Predicting octane number from microscale flame dynamics

Combustion and Flame 208 (2019) 5–14

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Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Predicting octane number from microscale flame dynamics Clara L. Druzgalski∗, Simon Lapointe, Russell Whitesides, Matthew J. McNenly Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

a r t i c l e

i n f o

Article history: Received 2 March 2019 Revised 24 April 2019 Accepted 23 June 2019

Keywords: Micro flow reactor Flames with repetitive extinction and Ignition (FREI) Fuel testing Octane number Neural network

a b s t r a c t The standard method for measuring the octane number of fuels requires large sample volumes ( ∼ 1L) and access to a Cooperative Fuel Research (CFR) engine. This method reliably quantifies the knock resistance of fuels in spark ignition engines, however the large sample volume requirement prevents testing of new experimental fuels (often produced in quantities of just ∼ 1 mL), and the large equipment size impedes mobile, decentralized testing of remote fuel supplies. When direct measurements of octane number are impractical, other methods are needed. Micro flow reactors have shown promise in measuring ignition characteristics that are sensitive to octane number, and they are compact and operate on small volumes ( ∼ 1 mL). This study uses simulations to demonstrate that measurements of the unsteady flame dynamics in a micro flow reactor can provide valuable data for accurate octane number predictions. Simulations of the flow reactor are used to obtain ignition characteristics for over 200 ethanol-toluene primary reference fuels (ETPRF) and 21 biofuel blends. A feed forward neural network is trained using the micro flow reactor ignition characteristics, fuel properties, and known research octane number (RON) and motor octane number (MON) for the ETPRF fuels. The neural network is able to predict the RON and MON of the biofuel blends to within 2 octane number on average. Prediction results are compared to other methods available in the literature. Additional neural network models are trained that show improved prediction accuracy as additional fuel training data becomes available. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Measurements of fuel ignition behavior are important to prevent engine damage, to control the quality of a fuel supply, and to discover new transportation fuels. The current standard for fuel quality testing in spark ignition engines is to measure the octane rating using a Cooperative Fuel Research (CFR) engine [1,2]. The CFR engine is widely used at refineries to rate fuel for sale within the U.S., but it can be impractical for fuel testing in other settings. The equipment is large, making it difficult to rate remote fuel supplies, and the sample volume requirement of ∼ 1 L is too large for testing experimental biofuels for which only small samples ( ∼ 1 mL) are manufactured. Studies have demonstrated different approaches for predicting the octane number of fuels without direct CFR engine tests. Knop et al. [3] used linear mixing rules for octane number prediction of pure component mixtures. Such mixing rule techniques are only applicable to mixtures of well tested components, and even where applicable, can lead to large prediction errors due to the nonlinear blending behavior of fuel components. Other studies have used

∗

Corresponding author. E-mail address: [email protected] (C.L. Druzgalski).

simulated ignition delay times (IDT) of stoichiometric fuel/air mixtures to predict octane number for a variety of reference fuels and mixtures [4–6]. IDT correlations require an accurate chemical mechanism and therefore cannot be used to predict new/unknown fuels for which the chemistry has not been previously characterized. Ignition quality testers (IQTs) have also been used to measure fuel ignition behavior and predict octane number via correlations [7,8]. However, IQTs require sample volumes of 20–100 mL which still restricts the testing of experimental fuels. In a recent study, Jameel et al. [9] used nuclear magnetic resonance (NMR) spectroscopy data and a neural network to predict RON and MON for a group of fuels that includes pure hydrocarbons, hydrocarbonethanol blends, and gasoline-ethanol blends. NMR spectroscopy doesn’t directly measure ignition behavior but it can used to determine the chemical composition in terms of functional groups from small samples of ∼ 50 μL. Recent research on micro flow reactors has shown promise in addressing unmet needs for fuel testing: they are inexpensive, portable, use microliter sample volumes, and have demonstrated sensitivity to octane number [7,10]. Fundamental studies of combustion in narrow channels with a temperature gradient have established a connection between flame behavior and octane number. Hori et al. [11] studied the octane number dependence of weak flames in mixtures of primary reference fuels (PRF, iso-octane and

