Numerical and Experimental Investigation of n-Heptane Autoignition in

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Numerical and Experimental Investigation of n-Heptane Autoignition in the Ignition Quality Tester (IQT) Gregory E. Bogin, Jr.,†,* Anthony DeFilippo,‡ J. Y. Chen,‡ Gregory Chin,‡ Jon Luecke,§ Matthew A. Ratcliff,§ Bradley T. Zigler,§ and Anthony M. Dean† †

Colorado School of Mines University of California, Berkeley § National Renewable Energy Laboratory ‡

ABSTRACT: Development of advanced compression ignition and low-temperature combustion engines is increasingly dependent on chemical kinetic ignition models. However, rigorous experimental validation of kinetic models has been limited under engine-like conditions. For example, shock tubes and rapid compression machines are usually restricted to premixed gas-phase studies, precluding the study of heterogeneous combustion and the use of low-volatility surrogates for commercial diesel fuels. The Ignition Quality Tester (IQT) is a constant-volume spray combustion system designed to measure ignition delay of low-volatility fuels, having the potential to validate ignition models. However, a better understanding of the IQT’s fuel spray and combustion processes is necessary to enable chemical kinetic studies. As a first step, n-heptane was studied because numerous reduced chemical mechanisms are available in the literature as it is a common diesel fuel surrogate, as well as a calibration fuel for the IQT. A modified version of the KIVA-3V software was utilized to develop a three-dimensional computational fluid dynamics (CFD) model that accurately and efficiently reproduces n-heptane ignition behavior and temporally resolves temperature and equivalence ratio regions inside the IQT. Measured fuel spray characteristics (e.g., spray-tip velocity, spray cone-angle, and flow oscillation) for n-heptane were programmed into the CFD model. Sensitivity analyses of fuel droplet size and velocity showed that their effects on ignition delay were small compared to the large chemical effects of increased chain branching in the isomers 2-methylhexane and 2,4dimethylpentane. CFD model predictions of ignition delay using reduced/skeletal chemical mechanisms for n-heptane (60-, 42-, and 33-species, and one-step chemistry) were compared, again indicating that chemical kinetics control the ignition process.

’ INTRODUCTION Enhanced understanding of kinetic pathways to autoignition has become increasingly important to the development of advanced combustion engines and alternative fuels. Homogeneous charge compression ignition (HCCI) and other forms of low temperature combustion (LTC) strategies strongly depend on fuel autoignition kinetics to control combustion timing.1 In addition, the autoignition characteristics of renewable biofuels are currently of great interest.2,3 Development of accurate chemical kinetic models for the ignition of diesel and biodiesel model compounds relies on well-characterized experiments;4 however, rigorous experimental validation of these kinetic models has been limited for a variety of reasons. For example, shock tubes and rapid compression machines are typically limited to premixed gas phase studies (e.g., refs 5 7), although there has been some recent progress in studying low vapor pressure fuels with these devices.8 10 Nevertheless, research platforms capable of investigating autoignition in a well-characterized, nonhomogeneous combustion environment could accelerate the validation of reduced kinetic models for advanced engine research. Because of their experimental and modeling simplicity relative to engine-based studies, constant volume devices have been used extensively to study the combustion of a wide range of liquid fuels, providing detailed information about fuel spray physics and fuel chemistry effects on the overall combustion event,11 27 demonstrating their potential for developing a research platform r 2011 American Chemical Society

capable of measuring the complex interactions between spray physics and fuel chemistry of low-volatility fuels. The Ignition Quality Tester (IQT) is a constant-volume combustion apparatus developed to measure ignition qualities of diesel-type fuels.28 32 The American Society for Testing and Materials (ASTM) method D6890-0833 was developed to correlate the IQT average ignition delay with the cetane number from the ASTM D613 engine test method;34 it permits rapid calculation of a derived cetane number (DCN) with high repeatability ((0.85 DCN) in the 34 61 DCN range. D6890 is reliable for middle distillate petroleum fuels and some nonconventional diesel fuels.35 37 However, the correlation does not hold for some single-component and secondary reference fuels, and it is possible that oxygenated biofuels with significantly different chemistry from petroleum fuels will also not correlate with D613. A better understanding of the IQT combustion process may lead to its use as a validation platform for kinetic models of fuel surrogates and blends because it provides a well-controlled environment for such tests and requires only small (50 mL) quantities of fuel as compared to a traditional engine. In this study, measurements (e.g., cone angle, spray tip velocity, spray penetration, etc.) of IQT spray events at ambient conditions were used to obtain the physical spray characteristics necessary for further development of an earlier version of a three-dimensional Received: July 26, 2011 Revised: October 10, 2011 Published: October 13, 2011 5562

