dataesr/scientific-paragraphs-categorization huggingface dataset:
For the first moment hypothesis, four progress variable, c, definitions identified by PCA are selected as conditioning variables to investigate the conditional fluctuations and normalised RMS of various species and temperature from all three databases at all axial locations. The results indicate that two control variables based on mixture fraction, Z, and progress variable significantly reduce the conditional fluctuations of scalars compared to a single variable. The selection of progress variables had minimal effects on the RMS of conditional fluctuations for all tested conditions, although a slight reduction of conditional fluctuations was found for the temperature-based progress variable, which can potentially help the further extension of CMC-based models in different flame configurations.
Subsequently, doubly CSE (DCSE) with mixture fraction and progress variable as conditioning variables have been developed to simulate partially-premixed flames, lifted flames, and spray flames  [31, 32]. The CSE and DCSE concepts have also been examined in a-priori analysis in DNS for high-pressure conditions  [33]. The results highlighted that DCSE and double conditioning are likely to be needed for cases closer to real practical combustion applications. Similar to the flamelet approaches, when choosing the conditioning variables for CMC approaches, the mixture fraction definition from Bilger is well accepted by the community, where the choice of progress variable and particularly its effects on conditional variable fluctuations needs more studies. Recently, Bushe  [34]  and Mousemi & Bushe  [35]  examined the conditional moment closure hypothesis over the Sandia/TUD, the Sydney Swirl burner, and Cambridge/Sandia stratified swirl burner databases.
Methodology 2. 1. Experimental setup Experimental measurements of premixed and stratified CH 4 /Air flames from the Cambridge/Sandia swirl burner (referred to as SwB) are used in this study. Multiscalar data of nine turbulent flames are examined under: (i) various ratios of stratification, and (ii) various swirl intensity conditions, depicted in Table  1. The burner, shown schematically in Figure  1 , features a large co-flow of pure filtered air preventing ambient air from entering the reaction zone, and two concentric outer (subscript  o) and inner (subscript i) annuli supplying the fuel/air mixture. The annuli's velocities were chosen to maximise the Reynolds numbers in the flows with Re i = 5,960 and Re o = 11,500. A variable degree of swirl allows the burner to mimic the flow conditions found in many practical systems.
Data-processing Three data-sets have been constructed to investigate the effects of spatial coordinates, swirl flow ratio, and stratification factor on the conditionally-averaged reactive scalars, depicted in Table  2. In the first case, the data collected from all nine flames are grouped together to create a general conditional domain for each of the scalars (SwB|all). Here, it is assumed that the conditional averages are independent of spatial coordinate, swirl flow ratio and stratification factor. The second data-set (SwB|Hstratified) combines the measurements of three flames exhibiting varying swirl flow ratio intensities with a single high stratification factor to investigate the dependence of conditional averages on swirl. For the third case, data from 3 flames with different stratification factors and a fixed high swirl flow ratio are grouped to investigate the dependence of conditional averages on stratification (SwB|Hswirl).
Label Scalar(s) φ k Mark c 1 Temperature c 2 Y CO2 c 3 Y CO2 + Y CO • c 4 Y CO + Y H2 + Y H2O + Y CO2 ♦ these points are considered to be unphysical. After executing all previous steps, each database consists of 5,518,536 point-based measurements for SwB|all, 1,887,496 for SwB|Hstratified and 1,901,113 for SwB|Hswirl. To examine the conditional space of Cambridge/Sandia flames, the methodology proposed in  [34, 40]  is followed and applied to all three data-sets. The conditional averages are obtained via a discrete process involving binning, dividing each progress variable dimension into 30 bins. This is justified given that more bins increase the possibility of having intervals with an insufficient number of data points which imposes unrealistically small fluctuations around the mean value  [40].
