Correction for particle loss in a regulatory aviation nvPM emissions system using measured particle size

To

To reduce the adverse impact of civil aviation on local air quality and human health, a new international standard for non-volatile Particulate Matter (nvPM) number and mass emissions was recently adopted.A system loss correction method, which accounts for the significant sizedependent particle loss, is also detailed to predict nvPM emissions representative of those at engine exit for emissions inventory purposes.As Particle-Size-Distribution (PSD) measurement is currently not prescribed, the existing loss correction method uses the nvPM number and mass measurements along with several assumptions to predict a PSD, resulting in significant uncertainty.
Three new system loss correction methodologies using measured PSD were developed and compared with the existing regulatory method using certification-like nvPM data reported by the Swiss and European nvPM reference systems for thirty-two civil turbofan engines representative of the current fleet.Additionally, the PSD statistics of three sizing instruments typically used in these systems (SMPS, DMS500 and EEPS) were compared on a generic aero-engine combustor rig.
General agreement between the three new PSD loss correction methods was observed, with both nvPM number-and mass-based system loss correction factors (k SL_num and k SL_mass ) within ±10% reported across the engines tested.By comparison, the existing regulatory method was seen to underpredict k SL_num by up to 67% and overpredict k SL_mass by up to 49% when compared with the measured-PSD-based methods, typically driven by low nvPM mass concentrations and small particle size.In terms of the particle sizing instrument inter-comparison, an agreement of ±2 nm for the GMD and ±0.08 for the GSD was observed across a range of particle sizes on the combustor rig.However, it was seen that these differences can result in a 19% bias for k SL_num and 8% for k SL_mass for the measured-PSD-based methods, highlighting the need for further work towards the standardisation of PSD measurement for regulatory purposes.

Introduction
Combustion-generated pollutants have been increasingly studied and regulated owing to their adverse health and climate impacts, with the aviation sector globally contributing to ~3.5% of effective radiative forcing (Lee et al., 2021).While the effect of combustion-generated gases on health and the environment is well established, the impact of particulate matter (PM) is less known (Bendtsen et al., 2021).Adverse health effect of particles is strongly linked to their size, with the relatively small PM emitted by aviation gas turbine engines (mean electrical mobility diameter typically between 15 and 40 nm (Boies et al., 2015;Delhaye et al., 2017;Durand et al., 2021;Durdina et al., 2019)) capable of penetrating deep into the lungs and reaching the systemic circulation (Bendtsen et al., 2021;Jonsdottir et al., 2019).
In response to the aforementioned concerns, a non-volatile PM (nvPM) certification requirement and emissions standard was adopted by the International Civil Aviation Organization (ICAO) for civil aviation turbofan and turbojet engines with rated thrust >26.7 kN (ICAO, 2017), replacing the legacy smoke number standard.In the standard, nvPM are defined as particles present at the aircraft engine exit plane which do not volatilise when heated to 350 • C. To afford traceable and repeatable measurement of nvPM in various sized engine testing facilities, a long (~30-35m) standardised sampling and measurement system is prescribed, which samples exhaust directly at the aircraft Engine Exit Plane (EEP) before diluting, cooling and conditioning (SAE International, 2020, 2021).This, combined with the small size of nvPM emitted from commercial aircraft engines, results in significant particle loss prior to measurement, up to 50% for nvPM mass and 90% for nvPM number (SAE International, 2019).
Accurate particle loss correction is therefore critical for predicting nvPM emissions at the source (i.e., EEP) relevant for modelling and air quality emission inventories, and improving combustion technologies, even if currently not required for engine nvPM emissions certification.Hence, a system particle loss correction methodology was recently added to the ICAO Annex 16 vol II (ICAO, 2017).However, particle loss is known to be size-dependent, and particle size measurement is not currently prescribed.Therefore, the current system loss correction methodology requires the use of the reported nvPM number and mass, along with several limiting assumptions, to derive a particle size distribution (PSD) and associated losses, which results in uncertainty in the reported EEP nvPM emissions available in the ICAO Engine Emissions Databank (EEDB, 2021).Limited studies report EEP nvPM concentrations (i.e., fully corrected for system loss) and these employ different correction methodologies (Corbin et al., 2022;Durdina et al., 2021;Harper et al., 2022;Saffaripour et al., 2019).Particle size measurement is currently not prescribed in the aerospace regulatory standard due to issues associated with the definition of and traceable measurement of nvPM size.The impact of the representativeness of the fractal nvPM witnessed in gas turbine exhaust, along with a lack of standard measurement and calibration practices for size instruments, therefore need further investigation.However, fast-sizing instrument capabilities have significantly improved in the last decades, with PSD becoming critical engineering information for combustor design and environmental impact assessment.PSD measurement can also facilitate system loss correction, reducing uncertainties compared to the existing system loss method which requires several assumptions (e.g., particle density, lognormality, GSD) and uses nvPM mass and number measurements as input.Recently, three commercially available size spectrometers have been demonstrated on ICAO compliant nvPM systems (Durand et al., 2021;Kinsey et al., 2021;Xue et al., 2015), namely: the scanning mobility particle sizer (SMPS, TSI Inc.), the differential mobility spectrometer (DMS500, Cambustion Ltd) and the engine exhaust particle sizer (EEPS, TSI inc.), all reporting size as electrical mobility diameters, which is typically used for theoretical particle penetration efficiency calculation (Baron et al., 2011;Durand et al., 2020).Other real-time particle size measurement instruments measuring in aerodynamic space are available (ELPI, Dekati Ltd.; APS, TSI Inc.; AMS, Aerodyne Research Inc.), with the aerodynamic diameter being a more relevant parameter for assessing the impact of PM on health (D.Kittelson, Khalek, et al., 2022).Few studies have compared the sizing performance of particle size instruments for combustion aerosol (Xue et al., 2015;Zimmerman et al., 2014).