https://doi.org/10.1016/j.combustflame.2019.06.019 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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C.L. Druzgalski, S. Lapointe and R. Whitesides et al. / Combustion and Flame 208 (2019) 5–14

n-heptane). Kamada et al. [10] studied the RON dependence of weak flames in natural gas components (methane, ethane, propane, and n-butane). Kikui et al. [12] studied n-butane weak flames at pressures up to 12 bar. These research studies focused on weak stable flames at ambient to moderate pressures. Dynamic flames with repetitive extinction and ignition (FREI) provide an even richer data set of easily measurable metrics such as ignition and extinction locations and frequency that have demonstrated sensitivity to octane number at engine relevant conditions [13]. The objective of this study is to demonstrate that measurements of the unsteady flame dynamics in a micro flow reactor can be used for accurate octane number predictions. Practically, the ability to predict the octane number using only a small volume of fuel ( ∼ 1 mL) is a valuable screening tool in a variety of scenarios. For example, testing fuel supplies on location can be a challenge. Direct access to a CFR engine is often not possible and the time delay of shipping fuel samples may be unacceptable. Micro flow reactor measurements can alleviate this pain point by providing a portable, inexpensive means of testing fuel samples. On-demand fuel screening is also advantageous in the development of new fuels. Laboratories that develop experimental biofuels often produce thousands of distinct blends in quantities of ∼ 1 mL. It is economically impractical to scale production of thousands of fuel samples from 1 mL to the 1–2 L required for CFR engine tests. Decisions on promising blends must therefore be made on incomplete information. Micro flow reactor measurements could be used to quickly and inexpensively predict the octane number of the small samples, providing valuable information to determine which fuels are candidates for larger-scale production. Currently, there are no published experiments that provide flame propagation and ignition data for fuels in micro flow reactors at pressures above 10 bar. Therefore, flow reactor simulations at engine relevant pressure (25 bar) are performed at a range of conditions for over 200 ethanol-toluene primary reference fuels (ETPRF) and 21 biofuel blends (7 biofuels, including ethanol, at 3 blend levels). Experimentally measured research octane number (RON) and motor octane number (MON) are obtained for all the ETPRF and biofuel blends from available literature [3,4,14–22]. The biofuel blends are selected from a study that identified highperformance biofuels for advanced spark ignition engines [22]. In that study, biofuels were blended into a multi-component surrogate fuel (representing a petroleum-derived base blend stock) at up to 30% biofuel by volume and key fuel properties, RON, and MON were measured and reported. Simulated micro flow reactor data and experimentally measured octane numbers are used to form a dataset to determine the relationship between the input features (fuel properties and ignition locations at a range of micro flow reactor conditions) and the target outputs (RON and MON). Feed forward neural network models are developed and trained on the ETPRF dataset. The trained networks are used to predict the RON and MON of fuels in the biofuel blend dataset, demonstrating the model’s ability to generalize and make accurate predictions for new fuels. Additional neural network models are trained to demonstrate the impact of including biofuel blends in the training set. Predicting the RON and MON of blends (typically composed of some well-characterized compounds and some lesser known compounds) represents a practical use-case for this technology, which can be used for new fuel discovery for spark ignition engines. RON and MON predictions are compared with other methods available in the literature. The following sections provide a description of the flow reactor, an overview of the computational strategy, details of the physics model and neural network model, and results demonstrating that ignition characteristics from the micro flow reactor can be used to predict the RON and MON of small fuel samples.

Fig. 1. Schematic of the micro flow reactor. The mixture of fuel and air enters the tube at flow rate m˙ . The heater creates a temperature profile along the wall of the tube Twall . At certain operating conditions, a periodic unsteady behavior exists where the mixture ignites at the ignition temperature, a flame travels upstream, and extinguishes at a lower temperature.