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Figure 2. Schematic of the IQT combustion chamber. Figure 1. Typical combustion pressure and needle-lift traces used to determine ignition delay; n-heptane, m = 78 ( 2 mg/inj, ignition delay = 3.78 ms (STDEV = 0.050) for 32-injection test run, P = 2.1 MPa, T ≈ 818 K (near nozzle).

computational fluids dynamics (CFD) model using KIVA-3V.38 Fuel properties (e.g., density, viscosity, surface tension, vapor pressure, etc.) are included in the KIVA-3V fuel database. Chemical kinetics were then applied to the combustion simulation and compared to IQT pressure traces; this modeling technique differs significantly from the previous models which used empirical global kinetics and minimal spray characteristics.26 These simulations demonstrated the dominance of autoignition chemistry on nheptane combustion in the IQT. In addition, the model allows comparison of the relative contributions of droplet breakup, droplet evaporation, and chemical ignition delay to overall ignition delay. The overall ignition delay measured in the IQT is a combination of spray physics and fuel chemistry; therefore, injector needle geometry and fuel chain branching studies were conducted to determine their effects. The hypothesis tested in these studies is that the overall ignition delay of n-heptane in the IQT is dominated by chemical kinetics over spray physics for the conditions investigated in this study. This hypothesis derives in part from the knowledge that compared to typical diesel engine operation, the ignition delay in the IQT is relatively long (on the order of several milliseconds). This allows more mixing of fuel and air leading to a combustion event that is closer to partially premixed charge compression ignition (PCCI) and is therefore more likely to be controlled by chemical kinetics rather than spray physics. This detailed characterization study was the first step to realizing the potential of using the IQT as a validation tool for ignition kinetic mechanisms.

’ EXPERIMENTAL SETUP AND COMPUTATIONAL MODEL IQT Overview. The IQT is a bench-scale, constant-volume combustion apparatus with a spray injection system designed for the direct measurement of liquid fuel ignition delay. Experimental parameters such as initial charge pressure, chamber wall temperature, air temperature, oxygen concentration, and mass of fuel injected are well controlled, thus facilitating accurate implementation into a numerical model. A pneumatically driven mechanical fuel pump and a single-hole S-type delayed (inward-opening) pintle nozzle inject the fuel. A pressure transducer installed in the combustion chamber measures the pressure rise during the combustion cycle; the time interval between the start of injection

(SOI) and the rise in combustion pressure to the “pressure recovery point” (138 kPa above the initial chamber pressure prior to injection) defines ignition delay28,29 (see Figure 1). The experimentally determined injection pressure is 22.5 MPa during the main injection period. Electric heaters embedded in the outer wall of the stainless steel combustion chamber30 maintain a constant charge temperature of approximately 818 K near the nozzle tip and 861 K near the middle of the chamber (along the axial axis), as shown in Figure 2. A temperature gradient along the axial direction of the combustion chamber results from heat transfer to coolant surrounding the injector nozzle at one end and the piezo-electric pressure transducer at the other end of the chamber. The air temperature increases by approximately 43 K at 7 cm down range (from the injector toward the center of the chamber, Figure 2). The 0.21 L chamber volume was pressurized to approximately 2.1 MPa (21% O2 in N2) prior to injection of the fuel (∼78 mg/inj), resulting in an overall lean equivalence ratio of 0.7.29,33 n-Heptane (g99.5%, Fluka) was used as the reference fuel having an ignition delay time of 3.78 (STDEV = 0.050) ms over a 32-injection test run.33 2-Methylhexane (g98%, Fluka) and 2,4-dimethylpentane (99%, SigmaAldrich) are the heptane isomers used to study the effects of fuel chemistry (i.e., chain branching) while minimizing changes in stoichiometry, viscosity, density, etc., at the D6890 operating conditions.

Spray Characterization of the IQT Fuel Injection System. Utilization of the IQT to validate ignition kinetic models requires a thorough characterization of the injection and combustion processes. For example, the transient physical behavior of the fuel spray as a function of time-resolved needle lift is required for realistic modeling of the coupled fuel spray physics, air entrainment, and combustion chemistry. The spray cone angle and velocity were determined experimentally under ambient conditions via high-speed, charge-coupled device (CCD) imaging. The IQT’s injection system was mounted in a fume hood and controlled with the system’s software to study n-heptane fuel spray under ambient conditions (Ta = 295 297 K, Pa = 87 kPa). The injection pressures (22.5 MPa at 0.69 mm needle lift) were the same used during normal operation of the IQT. The injection pressures are based on a correlation of fuel pressure with needle-lift displacement as measured using an external diesel injector test rig (Kiene Diesel Nozzle Tester DT1300) with varying shim thickness in the fuel injector which controls the fuel pressure required for opening the injector needle to allow fuel to exit the fuel injector. The fuel pressure settings used on the external diesel injector test rig were utilized to develop a correlation of fuel pressure with needle lift displacement, as well as for autoignition experiments in the IQT. The needle-lift sensor was attached to the injector body during imaging to correlate the position of the injector needle with the fuel spray. A Photron SA3 (120k-M2) high-speed digital camera captured 5563

