Francesca Vittorioso

Vincent Guidard

Nadia Fourrié

Javier Andrey-Andrés

Andrey-Andrés Preparing

Preparing the assimilation of IASI-NG in NWP models: a first channel selection

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. Introduction

As the EUMETSAT Polar System-Second Generation (EPS-SG) is being prepared, a new generation of the hyperspectral Infrared Atmospheric Sounding Interferometer (IASI) has being designed. The IASI New Generation (IASI-NG) will measure at 16921 wavelengths in each sounding pixel, benefiting of a spectral resolution and a signal-to-noise ratio improved by a factor 2 compared to its predecessor [START_REF] Crevoisier | Towards IASI-New Generation (IASI-NG) : impact of improved spectral resolution and radiometric noise on the retrieval of thermodynamic, chemistry and climate variables[END_REF]]. Measurement precision will be improved as well starting from the 1 K in temperature and 10% in humidity IASI precision. The IASI-NG characteristics will lead to huge improvements in detection and retrieval of numerous chemical species and aerosols, and in thermodynamic profiles retrievals, as well as providing, like its predecessor, a huge contribution to Numerical Weather Prediction (NWP). The high amount of data resulting from IASI-NG will present many challenges in the areas of data transmission, storage and assimilation. Moreover, the number of individual pieces of information will be not exploitable in an operational NWP context and the choice of an optimal data subset will be needed. For all these reasons, an appropriate IASI-NG channel selection is going to be performed aiming to select the most informative channels for NWP.

II. Observing System Simulation Experiment (OSSE) construction and 1D-Var retrievals

III. Case study

The first step of the present effort has been planned to be carried out on nadirover seaclear sky conditions. A subset of 1099 of the 318 391 observations matching these criteria, have been judged to be a representative sample of the overall data. The new subset contains observations for:

V. A first channel selection

This step has been based on a methodology suggested by [START_REF] Rodgers | Information contentand opyimisation of high spectral resolution measurements[END_REF] and proved to be a good a priori method for determination of an optimal channel set by [START_REF] Rabier | Channel selection methods for Infrared Atmospheric Sounding Interferometer radiances[END_REF]. The method relies on evaluating the impact of the addition of single channel on a figure of merit. This latter is normally a quantity reflecting the improvement of the analysis error covariance matrix A over the background error covariance matrix B (e.g. DFS or Entropy Reduction -ER ).

In this very first stage, only one among the case study profiles has been picked up (Augustnightmid-latitudes) and the figure of merit chosen to iterate the procedure is the Total DFS (Temperature + Humidity + Skin Temperature DFS). The iterative method has been implemented at this stage so that it stops when the maximum DFS does not reach any significant variations anymore. Based on an analysis of the Total DFS growth rate at each iteration, it has been decided to narrow the choice down to the channels showing a percentage of this parameter greater than 0.01% (i.e. the channels for which the Total DFS no longer varies after the fourth decimal place). These thresholds are: 665 channels for BAND 1 and 758 for BAND 2. The research results are shown here below in Figure 4 and 5. More in details, it is possible to observe the Total DFS growth with the amount of selected channels, the trend of the Temperature and Humidity Jacobians for the subset of channels selected via the growth rate criterion and finally the distribution of the selected channels on the interested spectrum areas.

(3) Data perturbation: -Observations:

[Instrument Noise] x [Random Noise] -Background: [B Matrix] x [Scaling Factor] x [Random Gaussian Noise]

IV. Propaedeutic study towards a channel selection

Tests performed on 1D-Var output retrieved profiles, showed a good improvement in results if a full covariance matrix of the observation errors (R matrix) was provided in input. Thus, in order to estimate full structure R matrices, a diagnostic procedure introduced by Desroziers et al.

(2005) has been applied to different regions of the spectrum that IASI-NG is able to characterize, mainly focusing on the BAND 1 and BAND 2, that are the most relevant for assimilation. 2448 and 3112 channels have been considered for band 1 and band 2, respectively. For both bands the process has been iterated until its convergence and the 1D-Var has been run giving in input the last diagnostic iteration R matrix.

The Rate of Improvement for Standard Deviations (computed on the 1099 profiles of the whole case study dataset) has been computed for both bands using 1D-Var output. Figure 3 shows the good improvement in results. For what concerns temperature, the improvement is more pronounced for BAND 1, that is the "temperature band". Concerning humidity, on the other hand, the better results are in the high troposphere if considering BAND 2. The reverse is true in low troposphere, due to the different sensitivity of the involved channels. The Degrees of Freedom for the Signal (DFS) values have been computed as well and are here shown in Table 1.  May and August  polar, mid-latitudes and tropical regions  day and night located as in Figure 2.

VI. Future works

The next step of the present study aims to refine and test this first channel selection. The procedure of section V will be spread to the whole dataset of atmospheric profiles selected as case study in section III. Another method will also be applied, based on selecting the most relevant channels relying on the characteristics of their weighting functions.

channels selected

Four

  dates in the middle of each season from 2013 have been selected: February 4th, May 6th, August 6th and November 4th [Andrey-Andrés et al. (2017)]. The full IASI orbit for each one of these dates has been computed for a total of 5242448 simulations for each instrument (IASI scan geometry is used for IASI-NG). The experiment was carried out into four steps: (1) construction of the input database; (2) spectra simulation for both IASI and IASI-NG; (3) data perturbation; (4) introduction of perturbed input data into 1D-Var . Météo France -Preprocessing: -IASI position -Instrument and solar angles MACC data (from ECMWF):-Vertical profiles of T, q, O 3 , CO, SO 2 -Surface P and T LMDz Model:-Profiles of CO 2 and CH 4

Figure 1 :

 1 Figure 1: IASI observations (5.242.448), Clear Sky over sea (318.391) and Clear Sky over land (404.791 cases).

Figure 2 :

 2 Figure 2: Subset of selected observations for preparing the IASI-NG channel selection: May/day, May/night, August/day, August/night data.

Figure 3 :

 3 Figure 3: 𝑅𝑎𝑡𝑒 𝑜𝑓 𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 = 𝑅 -𝑇 -𝐵 -𝑇 • (𝐵 -𝑇) -1 for Standard Deviations computed from the results obtained with the last iteration diagnostic matrices.

Table 1 :

 1 DFS values computed for retrieved profiles resulting from the use of the full R Matrix from diagnostic convergence iterations (7th iteration in BAND 1 and 10th iteration in BAND 2). Preparing the assimilation of IASI-NG in NWP models: a first channel selection Francesca Vittorioso, Vincent Guidard, Nadia Fourrié, Javier Andrey-Andrés CNRM UMR 3589, Météo-France & CNRS, GMAP/OBS, Toulouse, France francesca.vittorioso@meteo.fr BAND 1 BAND 2

Figure 4 :

 4 Figure 4: Main channel selection results for BAND 1. Top Right: Total DFS growth with the amount of channels selected (the contribute of Temperature, Humidity and Skin Temperature DFS at each iteration are shown as well). . Bottom Left: Temperature and Humidity Jacobians for the 665 channels selected. Bottom Right: position on the spectrum of such 665 channels.

Figure 5 :

 5 Figure 5: Main channel selection results for BAND 2. Top Left: Total DFS growth with amount of channels selected and contribute of Temperature, Humidity and Skin Temperature DFS . Bottom Right: Temperature and Humidity Jacobians for the 758 channels selected. Bottom Left: position on the spectrum of such 758 selected channels.

Acknowledgements

This research has received funding from CNES in the framework of the IASI-NG project.


Nicolas Reuge
email: reuge@free.fr

Gerard L Vignoles

Hélène Le Poche

Francis Langlais
email: langlais@lcts.u-bordeaux.fr

MODELLING OF PYROCARBON CHEMICAL VAPOR INFILTRATION

The chemical vapor infiltration (CVI) of pyrocarbon is used to produce carbon matrix of C/C composites. This process involves complex physico-chemical phenomena such as the transport of gas mixtures (hydrocarbons and hydrogen) in the reactor and inside the fibrous preform, chemical reactions (pyrolysis and deposition), and the structural evolution of the preform. A global modelling approach has been developed for isobaric CVI. The most difficult point is to find a realistic chemical model for pyrocarbon deposition chemistry, simple enough to be implemented in a 2D or 3D fluid dynamics code. Such a model is proposed in this study, featuring a group of light species leading to smooth laminar pyrocarbon, a group of heavier species (polycyclic hydrocarbons) leading to rough laminar pyrocarbon, and associated homogeneous and heterogeneous reaction kinetics. This model has been developed and validated according to results of pyrocarbon CVD experiments from propane, and isothermal, isobaric CVI in a 1D model porous medium made of compact stacks of 100 µm diameter filaments.

