of fuel anti-knock index and cooled EGR on engine performance and efficiency. SAE Int J Engines2012; 5: 1229–1241.

10.

Finney

Kaul

Daw

Wagner

Edwards

Boyd Green

. Invited review: a review of deterministic effects in cyclic variability of internal combustion engines. Int J Engine Res2015; 16(3): 366–378.

11.

Ozdor

Dulger

Sher

. Cyclic variability in spark ignition engines: a literature survey. SAE technical paper 940987, 1994.

12.

Kokjohn

Reitz

. Reactivity controlled compression ignition and conventional diesel combustion: a comparison of methods to meet light-duty NO_x and fuel economy targets. Int J Engine Res2013; 4: 360–374.

13.

Kimura

Aoki

Ogawa

Muranaka

Enomoto

. New combustion concept for ultra-clean and high-efficiency small DI diesel engines. SAE technical paper 1999-01-3681, 1999.

14.

Yao

Zheng

Liu

. Progress and recent trends in homogeneous charge compression ignition (HCCI) engines. Prog Energ Combust2009; 35(5): 398–437.

15.

Dec

Yang

. Boosted HCCI for high power without engine knock and with ultra-low NO_x emissions-using conventional gasoline. SAE Int J Engines2010; 3: 750–767.

16.

Manente

Johansson

Tunestal

. Partially premixed combustion at high load using gasoline and ethanol, a comparison with diesel. SAE technical paper 2009-01-0944, 2009.

17.

Sellnau

Moore

Sinnamon

Hoyer

Foster

Husted

. GDCI multi-cylinder engine for high fuel efficiency and low emissions. SAE Int J Engines2015; 8: 775–790.

18.

Kokjohn

Hanson

Splitter

Reitz

. Fuel reactivity controlled compression ignition (RCCI): a pathway to controlled high-efficiency clean combustion. Int J Engine Res2011; 12(3): 209–226.

19.

Moran

Shapiro

. Fundamentals of engineering thermodynamics. 5th ed. Hoboken, NJ: John Wiley & Sons, 2004, p.875.

20.

Patterson

Hampson

. Heat release design method for HCCI in diesel engines with simulation. SAE technical paper 2008-28-0006, 2008.

21.

Herold

Wahl

Regner

Lemke

Foster

. Thermodynamic benefits of opposed-piston two-stroke engines. SAE technical paper 2011-01-2216, 2011.

22.

Teh

Miller

Edwards

. Thermodynamic requirements for maximum internal combustion engine cycle efficiency. Part 1: optimal combustion strategy. Int J Engine Res2008; 9(6): 449–465.

23.

Foster

. Low temperature combustion—a thermodynamic pathway to high efficiency engines. National Petroleum Council Fuels Study, 28November2015, https://www.npc.org/FTF_Topic_papers/6-Low_Temperature_Combustion.pdf

24.

Lavoie

Ortiz-Soto

Babajimopoulos

Assanis

. Thermodynamic sweet spot for high-efficiency, dilute, boosted gasoline engines. Int J Engine Res2012; 14: 260–278.

25.

Caton

. The thermodynamic characteristics of high efficiency, internal-combustion engines. Energ Convers Manage2012; 58: 84–93.

26.

McBride

Zehe

Gordon

. NASA Glenn coefficients for calculating thermodynamic properties of individual species, https://www.grc.nasa.gov/WWW/CEAWeb/TP-2002-211556.pdf

27.

Payri

Olmeda

Martin

García

. A complete 0D thermodynamic predictive model for direct injection diesel engines. Appl Energ2011; 88(12): 4632–4641.

28.

Splitter

Szybist

. Experimental investigation of spark-ignited combustion with high-octane biofuels and EGR. 2. Fuel and EGR effects on knock-limited load and speed. Energ Fuel2014; 28(2): 1432–1445.

29.

Kalaskar

Splitter

Szybist

. Gasoline-like fuel effects on high-load, boosted HCCI combustion employing negative valve overlap strategy. SAE Int J Fuels Lubr2014; 7: 82–93.

30.

Szybist

Chakravathy

Daw

. Analysis of the impact of selected fuel thermochemical properties on internal combustion engine efficiency. Energ Fuel2012; 26(5): 2798–2810.

31.

Morgan

Smallbone

Bhave

Kraft

Cracknell

Kalghatgi

. Mapping surrogate gasoline compositions into RON/MON space. Combust Flame2010; 157(6): 1122–1131.

32.

Ghojel

. Review of the development and applications of the Wiebe function: a tribute to the contribution of Ivan Wiebe to engine research. Int J Engine Res2010; 11(4): 297–312.

An assessment of thermodynamic merits for current and potential future engine operating strategies *

Abstract

Keywords

Introduction

Methods

Thermodynamic model

Experimental platforms and conditions

Results and discussions

Thermodynamic implications of combustion phasing and duration

Thermodynamic implications of stoichiometric operation

Thermodynamic implications of lean operation

Conclusion

Footnotes

Appendix 1

Appendix 2

Acknowledgements

Funding

References