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Table 1. Fuel Spray Parameters for KIVA-3V Model fuel fuel temperature (K)

n-heptane 323 ( 1

air temperature (K)

861 ( 2 (uniform)

mass of fuel injected (mg/inj)

78 ( 2

injection duration (ms) cone angle

1.8 2 7 35° [injection period]

initial SMD droplet size

120 μm (est)

spray tip velocity (m/s)

(0 182) [injection period]

Figure 3. High-speed images of the fuel spray during typical injection process; n-heptane, Pf = 22.5 MPa, Pa = 87 kPa, Ta = 295 297 K; aSOI (after start of injection); d (spray penetration distance). The typical IQT ambient air pressure is 2.1 MPa. Figure 5. Isometric view shows the block structure of the ∼60 000 cell IQT grid.

Figure 4. Schematic of the S-type pintle injector nozzle. the fuel spray at 10 000 fps, resulting in a 0.1-ms time-step and 512  256 resolution for a main injection period of approximately 2 ms. Imaging continued over a period of 4 6 ms to capture secondary fuel spray injections. Photron FASTCAM Viewer software was used to determine the spray-tip velocity based on the penetration depth for each time step of 0.1 ms, along with the cone angle. The high-speed imaging also provided insight into the varying profile of the fuel spray and captured the complex spray patterns that develop during the injection process (Figure 3). The shape of the fuel spray is due to the use of a single-hole S-type-delayed (inward opening) pintle nozzle (standard injection nozzle for the IQT) (Figure 4). The nozzle is 13.5 mm wide with a nozzle hole of 1.1 mm in diameter, the pintle width is 0.82 mm. The geometry of the injector needle-pintle tip allows a small fraction of fuel to exit at the beginning of injection, followed by the bulk of the fuel exiting the nozzle at a higher velocity and wider angle. The mass flow rate is calculated based on discharge coefficient, Bernoulli’s equation, orifice exit area, and density of the fuel.39 The orifice exit area is calculated from knowing the diameter of the nozzle opening and the diameter of the pintle along with the change in diameter of the pintle as a function of needle displacement based on pintle geometry and using the needle-lift sensor. With the displacement of the injector needle as a function of time, the orifice exit area as a function of time can be calculated providing an “effective orifice area” (0.12 0.41 um2). The calculated mass flow rate (5.7 44 mg/ms during the displacement of the injector needle) is averaged and converted to a mass flow rate per injection based on needle-lift measurements and highspeed imaging which were used to determine the time the needle is open

for the injection of fuel. This provides a theoretical mass of fuel injected which was then compared to the measurements of the mass injected; the theoretical mass of fuel injected based on mass flow rate calculations were within 7% of the mass of fuel per injection measured. These calculations are used to provide a validation of the fuel spray velocities used in the model which are based on the spray-tip velocities measured using the high-speed imaging. The injection velocity is not directly measured, and thus, the spray-tip velocity obtained from high-speed imaging is used as an estimate of the injection velocity for the spray model and as a comparison to the calculated injection velocity using Bernoulli’s equation. The fuel spray parameters from both experiments and imaging (Table 1) were utilized in the numerical model (discussed in detail in Numerical Model). The inability to measure fuel droplet size required an estimation of the initial Sauter mean diameter (SMD) droplet size; the initial SMD droplet size was estimated at 120 μm (reference case) based on the annular spacing of the orifice of the injector nozzle. A parametric study of various droplet sizes was studied numerically and is discussed later in the results. The mass of fuel injected is an average of three test collections of the fuel (each test comprising 10 injections).40 Numerical Model. KIVA-3V is a three-dimensional CFD model that was selected to model the combustion processes in the IQT because of its ability to solve unsteady equations of motion of turbulent, chemically reactive mixtures of ideal gases that are coupled with equations for a single-component vaporizing fuel.41 The reacting fuel spray was simulated using a modified version of the KIVA-3V software.42 The code couples Lagrangian particle tracking of liquid spray droplets with Eulerian simulation of three-dimensional fluid flow governed by the Navier Stokes equations. These equations were solved on a structured grid domain of 59 868 cells generated using ANSYS ICEM CFD commercial software (Figure 5). A uniform temperature of 861 K is used as the initial air temperature inside the IQT. The original KIVA-3V chemical solver is replaced with Chemkin II for these studies. A stiff solver, dvode, developed by Lawrence Livermore National Laboratory (LLNL) is used to compute the change of species due to chemical reactions. The chemistry and fluid dynamics are solved sequentially. The maximum time step in the simulation is limited to 2  10 5 s (0.02 ms), while the IQT ignition delays are on the order of several milliseconds. During the ignition, the time step is automatically reduced by detecting 5564

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Figure 6. Comparison of the spray model and experimental data obtained from high-speed imaging at ambient conditions: n-heptane, Pf = 22.5 MPa, Pa = 87 kPa, Tf = 323 ( 1 K, Ta = 298 303 K. The experimental data and numerical results are represented by the open symbols and solid lines, respectively.