INTRODUCTION

Carbon/carbon (C/C) composite materials are used in high-temperature applications, such as rocket nozzle, heat shields, airplane braking, and furnace components. For a high thermal and mechanical quality, CVI-processed pieces are preferred. CVI 1 stands for Chemical Vapor Infiltration, a process derived from CVD (chemical vapor deposition), in which a preform made of carbon fibers is densified by a pyrocarbon (pyC) deposit originated in the cracking of gaseous hydrocarbons, usually at high temperatures (ca. 1000-1300 K) and low pressures. This process allows the fabrication of complex pieces without damaging the carbon fibers and results in excellent mechanical and thermal properties.

Hydrocarbon pyrolysis is known to lead to various nanotextural forms of pyrocarbon in the context of CVD and/or CVI 2,3 . Among them, two varieties, referred to as Rough Laminar (RL) and Smooth Laminar (SL) because of their appearances when imaged by Polarized Light Optical Microscopy (PLOM), differ by their degree of structural anisot-ropy, and have distinct mechanical and optical properties. Moreover, only the RL form is graphitizable by high-temperature post-treatment 3,4 . A key issue in pyC CVD/CVI is the control of the deposit nanostructure during processing. It has been shown [START_REF] Diefendorf | Deposition of pyrolytic carbons[END_REF][START_REF] Lieberman | [END_REF][7] that processing parameters such as temperature, pressure, and composition ratios are important for this.

Another crucial issue in C/C composite quality monitoring is the precise knowledge of the deposition kinetics as a function of the process parameters : temperature, pressure, residence time, gas composition, and surface-to-volume ratio S/V. Numerous experimental studies [8][9][10][11][12][13][14][15] have been devoted to the determination of kinetic laws in various physico-chemical conditions and reactor configurations, either in CVD (plain substrate, low S/V ratio), or in CVI (porous substrate, high S/V ratio). All of them have tried to identify some "ultimate precursor" of pyC, either light, aliphatic species, or heavy aromatic compounds such as PAHs (Polycyclic Aromatic Hydrocarbons). It has been proved, from mass spectroscopy 16 , gas chromatography 17,18 and FT-IR 19,20 measurements of the gas-phase composition, that the hydrocarbon pyrolysis follows a long chain of homogeneous reactions, starting from light species and leading to large PAHs, in a so-called "maturation" process. The pyrocarbon deposits come from both light and heavy hydrocarbons, and their nanostructure undergoes transitions from SL to RL and vice-versa when the residence time increases 21,22 . Scaled partial pressures of various species from computations (ref. [23]).

A kinetic modeling study based on a detailed gas-phase mechanism has confirmed the maturation phenomenon and its importance on one of the SL/RL transitions (from SL to RL when residence time and/or temperature increases), in the case of propane de-composition at 2 kPa in a tubular furnace and CVD conditions 23 . It appeared that only the heaviest species in the detailed model were associated to RL pyrocarbon growth, while many lighter ones were related to SL (see figures 1 and 2).

In order to bring all those results in a coherent and yet easy-to-use kinetic model, a simplified scheme will be presented for propane pyrolysis and SL/RL pyrocarbon deposition, suited to comparison with experiments of CVD and CVI for moderate to high residence times (0.1 to 10 s), low pressures (0.5 to 5 kPa), moderate temperatures (900°C to 1200°C) and propane as precursor gas. This model will be constructed from a synthesis of experimental results. Its parameters will be identified in a CVD configuration as a first guess; then, CVI results on model pores will be used to refine the parameter set and even update the whole model.

MODEL SETUP

The basic idea arising from experimental studies 18,21 is a description of homogeneous maturation as a set of reactions in series, with SL and RL deposition reactions in parallel. In the case of propane as a single precursor, the following scheme has been proposed :

where B and C are two groups of gas-phase species, respectively light and heavy. From numerical computations of gas-phase pyrolysis 23 , it appears that the species in group C would be C 14 H 10 or heavier, while species in group B would be lighter ones, from C 2 H 2 to C 6 H 6 . Actually, these light species, and especially the C 2 H x group, represent most of the decomposition products that are present in the gas-phase, so it is chosen to lump them together into a single species :

The value of α, β, and x have been fixed to 3/2, 1/2, and 14/3 in order to fit the actual mass and mole balances that are obtained from these computations 23 . On the other hand, C 14 H 10 is chosen as being representative of group C, so that reaction #3 reads : However, up to this point, one essential feature of gas-phase maturation is not reproduced in such a model : as soon as propane gets decomposed, group C species This completes the specification of a model frame containing maturation, and concurrent SL and RL deposition in the given set of experimental conditions. In the following, it will be intended to identify all kinetic parameters : activation energies, preexponential factors, and reaction orders.

C 3 H 8 α C 2 H x + β

MODEL PARAMETRIC IDENTIFICATION ON CVD CONFIGURATION

Direct identification from experimental results

The first information that may be used for parametric identification is the evolution of propane with time and temperature : actually, its decomposition is so fast that it can be considered as completely decomposed when pyC deposition begins to occur. Accordingly, no attempt is made here to give a kinetic law for reaction #1, but rather consider it as complete. Second, the heterogeneous deposition kinetics of reaction #2 may be deduced from the knowledge of the apparent kinetics in the regime where SL pyC is deposited (see figure 1). For high enough residence times, propane decomposition is indeed complete, and the reaction order is nearly zero. This can be interpreted as an adsorption-reaction scheme where the surface sites are saturated 23 ; consequently the order and activation energies of reaction #2 may be directly identified. As far as the next kinetic regime is concerned, the apparent order is nearly 2, with a widely varying activation energy : under the hypothesis that the homogeneous reactions are rate-limiting in this regime, this order will be affected to reaction #3. Indeed, this may be the sign of a limiting bimolecular step such as the most frequently cited ones for benzene synthesis during pyrolysis.

1D CVD computations

The identification of the other parameters is not feasible from a direct interpretation of experimental results ; so, a 1D CVD numerical solver has been used in order to check out trial parameter sets. This solver is a simplification of a previously described one 24 . It has turned out that various parameter sets may be chosen, with a similar correlation quality. First, an activation energy is chosen for the heterogeneous reaction #4 ; then a pre-exponential factor for the same reaction is obtained, and the fitting procedure is ended with the determination of the two missing parameters, which are the activation energy and pre-exponential factor of reaction #3.

FIGURES 3 & 4 Comparison of deposition rates vs. residence time between experimental results and 1D

CVD computations. P = 2 kPa, S/V = 118 m -1 in hot zone , precursor : propane. T = 950°C (fig. 3), 1035°C (fig. 4) Figures 3 and4 show the results of the simulations with two distinct choices for E a (4), at the two extremes of the admissible range (10 and 230 kJ.mol -1 ). In both cases, the fitted activation energy for reaction #3 is similar (340 and 320 kJ.mol -1 , respectively). So far, one degree of freedom remains : one has no indication of the actual value of the activation energy of reaction #4. We will see that model-pore CVI results help in addressing this point.

MODEL PARAMETRIC IDENTIFICATION ON CVI CONFIGURATION

Model-pore infiltrations

Since the precise knowledge of transport and internal surface properties is required for a CVI computation, it has been chosen to design a model porous medium built with a compact stacking of 108 µm-diameter SiC filaments, contained in a carbon crucible (figure 5). The mean pore diameter is ≈ 12 µm before deposition, a suitable value for CVI studies. It has been possible to compute all relevant transport properties in the direction parallel to the fibers, using geometrical evaluations for S/V and a previously described Monte-Carlo transport simulation software for Knudsen transport 25 , while for binary dif-Deposition rate (µg. cm -2 .min -1 ) Deposition rate (µg. cm -2 .min -1 ) fusion the tortuosity is known to be unity, and viscous transport is considered negligible. Five experimental conditions have been chosen : T = 950°C with t s = 0.5 s (MP1), 1.5 s (MP2) and 10 s (MP3), and T=1035°C with t s = 0.25 s (MP4) and 2 s (MP5), in a way that the SL/RL transition be susceptible to appear on the deposits. The thickness profiles (figure 7) all display a sharp slope change for depths no longer than 2 mm. The values at the pore entrances were identical to the CVD values, showing that the porous medium did not interact strongly with the free-medium. The measured extinction angles in PLOM (figure 8) display a decrease, approximately at the same depth as the thickness slope break. Another striking fact is that the plateau obtained in CVD curves does not appear in the CVI experiments (especially MP1 where it would be expected) : this would tend to invalidate the hypothesis of a Langmuir-Hinshelwood scheme, and suggest that this plateau would be the superposition of two reactions, one with an increasing rate and another with a decreasing rate, which do not depend in the same way on S/V.

Model modifications and discussion

One-dimensional CVI computations have been performed in order to reproduce the deposit thickness profiles, and particularly the slope break. An extra hypothesis has been used : the species B leading to SL deposition would be actually divided into two groups B1 and B2, of neatly different reactivities. B2 (and also C when RL is deposited) would be responsible for the rapid initial thickness decrease, the rest of the profile would be due to B1. Also, the idea of a zero-order deposition rate has been removed. By setting the kinetic parameters, the inlet partial pressures of the reactants appeared as a consequence of the fitting procedure. The fitted profiles were adequate when the sum of the partial pressures p(B1) + p(B2) was much lower than the expected p(B) from CVD experiments ; accordingly, the group B has been split into three contributions, B0, B1 and B2, the species B0 being considered as unable to yield directly any pyC deposit.

