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Initial conditions of the working fluid (air-fuel mixture) within an engine cylinder, namely, mixture composition and temperature, greatly affect the combustion characteristics and emissions of an engine. In particular, the percentage of residual gas fraction (RGF) in the engine cylinder can significantly alter the temperature and composition of the working fluid as compared with the air-fuel mixture inducted into the engine, thus affecting engine-out emissions. Accurate measurement of the RGF is cumbersome and expensive, thus making it hard to accurately characterize the initial mixture composition and temperature in any given engine cycle. This uncertainty can lead to challenges in accurately interpreting experimental emissions data and in implementing real-time control strategies. Quantifying the effects of the RGF can have important implications for the diagnostics and control of internal combustion engines. This paper reports on the use of a well-validated, two-zone quasi-dimensional model to compute the engine-out NO and CO emission in a gasoline engine. The effect of varying the RGF on the emissions under lean, near-stoichiometric, and rich engine conditions was investigated. Numerical results show that small uncertainties (~2–4%) in the measured/computed values of the RGF can significantly affect the engine-out NO/CO emissions.

The initial temperature, cylinder pressure, and composition of the working fluid (air-fuel mixture) play an important role in determining the combustion characteristics and consequently the emissions from an engine. Characteristics such as ignition delay, flame speed, and combustion stability are affected to varying degrees by the initial conditions of the mixture, depending on the engine operating conditions (e.g., engine speed, load, and ignition timing). These combustion characteristics have a direct impact on the engine-out emissions. Factors such as ambient temperature, air humidity, and residual gas introduce a degree of uncertainty in determining the exact initial conditions of the air-fuel mixture in the cylinder at the start of the compression stroke of an engine. The hot burned gas trapped in the clearance volume at the end of the exhaust stroke of the previous engine cycle is referred to as the residual gas [_{x} with a small addition of moisture _{2}, H_{2}O, nitrogen, and excess O_{2}, along with other minor combustion products such as NO, CO, and OH, and is typically above 350°C (depending on the engine operating conditions). The amount of residual gas depends on the compression ratio, valve location, and valve overlap. The residual gas (from the previous cycle) mixes with the fresh incoming charge of air and fuel inducted into the engine in the next cycle, thus altering the average temperature and mixture composition. In spark-ignited engines, the values of the RGF are estimated to be between 3% and 7% under full-load conditions but can be as high as 20% under part-load conditions. The RGF is smaller in Diesel engines on account of the larger compression ratio [_{2} can be present. The concentration of O_{2} in the engine cylinder has a strong impact on the flame propagation and kinetics (chemical effect). Furthermore, CO_{2} and H_{2}O (major components of the RGF) have higher specific heats than do N_{2} and O_{2} (main components of incoming air). As a result, the mixture-averaged ratio of specific heats (_{2} and H_{2}O in the initial engine charge can also affect the combustion kinetics and hence the ignition delay. Given these considerations, understanding the role of residual gas is important from an emissions standpoint. Several investigations, both experimental and numerical, have been conducted to determine the RGF [

Reported here is a systematic investigation of the sensitivity of engine-out NO and CO emission to small uncertainties in the measured/estimated values of RGF. In the absence of experimental data, numerical investigations can provide useful insight into effects of RGF on engine-out emissions. Conducting detailed multidimensional engine simulations with detailed chemistry require large computation resources. A typical parallel computation conducted on a single-cylinder engine over one cycle requires about 24–48 hours on about 30–50 cores. The prohibitively large computational resources required for multidimensional simulations preclude their use in conducting large parametric studies required for design/optimization. Reduced order models are ideally suited for conducting parametric studies in such cases. In this numerical study, a well-validated, fast, robust, two-zone quasi-dimensional model was used. A single-cylinder gasoline engine operating under lean (_{2} concentration in the working fluid. The fuel mass, initial cylinder pressure, and RPM were fixed for each of these air-fuel mixtures (lean to rich conditions). The RGF was varied from 0% (no RGF) to 7% in each case, and the temporal variation of NO and CO for each of these cases was computed by using reduced-order rate models. A small range of RGF variation was used in this study to assess the sensitivity of NO and CO emissions to small inaccuracies in experimental measurements/numerical estimates. Fast and robust quasi-dimensional models can be used not only for detailed analyses of a single engine cycle but also for analysis of complete engine drive cycles [

This paper is organized as follows. Sections

This section describes the two-zone quasi-dimensional model used to compute the temporal variation of the average cylinder pressure along with the burned and unburned gas temperature in a spark-ignited engine. The modified reaction rate-controlled models for NO and CO are also described in this section.