Figure 8. Chemical mechanism dependency of CFD model predictions of n-heptane ignition delay in the IQT: Pair = 2.1 MPa, Tair = 861 K, overall Φ = 0.7, Tfuel = 323 K, n-heptane ignition delay (3.78 ms, STDEV = 0.050) for 32-injection run.

Figure 7. Visual comparison of the fuel spray: n-heptane, Pf = 22.5 MPa, Pa = 87 kPa, Tf = 323 ( 1 K, Ta = 298 303 K. Spray-tip velocities and penetration distances are shown in Figure 6 aSOI (after start of injection). temperature changes to resolve the stiff increase in temperature. Therefore, the coupling between evaporation and chemistry should be sufficient for the present cases. It was assumed that the effects of turbulence were moderate compared to those in a reciprocating engine because the fuel was injected into quiescent air in a constant volume chamber. The effects of turbulence

were accounted for using a k ε turbulence model (based on turbulent kinetic energy and dissipation rate)41,43 and modified to account for spray/turbulence interactions.42 The effects of the interaction of turbulence and chemical reactions on autoignition in the IQT system are currently being studied using the Eddy Dissipation Concept.44,45 The model of the fuel spray break-up process is based on the concept that in a dense fuel spray the atomization of the injected liquid and subsequent breakup of drops are indistinguishable processes.46 The injection process assumes that breakup is due to instabilities formed on the surface of a cylindrical liquid jet and that droplet breakup can also occur due to interactions of two fluids (e.g., liquid and gas), which were modeled using Patterson and Reitz’s Kelvin Helmholtz Rayleigh Taylor (KH-RT) spray breakup model (replacing KIVA-3V’s basic spray model)47 as implemented in KIVA-3V by Professor H.-L. Tsai.48 Droplet collisions and coalescence are important for dense sprays, which are applicable to injections of fuel into engines49 52 as well as constantvolume combustion chambers, and these conditions are implemented in the model.41,53 In addition to the spray breakup model, a lookup table (based on experiments and calculations) coded for this analysis specifies the time-varying liquid injection velocity, mass flow rate, and spray cone angle to simulate the fuel spray experiments under ambient conditions to allow proper tuning of the spray break-up parameters before testing the model under the operating conditions of the IQT. Single-step and three reduced or skeletal chemical mechanisms simulating n-heptane combustion were studied. Mechanisms include a 33-species (sp) primary reference fuel (PRF) mechanism from Nissan,54 a 42-sp n-heptane mechanism created by adding nitrogen oxides (NOx) reactions and removing iso-octane reactions from a 41-sp PRF 5565

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Energy & Fuels mechanism developed at the University of Wisconsin—Madison,55 and a 60-sp n-heptane mechanism developed at the University of California—Berkeley (UCB).

’ RESULTS Modeling Fuel Spray Dynamics. The spray model was adjusted at ambient conditions because high-speed imaging provided a visible time history of flow structure without the confounding effects of chemical reactions; the experiments were also limited to ambient pressures due to the inability to capture visual images of the fuel spray at elevated pressures within the IQT. The spray velocity is adjusted at elevated pressures based on calculations from Bernoulli’s equation. Defining the spray required setting the initial SMD droplet diameter, spray velocity, spray cone angle and thickness, and fuel temperature. The characteristic Kelvin Helmholtz breakup time directly scales with the input coefficient, B1, which accounts for the internal effects of the injector (e.g., L/D ratio, cavitation at high injection

Figure 9. Zero-dimensional modeling results of n-heptane ignition in a WMR showing ignition delay dependence on Φ.

