I A Mulla

J Yon

D Honor\'e B

C Lacour

A Cessou

B Lecordier
email: bertrand.lecordier@coria.fr

Comprehensive characterization of sooting butane jet flames, Part 2: temperature and soot particle size

Keywords: turbulent sooting flames, butane, soot, SMPS, soot particle size

The present work investigates the effect of jet-exit Reynolds number (Re) on soot particle size and flame temperature in n-butane jet flames. Correlation of temperature with soot volume fraction (f v ), soot precursor (polycyclic aromatic hydrocarbons or PAH), and reaction zone (OH) is also examined. The investigated flames (Re = 5000 to 21500) are identical as of the companion work (Part 1). The temperature was measured in a low-sooting region using a fine-wire thermocouple. The soot particle size distribution was obtained using a scanning mobility particle sizer (SMPS). Temporal evolution (with 0.1 s resolution) of f v in the extracted aerosol sample was monitored with a Pegasor particle sensor (PPS). f v from LII and PPS are compared, and the reasons for differences are discussed in detail. The radial location of peak temperature is biased towards the fuel-rich side. At Re 5000, peak-PAH occurs at 650 K, whereas in lifted turbulent flame (Re 21500), peak-PAH shifts to 940 K. PAH formation temperature is influenced by air/fuel mixing. Despite the variation of turbulence level (Re = 5000 -21500), peak-f v in the soot inception region occurs at a nearly identical temperature of 1400 K. Peak-f v shifts towards lower temperature with increasing height, likely due to oxidation by diffused OH. The soot mode diameter (D m ) was measured along the axis. D m increases with height and reaches a maximum near peak-f v region. D m at moderate Re

Introduction

This is the second paper of a two-part series on the characterization of sooting n-butane jet flames. In turbulent flows, to predict soot formation, turbulence and soot chemistry processes are modeled. These models are generally assessed against an experimental database. Therefore, the database-oriented works have been reported in turbulent sooting flames, both in jet [1--3] and swirl stabilized [4--7] flame configurations. These databases proved to be valuable in the assessment of numerical models in turbulent jet [START_REF] K\"ohler | Experimental characterization and numerical simulation of a sooting lifted turbulent jet diffusion flame[END_REF][START_REF] Rodrigues | Coupling an LES approach and a soot sectional model for the study of sooting turbulent non-premixed flames[END_REF] and swirl [9--12] flames. These past studies primarily focused on ethylene fuel owing to high soot yield and well-established chemical kinetics. However, investigations of soot formation in larger alkanes such as n-butane are necessary to develop soot chemistry models for fuels of practical relevance. Thermochemical and combustion characteristics of n-butane are similar to the fuels of practical interest [START_REF] Marinov | Aromatic and polycyclic aromatic hydrocarbon formation in a laminar premixed n-butane flame[END_REF][START_REF] Pitz | Chemical kinetics of the high pressure oxidation of n-butane and its relation to engine knock[END_REF]. n-butane is the smallest paraffin that mimics oxidation of larger paraffins contained in gasoline [START_REF] Huang | Dilution limits of n-butane/air mixtures under conditions relevant to HCCI combustion[END_REF]. Therefore, to validate soot models intended for practical fuels, there is a need for a benchmark database with surrogate fuels besides ethylene. For these reasons, we comprehensively characterized sooting n-butane jet flames using a range of experimental methods. The companion paper [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF], focuses on the effect of jet-exit Reynolds number (Re) on soot concentration, soot precursors, and reaction zone. Laser-induced fluorescence (LIF) and laser-induced incandescence techniques (LII) were used to obtain the data non-intrusively. The present paper (Part 2) investigates the effect of Re on soot size and soot-temperature correlations in identical n-butane jet flames [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF], including the turbulent flow condition.

In Part 1 [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF], previous studies in turbulent sooting jet flames are reviewed in detail. Therefore in this part, the literature focused on temperature and soot size are discussed. For a given fuel, the soot formation process depends on the following local conditions, namely mixing field, velocity field, residence time, and temperature. In turbulent flame, many of these local properties fluctuate simultaneously, which poses difficulty in assessing the impact of an individual parameter on soot formation. The temperature is one of the most important quantities which governs soot formation and oxidation. The investigation by Coppalle and Joyeux [START_REF] Coppalle | Temperature and soot volume fraction in turbulent diffusion flames: Measurements of mean and fluctuating values[END_REF] provided correlations between temperature and soot volume fraction (f v ) in ethylene jet flames at different Re. The authors [START_REF] Coppalle | Temperature and soot volume fraction in turbulent diffusion flames: Measurements of mean and fluctuating values[END_REF] used an optical probe, which provided extinction-based f v , while the temperature was deduced through two-color pyrometry. Such optical probe-based f v and temperature were also reported by Shaddix et al. [START_REF] Shaddix | Joint temperature-volume fraction statistics of soot in turbulent non-premixed jet flames[END_REF]. Although the technique provides simultaneous measurements, the probe perturbation and low spatial resolution are the limitations. Chan et al. [START_REF] Chan | Simultaneous imaging of temperature and soot volume fraction[END_REF] reported temperature and soot concentration in laminar flames using two-line LIF thermometry and LII. The flame wrinkling was demonstrated [START_REF] Chan | Simultaneous imaging of temperature and soot volume fraction[END_REF] to have an impact on soot-temperature correlations. A similar measurement technique was applied to turbulent flames [START_REF] Mahmoud | Simultaneous planar measurements of temperature and soot volume fraction in a turbulent non-premixed jet flame[END_REF], where a strong correlation between soot presence and a certain temperature range was noted. Kohler et al. [START_REF] K\"ohler | Sooting turbulent jet flame: characterization and quantitative soot measurements[END_REF] measured temperature in turbulent ethylene jet flame using coherent anti-stokes Raman scattering. Gu et al. [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF] investigated a similar flame by simultaneously measuring temperature, f v , and soot size. Joint statistics between various parameters, including f v and temperature, were reported. A similar measurement approach was employed by Kruse et al. [START_REF] Kruse | Experimental investigation of soot evolution in a turbulent non-premixed prevaporized toluene flame[END_REF] to investigate soot oxidation in turbulent toluene flame. Park et al. [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF] compared the temperature deduced from Krypton LIF with the fine-wire thermocouple measurements. An excellent agreement between the thermocoupleand LIF-based measurements was demonstrated. Park et al. [START_REF] Park | Relationship between soot and scalar dissipation rate in the soot-inception region of turbulent non-premixed jet flames[END_REF] used Krypton LIF to investigate f v and temperature correlations in the soot inception region of nitrogen-diluted ethylene flame. These investigations [19--24] suggest a preferred temperature range (typically, 1200 -1600 K) where f v peaks. Besides ethylene flame, it is of interest to assess such soot-temperature correlations in n-butane flames since its oxidation chemistry is similar to that of larger paraffins present in practical fuels. In the present work, the temperature was measured in lowsooting regions using a fine-wire thermocouple. The mean temperature profiles are compared with the time-averaged f v from LII to investigate correlations.

Soot particle size can also be used to validate simulation models, as in Ref. [START_REF] Gkantonas | Comprehensive soot particle size distribution modelling of a model rich-quench-lean burner[END_REF]. The soot particle diameter can be measured either in a traditional ex-situ manner or using non-intrusive optical techniques. Time-resolved LII (TR-LII) can provide the primary diameter (d p ) of soot aggregates but not the aggregate size. To obtain the soot aggregate size, TR-LII and elastic scattering techniques were combined [START_REF] Reimann | 2D aggregate sizing by combining laser-induced incandescence (LII) and elastic light scattering (ELS)[END_REF] to obtain the radius of gyration (R gy ) and the number of primary particles per aggregate (N p ). Such complete description (f v , d p , R gy and N p ) of soot concentration, soot size, and morphology has been reported in laminar ethylene flame [START_REF] Reimann | 2D aggregate sizing by combining laser-induced incandescence (LII) and elastic light scattering (ELS)[END_REF]. In turbulent ethylene flame, Gu et al. [START_REF] Gu | Particle size distribution of nascent soot in lightly and heavily sooting premixed ethylene flames[END_REF] reported the axial variation of soot primary diameter (d p ), based on TR-LII. The d p measurements were also reported in toluene flame [START_REF] Kruse | Experimental investigation of soot evolution in a turbulent non-premixed prevaporized toluene flame[END_REF].