A numerical model used to compute the temporal variation of temperature and pressure in a single-cylinder diesel engine was described in detail in [

The energy equation describing the variation of pressure with crank angle is as follows.

The instantaneous values of volume

The convective heat transfer coefficient is expressed by the well-known Woschni correlation and is expressed as [

The velocity of the burned gas

Mixture-averaged values of specific heat of the working fluid were averaged by using mole fractions as follows.

The average gas temperature was obtained as follows:

The moles of CO_{2}, H_{2}O, O_{2}, and N_{2} produced in CAD _{2} : O_{2} moles in air (typically 3.76).

The total number of moles of any species (CO_{2}, H_{2}O, O_{2}, and N_{2}) in the burned zone at any crank angle _{2}, and N_{2}, are known, the composition of the burned zone (and hence unburned zone) can be computed based on (

The extended Zeldovich mechanism was used to derive a rate expression for the time rate of change of NO concentration. Details of the mechanism and rates can be found in [_{2}, NO, H, OH, and O_{2} are used in computing the RHS of (

Since the concentration

From SOI to EOC, the burned volume

The rate constants and equilibrium concentrations of species used in evaluating (^{3}).

The modified rate-controlled CO model used in this work is an adaptation of the model discussed in [

Details of (

The two-zone quasi-dimensional model described above was used to study the performance and emissions of a single-cylinder gasoline engine. Iso-Octane (C_{8}H_{18}) was used as a surrogate for gasoline for the sake of simplicity. In (_{2} : O_{2} ratio in air, is taken to be 3.76 and _{2}, H_{2}O, N_{2}, and excess O_{2} (for lean cases). The initial cylinder temperature at BDC was computed as a mass-averaged temperature of the incoming air and assumed percentage RGF. The initial cylinder gas composition (moles of O_{2}, N_{2}, H_{2}O, CO_{2}, and fuel) was computed on the basis of the pressure (at BDC), mass-averaged temperature, equivalence ratio, and the RGF.

The numerical procedure to obtain the cylinder pressure in a diesel engine is explained in detail in [

The engine dimensions and operating conditions used in this work are shown in Tables

Engine dimensions (in mm).

Bore | 59 |

Stroke | 103 |

Compression ratio | 8.1 |

Length of connecting rod | 255 |

Operating conditions used in this work.

Speed (rpm) | 1100 |

Inlet air temperature | 30°C |

RGF temperature | 350°C |

Spark timing | 26 btDC |

The burned zone comprised CO_{2}, H_{2}O, excess O_{2}, and the corresponding amount of N_{2}, whereas the unburned zone comprised the unburned fraction of fuel, O_{2}, and N_{2}. Equations (

Knowing the temporal variation of temperature, pressure, and elemental composition of the burned zone (from (_{2}, CO, CO_{2}, and N_{2} at every crank angle. Computation of equilibrium concentrations is very time-consuming. For this purpose, a fast, accurate, and robust solver based on the equilibrium constant method described in detail in [

The two-zone model described in Section _{2} and O_{2} and also the temperature of the burned gas mixture. While the temperature of the burned gas mixture is higher under near-stoichiometric conditions (as compared to lean mixtures), the concentrations of N_{2} and O_{2} of lean mixtures are higher than that of near-stoichiometric mixtures. Given the opposing effects of temperature and species concentration of N_{2} and O_{2} on the NO formation rate, the maximum NO formation occurs for 0.8 <

Temporal cylinder pressure (simulation and experimental data).

Comparison of predicted engine-out NO with experimental data for various equivalence ratios.

Comparison of predicted engine-out CO with experimental data for various equivalence ratios.

Experiments investigating the impact of the sensitivity of RGF on engine-out emissions are unavailable. Hence this section discusses the impact of variations in the RGF on engine-out NO and CO based on the numerical results obtained using the well-validated quasi-dimensional model described in Section

As discussed earlier, the cylinder pressure at BDC was kept constant for a given equivalence ratio, for all RGF fractions considered. Since the cylinder pressure at BDC can be computed using the ideal gas law

An increase in the percentage of RGF at BDC, implies an increase both in the mass of the residual gas (_{2} and O_{2} in the working fluid.

Figure

Variation of initial cylinder air mass with RGF.