Experiments MP1 and MP4 were used to obtain the deposition kinetics for SL deposition, and experiments MP2, MP3 and MP5 were used to obtain the kinetics for RL deposition and pore inlet values of p(C). The latter ones have revealed to be only compatible with high values of E a (3), so the uncertainty remaining after CVD experiments has been removed. There remains only to correlate the relative amounts of B1 and B2 to the experimental conditions. It is to notice that B1 has an evolution with T and t s very close to C 2 H 2 according to 23 , while B2 is present in small, constant amounts whatever the experimental conditions.

The CVI model obtained is summarized in Table 1

FIGURE 1

 1 FIGURE 1 Deposit rate vs. residence time. Precursor : propane, T = 950°C, P = 2 kPa.

FIGURE 2

 2 FIGURE 2Scaled partial pressures of various species from computations (ref.[23]).

Figure 6 FIGURE 5

 65 Figure 6 summarizes these results.

FIGURE 7

 7 FIGURE 7Deposit thickness profiles for 5 CVI experiments in model porous substrates.

FIGURE 8 PLOM

 8 FIGURE 8 PLOM extinction angle profiles for 5 CVI experiments in model porous substrates.

TABLE 1 :

 1 . The correlation index (residual of mean squares) has been always superior to 0,965 either in CVD or in CVI experiments. *(C) = 119,1 -0.21 T + 9.07 10 -5 T 2 (see text) 5. Summary of the model parameters.

		Balance	Pre-exp. factor A	Order	E a (kJ.mol -1 )
	#1.1 C 3 H 8 à B + 14/3 H 2 ,	1.59. 10 6 s -1	1	260
	#1.1	Repartition betw. B0, B1, and B2
	#1.2 #2.1 B1 à 2 C(s) + 7/3 H 2 (tabulated from the C 2 H 2 results of ref.[23]) 31.4 m.s -1 14148 m.s -1 #2.2 B2 à 2 C(s) + 7/3 H 2 #3 29.9 10 11 (mol.m -3 ) -0.8 s -1 1.8 1 1 7 B à C + 34/3 H 2 #4 C à 14 C(s) + 5 H 2 7.10 7 m.s -1 1 w. thresh. 230 120 120 320
		Threshold : p

CONCLUSION

A first attempt to provide a complete, coherent model for both CVD and CVI of pyrocarbon from propane has been presented. It appeared that model-pore densifications brought out numerous additional informations, sometimes in apparent contradiction with CVD results. This arises essentially in the large difference in S/V ratio, and consequently of the heterogeneous-to-homogeneous reaction ratio between both. A deposit thickness slope break has led to the necessary assumption that at least two distinct species groups are responsible for SL pyC deposition, a fact that may also explain a pseudo-plateau in rate vs. residence time CVD data.

ACKNOWLEDGEMENT

The authors wish to acknowledge Snecma Moteurs for financial support.


G D Maclean

Ciccarelli

A Comandini

N Chaumeix

J D Maclean

G Ciccarelli

Combustion properties of n-heptane/hydrogen mixtures

Combustion properties of n-heptane/hydrogen mixtures

Introduction

Current diesel engines use high levels of exhaust gas recirculation to decrease the combustion temperature and minimize the production of NOx. In addition, common rail high pressure fuel injection is used to produce a very fine fuel spray to reduce the production of soot and unburned hydrocarbons. In the latest diesel engines, the use of multiple fuel injections per cycle further reduces the amount of soot. The use of supplemental hydrogen gas mixed with diesel (i.e., hydrogen-enriched diesel) fuel has the potential to decrease these emissions. In fact, the presence of hydrogen reduces the carbon-to-hydrogen ratio and 2 enhances particle oxidation (producing higher concentrations of H and OH radicals and, for certain operating conditions, higher in-cylinder temperatures). Hydrogen-diesel fuel co-combustion also mitigates the effects of the over-mixing of diesel vapor with air which leads to compositions below the flammability limit and thus to significant concentrations of unburned hydrocarbons leaving the exhaust port. The presence of hydrogen favors flame initiation even in areas of the chamber where the diesel fuel is deficient. On the other hand, the percentage of diesel fuel replaced by hydrogen is limited by abnormal combustion behaviors [START_REF] Szwaja | Hydrogen combustion in a compression ignition diesel engine[END_REF][START_REF] Tsujimura | The utilization of hydrogen in hydrogen/diesel dual fuel engine[END_REF][START_REF] Liew | An experimental investigation of the combustion process of a heavy-duty diesel engine enriched with H2[END_REF]. Since the first pioneering investigations in the eighties [START_REF] Gopal | Use of hydrogen in dual-fuel engines[END_REF], numerous dieselengine studies focused on the effects of hydrogen addition on the exhaust gas composition have been performed. Savaranan and Nagarajan [START_REF] Saravanan | An experimental investigation of hydrogen-enriched air induction in a diesel engine system[END_REF] analyzed the emissions from a four-stroke, single-cylinder stationary diesel engine at different brake loads and percentages of hydrogen (between 0% and 90%). The authors measured a reduction in the particulate matter (PM) with increasing amounts of hydrogen (up to about 70% decrease) and in the smoke (caused by poor combustion). In a subsequent study [START_REF] Saravanan | Performance and emission studies on port injection of hydrogen with varied flow rates with Diesel as an ignition source[END_REF], the authors obtained a reduction in the smoke due to particulate matter of around 44% for an optimal hydrogen flow rate of 7.5 lpm. Decrement in PM emissions were also observed by Sandacı and Karagoz [START_REF] Sandalci | Experimental investigation of the combustion characteristics, emissions and performance of hydrogen port fuel injection in a diesel engine[END_REF] (smoke emission values decreased by 57.8%, 70.4%, and 75.2% with 16%, 36%, and 46% hydrogen energy content of total fuel, respectively) similar to other results obtained using the same water cooled, naturally aspirated CFR engine [START_REF] Karagöz | Engine performance and emission effects of diesel burns enriched by hydrogen on different engine loads[END_REF] and [START_REF] Karagöz | Effect of hydrogen enrichment on combustion characteristics, emissions and performance of a diesel engine[END_REF], and by Deb et al. [START_REF] Deb | An experimental study on combustion, performance and emission analysis of a single cylinder, 4-stroke DI-diesel engine using hydrogen in dual fuel mode of operation[END_REF] (smoke emission reduced by 37% and 66% with 11% and 42% hydrogen content). Talibi et al. [START_REF] Talibi | Effect of hydrogen-diesel fuel co-combustion on exhaust emissions with verification using an in-cylinder gas sampling technique[END_REF] performed experiments on a naturally aspirated, singlecylinder, direct injection, compression-ignition engine fixing the diesel fuel injection period and varying the hydrogen supplied to the engine. A decrease in soot emissions was observed at low engine loads, while at high loads the displacement of intake oxygen by hydrogen is the predominant factor, that leads to a slight increase in PM. A study by Tsolakis et al. [START_REF] Tsolakis | Dual Fuel Diesel Engine Operation Using H2. Effect on Particulate Emissions[END_REF] showed how the addition of hydrogen to a dual fuel diesel engine operating with reformed exhaust gas recirculation leads to reduced total particle number and mass, but it does not significantly affect particle size and mass distribution. On the other hand, the works by Zhou et al. [START_REF] Zhou | Combustion, performance, regulated and unregulated emissions of a diesel engine with hydrogen addition[END_REF][START_REF] Zhou | Diesel-hydrogen dual-fuel combustion and its impact on unregulated gaseous emissions and particulate emissions under different engine loads and engine speeds[END_REF] indicate that the decrease in PM emissions is due to the decrease in both particle number and particle size as the hydrogen content increases from 10% to 40%. PM reduction was also obtained by Chaichan [START_REF] Chaichan | The Effects of Hydrogen Addition to Diesel Fuel on the Emitted Particulate Matters[END_REF], although in this case a smaller effect was observed due to the high sulfur content in the diesel fuel. Different considerations apply for the case of the unburned hydrocarbon (HC) emissions. For example, the data obtained by Talibi et al. [START_REF] Talibi | Effect of hydrogen-diesel fuel co-combustion on exhaust emissions with verification using an in-cylinder gas sampling technique[END_REF], Savaravnan and Nagarajan [START_REF] Saravanan | An experimental investigation of hydrogen-enriched air induction in a diesel engine system[END_REF], and by Köse et al. [START_REF] Köse | An experimental investigation of effect on diesel engine performance and exhaust emissions of addition at dual fuel mode of hydrogen[END_REF] show a decrease of HC emissions with increasing H 2 enrichment, as in the study by Bari and Esmaeil [17] who evaluated the performance of a conventional diesel engine with addition of O 2 /H 2 mixtures. Other studies have shown the contrary [START_REF] Sandalci | Experimental investigation of the combustion characteristics, emissions and performance of hydrogen port fuel injection in a diesel engine[END_REF][START_REF] Karagöz | Engine performance and emission effects of diesel burns enriched by hydrogen on different engine loads[END_REF][START_REF] Karagöz | Effect of hydrogen enrichment on combustion characteristics, emissions and performance of a diesel engine[END_REF][START_REF] Deb | An experimental study on combustion, performance and emission analysis of a single cylinder, 4-stroke DI-diesel engine using hydrogen in dual fuel mode of operation[END_REF] even if the total HC emissions remain much lower than the regulation limits. In reality, the effect on the HC emissions may depend on the quantity of H 2 introduced, as shown by Zhou et al. [START_REF] Zhou | Combustion, performance, regulated and unregulated emissions of a diesel engine with hydrogen addition[END_REF]. While a consensus has been reached in the case of solid particle emissions, the effect of hydrogen-enriched diesel combustion on NOx is not as clear, since it strongly depends on the operating conditions and the temperatures attained in the combustion chamber. In general, a mild to considerable increase in NOx emissions is expected for increase in the chamber temperature caused by the presence of hydrogen [START_REF] Deb | An experimental study on combustion, performance and emission analysis of a single cylinder, 4-stroke DI-diesel engine using hydrogen in dual fuel mode of operation[END_REF][START_REF] Talibi | Effect of hydrogen-diesel fuel co-combustion on exhaust emissions with verification using an in-cylinder gas sampling technique[END_REF][START_REF] Zhou | Diesel-hydrogen dual-fuel combustion and its impact on unregulated gaseous emissions and particulate emissions under different engine loads and engine speeds[END_REF][START_REF] Köse | An experimental investigation of effect on diesel engine performance and exhaust emissions of addition at dual fuel mode of hydrogen[END_REF]. On the other hand, various studies showed that NOx can be reduced by lowering the combustion temperature at specific operating conditions [START_REF] Saravanan | An experimental investigation of hydrogen-enriched air induction in a diesel engine system[END_REF][START_REF] Masood | Computer simulation of hydrogen-diesel dual fuel exhaust gas emissions with experimental verification[END_REF][START_REF] Christodoulou | Experimental investigation of the effects of simultaneous hydrogen and nitrogen addition on the emissions and combustion of a diesel engine[END_REF]. In general, at low loads the NOx emissions decrease with increasing hydrogen content, while the opposite trend is observed at high loads [START_REF] Saravanan | Performance and emission studies on port injection of hydrogen with varied flow rates with Diesel as an ignition source[END_REF][START_REF] Karagöz | Engine performance and emission effects of diesel burns enriched by hydrogen on different engine loads[END_REF][START_REF] Zhou | Combustion, performance, regulated and unregulated emissions of a diesel engine with hydrogen addition[END_REF][START_REF] Saravanan | Combustion analysis on a DI diesel engine with hydrogen in dual fuel mode[END_REF]. Moreover, various studies show how for similar loads the addition of small amounts of hydrogen does not modify the NOx emissions while for the case of large H 2 quantities NOx increases considerably [START_REF] Sandalci | Experimental investigation of the combustion characteristics, emissions and performance of hydrogen port fuel injection in a diesel engine[END_REF][START_REF] Karagöz | Effect of hydrogen enrichment on combustion characteristics, emissions and performance of a diesel engine[END_REF]. Finally, in view of the necessity to reduce fossil fuel consumption, an increase in the thermal engine efficiency was observed in the majority of the abovementioned studies, due mainly to better mixing between H 2 and air compared to the liquid fuel case and faster burning characteristics (and consequently smaller heat transfer to the walls). Other applications of dual-fuel combustion can be envisioned, for example, in the case of homogeneous charge compression ignition HCCI engines, for which an extensive review has been recently presented by Hairuddin et al. [START_REF] Hairuddin | A review of hydrogen and natural gas addition in diesel HCCI engines[END_REF]. Several studies have also investigated the combination of hydrogen addition to diesel fuel and exhaust gas recirculation (EGR) techniques to further decrease the engine temperature and consequently the NOx emissions [START_REF] Banerjee | Hydrogen-EGR synergy as a promising pathway to meet the PM-NOx-BSFC trade-off contingencies of the diesel engine: A comprehensive review[END_REF][START_REF] Bose | An experimental investigation on engine performance and emissions of a single cylinder diesel engine using hydrogen as inducted fuel and diesel as injected fuel with exhaust gas recirculation[END_REF][START_REF] Miyamoto | Effect of hydrogen addition to intake gas on combustion and exhaust emission characteristics of a diesel engine[END_REF].