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pressures). Thus, B1 must be empirically specified, although it is expected to fall in the range of 1.73 to 60.47 The instantaneous injected mass flow rate was assumed to be proportional to the measured instantaneous injector needle lift, with the flow rate normalized such that the integral of mass flow rate gives a total injected mass of 78 mg. The time history of injector needle lift also leads to a specification of initial droplet diameter, with the initial Sauter mean diameter set equal to the annular spacing of the orifice (120 μm) of the injector nozzle during the main injection event when majority of the fuel exits the nozzle. With other injection parameters specified (i.e., measured cone angle, calculated initial droplet size, measured velocity, and measured fuel temperature), B1 was adjusted in the KIVA-3V model until the time history of spray penetration depth and spray tip velocity matched the spray penetration depth and spray tip velocity measurements at ambient conditions (Figure 6), which provided a B1 value of 40. The present KIVA-3V model captures the physical shape of the fuel spray reasonably well, as shown by comparison with the images in Figure 7. Further improvement of the fuel spray transient shape during the injection process is an iterative and ongoing process with continued experimental investigation of the fuel spray. Transitioning from ambient conditions to the IQT combustion chamber environment (Pair = 2.1 MPa and Tair = 823 863 K) requires an adjustment of spray velocity (ν) in the model, as the pressure drop across the injector will be smaller and produce a slower initial injection velocity. Bernoulli’s equation accomplishes this scaling by relating fuel injection pressure, air pressure within the chamber, and the density of the fuel injected. The cone angle of the spray at ambient conditions is assumed to be relatively unchanged with higher pressures in the combustion chamber based on the injection pressures and fuel type.56 Implementing Chemical Kinetics in the CFD Model. Having modeled the spray physics, chemical reaction mechanisms for n-heptane were incorporated into the three-dimensional KIVA3V model. The results of single-step, 33-,54 42-,55 and 60-sp (UCB) mechanisms on the predicted ignition delay behavior are shown in Figure 8. Under normal operating conditions (Pair = 2.1 MPa, Tair = 861 K) of the IQT, the 42-sp n-heptane mechanism

Figure 10. Comparison of predicted ignition delay using KIVA-3V (42-sp mechanism) and IQT experimental data across a wide range of temperatures for two pressures: n-heptane, Pair = 2.1 MPa, 1.5 MPa, Φ = 0.5. Experimental error bars decrease significantly below 1/T = 1.35. 5566

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Figure 11. Role of autoignition shown by the time evolution of the temperature contour plots (left) and the corresponding plots of temperature vs equivalence ratio (right), demonstrating that the onset of combustion occurs primarily in the rich regions around Φ ≈ 2.

predicted an ignition delay time of 4.1 ms which was within 8.5% of the experimental ignition delay time of 3.78 ms; while the 60-sp and 33-sp mechanism predicted ignition delays that had a 20.6% and 45.5% difference from the measured ignition delay, respectively, Differences in the modeled ignition delays between these chemical mechanisms probably result from variance in the autoignition reactions and their reaction rates. Supporting evidence comes from simulations with these mechanisms using the Senkin zero-dimensional well-mixed reactor (WMR) model,57 initially at 861 K and 2.1 MPa (Figure 9). The order from fastest

to slowest predicted ignition delay using the zero-dimension model in Figure 9 was the 1-step, 60-, 42-, and the 33-sp which agrees with the order of predicted ignition delays using the KIVA3V model. In addition to the reduced mechanisms, the full detailed n-heptane mechanism from LLNL was employed as a reference.58 The separation of the predicted ignition delay times increase as the fuel/air mixture becomes richer (Φ > 1), which is where autoignition is predicted to occur within the IQT(discussed in detail later in this section of the paper). The widely varying chemical ignition delays in the zero-dimensional 5567

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Figure 12. Projected lifetime for a single droplet decreases as droplet velocity increases and as droplet initial diameter decreases. Model predictions are based on a single droplet using a MATLAB code with KH-RT breakup algorithm.

simulations emphasize the importance of accurately capturing the chemical kinetics. The 42-sp n-heptane mechanism in the KIVA-3V model predicted an ignition delay time that was within 8.5% of the experimental ignition delay time for the IQT under normal operating conditions. Due to the performance of the 42-sp under normal operating conditions of the IQT, the model was validated across a wide range of temperatures and various pressures to test the adequacy of the 42-sp n-heptane mechanism as a sufficient reduced mechanism to use in the KIVA-3V model. The 42-sp n-heptane mechanism performed extremely well in predicting the ignition delay measured in the IQT within the experimental range for majority of the temperatures tested at 2.1 and 1.5 MPa as seen in Figure 10. The performance of the 42-sp mechanism was deemed sufficient as a reduced n-heptane model for the operating conditions of interest within the IQT and was used as the default mechanism for modeling of the IQT. The 42-sp mechanism was developed and validated specifically for direct injection heavy-duty diesel engine conditions, including tuning to capture the rich onset of autoignition in regions where fuel evaporation had locally cooled the mixture.55 In contrast, the 33- and 60-sp mechanisms were both developed specifically for HCCI conditions; the conditions by which each of the mechanisms were reduced may be one of the main reasons for the differences in the prediction of the ignition delay. It is believed that the fuel air mixture is partially premixed before ignition occurs and not completely homogeneous in the IQT when using nheptane as a fuel due to the relatively short ignition delay time, thus locally rich zones may be present which may result in a partially premixed conditions instead of homogeneous conditions. Evidence of the governing effects of autoignition chemistry on the predicted combustion event can be seen in an evolution of the KIVA-3V model at the onset of ignition. Dispersed locations within the chamber ignite as favorable conditions for autoignition are met, and no single propagating diffusion flame front dominates the process (Figure 11). The observed rich onset of autoignition near Φ = 2 for n-heptane is well-documented in the literature55,59 for charge mixtures that have been evaporatively cooled. Experimental evidence of locally fuel-rich zones in the IQT, consistent with KIVA-3V model prediction, comes from gas chromatography/mass spectrometer (GCMS) analysis of the exhaust emissions from n-heptane combustion. This analysis revealed the presence of benzene and naphthalene, which are indicative of fuel-rich combustion60 and are soot