A scanning mobility particle sizer (SMPS) is an ex-situ technique which can provide the soot particle size distribution (PSD) and concentration. Note that SMPS measures the size of a soot aggregate (mobility diameter, d m ). Thus, the SMPS-derived aggregate size (d m ) will differ from LII-deduced d p . In lowsooting n-butane laminar flames [START_REF] Betrancourt | Investigation of the size of the incandescent incipient soot particles in premixed sooting and nucleation flames of n-butane using LII, HIM, and 1 nm-SMPS[END_REF], a good agreement between LII-and SMPSbased soot sizes is demonstrated. Agreement between mode d m and d p in [START_REF] Betrancourt | Investigation of the size of the incandescent incipient soot particles in premixed sooting and nucleation flames of n-butane using LII, HIM, and 1 nm-SMPS[END_REF] suggests no soot aggregation in a nascent soot particle. Several studies have reported soot PSD in laminar ethylene flame using SMPS. Zhao et al. [START_REF] Zhao | Measurement and numerical simulation of soot particle size distribution functions in a laminar premixed ethylene-oxygen-argon flame[END_REF] observed a unimodal PSD in the inception region, which subsequently developed a bimodality with increasing height above the burner. The bimodality was solely associated with primary particles [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF]. The work of Gu et al. [START_REF] Gu | Particle size distribution of nascent soot in lightly and heavily sooting premixed ethylene flames[END_REF] showed that the PSD shapes are highly sensitive to the flame temperature and equivalence ratio. Such PSD studies in n-butane flames are relatively few [START_REF] Camacho | Evolution of size distribution of nascent soot in n-and i-butanol flames[END_REF], even in laminar flows.

In turbulent flames, very few studies report the SMPS-based soot particle size. Soot PSD has been measured in swirl-stabilized ethylene flames by De Falco et al. [START_REF] Falco | Soot particle size distribution measurements in a turbulent ethylene swirl flame[END_REF]. Chowdhury et al. [START_REF] Chowdhury | Time-averaged probability density functions of soot nanoparticles along the centerline of a piloted turbulent diffusion flame using a scanning mobility particle sizer[END_REF] and Boyette et al. [START_REF] Boyette | Soot particle size distribution functions in a turbulent non-premixed ethylene-nitrogen flame[END_REF] measured the soot particle size in turbulent nitrogen-diluted ethylene jet flames. The nitrogen dilution was necessary to avoid the blockage of the sampling orifice due to soot deposition. In undiluted flames (present case), a larger soot yield can result in uncertainty if the sampling orifice gets clogged. Therefore, it is necessary to monitor the temporal evolution of soot concentration in the extracted sample.

Thus, along with SMPS, we also employ a Pegasor particle sensor (PPS) to monitor the soot concentration temporally with 0.1 s resolution. Soot concentration from PPS is used to incorporate the orifice blockage correction of the SMPS data. PPS has generally been used to measure particulate emissions from internal combustion engines [33--35]. In fundamental combustion research, PPS

has not yet been used widely.

The primary intention of the present work is to report a part of the comprehensive database needed for the validation of soot models relevant to turbulent n-butane flames. Further objectives are to i) Investigate correlations between temperature and various parameters reported in Part 1 [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF], namely f v , PAH, and OH, on the time-averaged basis, and ii) Assess the effect of jet-exit Re on soot particle size.

Experimental methods

Burner and Flame condition

The measurements were performed in n-butane non-premixed jet flames at atmospheric pressure. The burner geometry and flame conditions are detailed in Part 1 [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. n-butane was issued through a 2.4 mm tube in the co-flowing air.

The flames were enclosed in a square duct (400 mm wide and 750 mm high) through which co-flow air was issued. The air co-flow was maintained at 5 g/s, which is high enough to ensure the over-ventilated flame condition. The flow rates were regulated by Coriolis-calibrated thermal mass flow controllers [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF].

The uncertainty in flow rates is estimated to be within \pm 1%. Three n-butane flames (Re 5000, 7200, and 21500) out of the four cases investigated in [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF] are considered. The Re 2100 flame was not suitable for intrusive measurements due to large soot concentration and low jet momentum, which could result in significant probe-induced perturbations.

Re is defined based on the jet-exit bulk velocity and tube diameter. Generally, the turbulence level increases with Re [START_REF] Deo | The influence of reynolds number on a plane jet[END_REF]. Therefore, Re has been used [START_REF] Sun | Planar laser-induced incandescence of turbulent sooting flames: the influence of beam steering and signal trapping[END_REF][START_REF] Lee | Measurements of soot, OH, and PAH concentrations in turbulent ethylene/air jet flames[END_REF] as a global parameter to represent the overall turbulence level. Re was varied from 2100 to 21500 by changing the fuel flow rate from 0.03 to 0.3 g/s.

Consequently, Re variation was accompanied by a change in residence time since the bulk velocity (flow rate) was altered. Therefore, to assess the effect of local turbulence, the velocity field needs to be measured (e.g., [START_REF] Narayanaswamy | Simultaneous LII and PIV measurements in the soot formation region of turbulent non-premixed jet flames[END_REF]). In the present work, the local velocity was measured only for Re 21500 in the jet-exit region.

Thus, the effect of local turbulence on soot could not be assessed explicitly.

Re 5000 flame was attached to the fuel tube, while Re 7200 and 21500 flames were lifted with 11 and 53 mm lift-off heights, respectively [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. From the modeling point of view, a database of the attached flame is preferred [START_REF] Shaddix | Understanding and predicting soot generation in turbulent non-premixed jet flames[END_REF] due to difficulty in modeling lifted flames owing to the partial premixing at the flame base. In general, a pilot flame has been used [START_REF] Shaddix | Understanding and predicting soot generation in turbulent non-premixed jet flames[END_REF] to avoid the lift-off at high Re; however, the pilot flame is argued [START_REF] K\"ohler | Sooting turbulent jet flame: characterization and quantitative soot measurements[END_REF] to introduce modeling complexities.

Another approach is to use an additive in fuel or oxidizer stream, such as H 2 [START_REF] Mahmoud | The effect of exit reynolds number on soot volume fraction in turbulent nonpremixed jet flames[END_REF] or O 2 [START_REF] Franzelli | Time-resolved spatial patterns and interactions of soot, PAH and OH in a turbulent diffusion flame[END_REF] to keep the flame attached. This approach was not used in the present work since the database with pure n-butane was intended. Instead, we provide the precise velocity and mixing fields in a lifted part of the flame (for Re 21500) as boundary conditions.

Laser diagnostics

The present paper uses the soot concentration, soot-precursor (PAH), and flame location (OH) data obtained in the companion work [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. A brief description of the measurement methods is provided here, while detailed information can be found in [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. Soot volume fraction was measured using the LII technique. Soot particles were heated by a 1064 nm wavelength pulse (from a Nd:YAG laser), and the resulting incandescence signal was acquired at 400 nm.