The results obtained for hydrogen-enriched diesel are very promising and emphasize how the technique may have a practical role in reduction of harmful pollutants from transportation engines. To help the engine manufacturers design solutions for an efficient implementation of this technology, the fundamental properties of the hydrogen-enriched diesel fuels need to be investigated not only in engines, but also in research reactors where the chemistry can be easily isolated and studied. In particular, due to the complexity of the real fuels, surrogate mixtures composed of few compounds which mimic the chemical and physical properties of the real fuel are often used in order to simplify CFD engine calculations [START_REF] Pitz | Recent progress in the development of diesel surrogate fuels[END_REF]. In the past, n-heptane has been proposed as a single-component surrogate fuel for diesel [START_REF] Guo | An Experimental and Modeling Study of HCCI Combustion Using n-Heptane[END_REF], and it is the most common component used in multi-component surrogate formulations, including the widely used primary reference fuel PRF and toluene reference fuel TRF. Due to its importance, n-heptane chemistry has been studied in detail both experimentally and numerically, in particular regarding its combustion properties, i.e. ignition delay times and laminar flame speeds, as relevant to the functioning of modern combustion devices. Several shock tube studies on n-heptane/air mixtures were implemented for the measurement of ignition delay times over a wide range of temperatures (720-1400 K), pressures (2-60 atm), and stoichiometric conditions (φ between 0.1 and 3) [START_REF] Ciezki | Shock-tube investigation of self-ignition of n-heptane-air mixtures under engine relevant conditions[END_REF][START_REF] Fieweger | Shock-tube investigations on the self-ignition of hydrocarbon-air mixtures at high pressures[END_REF][START_REF] Fieweger | Self-ignition of S.I. engine model fuels: A shock tube investigation at high pressure[END_REF][START_REF] Gauthier | Shock tube determination of ignition delay times in fullblend and surrogate fuel mixtures[END_REF][START_REF] Herzler | Shock tube study of the ignition of lean n-heptane/air mixtures at intermediate temperatures and high pressures[END_REF][START_REF] Shen | A Shock Tube Study of the Ignition of n-Heptane, n-Decane, n-Dodecane, and n-Tetradecane at Elevated Pressures[END_REF][START_REF] Hartmann | Experiments and modeling of ignition delay times, flame structure and intermediate species of EHN-doped stoichiometric n-heptane/air combustion[END_REF]. These studies were extended to lower temperature conditions (600-960 K) using rapid compression machine measurements at stoichiometric and fuel lean conditions and pressures between 3 and 20 atm [START_REF] Minetti | A rapid compression machine investigation of oxidation and auto-ignition of n-Heptane: Measurements and modeling[END_REF][START_REF] Karwat | Low-temperature speciation and chemical kinetic studies of n-heptane[END_REF][START_REF] Cox | Extents of alkane combustion during rapid compression leading to single-and two-stage ignition[END_REF][START_REF] Griffiths | Spontaneous ignition delays as a diagnostic of the propensity of alkanes to cause engine knock[END_REF][START_REF] Tanaka | Two-stage ignition in HCCI combustion and HCCI control by fuels and additives[END_REF][START_REF] Silke | The influence of fuel structure on combustion as demonstrated by the isomers of heptane: a rapid compression machine study[END_REF]. Other ignition delay time measurements with shock tube devices were also performed in argon bath gas for dilution factors between 64% and 99%, pressures between 1 and 15 atm, fuel-lean, and for stoichiometric and fuel-rich conditions [START_REF] Vasu | OH time-histories during oxidation of n-heptane and methylcyclohexane at high pressures and temperatures[END_REF][START_REF] Vermeer | Auto-ignition of hydrocarbons behind reflected shock waves[END_REF][START_REF] Coats | Investigation of the ignition and combustion of n-heptane-oxygen mixtures[END_REF][START_REF] Burcat | Shock Initiated Ignition in Heptane-Oxygen-Argon Mixtures[END_REF][START_REF] Colket | Scramjet Fuels Autoignition Study[END_REF][START_REF] Horning | Study of the High-Temperature Autoignition of n-Alkane/O/Ar Mixtures[END_REF][START_REF] Imbert | Ignition Delays of Heptane/O2/Ar Mixtures in the 1300-1600 K Temperature Range[END_REF][START_REF] Smith | Autoignition of heptanes; experiments and modeling[END_REF][START_REF] Akih-Kumgeh | Comparative Study of Methyl Butanoate and n-Heptane High Temperature Autoignition[END_REF]. In addition, regarding the laminar flame speed, n-heptane has been extensively studied in the literature by means of various experimental techniques, including Bunsen burners, horizontal tubes, counterflow flames, spherical bombs, stagnation jets, and heat flux burners [START_REF] Gerstein | Flame Propagation. II. The Determination of Fundamental Burning Velocities of Hydrocarbons by a Revised Tube Method[END_REF][START_REF] Heimel | Effect of initial mixture temperature on the burning velocity of benzene-air, nheptane-air, and isooctane-air mixtures[END_REF][START_REF] Gibbs | Effect of Molecular Structure on Burning Velocity[END_REF][START_REF] Davis | Laminar flame speeds and oxidation kinetics of iso-octane-air and n-heptane-air flames[END_REF][START_REF] Kwon | Flame/Stretch Interactions of Premixed Fuel-Vapor/O/N Flames[END_REF][START_REF] Huang | Laminar flame speeds of primary reference fuels and reformer gas mixtures[END_REF][START_REF] Kumar | Laminar Flame Speeds of Preheated iso-Octane/O2/N2 and n-Heptane/O2/N2 Mixtures[END_REF][START_REF] Smallbone | Experimental and modeling study of laminar flame speed and non-premixed counterflow ignition of n-heptane[END_REF][START_REF] Jerzembeck | Laminar burning velocities at high pressure for primary reference fuels and gasoline: Experimental and numerical investigation[END_REF][START_REF] Ji | Propagation and extinction of premixed C5-C12 n-alkane flames[END_REF][START_REF] Chong | Measurements of laminar flame speeds of liquid fuels: Jet-A1, diesel, palm methyl esters and blends using particle imaging velocimetry (PIV)[END_REF][START_REF] Kelley | Laminar flame speeds of C5 to C8 n-alkanes at elevated pressures: Experimental determination, fuel similarity, and stretch sensitivity[END_REF][START_REF] Van Lipzig | Laminar burning velocities of n-heptane, iso-octane, ethanol and their binary and tertiary mixtures[END_REF][START_REF] Sileghem | Laminar burning velocity of gasoline and the gasoline surrogate components iso-octane, n-heptane and toluene[END_REF][START_REF] Dirrenberger | Laminar burning velocity of gasolines with addition of ethanol[END_REF]. Considering the latest, more reliable datasets, the experimental results cover a wide range of pressures (0.5-25 atm), temperatures (298-470 K), and equivalence ratios (0.6-1.7). The objective of this study is to experimentally analyze the effects of hydrogen addition to the fundamental combustion properties of n-heptane using wellcharacterized kinetic experimental apparatuses. Aggarwal [START_REF] Aggarwal | Ignition characteristics of heptane-hydrogen and heptanemethane fuel blends at elevated pressures[END_REF] used chemical kinetic model simulation to study the ignition of n-heptane/H 2 and n-heptane/CH 4 mixtures. On the other hand, to the best of our knowledge, this work provides for the first time data which will be essential to validate chemical kinetic models for use in dual-fuel engine design codes. Kinetic analyses will also be performed based on kinetic models available in the literature.