2. The micro flow reactor The simulated flow reactor consists of a cylindrical tube, a control mechanism to specify the inlet flow rate m˙ of the mixture, and a heat source to impose a controlled wall temperature profile Twall (x) along the length of the tube (Fig. 1). The equivalence ratio and N2 /O2 dilution level of the mixture can also be adjusted using flow controllers. As the mixture moves downstream, it is exposed to an increasing wall temperature. At the ignition temperature, the mixture will auto-ignite and a flame will appear. Depending on the inlet flow rate, one of three flame types is observed: a thin stable flame (observed at high m˙ ), a thicker weak flame that is also stable (observed at low m˙ ), or a dynamic flame with repeated extinction and ignition (FREI, observed at intermediate m˙ ). The FREI regime contains critical combustion information at engine-relevant conditions such as sensitivity to chemical kinetics [13]. The fast response time of FREI allows many conditions to be tested for a given sample. The FREI regime only appears under specific conditions that depend on parameters such as the inlet flow rate, imposed temperature profile, tube diameter, pressure, and the fuel itself. The operating conditions of the device must be carefully designed to distinguish between mixtures with similar ignition chemistry, and to collect sufficient data for inference. In this work, simulations of the micro flow reactor are used to quickly and inexpensively run virtual experiments to obtain ignition locations at different conditions for many fuels. This data provides a rich set of ignition information for different fuels, and can be used to establish a relationship between the micro scale flame dynamics and the accepted ASTM standard for RON and MON [1,2]. In practice, measurements from the experimental apparatus would be used to characterize unknown fuels. Currently, experiments of FREI in a micro flow reactor at high pressure (20–30 bar) are under development by Schoegl et al. [23]. 3. Computational strategy The objective is to predict the octane number of new fuels using data from the flow reactor. To accomplish this, it must be demonstrated that (a) the flow reactor provides data that is measurably distinguishable between fuels, (b) the quantities measured in the flow reactor are sensitive to changes that affect the octane number, and (c) the flow reactor data can be used to predict the octane number with sufficient accuracy. Questions (a) and (b) have been studied in previous work [13,24,25]. To demonstrate (c) a sufficiently large dataset of fuels with micro flow reactor ignition characteristics, fuel properties, and experimentally measured RON and MON is needed to determine if a robust relationship exists between combustion metrics in the flow reactor and combustion metrics in an engine.

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Table 1 Composition and properties of the gasoline surrogate used for the biofuel blends. Table reproduced from McCormick et al. [22]. Isooctane, vol% n-Heptane, vol% Toluene, vol% 1-Hexene, vol% RON MON Anti-knock index

55 15 25 5 90.3 84.7 87.5

Prior to testing a prototype of the micro flow reactor at engine relevant pressures, its potential is assessed through numerical simulations. A validated simulation methodology is used to run virtual experiments of the flow reactor and generate ignition data on fuels for which experimentally measured RON and MON data is readily available. The fuels simulated include 238 ETPRF fuels and 21 biofuel blends. The biofuel blends are comprised of a gasoline surrogate (composition shown in Table 1) blended with each of the 7 biofuels at 3 different blend levels: 10%, 20%, and 30% biofuel by volume. The seven biofuels are: ethanol, methanol, 2methyl-1-butanol, methyl-ethyl-ketone, n-propanol, 1-butanol, and 2-butanol. The RON and MON of the biofuel blends are obtained from McCormick et al. [22]. The datasets are used to train and test feed forward neural network models. The trained models demonstrate that a generalizable relationship exists between the ignition characteristics at a range of FREI conditions and the RON and MON. The physics model and neural network models are described in detail in the following sections. The motivation, computational framework, and main results are summarized in Fig. 2. 3.1. The physics based model The physics-based model of the micro flow reactor is based on a computationally efficient 0-D plug flow reactor model proposed by Ayoobi and Schoegl [26]. The fluid density, velocity, temperature, and species mass fractions are assumed to only vary in time. The advection of a premixed fuel/air fluid particle is considered inside the heated channel. The location of the particle at a given time can be determined from the advection velocity, which is computed from the inlet mass flow and the local density:

ρU = (ρU )inlet .

(1)

The governing equations are the unsteady low-Mach temperature and species transport equations along with the ideal gas equation of state:

ρ cp ρ

 ∂T =− ω˙ i hiWi − Qw , ∂t i

∂ Yi = ω˙ iWi , ∂t

pW = ρ RT .