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precursors. Soot was also visible in the exhaust system, something that would not be expected in a completely homogeneous combustion with an overall lean equivalence ratio (Φ ≈ 0.7). Numerical Comparison of the Relative Effects of Spray Physics on Ignition Delay. Success in validating ignition kinetics with the IQT requires that the ignition delay be dominated by the chemical reactions and that effects of spray fluid mechanics be relatively minor. The overall ignition delay time from SOI can be approximated simplistically by a sequential combination of breakup time, evaporation time, and chemical reaction time. (In reality, these processes overlap and interact continuously, e.g., initial sites of chemical autoignition may influence remaining liquid fuel spray.) Serially solved simplified models for n-heptane (WMR, single-droplet) generated a characteristic droplet breakup time of 0.2 ms, an evaporation time ranging from 0.5 to 1 ms, and an ignition chemistry time ranging from 1.0 to 1.8 ms. A single droplet breakup was modeled considering both Kelvin Helmholtz and Raleigh Taylor instabilities.47 The KH-RT breakup algorithm61 was coded into MATLAB and applied to a single droplet 120 μm in diameter traveling at an initial velocity of 120 m/s, which is typical of a droplet injected into the KIVA3V model. Correct quantification of momentum transfer from the droplet to the surrounding air complicates the analysis, as the relative droplet velocity in the surrounding air governs breakup events. Varying momentum transfer rates resulted in similar breakup times (0.2 ms). However, the final droplet size and droplet velocity varied; therefore, they were studied while analyzing droplet evaporation. Droplet vaporization is the next critical step in spray combustion, as it generates the vapor necessary for gas-phase combustion. Droplet diameter decreases as heat transfer from the surrounding gases evaporates the liquid fuel. The lifetime of a droplet is governed by the rate of heat transfer to the droplet and its initial size, thus heating and vaporization times are shorter for smaller droplets.60 Droplets with higher Reynolds numbers (e.g., higher velocity) have shorter lifetimes due to convective effects (e.g., convective boundary layers), which increase the heat transfer and mass transfer rates. In addition, shear forces on the liquid surface cause internal circulation, which increases the heating of the liquid, resulting in higher vaporization rates.62 Numerical simulations of droplet evaporation, varying initial diameter and velocity, demonstrate the relative impact of velocity and size on droplet lifetime as shown in Figure 12. The numerical model suggests that a droplet that has already experienced breakup and drag from interactions with the surrounding fluid will completely vaporize in 0.5 1 ms, depending on the size and speed of the droplet after breakup and momentum transfer to the surrounding fluid. With the effects of droplet size and velocity on droplet lifetime for a single droplet determined using the MATLAB model, sensitivity analyses were performed for initial droplet size and velocity (based on typical diesel injection spray conditions) using the KIVA-3V model to examine the relative impact of spray physics on the predicted ignition delay time (see Table 2). Doubling the initial droplet size (120 240 μm) increased ignition delay by 5% while halving the initial droplet size (120 60 μm) reduced ignition delay by 4.3%. The change in ignition delay as a function of droplet size results from the dependency of evaporation on heat transfer (i.e., smaller droplets require less heat transfer to evaporate). Doubling the initial velocity of the 60 μm droplet reduced the ignition delay by 15% (conditions not representative of the IQT fuel injection system); this analysis was performed to determine an upper limit for the 5568

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required change in fuel spray conditions that would produce a significant change in ignition delay. Convective effects (e.g., convective boundary layers) increase the heat and mass transfer rate such that droplets moving faster have shorter lifetimes. Experimental Comparison of the Relative Effects of Spray Physics and on Ignition Delay. An experimental study of the effect of spray physics on ignition delay involved injector needle modifications that increased the effective nozzle orifice diameter from 0.25 to 0.81 mm which is an increase of more than a factor of 3. The resulting increase in measured ignition delay from the increase in effective nozzle orifice was from 3.78 to 4.01 ms which results in an increase of ignition delay of approximately ∼6%. Thus, a significant increase in the nozzle diameter (and therefore droplet diameter) resulted in a fairly small increase in the overall ignition delay. Investigation of the effect of injection pressure on ignition delay was conducted over a moderate range of injection pressures. Increasing the injection pressure from 18.4 to 27.6 MPa (original nozzle diameter of 0.25 mm) resulted in minor changes (within the standard deviation of the measured points) with an overall reduction in the average ignition delay of approximately 2.6%, as shown in Table 3. Lastly, the mass of fuel injected into the IQT was varied significantly from 59 to 103 mg (an increase of 75%) resulting in a moderate increase in ignition delay from 2.9 to 3.3 ms (approximately 14%), over the range of mass injected. The relatively small measured and modeled effects of spray physics on ignition delay underscore Table 2. Predicted Ignition Delay Time (Pair = 2.1 MPa, Tair = 861 K) droplet

ignition delay;

velocity

size SMD

KIVA-3V

change in ignition

(m/s)