Experimental and modeling techniques

Spherical reactor facility

The technique has been presented in detail in previous publications [START_REF] Nativel | Laminar flame speeds of pentanol isomers: An experimental and modeling study[END_REF][START_REF] Comandini | Experimental and modeling study of styrene oxidation in spherical reactor and shock tube[END_REF]. The spherical reactor is a stainless steel vessel composed of two concentric spheres with optical access guaranteed by the presence of 4 quartz windows (100 mm optical diameter). The diameter of the internal sphere is around 47.5 cm, which results in a volume of 56 liters. The gaseous mixtures of interest are prepared directly inside the vessel using the partial pressure method. Two MKS Baratron capacitive manometers (Type 631) of different full scales (100 Torr and 1000 Torr) are connected directly to the bomb for measurement of the partial pressures of the fuel and the air according to the required pressure ranges. The use of the two manometers minimizes the maximum error in the mixture preparation, estimated to be 0.5% for the single measurements and thus 1% for the equivalence ratios. The vacuum limit of the reactor is around 10 -2 Torr and the gases left in the reactor are mainly composed of N 2 , H 2 O, and CO 2 . The effect of the residual gases is then minimal. In the present work three different experimental datasets were obtained with 0%, 25%, and 50% of hydrogen in n-heptane. The composition of the air is 0.209 O 2 + 0.791 N 2 (laboratory dry air), while the purities of n-heptane and hydrogen were 99.8% (Sigma-Aldrich) and 99.999% (Alphagaz 1, Air Liquide), respectively. The high quality of the fuels reduces the risk of contaminations. All the experimental results were obtained at an initial pressure and temperature of 100 kPa and 294±1 K, respectively. After the mixture preparation inside the reactor, the flame is initiated at the center of the sphere by a spark obtained with two tungsten electrodes located on the same diameter of the sphere but of course in opposite directions. The distance between the tips of the two electrodes was adjusted in order to obtain, for each equivalence ratio, flames which were spherical and unperturbed by the presence of the electrodes. The spherical bomb is coupled to a Z-type single-pass schlieren system for visualization of the flame, a high-speed camera (Phantom v1610) with fixed frame rate of 25000 fps for image recording, and a Kistler pressure transducer (Kistler 601A) for monitoring of the pressure during the combustion process. Figure 1 shows the stoichiometric (50% n-heptane + 50% H 2 ) / air flame as a function of time. As mentioned above, the flame propagates starting from the center of the sphere till it reaches the limit of the window, which is also the last point which can be used for measuring the flame propagation speed. It is important to notice how the flame is spherical along the entire observation window while its surface is only slightly disturbed by the electrodes. The separation between the burned and the fresh gases is easily identifiable. These characteristics are essential in order to obtain accurate measurements of the radii and to guarantee the validity of the fundamental assumptions on which the expanding flame theory is based. The different signals are synchronized, thus the pressure rise due to the gas expansion can be directly correlated with the flame propagation. As shown in Figure 1, the combustion in closed vessels leads to a large increase of the pressure (in the present case, the maximum pressure is around 7 bar at 0.1 seconds). On the other hand, the pressure over a much shorter time (between 2.44 and 13.44 ms in the specific case) is nearly constant (graph at the bottom-right of Figure 1). In particular, the pressure rise between the times of the first and the last images used for deriving the flame speed is between 0.5% and 0.9% in the present experiments, thus it is accurate to assume that the flame propagates at nearly constant pressure conditions. This is possible because the volume of the burned gases which corresponds to the diameter of the windows is much smaller than the total volume of the sphere (around 0.8%).

- =         ⋅         ( 1
)
where к is the stretch rate. Finally, the fundamental value of the unstretched laminar flame speed of the unburned gases, 0 u S , was derived using the simple continuity equation which for the case of constant pressure conditions simplifies to

σ 0 b 0 u S S =
. In this equation the value of sigma is defined as σ = ρ u /ρ b where ρ u and ρ b are the unburned and burned gas densitiesas calculated using COSILAB [START_REF] Cosilab | The Combustion Simulation Laboratory, Version 3.3.2[END_REF]. Based on the uncertainties in the radii (± 1 pixel), an error of around ±0.6 cm/s in the flame speed measurements was estimated.

The measured unstretched spatial laminar burning speed obtained using the non-linear method (NQ) corresponding to eq. 1 is shown in Figure 2 for different equivalence ratios. The scales of the x-and yaxes are identical for all the graphs. This allows a direct visual comparison between the different cases, not only in terms of unstretched flame speed (defined as the intersection between the fitting curve and the y-axis) but also in terms of experimental trends. The slope of the fitting curve is directly related to the Markstein length, which clearly decreases with increasing equivalence ratios (L b is even negative valued for φ = 1.35). Also shown in Figure 2 is the linear relation between burning speed and stretch rate