Suppose that ensembles are split across all axial positions, the number of conditioning scalars needed to accurately represent the chemical state is reduced, where a single control variable could perhaps be sufficient to separate the conditional averages from spatial coordinate, swirl and/or stratification effects. This approach is of particular interest for CMC-based models as it can be seen as a viable alternative to bypass the challenges associated with joint-PDFs defined by a minimum of two scalars. If the conditional average is a good representation of the local thermo-chemical state, then it is expected that the mean of the conditional fluctuations will be zero. However, the RMS of those fluctuations is clearly not, as shown by Bushe  [34]  using the Sandia/TUD database and the Sydney swirl burner.
The dimensionality reduction is undertaken by truncating A, such that only the first q PCs that account for the maximum variance are retained, with q < Q. The original data-set X is retrieved as X X q = q A T q  (7)  where X q is the approximation of X based on the first q eigenvectors of A, and q is the (n × q) matrix of the principal component scores. Detailed mathematical formulation of PCA is not elaborated here where more details can be found in the literature  [47]. Principal component analysis requires high-fidelity data-sets to generate the PC-basis and accurately describe the thermo-chemical state-space. The experimental measurements of all three data-sets fed to PCA have been cleaned out following the steps presented previously. It should be noted that the mixture fraction and the progress variables have been excluded from the databases before being passed to PCA.
Parente & Sutherland also  [52]  showed that the square root of the standard deviation enhances the temperature scalar in carrying most of the data variance, and thus, forcing the first principal component to align with temperature. For this reason, the temperature was excluded from the three databases passed on to PCA. The real utility in PCA comes by founding correlations among the variables defining the state-space. A new coordinate system is identified in the directions of maximal data variance, allowing less important dimensions to be eliminated while maintaining the primary structure of the original data. In that sense, one can suppose applying PCA to a given reactive flow where no prior knowledge about the physical and chemical phenomena is known, and help identify the adequate number of control variables needed to accurately quantify the thermo-chemical state-space within a manifold.
Principal component analysis The PC analysis was individually performed on all three databases with all radial and axial locations grouped together. Figure  2  illustrates the variance accounted by each PC using Equation  (8). To clarify, figures depicting PCA results do not include the temperature scalar within the analysis. Regardless of the scaling method adopted, a single principal component seems to account for the largest amount of variance present in all three datasets, with ∼ 0. 9 using Pareto and ∼ 0. 8 with AS. The variance explained by PC1 is in good agreement with the threshold proposed by Parente et al. [46]. Their study showed that by accounting for ∼ 0. 9 of the total variance, all main species and temperature can be recovered with satisfactory levels of approximation. Consequently, the physical interpretation of all other principal components is omitted in this work, as is it believed to be out of the scope of this study.
In order to determine the underlying structure of PC1, the weights of the original variables characterising the three databases (i. e. matrix A) are presented in Figure  3  for both scaling methods. Regardless of the scaling method used, it is interesting to note that PCA is able to automatically distinguish reactants from products, with PC1 being negatively and positively correlated with reactants and combustion products, respectively. Regardless of the data-set, it appears that the mass fractions of CO 2 and O 2 have the most important contributions to PC1-Pareto, and to a larger extent Y H2O , with coefficients equal to approximately 0. 6, 0. 65 and 0. 35, respectively. This trend is also apparent for PC1-AS, with the latter having non-negligible weights on intermediate species, as opposed to Pareto, which clearly emphasises main species.
As expected, this behaviour is clearly accentuated by adopting the Pareto method. A supplementary analysis was carried out by including temperature in SwB|all and using only Auto-scaling, as PC1-Pareto will be constrained to align with temperature. Figure  5  illustrates the dominant contributions to PC1-AS. The temperature scalar and the same three species mass fractions have the largest weights on PC1, with ∼ 0. 4, suggesting that PC1, regardless of the scaling method adopted, is correlated with temperature. After identifying the structure of the first principal component, the first-moment conditional fluctuations analysis of all three databases is carried out to investigate which of the proposed progress variables can sufficiently accurately characterise the composition space. As suggested by PCA, particular attention is brought to the temperature-based progress variable c 1.