(μm)

(ms)

delay (%)

140

240

4.41

+5

140

120

4.2

base case

140

60

4.02

4.3%

280

60

3.42

15% (from 4.02 ms)

the high relative importance of ignition chemistry on the measured ignition delay time in the IQT. Experimental Comparison of the Relative Effects of ChainBranching on Ignition Delay. The effects of chemical structure on ignition delay were studied experimentally using the heptane isomers 2-methylhexane and 2,4-dimethylpentane. These isomers were selected to study the effects of methyl branching while minimizing changes in density, stoichiometry, and viscosity as well as combustion properties such as laminar burning velocities and adiabatic flame temperatures. 2-Methylhexane and 2,4dimethylpentane both have lower boiling points and heats of vaporization compared to n-heptane (see Table 4). If spray physics dominate the ignition process over fuel chemistry in the IQT, then these two isomers might be expected to have shorter ignition delays due to a lower boiling point and heat vaporization which would reduce the energy and time required to vaporize the fuel and produce favorable mixture conditions in a shorter time for autoignition to occur. It is well-known that increasing chain branching reduces cetane number (increases the ignition delay)63 arising from the specifics of each compound’s detailed ignition chemistry. Consistent with the fuel responses in the Cooperative Fuel Research (CFR) engine used in ASTM D613, the ignition delays of the heptane isomers measured in the IQT increased significantly (compared with the changes shown earlier due to physical effects) with increasing chain branching (see Figure 13). 2-Methylhexane and 2,4-dimethylpentane had measured ignition delay times that were longer by 26.5% and

Table 3. Measured Ignition Delay Time (Pair = 3.0 MPa, Tair = 861 K) injection pressure (MPa)

ignition delay; IQT (ms)

18.4

3.08 (STDEV = 0.074)

21.8

3.05 (STDEV = 0.059)

25.4

3.07 (STDEV =0.064)

27.6

3.00 (STDEV = 0.048)

Figure 13. Combustion pressure traces for heptane, 2-methylhexane, and 2,4-dimethylpentane: Pair = 2.1 MPa, Tair = 855 K, averaged over 10 injections.

Table 4. Fuel Properties for n-Heptane, 2-Methylhexane, and 2,4-Dimethylpentane fuel properties 3

65

viscosity (10 Pa 3 s) 298 K boiling point (°C)b,c vapor pressure (kPa)b

n-heptane

2-methylhexane

2,4-dimethylpentane

0.387 98

0.357 88 90

0.368a 81 82

5.3 (293 K)

5.3 (288 K)

11.1 (294 K)

density (kg/m3)b

0.684

0.678

0.673

heat of vaporization (kJ/mol) 298 Kc

36.6

34.9

32.9

56

38

18

DCN (IQT) D6890-08

53.9 (STDEV = 0.73)

43.6 (STDEV = 0.64)

28.6 (STDEV = 0.46)

ignition delay (ms) D6890-08

3.77 (STDEV = 0.055)

4.77 (STDEV = 0.080)

7.79 (STDEV = 0.108)

cetane number63

a

Average of measured viscosities for 2,2-dimethylpentane and 2,3-dimethylpentane.65 b Obtained from the chemical manufactures (Fluka and SigmaAldrich) and MSDS. c NIST database (webbook.nist.gov). 5569