The average laser fluence of 0.4 J/cm 2 was used to ensure the plateau regime of LII. The LII signal was imaged on an intensified CCD (ICCD) camera with a prompt gating of 50 ns relative to the laser pulse. To obtain the soot volume fraction, the LII signal was calibrated using a laser-extinction measurement at 1064 nm. To image OH and PAH distributions, the planar laser-induced fluorescence (PLIF) technique was used. The OH radical was excited using 283 nm wavelength (from a dye laser) with 0.05 J/cm 2 average fluence. The resulting OH fluorescence was imaged at 310 nm using an emICCD camera gated to 30 ns width. PAH is excited with 283 nm wavelength laser pulse at a reduced fluence (0.02 J/cm 2 ) to avoid the LII interference. The PAH-PLIF signal was acquired in a 350 -400 nm range with an ICCD camera gated to 50 ns width. These excitation and detection parameters provide the LIF signal primarily from 2-4 ring PAH [START_REF] Bejaoui | Laser induced fluorescence spectroscopy of aromatic species produced in atmospheric sooting flames using UV and visible excitation wavelengths[END_REF]. In all the above diagnostics, the signal was imaged at a magnification of 5.75 pixels/mm, which corresponds to 89 mm wide field-of-view (FOV). A total of 1000 to 2000 images (depending on height above the burner) were acquired at a 10 Hz rate. The time-averaged data sets of f v , OH-PLIF, and PAH-PLIF from [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF] are used in the present paper to investigate their correlations with temperature.

Temperature measurements

The gas temperature was measured using a fine-wire thermocouple. A Type-B thermocouple (Pt-30\%Rh / Pt-6\%Rh) was chosen due to its high temperature limit. Thermocouple wires of 50 \mu m diameter were butt-welded to form a junction. The junction was exposed to the flame, while the extension wires were shielded in a twin-bore ceramic tube. The thermocouple signal was amplified and digitized at a 3 kHz rate. The lowest measurable temperature was limited to 530 K due to a weaker thermocouple signal. The thermocouple was traversed through the flame using a 3-axis motorized stage. The translation stage and data acquisition system were integrated to automate the measurements. Any misalignment between the thermocouple translation and flame axes was minimized through a 2D temperature mapping at two different heights (planes). This provided the flame axis and its orientation with reference to the thermocouple translation coordinates.

Temperature measurements are intended to be quantitative. Therefore, various uncertainty sources, namely 1) calibration error, 2) catalytic effects, 3) local flame perturbations, and 4) radiation correction uncertainty, are assessed. The calibration accuracy was verified by measuring known temperatures (within the 570 -1060 K range) in a portable calibration furnace (Pegasus 1200B, AOIP).

The conduction heat losses through thermocouple wires can be neglected since the wire length was long (10 mm) relative to the diameter (50 \mu m). In reducing atmospheres, the platinum surface can act as a catalyst that may enhance exothermic reactions. A non-catalytic coating could have been used; however, such coating deteriorates the temporal response in turbulent flames. Therefore, the uncoated bare thermocouple was used. The catalytic effects in non-premixed flames were speculated to be insignificant due to lower radical concentration [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF]. This is confirmed by an excellent agreement between LIF-based temperature and thermocouple (uncoated) measurements that are reported by Park et al. [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF].

Nevertheless, we assessed the catalytic effects by traversing the thermocouple from oxidizer to fuel stream and vice-a-versa. The hysteretic effects were not significant in the present flames (see Fig. S1 in Supplement).

Since the thermocouple size was small (50 \mu m), no significant flame perturbations were noted, as evidenced from Fig. 1, where lift-off height and overall flame appearance with and without the thermocouple are identical. The measurements stations are marked on respective flame photographs in Fig. 2. The Re 5000 flame is attached, while other flames are lifted. The lift-off heights for Re 7200 and 21500 measured 53 and 11 mm, respectively, based on OH-PLIF data [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. Since the Re 2100 flame was highly sooting, the temperature was not measured. In remaining flames, measurements were limited to low-sooting regions, where time-averaged f v is below 0.1 ppm (deduced from LII measure-ments in [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]). The soot deposition can change the emissivity and diameter of the thermocouple junction, consequently resulting in a large uncertainty. To reduce the effect of soot deposition, the measurement duration was limited to 3 s at each location. In the case of soot deposition, the temperature was reported to decrease even within the first two seconds [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF]. Over the present 3 s duration, the temperature did not decay (see Fig. S2), which suggests negligible soot deposition. Additionally, no visible deposition was noted at the end of measurements. The radiation correction is necessary since the flame temperature is anticipated to be high (T ad = 2267 K). The correction is applied by considering a convection-radiation balance as detailed in Sec. S1.3 of the Supplement.

The detailed estimates of uncertainties owing to errors in radiation correction, positional error, and statistical uncertainty in mean temperature are provided in Sec. S1.4. The combined uncertainty in mean temperature at a peak value (2250 K) is estimated to be \pm 6%, while uncertainty is \pm 4% in the temperature range of 600 -1600 K.

Particle analyzers

A Pegasor particle sensor (PPS) was used to measure the soot concentration, whereas the scanning mobility particle sizer (SMPS) was employed to measure the soot particle size simultaneously. Both SMPS and PPS measurements require the extraction of an aerosol sample from the flame. Figure 3 shows the schematic of the experimental layout. The sample was drawn through a 1 mm orifice drilled in a probe tube of 4 mm inner diameter and 1 mm wall thickness.

To draw the sample, a mild vacuum was generated by a pump. The suction strength was controlled by a valve. The sample was quickly diluted with nitrogen (N 2 ) that was issued through the tube at a 10 liters per minute (lpm) flow rate. The N 2 dilution assists in quenching of reactions, and it also limits the soot aggregation. Apart from N 2 , additional dilution (with air) was achieved using two diluter units (VKL 10, PALAS) connected in tandem. This provided an additional dilution factor of 100. Such a heavy dilution is necessary to avoid the saturation of SMPS and PPS.

The probing system and dilution level were qualified using a well-characterized miniCAST soot (miniCAST 5200, Jing) generator. Soot generated by mini-CAST propane (0.06 lpm)/air (1.5 lpm) flame was very stable and reproducible.

The combustion products (including soot) were quenched by nitrogen gas (7 lpm).

The products were further diluted with air (20 lpm) within the miniCAST system. Next, the SMPS measurements were performed at various N 2 flow rates through the probe. Subsequently, 10 lpm was found to be enough to avoid soot aggregation in the sampling line, as inferred from the converged soot PSD, similar to [START_REF] Boyette | Soot particle size distribution functions in a turbulent non-premixed ethylene-nitrogen flame[END_REF][START_REF] Zhao | Analysis of soot nanoparticles in a laminar premixed ethylene flame by scanning mobility particle sizer[END_REF]. For the miniCAST configuration, PPS measurement showed remarkable stability in the soot concentration with time, indicating no blockage of the orifice. The dilution ratio (N 2 /sample) is determined to be 24:1 by comparing PPS measurements with the probe and directly without the probe.

Recall, the additional air dilution (\times 100) was used. Thus, the effective dilution ratio was 2400:1 by volume. The sample extraction set-up was identical (valve position, vacuum pump, etc.) as of the main campaign. Therefore, the dilution ratio deduced in miniCAST was used to calibrate the measurements performed in butane jet flames. Uncertainty in the dilution ratio is discussed subsequently in Sec. 3.3.

The sampling probe generally perturbs the flame through alteration of local temperature and upstream flow-field. Yet, a wealth of information can be extracted with fewer assumptions and lesser complexity than laser-based techniques. In laminar flames, perturbations are contained within a few mm upstream of the probe [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF]. In the turbulent flame, upstream perturbations are expected to be lower due to larger flow momentum. Figure S4 in the Supplement shows flame photographs with the probe, suggesting low global perturbations.

Although, a discrepancy exists between LII and probe-derived soot concentration, especially at low Re (discussed in Sec. 3.3).

PPS (PPS-M 2000HC PEMS, Pegasor

) provides the quasi-temporally resolved (0.1 s) soot concentration. In the PPS technique, soot particles interact with ionized air. The exiting charged particles provide an estimate of escaping current, which is proportional to the soot concentration. A detailed working principle can be found in Ref. [START_REF] Amanatidis | Measuring number, mass, and size of exhaust particles with diffusion chargers: The dual pegasor particle sensor[END_REF]. Once the escaping current (I pps ) is measured, soot mass concentration can be deduced as C s = K pps .I pps /Q v , where Q v is the sample flow rate (5 lpm) and K pps is a constant (1.05, based on Diesel soot applications [START_REF] Ntziachristos | Application of the pegasor particle sensor for the measurement of mass and particle number emissions[END_REF]). Next, the soot volume fraction can be deduced as f v -P P S = C s /\rho soot , where \rho soot is a soot particle density which is assumed to be 1700 kg/m 3 , based on a range of values reported in the literature (1500 [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF] -1900 [START_REF] Liu | Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence[END_REF] kg/m 3 ). The combined uncertainty in PPS is estimated to be \pm 56%. Individual error sources are discussed subsequently in Sec. 3.3.