(2)

(3) (4)

cp is the heat capacity, p is the thermodynamic pressure, W is the mixture molecular weight, and R is the universal gas constant. hi , cp,i , Wi , and ω˙ i are the enthalpy, heat capacity, molecular weight, and production rate of species i. The wall heat transfer term, Qw , is computed using Newton’s law of cooling

Qw =

4λNu (T − Twall ), d2

(5)

where λ is the conductivity, Nu is the Nusselt number, d is the tube diameter, and Twall is the local wall temperature. The

Fig. 2. Summary of the motivation, methodology, and main results of the present study.

species thermal conductivities, λ, are computed using Eucken’s formula [27] and the mixture-averaged thermal conductivity, λ, is obtained following Mathur et al. [28]. A constant Nusselt number of 4 is used. The equations are integrated in time with the scaled preconditioned GMRES method distributed as part of the CVODE package included in the SUNDIALS library [29]. An adaptive preconditioning strategy [30] is used to efficiently solve large detailed kinetic mechanisms. A comprehensive chemical mechanism for gasoline surrogates by Mehl et al. [31] is used. The mechanism contains more than 2800 species and 12,000 reactions. This kinetic mechanism has been validated with experimental measurements of ignition delay times, flame speeds, and speciation from flow reactors. While the exact values of the simulation could change with a different mechanism, the overall trends predicted are not expected to be strongly dependent on the chemical mechanism. The 0-D model was validated against a quasi 2-D thermal boundary layer model [13] and was found to predict the ignition location with reasonable accuracy. The validation is provided in the supplemental material. The operating conditions of the system are determined by the fuel/air mixture, heat source (temperature profile), pressure, and tube diameter. The fuel/air mixture is supplied at a controlled inlet velocity at ambient temperature. The wall temperature varies along the axial direction following

T (x ) =





T0 + T1 T1 − T0 x − x1 + erf , 2 2 σ1

(6)

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where T0 = 293 K, T1 = 1400 K, x1 = 71.2 mm and σ1 = 5.11 mm. The temperature profile was chosen for its simple analytic form and is similar to that used in previous studies of similar micro flow reactors [24,32–34]. The effect of heat release within the tube on the wall temperature profile is not considered since it is small compared to that of the large external heat source [24]. A pressure of 25 bar was chosen since it was found that the research octane number (RON) and motor octane number (MON) correlate best with simulated zero-dimensional (0-D) ignition delay times at 25 bar [6,35]. The tube diameter is 0.4 mm. For each fuel, 25 ignition locations are computed by sweeping over a range of mass flows and nitrogen dilution levels. The mass flow is varied from 2 · 10−7 kg/s to 6 · 10−7 kg/s and the N2 /O2 molar ratio is varied from 2 to 7 (air is 3.76). A low mass flow and a small N2 /O2 ratio will lead to ignition at a lower wall temperature than a high mass flow with a large N2 /O2 ratio. This ensures that ignitions occur at different locations along the channel, thereby covering a range of temperatures. A stoichiometric equivalence ratio is used in all cases. 3.2. Training data The physics-based model was used to simulate the ignition locations of over 200 ETPRF fuels. Experimental octane number measurements for these fuels were collected from the literature [3,4,14–21]. This information was used to create a database of training data for the neural network model. The amount of training data was limited by the availability of experimental RON and MON measurements. The database was used to train the RON neural network with 238 ETPRF mixtures, while the MON neural network was trained with 174 mixtures. In practice, the database would be created using experimental measurements from the micro flow reactor. Creating the initial database would require testing a large number of fuels, O (100 ), for the neural network to sufficiently generalize. This large number of fuel tests is both economically and practically feasible. Testing a fuel requires a sample volume of only ∼ 1 mL. Once the fuel sample enters into the micro flow reactor, the measured physical phenomena occurs quickly and repeats: the frequency of a FREI event is 10–10 0 0 Hz (depending on the fuel, mass flow rate, pressure, and wall temperature profile) [24,34]. Recording measurements at a range of conditions by sweeping across different mass flows and N2 /O2 ratios also occurs quickly as the typical response time for a flow controller is 100 ms. Once an initial database has been created, it can be improved over time by adding more fuel samples. 3.3. Neural network model Feed forward neural network models are developed to determine the nonlinear relationship between the input features (fuel properties and ignition locations) and the target outputs (RON and MON predictions). The neural network is built with PyTorch (version 0.3.1.post2), an open source machine learning platform [36]. 3.3.1. Neural network architecture The input layer to the neural network has 30 features: 25 ignition locations and 5 fuel properties: the density, heat of vaporization, and number of H, C, and O atoms. These fuel properties were chosen based on physical intuition, availability, and model performance. The inputs are normalized using min-max normalization. The network has 1 hidden layer with 20 nodes, and one output dimension (separate networks are trained for prediction of RON and MON). The exponential linear unit (ELU) is used as the activation