( κ ⋅ - = b 0 b b L S S
, [START_REF] Clavin | Dynamic behaviour of premixed flame fronts in laminar and turbulent flows[END_REF][START_REF] Matalon | Flames as gasdynamic discontinuities[END_REF], denoted as LS). The two solutions are very similar at fuel rich conditions, while they differ for the fuel lean cases. This is due to the fact that the linear model is not able to correctly reproduce the speed vs stretch relation for the entire range of equivalence ratios studied herein. Other extrapolation methods proposed in the literature [START_REF] Chen | On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames[END_REF][73][START_REF] Wu | Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames[END_REF] were also tested in order to confirm the accuracy of the present extrapolation methodology and estimate the associated uncertainties. The solutions of the NM-I model by Chen [START_REF] Chen | On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames[END_REF] (solid line) and the non-linear model in expansion form NE [73] (dash line) are presented in Figure 3 together with the NQ solution (circles). The maximum discrepancy between the results obtained with the NM-I and NE methods (which are almost superimposed) compared to the results derived from the NQ equation (symbols) is around 1.3%, which is well within the uncertainties of the measurements. Thus, the extrapolation model does not have an influence on the derivation of the laminar flame speeds. Wu et al. [START_REF] Wu | Uncertainty in stretch extrapolation of laminar flame speed from expanding spherical flames[END_REF] proposed a different criterion in order to discriminate the spherical expanding flame experiments which may be affected by large errors due to the extrapolation method. Based on such criterion, the product between the Markstein number and the Karlovitz number (Ma•Ka) must be below 0.15 for reliable measurements. This is the case for all the experiments presented here (Figure 4). It is important to underline how such a criterion was developed based on experimental databases for hydrogen and n-heptane fuels. The results presented in Figure 4 can be then considered without any doubt as a valid confirmation of the accuracy of the extrapolation method. Finally, the iterative procedure used to solve equation 1 was also tested. Chen [START_REF] Chen | On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames[END_REF] proposed a different formulation of equation 1 (NM-II) which can be solved with a least-square method. The two mathematical approaches give very similar solutions. Another physical aspect which may cause uncertainties in the measurement of the laminar flame speed is the heat radiation from the burned to the unburned gases. The simplified model by Yu et al. [START_REF] Yu | Radiation-induced uncertainty in laminar flame speed measured from propagating spherical flames[END_REF] provides a simple tool to estimate the effects of radiation on the experimental measurements from expanding flames. Based on this approach, the radiation-correction terms are around 0.5 cm/s for all the experimental conditions. If the corrections were applied to all the experimental points, a simple shift of the profiles by 0.5 cm/s would be obtained. Such a shift would not modify the effect of the hydrogen addition on the laminar flame speeds.

Shock Tube Facility

The shock tube has a 4.5 m long, 7.6 cm square cross-section driven-section and a 1.83 m long, 10.2 cm diameter driver. A 76.2 cm round-to-square transition section is included in the driven length. The double diaphragm technique was used to accurately obtain the desired shock Mach number. The diaphragm material is 2 mm thick, 1100 series aluminum, pressed with a four-petal shape to facilitate diaphragm opening (rupture pressure between 22.1 and 44.2 bar across the diaphragms). Three piezoelectric pressure transducers (PCB 113A24) are used to record the pressure inside the tube and consequently to obtain the incident shock wave velocity. The distance between successive pressure transducers is 0.31 m, with the last one located at the axial position of the reflection endplate. The incident shock wave velocities were subsequently used together with the initial conditions to calculate the pressure and temperature conditions behind the reflected shock waves by solving the conservation equations. The method used for the calculations assumes thermal equilibrium, no reaction before ignition, and variable specific heat ratio. Based on the dimension of the pressure transducer face there is a possible error of 1.74% on the shock speed, and therefore, the maximum estimated errors in the temperature and pressure conditions behind the reflected shock waves are 2.5% and 5.8%, respectively. A photodiode (Edmund Optics, S-050-H) with a 430±10 nm filter (Thorlabs, FB430-10) is attached to the endplate via an acrylic rod to detect luminescence from CH radicals. The onset of ignition was determined by the maximum slope in the pressure profiles, which also corresponds to a steep increase in the CH radical signals measured by the photodiode. Ignition delay times have been defined as the time between the arrival of the incident shock wave at the end plate and the onset of ignition. A typical pressure profile is presented in Figure 5, also shown is the ignition delay time. The shock tube is pumped down using an Edwards RV5 pump (designed vacuum of 2x10 -3 mbar). The fuel/air mixtures were prepared in a separate mixing chamber using the method of partial pressures to combine n-heptane, hydrogen and air at the desired ratios. In the present study, the percentage of hydrogen in the fuel mixture was varied from 0% to 20%, 50%, and 75%, for average equivalence ratios equal to 1.248, 1.000, and 0.832.

Chemical kinetic modeling

As mentioned in the previous sections, n-heptane has been the focus of numerous studies including the development and validation of detailed chemical kinetic models. Various models have nowadays reached excellent performances with respect to the simulation of both the ignition delay times and the laminar flame speeds of n-heptane/air mixtures, such as for example the LLNL model [START_REF] Mehl | Kinetic Modeling of Gasoline Surrogate Components and Mixtures Under Engine Conditions[END_REF] (654 species and 2827 reactions), the NUIG model [START_REF] Zhang | An updated experimental and kinetic modeling study of n-heptane oxidation[END_REF] (1268 species and 5336 reactions), or the CRECK model [START_REF] Pelucchi | Improved Kinetic Model of the Low-Temperature Oxidation of n-Heptane[END_REF] (300 species and 11790 reactions, including chemistry for iso-octane). These models are relatively large in terms of number of species and reactions which makes them impractical for use in engine codes. Even for simulations of laminar flame speed measurements the resulting computational costs are considerable. For these reasons, reduction schemes have been developed to diminish the size of the models based on specific targets. In view of their practical use in engine simulations and their reduced computational costs, two reduced chemical kinetic schemes were used in the present work to simulate the laminar flame, these include the models by Stagni et al. [START_REF] Stagni | Skeletal mechanism reduction through species-targeted sensitivity analysis[END_REF] and Cai and Pitsch [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF]. The two models provide very similar results compared to the non-reduced models, with-respect-to laminar flame speed measurements of gasoline PFR/toluene surrogates, including experimental results for the n-heptane component available in the literature. The iso-octane chemistry was removed by both models, which reduced their size to 236 species and 1165 reactions for the model by Cai and Pitsch [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF] and 106 species and 791 reactions for the model by Stagni et al. [START_REF] Stagni | Skeletal mechanism reduction through species-targeted sensitivity analysis[END_REF]. The present work includes the addition of hydrogen as a fuel, thus the corresponding C0 reactions were analyzed in detail. In particular, the model by Stagni et al. [START_REF] Stagni | Skeletal mechanism reduction through species-targeted sensitivity analysis[END_REF] does not contain the recombination reactions between two hydrogen atoms and two oxygen atoms as in the original CRECK model [START_REF] Frassoldati | A wide range modeling study of formation and nitrogen chemistry in hydrogen combustion[END_REF][START_REF] Ranzi | Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels[END_REF], thus, these reactions were added. The addition of such reactions did not change the simulation results for the n-heptane experiments. The validation of the two models against experimental hydrogen/air data at room temperature and atmospheric pressure from the literature is presented in Figure 6. The two models generate very similar results, in good agreement with the experimental data over the entire range of equivalence ratios, thus they can be used with confidence to model the hydrogen enriched n-heptane experiments. Cosilab software, version 3.3.2 [START_REF] Cosilab | The Combustion Simulation Laboratory, Version 3.3.2[END_REF] was used to perform the simulations. In particular, the one-dimensional freely-propagating flames were solved to derive the laminar flame speed. GRAD and CURV were imposed as 10 -5 , with a spatial domain between -10 and 100 mm, while multi-component transport properties and Soret effect were included in the calculations. The model by Cai and Pitsch [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF] was also used to simulate the ignition delay time together with the CRECK model [START_REF] Ranzi | Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels[END_REF]. In this case, the simulations were obtained with the homogeneous batch reactor module at adiabatic, constant volume conditions and at an initial pressure of 20 bar. Laminar Flame Speed (m/s)