As expected, the same trend is observed for the RMS of T around c 1. It is interesting to note that further downstream the axial position, the RMS of Y CO2 around c 1 are improved or off the same order of magnitude as the Y CO2 -based progress variable. Additionally, the RMS of Y CH4 obtained using any c k are unchanged and remain close to 10%. Assuming that RMS of conditional fluctuations of the order of 10% can be considered as 'relatively small'  [34] , one can suppose that using a single conditioning variable for this database might still give acceptable predictions of the considered reactive scalar for conditional moment closure models. However, using c k as a single conditioning variable gives poor results for intermediate species, i. e. CO and H 2 , where normalised RMS exceed 10% of the maximum value of that particular scalar in the regions near the burner's tip.
Moreover, the height of conditional fluctuations (in particular for intermediate species) seems to remain constant throughout all axial positions, as opposed to the trends observed with SwB|all. The local averages of the presented conditional fluctuations (cf. golden markers in Figure  A1 )  Figure 10. Normalised RMS of the conditional fluctuations of temperature and species mass fractions for the SwB|Hstratified database around the conditional average f | ξ = c k (x) (markers) using c k as the single conditioning variable and around the conditional average f | η = Z, ξ = c 1 , c 2 (x) using the mixture fraction and, the temperature-based progress variable (crosses) or the Y CO2 -based progress variable (pluses), and collecting all points at different radii together. are fixed at zero, suggesting that using either of the proposed c k as a conditioning variable should provide an accurate approximation of the turbulent reaction rate, i.
e. a closure utilising only the first term of a Taylor expansion of the reaction rate. Figure  10  provides further insights. The normalised RMS of all variables investigated for the considered database around one-condition (i. e. using c k ) exhibit similar results as seen with SwB|all. As expected, the RMS obtained using a single control variable have much higher swirl dependence at the inlet of the burner than two-condition conditional averages, in particular for methane, CO and H 2 mass fractions, emphasised by normalised RMS values above 10%. Further downstream the axial direction (i. e. z = 60, 70 mm), the normalised RMS are nearly of the same order of magnitude as both combinations of doubly conditioning, suggesting that adding the mixture fraction as a second control variable does not significantly affect the fit.
For the same species, the definition attributed to the progress variable seems irrelevant. The differences are more straightforward for major species and temperature, where all c k provide very good results. Based on these results, the temperature-based progress variable seems to be the most optimal choice (as concluded from the PCA analysis), followed by c 4 and c 3 , and with the Y CO2 -based progress variable being the worse among the tested reaction variables. These findings are consistent with recent results computed by analysing methane-air  [55]  and hydrogen-air  [21]  premixed flames. The normalised RMS around two-condition conditional averages are unchanged compared to the trends observed with the first database. The definition attributed to the progress variable as a second control scalar seems irrelevant for this case.
Once again, two-condition conditional averages are sufficient to describe the considered database and detach it from swirl and space. This suggests that a DCSE calculation of these flames (including SwB|all) using both mixture fraction and progress variable as conditioning variables might be successful. The contours of conditionally-averaged reactive scalars are illustrated in Appendix 1. The conditional averages of temperature and several species mass fractions around the mixture fraction and the temperature-based progress variable are shown in Figure  A2. Figure  A3  presents the conditional averages of the same scalars using Z and c 2. Similar conclusions drawn for SwB|all can be applied to the considered data-set. Regions with no available measurements are much more accentuated in both conditional domains, attributed to the exclusion of data from 6 flames that do not exhibit the desired characteristics of the current database.
Fixed high swirl, stratification sweep (SwB3, SwB7, SwB11) The conditional fluctuations around one-condition conditional averages of the variables describing the SwB|Hswirl database are studied to investigate the most optimal choice of progress variable definition to cancel stratification and spatial dependences, assuming high fixed swirl intensity. The conditional fluctuations of the scalars previously investigated are shown in Appendix 2-Figure  A4. Similar to SwB|all and SwB|Hstratified, the conditional fluctuations of Y CH4 , Y CO and Y H2 appear to be still affected by space and stratification effects, particularly at the inlet of the burner. All c k promote similar results, suggesting that another choice of scalar is perhaps more suitable. Just like c 2 for Y CO2 , the temperaturebased progress variable provide the lowest fluctuation heights for T and Y H2O , with c 2 and c 3 being the worse for the considered scalars.