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Energy & Fuels 106%, respectively. The process of spray physics and fuel chemistry are still coupled for these relatively short ignition delay times, and the effect of lower boiling point and lower heat of vaporization for the two isomers reduced the magnitude of the overall increase in ignition delay times produced by the two isomers that would have resulted if the system was completely homogeneous, like conditions found in RCMs and shock tubes. Although the spray physics are involved in the autoignition of the fuel, the results shown in Figure 13 are evidence that fuel chemistry involved with increasing chain-branching dominates over the physical effects of lower boiling point and lower heat of vaporization, at least for these relatively volatile compounds. Others have studied the effects of physical property variations on apparent reactivities of alcohol blends (i-butanols and ethanol) and have also determined that the relative reactivities were dominated by chemical kinetics, while the blend-specific physical properties had very little effect on relative ignitability.64 nHeptane physical properties (e.g., viscosity, surface tension, heat of vaporization, etc.) were modified in the KIVA-3V model to match that of n-hexadecane while keeping the chemical mechanism the same; this produced minor or no measurable effect on the predicted ignition delay. The heat of vaporization was then changed significantly (order of magnitude) to match that of ethanol; this modification produced a noticeable increase in the predicted ignition delay from 3.34 to 4.16 ms. The KIVA-3V model predicts that a large modification of the fuel’s physical property is required to have any significant effect on ignition delay for the same n-heptane chemistry. Overall, these analyses indicate that ignition delay in the IQT is dominated by chemical kinetics and not spray physics, indicating that the IQT has the potential for meaningful study of ignition kinetics. The numerical model indicates that by reducing droplet size and increasing droplet velocity the relative influence of the fuel spray physics will be further reduced, providing a more direct correlation with the chemical kinetics. The impacts of higher injection pressures and fuel injector design are currently being investigated, which will allow further investigation of spray physics and investigation of lower volatility fuels (e.g., diesel). A logical next step in the numerical modeling of the IQT would be utilization of a 2-methylhexane and 2,4-dimethylpentane reduced/skeletal mechanism for comparison with experiments.

’ CONCLUSIONS A KIVA-3V model was developed for n-heptane ignition in the IQT spray combustion system and compared to experimental results. The model predicts that the ignition delay is governed primarily by autoignition kinetics and that dispersed ignition events occur throughout the combustion chamber. KIVA-3V (using a 42-sp mechanism) predicted an ignition delay of 4.1 ms in comparison to the measured ignition delay of 3.78 ms under normal (ASTM D-6890) operating conditions for the IQT. Modeled differences show that the overall ignition delay changed significantly depending on the chemical mechanisms used. Thus, performing sensitivity analyses of the various chemical reactions and reaction rates in each mechanism should provide insight into the cause of the varying prediction of chemical ignition delay times. The efficacy of validating fuel combustion kinetic mechanisms during spray combustion using the IQT depends on the relative importance of the chemical reaction time to the overall ignition delay. An accurate understanding of the physics of the

ARTICLE

fuel spray is thus vital for capturing and examining the physical effects on the overall ignition delay time. The physics of the fuel spray implemented in the model are based on experimental characterization of the fuel spray and analytical estimation when necessary. The KIVA-3V model of the IQT allows comparison of the overall ignition delay through sensitivity analyses of various experimental parameters and the use of different reduced chemical mechanisms. The KIVA-3V model predicts that significant changes in droplet size and droplet velocity have a relatively small impact on ignition delay; this was verified experimentally using varying injector nozzle geometry. Experiments varying the injection pressure by more than 9 MPa resulted in a decrease in ignition delay of only 2.6%, which suggests that the spray physics has minimal impact on the ignition delay time for n-heptane. Experiments using the heptane isomers 2-methylhexane and 2,4-dimethylpentane confirmed that ignition delay increases significantly with increased chain branching. More importantly, these chemical structure effects are large compared to the small observed changes in ignition delay resulting from modifying the spray physics. These results indicate that ignition delay in the IQT is dominated by chemical kinetics and not spray physics for nheptane, which is a necessary condition for meaningful study and validation of ignition kinetic models. Simplified models of droplet breakup, evaporation, and chemical ignition solved serially provide insights into the relative effects of chemical mechanism, initial droplet size, and initial droplet velocity on the overall ignition delay. This leads to a better understanding of the predicted overall ignition delay from the KIVA-3V model in which physics and chemistry are coupled. The improved understanding of spray physics and combustion chemistry gained from these models may lead to a robust experimental system with engine-like conditions in which ignition kinetics studies can be performed. The KIVA-3V model predicts ignition delay within the experimental range for a wide range of temperatures using a 42-sp chemical mechanism for n-heptane, which was originally validated under spray combustion conditions in a diesel engine. Thus, for direct-injection, autoignition applications, the well-controlled conditions of the IQT make it a potentially attractive validation platform for ignition kinetics.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors thank the U.S. Department of Energy Vehicle Technologies Program and Fuel Technologies Program Manager Kevin Stork for their support of this fuels research. ’ REFERENCES (1) Wooldridge, M. S.; Walton, S. M.; He, X.; Zigler, B. T. Chemical Kinetics of Homogeneous Charge Compression Ignition and Other Low-Temperature Combustion Strategies. Proceedings of the 2006 Technical Meeting of the Central States Section of The Combustion Institute; Cleveland Ohio, May 21 23, 2006. (2) Letter Report on the Review of the Research Program of the FreedomCAR and Fuel Partnership, Phase 3, Committee on the Review of the Research Program of the FreedomCAR and Fuel Partnership, Phase 3, National Research Council, 2009. 5570

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