Results and discussions

Numerous studies on laminar flame speed of n-heptane/air mixtures provide a benchmark to confirm the validity of the spherical bomb technique. The n-heptane/air measurements were compared to the measurements at room temperature and atmospheric pressure available in the literature (see Figure 7). Also provided in Figure 7 is the normalized data taking into account the difference in initial temperature (294 K vs 298 K), pressure (100 kPa vs 101.3 kPa), and air composition. The normalization factors were estimated using the kinetic model by Cai and Pitsch [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF]: all the simulations were performed first at the conditions of the present study, then at the conditions of the data in the literature, from which normalization factors could be derived. Figure 7 clearly shows that the present data closely agree with the recent measurements by Dirrenberger et al. [START_REF] Dirrenberger | Laminar burning velocity of gasolines with addition of ethanol[END_REF] obtained with a flat flame adiabatic burner. The experimentally measured laminar flame speeds are reported in Figure 8, together with the simulations obtained with the two kinetic models. The blending of hydrogen with n-heptane leads to an incremental change in the laminar flame speed. The term "speed increment" is used to represent the difference between the laminar flame speed for the hydrogen/heptane and the heptane-only fuel. The change is substantial only when a large amount of hydrogen is present. Figure 9 contains the experimental and modeling increments obtained for different hydrogen enrichment. The experimental flame speed data was fit with a polynomial, see Figure 8. The fits accurately reproduce the experimental results, with discrepancies which are within the experimental error of a single measurement (less than 0.3 cm/s for more than 90% of the cases). The results in Figure 9 indicate that the addition of 25% of hydrogen in the fuel mixture generates an average increase of only 3% in the speed (0.9 cm/s on average, with maximum increment of ∼ 1.2 cm/s at φ ∼ 1.1). On the other hand, the laminar flame speeds of the (50% C 7 H 16 + 50% H 2 )/air mixtures are ∼10% higher than the n-heptane case (3.3 cm/s on average). In this case, the maximum increment is reached at φ ∼ 1.2, thus slightly shifted compared to the experiments with lower hydrogen mole fractions. From a modeling perspective, both models overpredict the measurements (Figure 8), although the error can be considered minimal (around 5% for the Cai and Pitsch model [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF] and between 6% and 14% for the Stagni et al. model [START_REF] Stagni | Skeletal mechanism reduction through species-targeted sensitivity analysis[END_REF], with higher discrepancies at fuel-rich conditions). A more important aspect evident in Figure 9 is that both models are capable to reproduce quite accurately the effects of the addition of H 2 . In particular, the correspondence between the results obtained with the Cai and Pitsch model [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF] (dash lines) and the experiments is remarkable for both profiles. The only discrepancy appears at fuel-rich conditions, where the experimental profiles bend at lower equivalence ratios and thus the speed increments are slightly over-predicted. The effect of hydrogen addition on the experimental Markstein length (derived from the solution of the non-linear equation) was also considered. The Markstein length L is related to the slope of the curves in Figure 2: the higher the slope, the larger the corresponding value of L. Figure 10a shows the renormalized burned Markstein length L′ (L′ = L b /σ). This value is consistent with the plots of the unstretched laminar flame speed of the unburned gases. Considering the curves which fit the experimental data, the addition of hydrogen slightly decreases the Markstein length at fuel-lean conditions, 6-8% and 16-18% for the (75% C 7 H 16 + 25% H 2 ) and (50% C 7 H 16 + 50% H 2 ) datasets compared to pure n-heptane, respectively. As an example, three different curves obtained at φ ∼ 0.95 are presented in Figure 10b. Even if the extrapolated flame speed is lower for the case of n-heptane (black line and symbols), the slope of the corresponding curve is clearly larger than the curves obtained with hydrogen enrichment. Although the estimated error in the determination of L′ is larger than the observed differences, the small discrepancy between the polynomial fits and the experimental data suggests that the error estimates on the single measurements may be conservative, larger than the actual values. Thus, hydrogen enrichment is expected to slightly change the response of the flame to the stretch as in engine applications (for fuel-lean conditions). Finally, for fuel-rich conditions the curves presented in Figure 10a converge, suggesting no effect of the hydrogen enrichment on the response of the flame to stretch. The chemical kinetic models were also used to determine how the fuel composition influences flame propagation. The results presented in the following paragraphs were obtained with the kinetic Cai and Pitsch model [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF], which provides better predictions of the measured laminar flame speed. The main factor which leads to the increase in the flame speed with increased percentages of hydrogen enrichment is the formation of larger amounts of radicals (in particular H, OH, and HO 2 ). The H and OH profiles are reported in Figure 11a for φ = 1.1. The addition of 25% hydrogen in the fuel leads to an increase of 2.8% and 1.7% in the maximum H and OH mole fractions, respectively; while for (50% C 7 H 16 + 50% H 2 ) the maxima increased by 8.2% and 2.7%. The radicals diffuse towards the unburned gas leading to faster consumption of the n-heptane (as shown in Figure 11a, where the profiles were normalized based on the fuel mole fraction of the 100% C 7 H 16 case) and a larger heat release rate (Figure 11b). In this case, the increase in the peak heat release rate is 2.5% and 8.2% for 25% and 50% hydrogen enrichment, respectively. These results agree with measurements made in IC engines [START_REF] Saravanan | An experimental investigation of hydrogen-enriched air induction in a diesel engine system[END_REF]. Although the adiabatic flame temperature changes only slightly (2272K, 2274 K, and 2277 K for 0%, 25%, and 50% hydrogen at stoichiometric conditions), the temperature profiles follow the same behavior of the fuel and the heat release rate; thus a steeper slope for higher hydrogen enrichment is observed in Figure 11b. From a practical point-of-view, the absolute mole fraction of the radicals, as presented in Figure 11a, determine the variation in the flame propagation speed in engines (for similar equivalence ratios), but such values are influenced by the different initial mole fractions of H atoms. The H atom profiles relative to the H atom content in the 100% C 7 H 16 case are reported in Figure S1 (Supplementary File). The difference in H atom concentration peaks becomes less marked than in Figure 11a, but the addition of hydrogen leads to an increase in the production of H atoms relative to the initial H content in the fuel. This suggests that the chemistry of hydrogen is more effective in producing H atoms compared to the n-heptane chemistry, which is of course an expected result. Although some of the pathways for the n-heptane consumption are more-or-less favored by the presence of hydrogen, the reactions which significantly affect the flame propagation speed remain unaltered. Figure 12 shows the sensitivity analysis of the laminar flame speed with respect to the reaction rate constants for φ = 1.1. All the coefficients increase when hydrogen is added to the fuel mixture, which is mainly due to presence of larger radical mole fractions (as shown in Figure 11a). On the other hand, the reaction order remains nearly identical. This is due to two facts: 1) the flame speed is mainly influenced by the H 2 /O 2 chemistry and by the small intermediates produced from the decomposition of n-heptane; 2) there is not a substantial variation in the pathways which leads to the formation of such small fragments. Such pathways are presented in Figure 13, for reactions leading to propene, allyl radical, ethylene, ethyl radical, and acetylene, intermediates whose chemistry significantly affects the flame propagation speed. The purpose of this figure is not to provide a comprehensive description of the n-heptane chemistry, but to show the effects of the presence of hydrogen on the decomposition of regular carbon-based fuels, in this case n-C 7 H 16 . The arrow thickness is proportional to the integrated reaction rates for the n-heptane/air mixture, while the numbers represent the percentage increase/decrease for the (50% C 7 H 16 + 50% H 2 ) fuel mixture compared to the pure n-heptane case (after normalization to take into account the number of C atoms in the fuels). For clarity, the figure has been divided into two parts, where the formation pathways for the compounds highlighted by dash lines (bottom graph) are reported on the upper graph. It is clear how hydrogen increases the rate of consumption of the fuel (as already observed concerning Figure 11), and consequently of the intermediates due to the increase in H, OH, and HO 2 concentrations. Only the fluxes proceeding through the thermal decomposition of the largest stable olefins (such as 1-hexene (C 6 H 12 ) and 1-pentene (C 5 H 10 ) forming C 3 H 5 + C 3 H 7 and C 3 H 5 + C 2 H 5 respectively) drop due to the considerable increase in the competing H-abstraction reactions by H, OH, and O radicals. Similarly, the fragmentation of the resonantly stabilized allyl radical to acetylene + methyl radical shows a decrease of 11.2% due to competition with reactions involving the H atoms (recombination to form propene and addition/fragmentation to form C 2 H 3 + CH 3 ).

Figure 13. Rate of consumption analysis, φ = 1.10. Arrow thickness proportional to the integrated reaction rates for C 7 H 16 /air mixture. Percentages represent the increment/decrement for the (50% C 7 H 16 + 50% H 2 ) fuel mixture compared to the pure n-heptane (after normalization to take into account the number of C atoms in the fuels). Dash lines for compounds whose formation is reported on the upper graph.

As for the case of the laminar flame speed, various studies on the ignition delay times of n-heptane/air mixtures have been completed in the past. The experiments presented herein were obtained at a nominal initial pressure of 20 bar, varying the equivalence ratio between 0.832 and 1.248. The comparison between the stoichiometric results and the ones available in the literature for similar pressure conditions by Ciezki and Adomeit [START_REF] Ciezki | Shock-tube investigation of self-ignition of n-heptane-air mixtures under engine relevant conditions[END_REF] and Gauthier et al. [START_REF] Gauthier | Shock tube determination of ignition delay times in fullblend and surrogate fuel mixtures[END_REF] are reported in Figure 14a. The experiments are in good agreement over the entire temperature range (730 K -1200 K), especially in the negative temperature coefficient (NTC) region between 810 K and 920 K, where the ignition time increases with increasing temperature. In the rest of the study, attention is focused on NTC region which corresponds to the post compression operating temperature in typical IC engines. The measured ignition delay time for nheptane/air for equivalence ratios between 730 K and 950 K is presented in Figure 14b. In general, there is slight decrease in the ignition delay for an increase in equivalence ratio from 0.832 to 1.0, but almost no change from 1.0 to 1.248. A similar trend was observed for different hydrogen enrichments. The experimental and modeling results for different hydrogen enrichment are presented in Figure 15.