The SMPS system (Classifier 3080 + CPC 3010, TSI) was used to obtain the soot particle size distribution. The aerosol sample was supplied to the instrument at 1 lpm flow rate, while the sheath flow rate was set to 10 lpm.

SMPS counts the particle concentration by a sequential selection of classes of

electrical mobility diameters over a specific range. Such scan duration is long (2 min for 7 -290 nm), and thus, SMPS is generally used in laminar flames [26, 28--30]. Nevertheless, for the size range of interest (mode diameter 7 -30 nm), the scan duration was short (23 s). The relative uncertainty in the particle size distribution shape is estimated to be 10% based on Ref. [START_REF] Boyette | Soot particle size distribution functions in a turbulent non-premixed ethylene-nitrogen flame[END_REF].

Results and discussion

Flame temperature

Temperature measurements were performed in low-sooting regions, where time-averaged f v was less than 0.1 ppm. Figure 4 shows the radiation corrected temperature profiles. In the case of turbulent flame (Fig. 4e), measurements for y < 60 mm were not performed since the flame was lifted. Recall, the present thermocouple could not measure temperature below 530 K. To eliminate biased results, a dataset containing even a single instant of T \leq 530 K was not retained. Therefore, the mean temperature is not available in some cases.

The peak flame temperature in Re 5000 flame at y = 10 mm in Fig. 4a measures 2261 K, while T ad is 2267 K. At y = 10 mm, the soot concentration is negligible. Nevertheless, the temperature in non-premixed flames is expected to be lower than T ad . Recall, at high temperature, \pm 6% uncertainty (detailed in S1.4) exists. The actual peak flame temperature is likely to be lower. In Re 7200 flame, peak temperature (in Fig. 4c) at y = 10 mm is lower due to a lifted flame base (see Fig. 2b). The lift-off height for this flame measures 11 mm with a standard deviation (\sigma ) of 0.6 mm based on the OH-PLIF data [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. At y = 10 mm, the flame leading edge spatially fluctuates. Therefore, the thermocouple is subjected to fluctuations between preheat and post-flame zones, which lowers the mean temperature. For a given Re, in general, the temperature decreases with increasing y. In Re 5000 flame (Fig. 4a), the radial peak temperature reduces by \sim 150 K with increase in height from y = 10 to 60 mm. The soot radiation effect [START_REF] Liu | ulder, Effects of gas and soot radiation on soot formation in a coflow laminar ethylene diffusion flame[END_REF] alone cannot explain the observed drop in temperature since the measurements were restricted to low f v regions. Recall that the plotted temperatures in Fig. 4 Temperature profiles become broader due to increased flame-brush thickness with Re. In Fig. 4, the thermocouple enters from left (r -) to right (r + ).

Temperature profiles are minutely asymmetric, which is attributed to the thermocouple perturbation towards r + side in Fig. 4. Even this mild asymmetry could influence the temperature correlations with OH, PAH, and soot. Thus, only the left side (r -) of the profile is retained for further analysis.

Temperature correlations

Temperature profiles are used to deduce correlations with soot concentration, soot-precursor (PAH), and reaction zone (OH) reported in the companion paper [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. To visualize the spatial trends, the profiles are extracted from the timeaveraged planar data. Figure 5 shows PAH-LIF, f v , and OH-LIF profiles at y = 100 mm, for Re 2100, 5000, and 7200 flames. Recall, temperature measurements in Re 2100 are not available. However, OH, PAH, and f v are available, and thus presented to enable comparison with other Re. For turbulent flame, the profiles at y = 250 mm (where f v is appreciable) are plotted. A peak asymmetry is noted in f v , which is attributed to possible beam steering and laser extinction along the path [START_REF] Sun | Planar laser-induced incandescence of turbulent sooting flames: the influence of beam steering and signal trapping[END_REF]. Therefore following Sun et al. [START_REF] Sun | Planar laser-induced incandescence of turbulent sooting flames: the influence of beam steering and signal trapping[END_REF] data only towards the laser-incident side is retained.

At Re 2100 (Fig. 5a), the radial order of the species from the jet axis is as following: PAH, soot, and reaction zone. A minute OH-LIF signal near the jet core is attributed to interference from 1-2 ring PAH, as discussed in [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. The radial order of species is the result of temperature and air/fuel mixing field. At a low oxygen concentration and a certain temperature range (700 - 1300 K [START_REF] Nakamura | Soot formation characteristics and PAH formation process in a micro flow reactor with a controlled temperature profile[END_REF]), PAH forms through pyrolysis of fuel. The smaller PAH gets converted to larger PAH with increasing temperature. Subsequently, larger PAH coagulate and go through thermochemical processes to eventually form a nascent soot particle [START_REF] D'anna | Particle formation in opposed-flow diffusion flames of ethylene: An experimental and numerical study[END_REF]. Next, soot particles grow through aggregation and surface reactions. Soot eventually gets oxidized in the vicinity of the flame, primarily through the OH route [START_REF] Guo | Optimized rate expressions for soot oxidation by[END_REF]. With an increase in Re , the PAH peak shifts from flame wing to the jet axis, while the annular structure of soot and reaction zone is preserved. The mass diffusion of the solid soot particles is negligible relative to the diffusion of gaseous species (PAH) [START_REF] Kronenburg | Modeling soot formation in turbulent methane--air jet diffusion flames[END_REF]. In the turbulent flame (Fig. 5d), the time-averaged profiles become much broader than that of the laminar flame. The broadening of profiles is related to the spatial fluctuations induced by turbulent structures.

Temperature correlation with OH

The radial peak locations of OH-LIF and temperature are compared for different flames in Fig. 6 at several heights. The temperature profiles are much broader than that of the OH, even in the laminar flame (Fig. 6a). The OH peak and temperature peak lie close to each other; however, the temperaturepeaks (and -profiles) are biased towards the fuel stream. In a non-premixed flame, combustion generally occurs at a stoichiometric surface, with products distributed on either side of the reaction zone. OH peaks in close vicinity of the stoichiometric surface but towards the fuel-lean side, as demonstrated by Donabar et al. [START_REF] Donbar | Reaction zone structure in turbulent nonpremixed jet flames---from CH-OH PLIF images[END_REF] in a turbulent jet flame. Consequently, OH and temperature peaks do not overlap. In premixed flames, temperature peaks at a fuel-rich condition (\phi = 1.05 for n-butane). The appreciable shift of the temperature peak relative to OH in Fig. 6 suggests the occurrence of peak-temperature at even richer \phi . The observation deduced from Park et al. [START_REF] Park | Relationship between soot and scalar dissipation rate in the soot-inception region of turbulent non-premixed jet flames[END_REF] indicates the occurrence of peak-temperature at \phi \sim 1.2 in a turbulent jet flame. In non-premixed flames, apart from chemical kinetics, convection and diffusion processes determine the peak-temperature \phi [START_REF] Turns | An introduction to combustion: Concepts and Applications[END_REF]. In the present flame, to identify \phi corresponding to the peak-temperature, the mixture fraction data is needed.

Temperature correlation with PAH

The PAH-LIF profiles are also compared with the temperature in Fig. 7 for different Re. In turbulent flame (Re 21500), no appreciable PAH is detected at lower height since the flame is lifted. In general, PAH concentration peaks in the fuel-rich low temperature zone. For quantitative comparison, temperature value at peak-PAH location is provided in Table 1. In the attached flame (Re 5000) at the base, PAH peaks at a much lower temperature (650 K). Since reactant premixing is nearly absent in the attached flame, pyrolysis of fuel (that assist in PAH formation) may take place at a lower temperature. PAH peak shifts towards higher temperature with increasing height. This trend is likely associated with the increased diffusion of air with residence time (which is proportional to height). The presence of oxygen can shift the PAH formation to a higher temperature.