function for the nodes. The Adam method is used for stochastic gradient-based optimization [37], with an L1 loss function. 3.3.2. Architecture and hyperparameter selection A neural network creates a mapping between the input features and the target outputs. This mapping is determined by the training data, the neural network architecture, and the hyperparameters. Determining a suitable neural network architecture and hyperparameter combination for a problem is a highly iterative process. Neural networks developed for other domains such as image classification, spam filtering, etc. have a substantial publication record with best practices on neural network architecture and hyperparameter tuning [38]. Intuition from these domains serve as a useful guide but the choice of hyperparameters often depend on the specific dataset, amount of data, and input features. For this problem, many neural network architectures and hyperparameters were tested. The data was split into a training set and test set. The training set, comprised of data from the ETPRF fuels, was used to determine an optimal neural network architecture and hyperparameter set by using 10-fold cross validation. The test set, comprised of the biofuel blend data, was used to evaluate the efficacy of the neural network models to predict RON and MON for this new set of fuels. Several activation functions were evaluated, starting with the rectified linear unit (ReLU) due to its prevalence in deep learning problems [39]. However, it was found that both exponential linear unit (ELU) and sigmoid activation functions outperform ReLU for this problem. Different loss functions were also compared, and it was found that the L1 loss function outperforms the L2 loss function which is attributed to the L2 loss functions’ bias towards heavily weighting outliers. Different optimization methods were also tested: traditional stochastic gradient descent and the Adam optimizer performed similarly well. Other hyperparameters such as the number of hidden nodes, learning rate, and iteration step were tuned iteratively. 3.4. The number of ignition measurements A neural network can accept any number of input features, but there is often a practical upper bound due to the expense of gathering data and running the neural network model. For each fuel, 25 ignition locations were computed by initializing simulations at a range of mass flow and nitrogen dilution levels. Measuring data for 25 different conditions in a flow reactor is technically feasible as the measured physical event occurs on a time scale of 1–100 ms and the response time for a flow controller occurs on a time scale of 100 ms. The number of input features was chosen to provide the neural network with a rich set of ignition information, while still remaining computationally and experimentally feasible. Reducing the number of input features can lower the cost of computation and data gathering. To explore the impact of reducing the number of measurements on prediction quality, the neural network was also trained with 9 ignition locations, instead of 25. The 9 input parameters were selected by sweeping over the same ranges of mass flow and N2 /O2 ratios, but with a larger step size. The results are reported in Fig. 3. The mean average error for RON and MON were higher for the 9 ignition location case, compared with the 25 ignition location case. Therefore, the remainder of the results were trained using 25 ignition locations. It is important to note that the same neural network architecture was used for the different input number cases. A different neural network architecture choice could improve prediction capability with fewer inputs. Determining the minimum number of input features required to predict an output without unacceptable degradation of prediction quality is an important topic in machine learning, and should be examined for this system in future work.

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Fig. 3. Average training and test error for RON and MON predictions. The training set is comprised of the ETPRF fuels; the test set is comprised of the biofuel blends. Using data from 25 ignition locations in the input layer led to better RON and MON predictions compared to the 9 ignition location case. Therefore, the remainder of the neural network cases use data from 25 ignition locations.

Fig. 4. Average training and test error for RON and MON predictions. The training set is comprised of the ETPRF fuels; the test set is comprised of the biofuel blends. A case with Gaussian noise was added to explore the impact of random error that can be present in experimentally measured data.