From the experiments, no discernable difference could be observed between the different datasets in the high temperature region, while in the NTC region the experimental data differs more significantly. In particular, the ignition delay times of (80% n-heptane + 20% hydrogen)/air mixtures nearly superimpose for pure n-heptane, and only with higher hydrogen enrichment does the ignition delay time increase (as was the case of the laminar flame speed). Similar results were obtained with the two kinetic models which are capable of reproducing, not only the effects of hydrogen addition, but also the magnitude of the experimental data. The Cai and Pitsch model [START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF] accurately predicts the experimental results over the entire temperature range, especially in the NTC region, while the increase in the ignition delay time in the NTC region is slightly overpredicted by the CRECK model [START_REF] Ranzi | Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels[END_REF]. Since the uncertainty in the experimental results does not allow to accurately determine the effects of hydrogen enrichment on the ignition delay time (many more points would be necessary in order to draw reliable fitting curves), the model by Cai and Pitsch which better fits the experimental curves was used for this purpose. The percentage increase in the ignition delay time for different hydrogen enrichment compared to the reference n-heptane/air is reported in Table 1 for temperatures between 750 K and 900 K (temperature range relevant to diesel engines). The data indicated is the average of the values for the three equivalence ratios investigated. In all cases, the effects of the hydrogen addition are slightly more marked at higher temperatures, although the mixtures composed of 80% n-heptane and 20% hydrogen are characterized by ignition delay times which differ by only ∼ 2% compared to the reference case. The percentage increase becomes larger with increased hydrogen enrichment, ∼ 8% and ∼ 27% for (50% C 7 H 16 + 50% H 2 ) and (25% C 7 H 16 + 75% H 2 ), respectively. These variations are mainly due to the drop in the concentration of the n-heptane and oxygen components in the initial mixture. For example, the n-heptane mole fraction at stoichiometric conditions diminishes by 1.6%, 6.0%, and 16% with the addition of 20%, 50%, and 75% of hydrogen, respectively. Therefore, the low temperature chemistry becomes less significant, as shown in Figure 16b where the mole fractions of the most abundant peroxy radical (3hepthyl peroxy, C 7 H 15 O 2 ) are present. The higher the concentration of initial hydrogen, the lower the mole fraction of the intermediate species formed through the low temperature kinetic mechanisms. This translates to a smaller increase in pressure and temperature conditions due to cool flame phenomenon (see Figure 16a), which directly affects the ignition delay times, i.e., the lower the temperatures reached due to the cool flame, the longer the delay.

Conclusions

The effect of hydrogen enrichment on the combustion properties of n-heptane/air has been investigated both experimentally, using complementary techniques, and numerically with kinetic models available in the literature. New laminar flame speed measurements in n-heptane/air, (75% n-heptane + 25% hydrogen)/air, and (50% n-heptane + 50% hydrogen)/air mixtures were obtained at an initial pressure of 1 bar and initial temperature of 294 K. The results show that the flame speed increases by roughly 3 % and 10 % with 25% and 5% hydrogen enrichment of n-heptane, accompanied by a slight decrease in the Markstein length. The experiments on the ignition delay times of fuel/air mixtures containing from 0% to 75% hydrogen enrichment were conducted at equivalence ratios of 0.832, 1.000, and 1.248, initial nominal pressures of 20 bar, with particular focus on the NTC region which is relevant to diesel engine post compression conditions. Only for large hydrogen enrichment does the ignition delay time become longer compared to the reference n-heptane/air case. The simulations accurately reproduce the experimentally measured laminar flame speed and the ignition delay time. The kinetics behind the change in the combustion properties of the n-heptane/hydrogen dual fuel were identified. From a practical pointof-view, the control of the ignition delay time and the heat release rate could be accomplished by adjustments in the operational parameters for optimal dual-fuel engine performance (for similar equivalence ratios).

Figure 1 .

 1 Figure 1. (50% n-heptane + 50% H 2 ) / air flame, stoichiometric conditions.

Figure 2 .

 2 Figure 2. Laminar burning speed, (50% n-heptane + 50% H2) / air. Solid line: NQ model; dash line: LS model.

Figure 3 .

 3 Figure 3. Laminar flame speed measurements obtained with different extrapolation methods for n-heptane/air measurements. Symbols: NQ, --NM-I, --NE.

Figure 4 .

 4 Figure 4. Criterion to estimate the extrapolation error by Wu et al. [74]: Ma Linear ⋅ Ka mid . Negligible error for -0.05 < Ma Linear ⋅ Ka mid < 0.15. 100% C 7 H 16 , 75% C 7 H 16 + 25% H 2 , 50% C 7 H 16 + 50% H 2 .

Figure 5 .

 5 Figure 5. Typical pressure profile; n-heptane/air mixture, φ = 1, T 5 = 811 K, P 5 = 20.8 bar.

Figure 6 .

 6 Figure 6. Laminar flame speed of H 2 /air. T in = 298 K; P in = 101.3 kPa: Kwon et al. [83], Aung et al. [84], Dowdy et al. [85], Tse et al. [86], Goulier et al. [87].

Figure 7 .

 7 Figure 7. Laminar flame speed of n-heptane/air. T in = 298 K; P in = 101.3 kPa: Dirrenberger et al. [63], Huang et al. [54], Davis et al. [52]. present work (T in = 294 K; P in = 100 kPa); p.w. normalized to 298 K (see text)

Figure 8 .

 8 Figure 8. Laminar flame speed of n-heptane/H 2 /air mixtures. Fuels: 100% C 7 H 16 , 75% C 7 H 16 + 25% H 2 , 50% C 7 H 16 + 50% H 2 . Lines represent modeling results using the model by: a) Cai and Pitsch [80], Stagni et al. [79].

Figure 9 .

 9 Figure 9. Increment of the flame speed for different hydrogen enrichment compared to the n-heptane/air case. Dashed lines: Cai and Pitsch model [80]; solid lines: Stagni et al. model [79].

Figure 10

 10 Figure 10. a) Markstein length L′; b) evolution of the spatial laminar burning speed, φ ∼ 0.95.

Figure 11 .

 11 Figure 11. Profiles for a) normalized C 7 H 16 (blue); OH (black), H (red); b) temperature (blue), heat release rate (black). φ = 1.1. Dash-dot line (100% C 7 H 16 ); solid line (75% C 7 H 16 + 25% H 2 ), dash line (50% C 7 H 16 + 50% H 2 ).

Figure 12 .

 12 Figure 12. Sensitivity analysis of the laminar flame speed with respect to the reaction rate constants, φ = 1.1.

Figure 14 .

 14 Figure 14. Ignition delay times of n-heptane/air mixtures. a) Comparison of stoichiometric mixtures with the literature: present work; Ciezki and Adomeit [27]; Gauthier et al. [30]; b) NTC region results (present work): φ = 1.000; φ = 1.248; φ = 0.832.

Figure 15 .

 15 Figure 15. Ignition delay times of n-heptane/H 2 /air mixtures for 3 different equivalent ratios and nominal pressures of 20 bar: a) & d) φ = 1.000, b) & e) φ = 0.832, c) & f) φ = 1.248. Fuels: 100% C 7 H 16 , 80% C 7 H 16 + 20% H 2 ,

Figure 16 .

 16 Figure 16. a) Pressure and b) 3-heptyl peroxy profiles predicted by the Cai and Pitsch model [80] for φ = 1 at an initial temperature of 850 K.

+0.8% +10.3% +0.8% +8.1% +3.2% -11.2%

			+5.1%
	+5.1%
		+5.1%
			+4.4%
				+5.0%
		+5.3%
		+5.3%
		+4.1%		+4.2%
		-5.0%		+6.0%
			+10.1%
	+8.8%		+0.6%
		+12.4%
		-5.0%		-8.8%
		+12.3%	+12.3%	+9.9%
	+4.8%	+8.5%		C 2 H 5 + CH 3
		-0.1%
				+4.3%	C 2 H 3 + CH 3
			+4.8%
		+5.0%
		+5.3%
		-8.8%	+5.3%
			+4.2%
	+9.5%	+1.4%
	CH 3 + CH 3	+5.6%
		+6.0%
		CH 3 + TXCH 2

Table 1 .

 1 , 80% C 7 H 16 + 20% H 2 , 50% C 7 H 16 + 50% H 2 , 25% C 7 H 16 + 75% H 2 . Dashed lines: Cai and Pitsch model[START_REF] Cai | Optimized chemical mechanism for combustion of gasoline surrogate fuels[END_REF]; solid lines: CRECK[START_REF] Ranzi | Hierarchical and comparative kinetic modeling of laminar flame speeds of hydrocarbon and oxygenated fuels[END_REF]. Average calculated increase in ignition delay time for different hydrogen enrichment compared to the C 7 H 16 /air reference case.

		20% H 2	50% H 2	75% H 2
	T = 900 K	2.2%	9.1%	29.9%
	T = 850 K	2.0%	8.4%	27.4%
	T = 800 K	1.9%	7.8%	25.7%
	T = 750 K	1.7%	7.2%	23.6%

Acknowledgments

The authors would like to thank Kevin Brialix for the support in running the laminar flame speed experiments. The work was partially financed by the Centre Nationnal de la Recherche Scientifique and Natural Sciences and Engineering Research Council of Canada.