The complete single step combustion of a hydrocarbon (lean and stoichiometric) can be represented as _{8}H_{18}, _{2} and 9 moles of H_{2}O.

Figures _{2}, H_{2}O, and CO in the burned gas zone normalized by the total number of fuel moles with no residual gas in the initial mixture (% RGF = 0). During the expansion stroke, the lean and stoichiometric cases show that the normalized moles of CO_{2} and H_{2}O are near the theoretically expected values and the moles of CO are insignificant. For rich mixtures, there is insufficient oxygen for complete combustion; hence the moles of CO_{2} and H_{2}O after combustion are below the expected theoretical values. Rich mixtures also show a significantly larger concentration of CO, compared to the lean and stoichiometric cases.

Variation of normalized moles of CO_{2} with crank angle.

Variation of normalized moles of H_{2}O with crank angle.

Variation of normalized moles of CO with crank angle.

Figure _{2} content of the fuel-air-RGF mixture. The reduction in the O_{2} content of the working fluid leads to incomplete fuel combustion. In other words, the lack of sufficient O_{2} in the mixture means that all fuel moles are not completely converted to the theoretically expected moles of CO_{2} and H_{2}O but produces a larger fraction of CO. CO is a fuel that can be combusted to generate additional thermal energy via the exothermic reaction [_{2} as shown in (

Effect of RGF and equivalence ratio on maximum burned gas temperature (K).

The percentage drop in the peak temperature is close to the percentage of RGF introduced into the mixture, both for stoichiometric and for rich mixtures. In other words, introducing a 3% RGF in the working fluid drops the peak temperature (of the 0% RGF mixture) by about 3%.

Figure _{2}) in the mixture (dilution effect of the RGF). Despite the increased peak temperature (for lean mixtures) the reduced mass of O_{2} and N_{2} in the initial working fluid lowers NO. The RGF acts as an internal exhaust gas recirculation (EGR) and hence leads to NO reduction. The percentage of RGF has a significant impact on the engine-out NO for both lean and rich mixtures. For instance, the numerical results show that, for lean mixtures, if the measured/estimated RGF = 5% with a ±2% error in the measurement/estimate, the error in the predicted NO is about 20%. The error is even more severe, if one were to note that, for lean mixtures, at RGF = 7%, there is about a 45% reduction in NO as compared with RGF = 0. Rich mixtures show about a 70% reduction in NO at an RGF of 7% as compared with RGF = 0. These results show that even a slight inaccuracy in the computed/measured value of the RGF fraction can have a significant impact on the engine-out NO.

Effects of RGF and equivalence ratio on engine-out NO (ppm).

Figure

Effect of RGF and equivalence ratio on engine-out CO (ppm).

Figure

Temporal variation of in-cylinder NO: (a) lean mixture and (b) rich mixture.

Figure _{2} and H_{2}O in the working fluid. As explained earlier, the higher specific heat values of CO_{2} and H_{2}O tend to decrease the mixture-averaged value of

Temporal variation of ratio of specific heats: (a) lean mixture and (b) rich mixture.

As noted earlier, the low computational time for a complete cycle simulation of quasi-dimensional codes enables their use for design/parametric studies. Fast robust solvers were developed to enable the quasi-dimensional code used in this work to complete an engine cycle simulation in 70 milliseconds on a 2.93 GHz, Intel E7500 processor. Since the code runs at near real-time speeds, large-scale parametric engine cycle studies can be conducted with minimal computational resources and wall-time.

A well-validated, two-zone, quasi-dimensional engine model was used to conduct a numerical study of the sensitivity of the engine-out NO and CO emissions to the uncertainty in the percentage of residual gas fraction. Rate-control models for the formation of NO and CO included the effect of changing cylinder volume. The mixture-averaged ratio of specific heat (_{2} and H_{2}O very close to the theoretically expected values, whereas rich mixtures yield a considerably higher concentration of CO as compared to lean and stoichiometric mixtures. The model also correctly predicts that the peak burned gas temperature occurs for the stoichiometric mixture for all RGF considered. The model also predicted the known trends of NO and CO emissions well. Inclusion of the volume correction term in the rate equations for CO and NO is necessary to capture the correct temporal variation of these species. Inclusion of the effects of mixture composition and temperature shows that the values of the mixture-averaged

The author declares that there are no conflicts of interest regarding the publication of this paper.

This material was based upon work supported by the US Department of Energy, Office of Science, under Contract no. DE-AC02-06CH11357.

_{X}emissions and performance of a light-duty diesel engine