3.5. Robustness to Gaussian noise An important difference between measurements computed from virtual experiments and measurements obtained from physical experiments is the lack of random and systemic errors in numerical results. To demonstrate that the present method can be used to predict RON and MON even in the presence of random errors, Gaussian noise, with 0 mean and a standard deviation of 0.05 mm, was added to the ignition locations in the training and test data. Gaussian noise was added before the normalization of the input features. For a given fuel, the change in ignition location due to different input conditions (mass flow and N2 /O2 ratios)

spans 1–3 mm. Therefore, the chosen standard deviation is equivalent to adding 1–5% Gaussian white noise to the data. The neural network architecture was trained and tested with this noisy data, and the results are shown in Fig. 4. While the addition of noise reduced the prediction accuracy, the method remains robust at predicting RON and MON of new fuel blends. The remainder of the figures presented in the Results section are free of Gaussian noise. The results in Fig. 4 demonstrate a low training error and a test error that, even in the presence of noise, is lower than other comparable methods (comparisons are shown in the Results section). The low test error indicates that the neural network is generalizing well from the training set to the biofuel blend test set. One of the

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Fig. 5. Absolute error of the RON and MON predictions for ethanol blends at 10, 20 and 30% ethanol by volume.

Fig. 6. Absolute error of the RON and MON predictions for methanol blends at 10, 20 and 30% methanol by volume.

most reliable methods to improve the performance of a neural network is to include more training examples. As more training data becomes available, this information can be included in the neural network to improve octane number predictions of the biofuel blends and extend the range of validity to fuels with properties that are very different from the ETPRF fuels. 4. Results The neural network architecture described in the preceding section is used to train separate models to predict the RON and MON. The models are trained on the ETPRF fuels, and for the 25 ignition location case, have a mean absolute error (MAE) on the training

data of 0.6 for RON and 0.3 for MON. The test set is comprised of the 21 biofuel blends, the MAE on the test data is 2.2 for RON and 1.9 for MON (Fig. 3). The experimental uncertainty for reproducibility across facilities is 0.7 for RON and 0.9 for MON [6]. The prediction errors for all 21 biofuel blends (7 fuels at 3 blend levels) are shown in Figs. 5–8. The ethanol and methanol blends predictions are compared to ignition delay time (IDT) correlation predictions from Naser et al. [7] and nuclear magnetic resonance (NMR) spectroscopy neural network predictions from Jameel et al. [9]. Naser et al. developed correlations to relate the RON and MON to constant volume, gas-phase ignition delay times. The correlations were validated with various ethanol-toluene primary reference fuels (ETPRF) mixtures as well as multi-component gasoline

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Fig. 7. Absolute error of RON predictions for 5 biofuels blended at 10, 20, and 30% by volume.

Fig. 8. Absolute error of MON predictions for 5 biofuels blended at 10, 20, and 30% by volume.

surrogate mixtures. In that work, ignition delay times at 20 bar and 750 K are used to predict the RON and ignition delay times at 20 bar and 820 K are used for the MON. Jameel et al. employed a neural network to predict the RON and MON from the fuel’s functional groups information. The functional groups were determined using NMR spectroscopy and the neural network was trained using pure hydrocarbons, hydrocarbon-ethanol blends, and FACE (fuels for advanced combustion engines) gasoline-ethanol blends. Figure 5 compares the RON and MON predictions for ethanol using the present micro flow reactor neural network, IDT correlations from Naser [7], and the NMR neural network [9]. The micro flow reactor neural network performs better than other available methods, with an average RON MAE of 1.4 and MON MAE of 1.2. Figure 6 shows the octane number prediction errors for methanol blends. The results across the methods are very mixed, all of the methods had a large spread in prediction error from less

than 1 octane number for some blends to ∼ 6 octane numbers for other blends. Prediction for the remaining alcohol blends using the micro flow reactor neural network are compared to predictions from the NMR neural network. The IDT correlations from Naser et al. are computed from a chemical mechanism [40] which does not contain some of the alcohol species used in the biofuel blends. Using a different mechanism would not be consistent with the correlations, therefore RON and MON comparisons using IDT correlations are only computed for methanol, ethanol, and methyl-ethyl-ketone. Figures 7 and 8 show the comparisons for RON and MON respectively. The micro flow reactor neural network has a lower absolute error than the NMR neural network for all blends. The variation in prediction ability across different fuels can in part be attributed to the small number of training examples. Access to more training examples can reduce variance and improve predictions.

