Journal of Combustion

Volume 2018, Article ID 7237849, 13 pages

https://doi.org/10.1155/2018/7237849

## Sensitivity of Emissions to Uncertainties in Residual Gas Fraction Measurements in Automotive Engines: A Numerical Study

Argonne National Laboratory, Lemont, IL 60439, USA

Correspondence should be addressed to S. M. Aithal; vog.lna.scm@lahtia

Received 21 January 2018; Revised 19 March 2018; Accepted 1 April 2018; Published 2 May 2018

Academic Editor: Constantine D. Rakopoulos

Copyright © 2018 S. M. Aithal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1]. While inlet air temperature and intake air humidity can be measured (albeit at a cost), there is no sensor to measure the amount of residual gas fraction (RGF). The RGF can only be inferred through simulations or an estimation [2]. The difficulties in ascertaining the exact values of the initial conditions of the fuel-air mixture can lead to inaccuracy in model prediction and also analyses and interpretation of experimental data [3–5]. For instance, the authors of [6] report a very controlled experimental study on the effects of intake air humidity on the performance and emissions of a turbo-charged 4-cylinder diesel engine at various engine speeds and loads. The authors of this study reported a 14% reduction in NO_{x} with a small addition of moisture ~ or 1.35%) thus highlighting the importance of the initial mixture composition on engine-out NO emissions. The residual gas consists of CO_{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 [7]. Based on the results shown in [6], it is clear that RGF will impact the initial mixture composition and temperature and consequently the engine-out emissions. RGF acts as an internal EGR (exhaust gas recirculation) and impacts engine-out emissions akin to external EGR via dilution, chemical, and thermal effects. Gasoline engines are usually operated close to stoichiometric; hence little oxygen is present in the residual gas, whereas in diesel engines (which typically run lean) considerable amounts of O_{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 (*γ*) of the working fluid is lowered, thus altering the temporal variation of cylinder pressure and temperature (thermal effect) [8]. The presence of CO_{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 [9–18]. Uncertainties in measurements, however, can lead to errors in the estimates of RGF. For instance, [19] points out that a 5% error in-cylinder pressure measurement can lead to a 2-3% error in the estimation of the RGF. Understanding the sensitivity of the engine-out emissions to the percentage of RGF in the engine cylinder is important from the standpoint of model calibration and engine data interpretation. Moreover, the sensitivity of emissions to the uncertainty in the RGF is also important for designing robust real-time controls to minimize emissions while maximizing performance and fuel economy. There is currently no experimental data or numerical investigation evaluating the sensitivity of engine-out NO and CO on the RGF and hence the focus of this numerical study.

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 (*ϕ* ~ 0.8), near-stoichiometric (*ϕ* ~ 1.0), and rich (*ϕ* ~ 1.12) conditions was investigated. Most gasoline engines run close to stoichiometric; however, the lean and rich cases also were studied in order to understand the impact of the RGF for extreme cases of O_{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 [20]. The ability to conduct sensitivity analyses on complete drive cycles in real-time is necessary because stringent emissions standards in the future will necessitate a cycle-by-cycle analysis of drive cycles. This work lays the foundation for both single-cycle and drive-cycle analyses to understand the impact of RGF on emissions and thus has potential for use in engine data interpretation and model calibration over a wide engine operating range.

This paper is organized as follows. Sections 2 and 3 briefly describe the model and the method of solution, respectively. Section 4 describes model validation while Section 5 discusses results for the single-cylinder gasoline engine. Section 6 briefly summarizes the main findings of this work.

#### 2. Mathematical Formulation

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.

##### 2.1. Two-Zone Model for Computing Temporal Variations of Temperature and Pressure

A numerical model used to compute the temporal variation of temperature and pressure in a single-cylinder diesel engine was described in detail in [8]. A similar methodology was used in this work to model a spark-ignited engine. Temporal variation of the engine pressure and temperature during the compression and power stroke was obtained by a numerical solution of the energy equation as in [8].

The energy equation describing the variation of pressure with crank angle is as follows.The amount of heat produced () due to the fuel burned from *θ* and is given by while the heat lost from the engine during the interval is given by The wall temperature in (3) was assumed to be constant at 400°K in this work.

The instantaneous values of volume and area () are given by the slider-crank model as discussed in [7, 8]

The convective heat transfer coefficient is expressed by the well-known Woschni correlation and is expressed as [21]where 3.26 is the scaling factor in the Woschni correlation.

The velocity of the burned gas in (4) is given byEffects of temperature and mixture composition on the thermophysical properties of the working fluid were included in the solution of the energy equation. Temporal variations of the thermophysical properties of all the species in the gas mixture were obtained by using thermodynamic coefficients from the CHEMKIN database. Computing the temporal variation of the thermophysical properties of the working fluid correctly as a function of mixture composition and temperature is extremely important in order to predict the engine pressure and temperature correctly as pointed out in [8]. Many quasi-dimensional models use constant values for the ratio of specific heats () during the compression and expansion strokes, which can lead to inaccuracies in computed engine pressure and consequently in the temperature and emissions. This situation is especially true for lean mixtures or engines running on high EGR fractions. Temperature dependent polynomial expressions for specific heat (), enthalpy (), and internal energy () of individual species in the working fluid were computed using the procedure discussed in [22].