Conversely, in a lifted flame (Re 7200), the PAH peak appears to be less sensitive to height. The oxygen content in the PAH formation zones may not be varying significantly in the y = 20 -120 mm region due to partial premixing.

At y = 20 mm, the PAH peak occurs at a much higher temperature than that in the attached flame. A partial premixing in the lifted region is likely responsible for the observed trend. In the turbulent flame (Re 21500), higher lift-off height (h lif t = 53 mm) and turbulence cause stronger premixing at the flame base.

Therefore, the peak-PAH occurs at an even higher temperature of 940 K. With increasing Re, the residence time decreases while mixing enhances. The results show that the PAH formation temperature is influenced by the air/fuel mixing and residence time.

Temperature correlation with soot concentration

The temperature-soot correlations are explored in a similar manner. For such correlations, generally, simultaneous measurements of temperature and soot have been performed. However, there is likely to be a notable (few ms) delay between a change in local flow conditions and soot response, as evidenced from time-resolved measurements of St\"ohr et al. [START_REF] St\"ohr | Time-resolved study of transient soot formation in an aero-engine model combustor at elevated pressure[END_REF]. Owing to longer soot reaction timescales (few ms), interpretation of instantaneous correlation is difficult in turbulent flames. The influence of soot response delay on time-averaged correlation is expected to be less significant than that of instantaneous correlation for a statistically stationary flow. To understand time-resolved soot-temperature correlation, high-speed simultaneous diagnostics is required where quantification is not trivial. Therefore, in this work, only time-averaged correlations are assessed.

Figure 8 shows the mean temperature and f v profiles in Re 7200 flame.

Soot lies closer to the fuel-rich zone, away from the peak temperature location.

The spatial trend between soot and temperature is similar to that reported in turbulent diluted ethylene flame by Park et al. [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF]. The width of the temperature profile is larger than the f v profile. This observation is similar to that of Gu et al. [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF]. In general, soot structures are highly localized due to a large Schmidt number of soot particles, which leads to a low soot mass diffusivity [START_REF] Bisetti | On the formation and early evolution of soot in turbulent nonpremixed flames[END_REF] relative to the thermal diffusivity of a gas. Consequently, the temperature profile width outgrows the soot profile width, as observed in Fig. 8. Similar to Re 7200 flame, the temperature and f v profiles are overlaid for other flames (but not shown for brevity).

Soot exists within a certain temperature range. To enable quantitative comparison, we deduce the mean gas temperature where time-averaged f v peaks. The present findings are compared with the measurements in ethylene flames, since such data in turbulent n-butane flame is not yet reported. Note that the stoichiometric T ad of n-butane flame is \sim 100 K lower than that of the ethylene. In turbulent ethylene lifted DLR jet flame (Re = 10000), the peak f v was reported [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF] to exist in a 1550 -1750 K range. This range is comparable to the T f pk v \approx 1600 K reported by Coppalle and Joyeux [START_REF] Coppalle | Temperature and soot volume fraction in turbulent diffusion flames: Measurements of mean and fluctuating values[END_REF] in ethylene flame at Re = 11800. In a different ethylene flame (Re = 20000, pilot stabilized) T f pk v \approx 1400 K was reported [START_REF] Shaddix | Joint temperature-volume fraction statistics of soot in turbulent non-premixed jet flames[END_REF]. Higher Re could lead to lower flame temperature due to increased flame-stretch. Additionally, measurements in [START_REF] Shaddix | Joint temperature-volume fraction statistics of soot in turbulent non-premixed jet flames[END_REF] were path integrated over a larger region (10 mm), resulting in lower resolution.

From a LIF-based temperature measurement in a diluted turbulent (Re = 8300) ethylene flame [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF][START_REF] Park | Relationship between soot and scalar dissipation rate in the soot-inception region of turbulent non-premixed jet flames[END_REF], peak f v was shown to occur in a 1300 -1500 K range in the soot inception region. This temperature range is lower compared to pure ethylene flames [START_REF] Coppalle | Temperature and soot volume fraction in turbulent diffusion flames: Measurements of mean and fluctuating values[END_REF][START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF], but lies closer to [START_REF] Shaddix | Joint temperature-volume fraction statistics of soot in turbulent non-premixed jet flames[END_REF]. Park et al. [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF] argued that with a diluted fuel, the flame temperature itself is lower, consequently resulting in a low T f pk v . In the present n-butane flames, T f pk v at the soot inception region (1400 K) is in agreement with a diluted ethylene flame of Park et al. [START_REF] Park | Mixture fraction, soot volume fraction, and velocity imaging in the soot-inception region of a turbulent non-premixed jet flame[END_REF][START_REF] Park | Relationship between soot and scalar dissipation rate in the soot-inception region of turbulent non-premixed jet flames[END_REF].

Soot concentration from PPS

The PPS-based soot concentrations are compared with that of LII from the companion work [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. Note, the use of PPS was primarily intended to monitor the temporal evolution of the soot sample during an SMPS scan. Figure 10 shows the temporal evolution of soot volume fraction in aerosol sample extracted from Re 7200 flame at y = 250 mm. The profile shows the initial spike as flame ignites. Subsequently, f v decreases due to the blockage of the probe orifice. The peak concentration associated with the flame transition is not retained. There exists a distinct post-peak transition marked by a circle (in Fig. 10), which is assumed to be the quasi-steady soot concentration before any obstruction of the orifice. This procedure is adapted for all the measurements. The blockage of the probe orifice is lesser in the turbulent case due to lower f v . The SMPS measurements are affected by the probe blockage over the scan time. Therefore, the SMPS data is corrected using PPS measurements, as detailed separately in Sec. S2.2 of the Supplement.

Soot concentrations obtained from PPS (f v - P P S ) are compared with that of the LII (f v - LII ). Figure 11 shows the axial (centerline) mean profiles of f v - LII along with f v - P P S . The objective of this comparison is to assess the impact of probe perturbation on the flame. Overall, there is a qualitative agreement between f v - P P S and f v - LII . At Re 5000, f v - P P S appears to be shifted towards lower height relative to f v - LII . However, this discrepancy reduces with increasing Re. As Re increases, higher jet momentum results in lower probe perturbations. Additionally, at higher Re, the flame width increases, which reduces the PPS probe sensitivity to radial misalignment as well as to probe-induced radial fluctuations of f v . These factors result in a better qualitative agreement between PPS and LII with increasing Re.

Although the qualitative trends are in agreement, absolute values of f v - P P S are much higher than f v - LII . The factor is 2.4 for Re 5000 and 7200 flames, whereas it measures 2.8 for Re 21500 flame. A discrepancy between in-situ (LII based) and ex-situ (SMPS based) f v values is reported recently [START_REF] Falco | Soot particle size distribution measurements in a turbulent ethylene swirl flame[END_REF]. The authors [START_REF] Falco | Soot particle size distribution measurements in a turbulent ethylene swirl flame[END_REF] argue that their LII measurements were biased towards larger soot particles (i.e., low LII sensitivity to smaller particles), and thus leading to lower LII-based f v relative to SMPS measurements. Note, f v - LII in Fig. 11 was in close agreement with the value (0.54 ppm) reported in [START_REF] K\"ohler | Sooting turbulent jet flame: characterization and quantitative soot measurements[END_REF][START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF]. 2) Uncertainty exists in the extinction coefficients K e used for LII calibration. K e varies with fuel and soot maturity (C-H composition) [START_REF] Williams | Measurement of the dimensionless extinction coefficient of soot within laminar diffusion flames[END_REF].

3) The excitation laser beam steering in a turbulent flame can also affect the LII signal [START_REF] Sun | Planar laser-induced incandescence of turbulent sooting flames: the influence of beam steering and signal trapping[END_REF]. 4)

Statistical uncertainty in the mean quantity arises due to fluctuations and a finite number of samples. The combined uncertainty (excluding K e ) from the above sources is estimated to be \pm 19% [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF].