As in the two previous databases, the local averages throughout all downstream locations are equal to zero, suggesting that the definition attributed to the progress variable is perhaps less relevant in a closure context than in an accurate representation of the chemical state. Surprisingly, Figure  11  shows that using a single conditioning variable for intermediate species, regardless of the definition attributed to c, equally well performs as Z,c(T) and Z,c(Y CO2 ), excluding the results obtained near the inlet of the burner (i. e. z = 10, 20 mm) where values deviate by a factor of ∼ 2, attributed to the recirculation zone and possibly the heat exchange with the bluff body. For these axial distances, this suggests that all investigated c k are enabling to decrease the functional dependence of conditional averages on spatial coordinates and stratification.
Additionally, the contours of two-condition conditional averages have also been added in Appendix 2. The conditional averages of temperature and mass fractions of several species around mixture fraction and the temperature progress variable are shown in Figure  A5. The conditionally-averaged scalars around Z and c 2 are illustrated in Figure  A6. No apparent differences can be identified among the conditional domains computed from each of the three databases (assuming the use of the same two control variables), suggesting that the conditional averaged scalars behaviour is not affected by the underlying characteristics and effects of the studied burner.
Conclusion Within this study, the Cambridge/Sandia swirl measurements are used in conjunction with principal component analysis (PCA) to attempt to find which set of control variables has the highest correlation with the reactive scalars. Three databases have been constructed to investigate the influence of swirl, stratification and spatial coordinates. Two scaling methods for the PCA model have been adopted, namely Pareto and Auto-scaling (AS). For all three data-sets, and regardless of the scaling method adopted, it was found that: (i) the first principal component (PC1) accounts for the largest amount of variance, and (ii) PC1 is well-aligned with temperature. The conditional spaces of Cambridge/Sandia flames are examined by investigating the conditional fluctuations of temperature and various species mass fractions obtained with single-conditional averages around four different progress variable definitions.
While conditional fluctuations of intermediate species and methane are unchanged using the progress variables tested, it was found that adopting a temperature-based progress variable provides minor improvements for major reactive scalars, in particular for temperature and H 2 O. For all three databases, the local averages of conditional fluctuations throughout all downstream locations are anchored at zero, suggesting that the definition attributed to the progress variable is perhaps less relevant in a closure context. Regardless of the data-set, the normalised RMS of the reactive scalars indicates that a single control variable based on c is unable to detach the thermo-chemical state from spatial coordinate, swirl or stratification, in particular for regions near the burner's tip characterised by an intense recirculation of the flow and significant heat exchanges with the bluff-body.
Acknowledgments The authors wish to express gratitude to  Professor Alessandro Parente  for having provided the impulse to pursue the work presented here. His various suggestions for improvements of the work are greatly appreciated. Special thanks are given to  Dr. M. S. Sweeney  for the high-quality measurements of the Cambridge/Sandia swirl burner and for making them available to the community. Substantial thanks go to  Professor Simone Hochgreb  and  Mr A. Mousemi  who kindly share the full point-based measurements with the authors. The authors would also like to acknowledge the funding support.
Transmission electron microscopy (TEM) was performed with a JEM-1400 flash microscope from JEOL (Tokyo, Japan) at the Centre Technologique des Microstructures, University Claude Bernard Lyon1. The TEM image could be used to observe the morphology of the particles. A drop of the sample was deposited onto a carbon grid and left until it dried. ImageJ software 8B calculated the gold nanoparticle size and polydispersity index (PDI) from TEM images of at least 200 particles. The absorbance of the gold nanoparticles was scanned with a range of 300-800 nm by a Jenway 7250 UV/Visible Spectrophotometer (Jenway, London, UK). FTIR spectroscopy was run at room temperature using a continuous Nicolet vacuum microscope (Thermo Fisher Scientific, Waltham, MA, USA) coupled with Nexus infrared spectroscopy (Nexus Analytics, Singapore) in specular reflectance mode with an MCT detector (Infrared Associates Inc.