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Fig. 9. Comparison of MAE for RON of the 20% biofuel blends. The red bar shows the MAE using the NMR spectroscopy neural network [9]. The blue bars show the present neural network with 4 training data cases: ETPRF fuels only, ETPRF and 10% blends, ETPRF and 30% blends, and ETPRF and 10 and 30% blends. The final bar is the training error when all biofuels are included in the training data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Comparison of MAE for MON of the 20% biofuel blends. The red bar shows the MAE using the NMR spectroscopy neural network [9]. The blue bars show the present neural network with 4 training data cases: ETPRF fuels only, ETPRF and 10% blends, ETPRF and 30% blends, and ETPRF and 10 and 30% blends. The final bar is the training error when all biofuels are included in the training data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

To demonstrate that more training data improves the neural network’s ability to accurately predict RON and MON, new training datasets are created by adding some of the biofuel blends. The original training dataset was comprised of only ETPRF, where no biofuels other than ethanol were present. In practice, as micro flow reactor measurements of biofuel blends are taken, this information can be added as additional training data so that the

octane number for other biofuel blend levels can be predicted with greater accuracy. The three new training sets created are: ETPRF and 10% biofuel blends (an extrapolative scenario), ETPRF and 30% biofuel blends (a large-gap interpolative scenario), and ETPRF and 10 and 30% biofuel blends (a small-gap interpolative scenario). The test set for all three cases is comprised of the 20% biofuel blends.

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Figures 9 and 10 show the average RON error and average MON error for the 20% biofuel blends. The red bar shows the prediction error using the NMR neural network, while each blue bar shows a different training scenario for the micro flow reactor neural network. The NMR neural network had an average RON and MON error of ∼ 5 octane number. The flow reactor neural network trained only on ETPRF fuels had an average error of ∼ 2 octane number. Including biofuels at blend conditions of 10% and 30% in the training set had a positive impact for predicting the octane number for 20% blends, reducing the MAE from ∼ 2 octane number to ∼ 1 octane number. The last blue bar shows the training error of the neural network is less than 1 octane number. The experimental uncertainty for reproducibility across facilities using the standard CFR engine is 0.7 for RON and 0.9 for MON [6].

5. Conclusion Combustion in a narrow channel with an imposed temperature gradient was studied to determine its potential as a fuel testing method. Simulations of the flow reactor were used to obtain ignition locations of over 200 ETPRF fuels and 21 biofuel blends. Experimental RON and MON values for these fuels were obtained from the literature. A feed forward neural network was developed with the fuels’ ignition locations and fuel properties (density, heat of vaporization, and number of H, C, and O atoms) as inputs and the octane numbers as outputs. The ETPRF fuels were used to train the neural network, while the biofuel blends formed the test set to demonstrate that RON and MON can be predicted accurately. The mean absolute error on the training data was 0.6 for RON and 0.3 for MON while the average error on the test set was 2.2 for RON and 1.9 for MON. The neural network was then trained using both ETPRF and some of the biofuel blends. Including information on the biofuel blends in the training data led to improved predictions with errors on the order of one octane number for both RON and MON. Predictions using the micro flow reactor neural network approach were compared to other prediction methods available in the literature. This data showed particular improvement over other methods for biofuel blends including species such as 2-methyl-1-butanol, methyl-ethyl-ketone, n-propanol, 1-butanol, and 2-butanol. This represents an important milestone in demonstrating the utility of the present micro flow reactor to predict the octane number of practical transportation fuels. The present study used simulations to generate the ignition data. Future work will use experimental measurements from a micro flow reactor to generate ignition, flame propagation, and flame extinction measurements for uncharacterized fuels at engine relevant pressures.

Acknowledgments The authors would like to acknowledge Prof. Ingmar Schoegl for providing a functional 0-D plug flow reactor simulation template to predict ignition locations and for sharing an experimentallymeasured micro flow reactor wall temperature profile. This work was supported through the Laboratory Directed Research and Development program, tracking no. 16-ERD-003, and the Co-Optimization of Fuels and Engines (Co-Optima) project sponsored by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE), Bioenergy Technologies and Vehicle Technologies Offices. The work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC5207NA27344.

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Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2019.06. 019.

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