The uncertainty in PPS can arise from the following sources. 1) There is inherent uncertainty in PPS-derived f v due to the transient nature originated from the probe blockage (recall Fig. 10). This uncertainty is estimated to be \pm 15%, based on the signal fluctuations.

2) The conversion of the PPS signal to the soot mass concentration involves soot particle size distribution assumption, which can lead to uncertainty up to \pm 30% [START_REF] Ntziachristos | Exhaust particle sensor for OBD application[END_REF]. Furthermore, soot mass concentration is converted to f v through an assumed density, as indicated in Sec. 2.4. The soot density typically varies from 1500 [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF] to 1900 [START_REF] Liu | Heat conduction from a spherical nano-particle: status of modeling heat conduction in laser-induced incandescence[END_REF] kg/m 3 with soot maturity. Therefore, we use 1700 kg/m 3 soot density accompanied by \pm 15% uncertainty.

3) The uncertainty due to an error in probe positioning and upstream perturbations are estimated to be within \pm 5 mm, which translates to f v uncertainty of \pm 15% based on LII fields [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. 4) The absolute dilution ratio between the aerosol sample and N 2 is estimated in a separate calibration burner (recall Sec. 2.4) at a different flow velocity and temperature than the jet flames. The flow velocity can affect the pressure upstream of the probe, while temperature influences the quench gas (N 2 ) expansion. Therefore, the dilution ratio could differ, which may be the major source of uncertainty. The dilution uncertainty could be high as \pm 40% [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF].

Total uncertainty from the above sources is estimated to be \pm 56% through This provides a base for technique-focused future works that could exploit PPS capabilities by addressing the aforementioned uncertainties. Unlike PPS, LII has been used widely (over a few decades) with a detailed understanding. Therefore, we retain only f v - LII for the forthcoming analysis. is not appreciable. Thus, the lowest y station is different than Re 5000 and 7200 flames. In turbulent flame, the probe orifice is the least blocked owing to a low time-averaged soot concentration. Consequently, \sigma gC and \sigma gU are in close agreement. As the blockage is moderate, both D gC and \sigma gC are reliable throughout the measured axial locations.

All the PSDs (Figs. 12 to 14) exhibit a single mode within the present measurement range. This unimodality is in agreement with the PSD reported in diluted ethylene jet flames [START_REF] Chowdhury | Time-averaged probability density functions of soot nanoparticles along the centerline of a piloted turbulent diffusion flame using a scanning mobility particle sizer[END_REF]. However, LES investigation [START_REF] Rodrigues | Coupling an LES approach and a soot sectional model for the study of sooting turbulent non-premixed flames[END_REF] in turbulent ethylene flame showed a bimodal PSD which is primarily prevalent downstream of the peak-f v location. The first mode [START_REF] Rodrigues | Coupling an LES approach and a soot sectional model for the study of sooting turbulent non-premixed flames[END_REF] occurs at a much smaller diameter(< 5 nm), while the detection limit of the present system is 7 nm. In turbulent toluene flame, Kruse et al. [START_REF] Kruse | Experimental investigation of soot evolution in a turbulent non-premixed prevaporized toluene flame[END_REF] also noted a bimodal distribution of d p in a soot oxidation region.

For a given Re, with increasing height (y), soot particles are observed to be distributed over a wider size range, consistent with [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF]. In inception regions (lower y), generally nascent soot particles exist without any aggregation. At a higher height, surface growth of primary soot particles takes place in addition to aggregation. This leads to a wider particle size distribution in downstream regions. Excluding the high-sooting and flame-tip regions, \sigma g in Re 5000 flame (Fig. 12) appears to increase from 1.5 to 1.6 nm with height. For Re 7200 flame, \sigma g varies over a larger range of 1.5 to 1.8 nm (Fig. 13). At Re = 21500 (Fig. 14), \sigma g varies from 1.7 nm near the inception region to 1.9 nm near the peak-f v region. In turbulent flame, soot particles are distributed over a wider size range, even at soot inception regions. Although the soot size range increases with Re, the mode diameter in turbulent flame measures less than that of the lower Re flames. Turbulence could reduce the soot growth and aggregation owing to reduced residence time, soot precursor (PAH) concentration, and gas temperature.

Soot particle size

The axial evolution of soot mode diameter (D m ) obtained from PSD is shown in Fig. 15 along with f v - LII . For all the cases in Fig. 15, the soot size increases with a height, similar to f v , until both reach a peak. Beyond a certain distance, [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF], confirms that the peak f v lies further downstream than that of the time-averaged f v . This explains the difference in axial trends of D m and time-averaged f v .

f v decreases, but
f v - LII reported in
Since the soot particle size in turbulent n-butane flame is not yet been re-ported in the literature, we compare the present measurements with ethylenefueled turbulent flames and with a laminar n-butane flame. The D m range of the present jet flames is close to the one interpreted from PSD reported for a laminar premixed n-butane flame [START_REF] Camacho | Evolution of size distribution of nascent soot in n-and i-butanol flames[END_REF]. In turbulent non-premixed ethylene jet flame, Gu et al. [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF] reported the primary soot diameter (d p ) based on timeresolved LII. The mean d p followed a similar trend as of the mean f v with height.

The most probable d p also showed an identical trend (and values) as of the mean d p with height. The peak in d p and f v occurred at the same location. A similar trend is noted in turbulent pre-vaporized toluene flame [START_REF] Kruse | Experimental investigation of soot evolution in a turbulent non-premixed prevaporized toluene flame[END_REF]. The present mode (most probable) diameter evolution shows a similar trend with f v as of [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF][START_REF] Kruse | Experimental investigation of soot evolution in a turbulent non-premixed prevaporized toluene flame[END_REF],

within the measurement uncertainty.

Apart from qualitative trends, the soot particle size from ethylene flame [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF] could be compared quantitatively with the present results while being aware of differences (in Re, fuel, soot size parameter). In ethylene flame [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF], the most probable d p varies in 8 -16 nm range. The mode diameter D m in the present turbulent n-butane flame (Re 21500) varies in 12 -24 nm range, which is 1.5 times of the most probable d p with ethylene. Based on the PSD reported in laminar ethylene [START_REF] Abid | On evolution of particle size distribution functions of incipient soot in premixed ethylene--oxygen--argon flames[END_REF] and n-butane flames [START_REF] Camacho | Evolution of size distribution of nascent soot in n-and i-butanol flames[END_REF], we assume soot size in n- Consequently, the correction uncertainties are minimal in D m , and therefore, we chose to use D m . The axial D g trend in [START_REF] Chowdhury | Time-averaged probability density functions of soot nanoparticles along the centerline of a piloted turbulent diffusion flame using a scanning mobility particle sizer[END_REF] shows continuous growth until a certain downstream distance near the flame-tip. Beyond which measurements were not available. Therefore, the peak transition from a monotonic trend could not be identified. Additionally, the axial peak-f v location in this flame is not known to assess f v and soot size correlation. The D g variation range in [START_REF] Chowdhury | Time-averaged probability density functions of soot nanoparticles along the centerline of a piloted turbulent diffusion flame using a scanning mobility particle sizer[END_REF] is rather small (3 -6 nm) relative to the mean d p (5 -16 nm) reported in pure ethylene flame [START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF]. The smaller soot size in [START_REF] Chowdhury | Time-averaged probability density functions of soot nanoparticles along the centerline of a piloted turbulent diffusion flame using a scanning mobility particle sizer[END_REF] is likely due to the dilution (65% N 2 ) of ethylene. Decrease in d p with N 2 dilution has also been reported by Sun et al. [START_REF] Sun | Effects of hydrogen and nitrogen on soot volume fraction, primary particle diameter and temperature in laminar ethylene/air diffusion flames[END_REF].