Two in-parallel columns, one at room temperature (molecular sieve 13X) for N 2 , O 2 , and CO and the other in the oven of the chromatograph (Porapak T) at 443 K for air, CO 2 , HCHO, CH 3 OCH 3 (DME), H 2 O, CH 3 OH (MeOH), HCOOCH 3 (MF) and CH 2 (OCH 3 ) 2 (DMM), performed the separation of the reactor effluents. Formic acid was never detected. The carbon balance was evaluated for each catalytic test and the data were rejected if the error was higher than 5%.
Catalytic activity Due to the high activity of tested catalyst, conversion was always higher than 10%. Thus, integral reactor was considered. The kinetics data were obtained for reaction mixtures containing 6% of methanol in air, reaction temperatures in the range 275-375 • C and contact times in the range 5-40 g cat. h/mol CH3OH. Only appreciable amounts of formaldehyde and CO were detected for all the prepared catalysts (Fig. 1A , Fig. 1B  and Fig. 1C ). For stoichiometric samples, coprecipitated and solgel like, measurable amounts of DME were also detected in the reactor outlet. The formation of dimethyl ether is more probable when large amounts of methanol are available on the catalyst surface (low methanol conversion) and the oxygen is scarce. The catalytic tests were performed with a large excess of oxygen and with high methanol conversion (low methanol availability) what explains the low selectivities towards dimethyl ether observed (Fig.
2 (32. 2 kW) in the primary zone. A 40% air addition through the secondary air inlets is considered resulting in a global value of 0. 86 at 39. 3 kW. When generating an experimental database on sooting turbulent flames, laser-induced incandescence (LII) measurements are classically employed to obtain time-averaged SVF fields  [20]. Even if feasibility of application at high-speed has been proven  [21, 22] , this technique is classically performed at low-frame rate to avoid non-linear effects caused by multiple exposure of soot to high power laser pulses. In the following, LII measurements published in  [23]  are considered, which were acquired at a rate of 3 Hz. Approximately 400 images, i. e. roughly 2 minutes of acquisition, were recorded. Soot LS measurements obtained from a high-speed PIV image sequence recorded within a previous study  [10]  are also considered.
The sequence was recorded at a rate of 9. 3 kHz over a duration of approximately 2 s corresponding to 20000 images. The field of view covers an area of 44×36 mm 2 in the primary reaction zone of the burner and the pixel resolution is ∆x=85 µm. The raw PIV images contain both dotted patterns of Mie scattering from PIV particles as well as the Rayleigh scattering signals from clouds of soot particles, which appear rather smooth. A specific image processing routine was developed and applied to discriminate the dotted regions representing PIV particles and smooth soot structures  [10]. The primary focus of the original work was application of stereo PIV, and information on soot scattering was derived as unexpected sideproduct. Thus, the laser sheet profile was not recorded and, consequently, image correction for the sheet profile of the kHz data to obtain quantitative interpretation of the LS signal is not possible.
Results for two different timeaveraging periods each at tav=100 ms and 1 s are plotted in Fig. 2. Time-averaged fields strongly differ when considering two different intervals of 100 ms (Fig. 2a ). Even worse, experimental results are not converged even for tav=1 s (Fig. 2b ). When considering the whole available dataset by averaging over 2 s, the field is still not symmetric. The physical processes underlying soot production thus have to be considered over longer times to obtain a statistical representation. This is because the selected configuration presents low frequency flow features and soot events are observed only for very specific thermo-chemical conditions of the gaseous phase, whose statistical representation requires a long time-averaging period  [12]. To obtain a rigorous validation of simulations, the LES would have to be performed over thousands of milliseconds.