Mixture-averaged values of specific heat of the working fluid were averaged by using mole fractions as follows.Following the procedure in [8], fuel combustion chemistry was modeled by a single-step global reaction. The combustion process of the premixed fuel-air mixture after the spark was modeled by using the well-known Wiebe function [7].where , , and are the instantaneous crank angle, the crank angle for the start of combustion, and the combustion duration, respectively. Further, is the fuel burned, is the total fuel at BDC, and is the fraction of fuel mass burned in each crank angle and is used to compute in (2). The Wiebe function constants; namely, “,” “,” and “” are functions of various parameters such as engine geometry, fuel type, air-fuel ratio, engine speed, and load.

The average gas temperature was obtained as follows:The Wiebe function can be used to compute the mass of fuel burned at each crank angle. The species in the burned and unburned zones are computed so as to ensure a total elemental balance (and hence mass balance) in the cylinder. Knowing the masses of the burned and unburned zones, the burned and unburned gas temperature were obtained aswhere the subscripts “” and “” represent unburned and burned quantities, respectively. It was assumed that there is no heat transfer between the burned and unburned zone, for the sake of simplicity. The volume fraction of the burned gas = can be obtained by using the following relationship [7].Following [7], was used for the sake of simplicity.

The moles of CO_{2}, H_{2}O, O_{2}, and N_{2} produced in CAD in accordance with the single-step global chemistry model are as follows.where is the number of carbon atoms, is the number of hydrogen atoms, and is the molecular weight of the fuel. In (13) and (14), *ϕ* and *β* denote the equivalence ratio and ratio of N_{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 *θ* iswhere the summation is over the crank angle interval from (SOI) to *θ*. Since the initial moles of fuel, O_{2}, and N_{2}, are known, the composition of the burned zone (and hence unburned zone) can be computed based on (11)–(15).

##### 2.2. Modified Rate-Controlled NO Model

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 [7] (page 573). Based on the extended Zeldovich mechanism, the expression for the time rate of change of NO is as follows.Following the simplifying assumptions in [7], Equilibrium concentrations of O, N_{2}, NO, H, OH, and O_{2} are used in computing the RHS of (17). Equation (17) holds true under constant volume conditions. In an IC engine, the volume of the cylinder varies with time.

Since the concentration , where is the number of moles of NO and is the instantaneous volume of the cylinder, the LHS of (17) can be rewritten as discussed in [23]which can be shown to yieldwhere is the rate of change of NO concentration at constant volume computed using (17). The second term on the RHS of (18) accounts for the decrease in NO concentration as a result of the increasing cylinder volume during the expansion stroke.

From SOI to EOC, the burned volume can be computed based on the procedure discussed earlier. After EOC, , where is the cylinder volume at crank angle Equation (19) is referred to as the modified reaction rate-controlled NO model in this work because it accounts for the rate of change of the engine volume in determining the NO concentration during the engine cycle.

The rate constants and equilibrium concentrations of species used in evaluating (19) are computed by using the burned gas temperature and pressure at a given crank angle. Effects of mixing between the burned and unburned gas and the temperature gradients in the burned gas region are neglected. Solution of (19) yields the temporal variation of NO concentration (in moles/cm^{3}).

##### 2.3. Modified Rate-Controlled CO Model

The modified rate-controlled CO model used in this work is an adaptation of the model discussed in [24]. Similar to (19), the modified CO model used in this work can be written as in (20) is the rate of change in concentration of CO at constant volume and is expressed as where is the calibration parameter. can be evaluated using the ratio between experimental data and model predictions obtained by setting for a given set of operating conditions. This calibrated value of is kept the same for all other operating conditions.

Details of (21) along with reaction rates are described in [24] (see Eq. 28). The concentration of all terms required to evaluate the RHS of (21) is equilibrium values at a given temperature and pressure corresponding to a given crank angle.

#### 3. Computational Details

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 (11) through (14), and ; *β*, the N_{2} : O_{2} ratio in air, is taken to be 3.76 and is the molecular mass of the fuel (114 gm/mole for Iso-Octane). Three different equivalence ratios (*ϕ*), namely, *ϕ* = 0.8 (lean), 1.0 (stoichiometric), and 1.12 (rich), were considered. The engine torque for each of these cases was kept constant at 17 Nm. The fuel mass and initial cylinder pressure at bottom dead center (BDC) were kept constant for each of these cases considered. The RGF was varied from 0% to 7% for all the equivalence ratios considered in this work. Since the RGF fraction considered in this work is small, it has an insignificant impact on the combustion characteristics (burn rate) and hence the same Wiebe parameters were used for all cases considered in this work for simplicity. The RGF was assumed to consist of CO_{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 [8]. The same procedure was adapted to obtain the pressure and temperature in an SI engine using the equations described above. Briefly, for a given set of operating conditions, namely, the prescribed mass of the fuel-air-RGF mixture and temperature at BDC, (1) was solved iteratively by using (2)–(10) to obtain the cylinder pressure from *θ* = −180 (BDC) to (crank angle for exhaust valve opening) in increments of 0.5°. was set at 140° in each of the cases considered. For a given pressure at a crank angle, the burned and unburned gas temperatures were obtained by using (9).

The engine dimensions and operating conditions used in this work are shown in Tables 1 and 2, respectively.