In the present undiluted n-butane flames, the soot size (D m ) ranges from 12 to 28 nm, as observed from Fig. 15. Soot particles much smaller (2 -4 nm)

than the present range have been reported [START_REF] Betrancourt | Investigation of the size of the incandescent incipient soot particles in premixed sooting and nucleation flames of n-butane using LII, HIM, and 1 nm-SMPS[END_REF] in low sooting laminar n-butane nucleation flames. The present SMPS set-up is unable to resolve such a small size which may occur in soot nucleation regions. In the attached flame (Fig. 15a), D m measures 20 nm near the inception region, whereas in lifted flames (Figs. The effect of lift-off originated partial premixing is investigated by Grader et al. [START_REF] Grader | Large-eddy simulation and analysis of a sooting lifted turbulent jet flame[END_REF] through LES. The impact of partial premixing is mainly relevant in the soot inception and growth regions. In the downstream locations (between soot growth and oxidation regions), combustion was shown to occur primarily in the non-premixed regime. This may be the reason for the substantial rise in D m with height in lifted flames despite the upstream partial premixing.

Conclusions

The present paper reports the temperature and soot particle size in n-butane jet flames. The effect of exit Re on correlations between temperature and various parameters, namely f v , soot-precursor (PAH), and reaction zone (OH), are investigated. The soot particle size distribution was obtained at different Re.

Additionally, soot concentration was measured using the ex-situ PPS device. In this manner, the present work examined the influence of Re on temperaturesoot correlations and soot particle size. The application of the PPS device is demonstrated for the first time to measure the in-flame soot concentration. Additionally, soot particle size in a turbulent n-butane flame is provided using SMPS. The data provided insights into the effect of upstream partial premixing and turbulence on soot size. The comprehensive database containing a wide range of parameters and boundary conditions, from the present and companion (Part 1) [START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF] papers, can contribute towards the development and validation of turbulence and soot-chemistry models for fuels of practical relevance. lations. Dg and \sigma g are specified in nm. ( ) without blockage correction, ( ) with correction.

  are time-averaged. In addition to mean, we also deduce root mean square (RMS) values. This data is provided in the Supplementary material. Since the thermocouple response time is estimated to be 10 ms, RMS values are indicative. Nonetheless, RMS can be compared on a relative basis across flames and measurement locations. The unsteadiness of the jet flames increases with height, as noted from increasing RMS values of temperature. Consequently, the thermocouple is subjected to spatial fluctuations between the peak (reaction zone) and moderate (preheat zone) temperature regions of the flame. Thus, the time-averaged temperature decreases with height. With increasing Re, the peak flame temperature drops, accompanied by the increased profile widths. The flame stretch increases with Re due to increased flame wrinkling (curvature) and flow strain, consequently lowering the instantaneous flame temperature. The mean temperature further reduces due to spatial fluctuations of the flame and associated time-averaging, as discussed earlier.

Figure 9

 9 Figure 9 shows temperature profiles at select heights, along with the radial location of peak f v and corresponding temperature (T f pk v ). In Re 5000 flame, T f pk v drops from 1400 to 1200 K with height in a y range of 30 to 120 mm. Note, the T f pk v trend is opposite of the temperature-PAH correlation where the temperature corresponding to peak-PAH increased with height. In Re 7200 flame, T f pk v decreases similarly from 1400 to 1300 K when y increases from 60 to 120 mm. The y range for Re 7200 is different than the Re 5000 case to account for varying soot inception heights. The plot for Re 21500 flame is not shown since measurable f v and T are available only at y = 120 mm. In this turbulent flame, peak f v occurs around 1400 K (at y = 120 mm). Despite the variation of turbulence level (Re), T f pk v at soot inception regions is almost identical with a value of 1400 K. This optimum temperature is the result of a competition between soot formation and oxidation reactions. Soot formation is dominated by larger PAH, while oxidation is primarily influenced by OH [26]. In the vicinity of flame, soot reaction with diffused OH can reduce the soot concentration. Consequently, f v peaks away from the high-temperature regions of the reaction zone. The possible reasons for the decrease in T f pk v with height are discussed next. The peak flame temperature itself decreases with height due to the timeaveraging of unsteady flame, as discussed earlier. Apart from this, the nascent soot during inception may require higher temperatures to form. Conversely, at downstream locations, the soot growth is facilitated by surface reactions and transported PAH from upstream regions. The residence time also increases

  is obtained from time-averaging, while f v - P P S is quasi time-resolved (averaged over 0.1 s). Additionally, spatial resolutions of LII and PPS differ. The in-plane magnification of LII is \sim 0.2 mm, while the out-of-plane resolution is expected to be \sim 0.2 mm based on the laser-sheet thickness. The PPS resolution is five times coarser (1 mm) than LII. The larger probe volume and finer temporal resolution of PPS eliminate the soot intermittency effect as the soot is always present in the sample. Additionally, due to ex-situ nature of PPS, soot sam-ple may always be present in the sampling line. In contrast, significant soot intermittency is noted in spatially well-resolved LII measurements. Soot intermittency can lower f v - LII when averaged unconditionally[START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF][START_REF] Lee | Measurements of soot, OH, and PAH concentrations in turbulent ethylene/air jet flames[END_REF][START_REF] Crosland | Simultaneous instantaneous measurements of soot volume fraction, primary particle diameter, and aggregate size in turbulent buoyant diffusion flames[END_REF]. To isolate the effect of intermittency, the LII data can be conditionally averaged by considering samples only with the soot presence. The conditionally averaged peak axial f v - LII measures nearly 3 times (2.8, 3.1, and 3.5 for Re 5000, Re 7200, and Re 21500 respectively) as of the time-averaged one[START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]. This factor is quite close to the ratio of time-averaged LII to PPS measurements shown in Fig.11. The peak axial values of soot concentration from PPS and that of the conditionally averaged LII data are indeed in a reasonable (\pm 15%) agreement.Various sources of uncertainty in soot measurement are discussed next. Although assumed to be robust, uncertainty in LII can arise from the following sources. 1) Uncertainty in extinction-based LII calibration due to beam steering was verified to be insignificant. The mean f v value in a lifted ethylene flame (Re = 8700) with the present LII set-up was available to enable validation with a similar flame (Re = 10000) reported in[START_REF] K\"ohler | Sooting turbulent jet flame: characterization and quantitative soot measurements[END_REF][START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF]. The mean peak f v (0.56 ppm)

  propagation. Further investigation and quantification are difficult to pursue with the available data owing to the turbulent flow. The PPS data is primarily used to correct the SMPS results for probe blockage. This correction can be accomplished even with a relative soot concentration since only the particle size distribution is intended from SMPS than the absolute concentration. The PPS technique has not yet been widely used in the fundamental soot research community. The agreement (within \pm 15%) between f v - P P S and conditionally averaged f v - LII appears very promising, despite various uncertainty sources.

3. 4 . Soot particle size 3 . 4 . 1 .

 4341 Soot particle size distributionThe soot particle size distributions (PSDs) at different heights (y) are shown in Fig.12for Re 5000 flame. Both raw and blockage-corrected PSDs are shown.The geometric mean diameter (D g ) and standard deviation (\sigma g ) are evaluated for both the corrected (C) and uncorrected (U) PSDs. Data within the entire range (7 -290 nm) of SMPS scan duration (120 s) is considered to evaluate D g and \sigma g .In high-sooting regions (y = 310 mm), large difference exists between \sigma gC and \sigma gU accompanied by much lower D gC . This could be attributed to larger probe blockage with time. The data with orifice blockage > 95% at the end of SMPS scan duration (120 s) is marked by *. A high blockage can lead to uncertainties in correction, especially for larger soot size (> 60 nm). Therefore, the corrected data at y = 310 and 370 mm should be interpreted with caution.As an alternative to D g , a mode diameter (corresponding to the peak of PSD) can be evaluated. Note that the uncertainty in mode diameter (D m ) due to blockage correction is not significant due to shorter SMPS scan duration over the range of interest (23 s until 30 nm, and 75 s until 60 nm). D m could be evaluated within \pm 5% uncertainty from a given PSD.Soot PSDs forRe 7200 flame are shown in Fig. 13. The orifice blockage correction in unsteady (intermittent) flame-tip region (y = 525 and 580 mm) and low-sooting region (y = 75 mm) leads to increased fluctuations in PSD. On the other hand, the correction in a severe blockage case leads to high \sigma gC with lower D gC at y = 250, 310, and 370 mm. Similarly, PSDs for Re 21500 flame are shown in Fig. 14. At lower measurement stations (y = 75 and 150 mm), soot concentration (along the axis)

  D m shows a plateau until further downstream; afterward, D m decreases with height. The reduction in D m and f v is due to oxidation of soot (mainly by OH) near the flame-tip region. Recall that the f v - LII is timeaveraged, and thus, can be affected by soot intermittency. Since D m is the most probable value, it is less affected by soot intermittency. Conditionally averaged

  butane flames to be similar as of ethylene. Consequently, the D m /d p ratio of 1.5 suggests a mild soot aggregation in the present flame. To conclude definitively, complementary (d p , D m , R gy , N p , etc.) information is needed in an identical flame. Next, we compare the present D m trends with the mobility diameters reported by Chowdhury et al. [31]. The authors reported an axial variation of geometric mean diameter (D g ) based on SMPS in diluted turbulent ethylene flame. Note that D g and D m need not be identical. D g in the present flame is listed on respective PSD provided in Sec. 3.4.1. D g measures consistently higher than D m , typically 1.1 to 1.3 times as of D m . The orifice blockage correction may lead to uncertainties in D g estimation for high sooting cases, as noted in Sec. 3.4.1. Recall, for D g evaluation, data over the entire scan range (120 s duration) is needed. Conversely, D m evaluation requires data until peak probability, which corresponds to a smaller time delay (23 s until 30 nm scan).

  15b and 15c) corresponding D m is \sim 12 nm. In lifted flames, partial premixing is anticipated. The soot size appears to be highly sensitive to the local fuel concentration. Partial premixing can reduce the fuel pyrolysis, which in turn decreases the concentration of PAH needed for the soot growth. Nevertheless, the smaller D m in lifted flame (Re 7200, Fig.15b) grows to a peak value of 28 nm, which is the same as of Re 5000 attached flame. At Re 5000 and 7200, D m rises sharply after the inception, similar to the f v trend. In turbulent flame (Fig.15c), D m rise trend is almost identical as of f v . Peak D m measures 24 nm, which is slightly lower than Re 5000 flame (28 nm). Increased Re reduces the soot size marginally. With an increase in Re, the residence time and temperature decrease, while air/fuel mixing enhances, which combinedly leads to lower D m .

  Time-averaged flame temperature decreases with Re due to increased flamestretch and averaging in an unsteady flame. For a given Re, the mean flame temperature decreases with height. The temperature and OH peaks are nearly aligned; however, the temperature peak is biased towards the fuel-rich side of the flame. Soot-precursor (PAH) peaks at a much lower temperature (650 K) in the attached flame (Re 5000) than in the lifted flame (850 K in Re 7200). In turbulent lifted flame (Re 21500), peak-PAH occurs at a higher temperature (940 K). Partial premixing of air/fuel in the lifted flames can significantly increase the temperature required for PAH formation. The mean temperature at peak-f v location (T f pk v ) was measured in low-sooting regions. T f pk v decreases from 1400 to 1200 K with height in Re 5000 flame. At downstream locations, the soot growth may be facilitated by surface reactions and transported soot-precursors from upstream regions, and thus resulting in the lower T f pk v . Despite the variation in turbulence level (Re = 5000 -21500), peak f v at soot inception region occurs at a nearly constant value around 1400 K. The soot-temperature correlation is governed by the competition between soot formation through larger PAH and oxidation by OH near the reaction zone. These competing processes dictate the value of T f pk v which is found to be less sensitive to Re in the soot inception region. To obtain further insights into the soot-temperature correlation, time-resolved (i.e., high-speed) simultaneous measurements will be beneficial where one can account for a soot response delay owing to longer soot reaction timescales.A quasi-instantaneous (averaged over 0.1 s) f v - P P S deduced from the ex-situ PPS technique is in qualitative agreement with the in-situ time-averaged f v - LII . However, f v - P P S measures 2.4 to 2.8 times of f v - LII . This difference is primarily attributed to the time-averaging of f v - LII in an intermittent field. If the soot intermittency is accounted for by conditional averaging of f v - LII , a reasonable quantitative agreement (within \pm 15%) between f v - LII and f v - P P S is noted.The mode diameter (D m ) of soot particle peaks around the same axial region as the peak f v . D m at a moderate Re (5000 or 7200) varies between 12 - 28 nm, whereas at Re 21500 peak-D m decreases marginally to 24 nm. Turbulence can reduce the soot growth and aggregation owing to a reduced residence time, soot precursor concentration, and temperature. Although D m decreases with Re, soot particles are distributed over a wider size range, possibly due to reduced soot aggregation. D m in turbulent flame (Re 21500) measures nearly 1.5 times of the primary diameter reported in a turbulent ethylene flame[START_REF] Gu | Simultaneous measurements of gas temperature, soot volume fraction and primary particle diameter in a sooting lifted turbulent ethylene/air non-premixed flame[END_REF], suggesting a moderate soot aggregation in the present flame.

Figure 1 :

 1 Figure 1: Re 7200 flame: (a) without thermocouple, and (b) with thermocouple at y = 30 mm.

Figure 2 :

 2 Figure 2: Flame photographs: (a) Re 5000, (b) Re 7200, and (c) Re 21500. Temperature measurement stations are marked by magenta lines.

Figure 3 :

 3 Figure 3: Probe sampling set-up for SMPS and PPS measurements.

Figure 5 :

 5 Figure 5: PAH-LIF, Soot concentration, OH-LIF mean radial profiles: (a) Re 2100 at y = 100 mm, (b) Re 5000 at y = 100 mm, (c) Re 7200 at y = 100 mm, and (d) Re 21500 at y = 250 mm. The profiles are extracted from the data reported in[START_REF] Mulla | Comprehensive characterization of sooting butane jet flames, Part 1: soot, soot-precursor, and reaction zone[END_REF]

Figure 7 :

 7 Figure 7: Temperature (dashed line) and PAH-LIF (solid line) mean radial profiles: (a) Re 5000, (b) Re 7200, and (c) Re 21500. The legend shows axial y location (in mm).

Figure 8 :

 8 Figure 8: Temperature (dashed line) and fv (solid line) profiles in Re 7200 flame at: (a) y = 30 mm, (b) y = 50 mm, and (c) y = 120 mm.

Figure 9 :Figure 10 :

 910 Figure 9: Temperature profiles where open circles mark the temperature at peak soot concentration location for: (a) Re 5000, (b) Re 7200. Axial y locations (in mm) are indicated in the legend.

Figure 11 :

 11 Figure 11: Axial fv profiles from LII (line) and PPS (symbols): (a) Re 5000, (b) Re 7200, and (c) Re 21500.

Figure 12 :

 12 Figure 12: Soot PSDs at different heights (y in mm) along the burner axis in Re 5000 flame.

Figure 13 :

 13 Figure 13: Soot PSDs at different heights along the burner axis in Re 7200 flame. ( ) without blockage correction, ( ) with correction.

Figure 14 :

 14 Figure 14: Soot particle size distribution at different heights along the burner axis in Re 21500 flame. ( ) without blockage correction, ( ) with correction.

Figure 15 :

 15 Figure 15: Soot mode diameter Dm (symbols) and fv-LII (line) variation along the axis: (a) Re 5000, (b) Re 7200, and (c) Re 21500.

Table 1 :

 1 Temperature at peak PAH radial location at different y (mm).

Acknowledgments

The project (ASMAPE) was funded by the French National Research Agency (ANR) under contract no. ANR-13-TDMO-0002. Dr. I.A. Mulla acknowledges support through Marie Sk\l odowska-Curie Individual Fellowship (ID: 747576)

The legend shows axial y stations (in mm) as marked in Fig. 2.

(