Symbol
In this study, the uncertainty associated with particle size measurement of two Cambustion DMS500, a TSI EEPS, and a TSI SMPS was assessed using aviation-like nvPM from a Rich-burn, Quick-mix, Lean-burn (RQL) generic combustor rig.Measured PSD was then used to develop three system loss correction methodologies deemed suitable for nvPM regulatory systems.The three measured-PSDbased system loss correction methodologies were subsequently assessed and compared with the currently prescribed system loss method using certification-like nvPM emissions data collected by the European (EUR) and Swiss (CH) nvPM reference systems covering thirty-two gas turbine engines from seven engine manufacturers, with rated thrusts from <26.7 kN (business aviation) to >300 kN (long haul) hence representative of the current commercial fleet.Finally, the impact of PSD measurement uncertainty on the measured-PSD-based system loss correction methodologies was evaluated.

Experimental nvPM data collection
This study compiles novel experimental nvPM datasets, collected over five years of emissions testing by the European (EUR) and Swiss (CH) nvPM reference systems, which were operated in compliance with both the ICAO standard (ICAO, 2017) and SAE ARP 6320 (SAE International, 2021) during full-scale engine and combustor rig testing.Further details of the two compliant systems are detailed in the literature (Crayford et al., 2014;Lobo et al., 2015Lobo et al., , 2020)).
To enable this study, additional PSD measurements were undertaken during all testing opportunities providing PSD statistics required for system loss correction, namely the statistical Geometric Mean Diameter (GMD), Geometric Standard Deviation (GSD) and PSD shape.During all certification-like engine testing data reported in this study, a Cambustion Differential Mobility Spectrometer (DMS500) measuring from 5 to 1000 nm was employed with the EU nvPM reference system and a TSI Scanning Mobility Particle Sizer (SMPS) composed of a long Differential Mobility Analyser (DMA) model 3081A, a bipolar Kr-85 charger model 3077A and a TSI 3776 Condensation Particle Counter (CPC) configured to measure typically from 7.9 to 242 nm was employed with the CH nvPM reference systems.
To first provide confidence in comparing PSDs reported from the two reference systems, a wider particle size instrument intercomparison was undertaken as part of the EU CleanSky2 RAPTOR programme.Four particle size instruments were employed, namely: two DMS500s (one from the EU nvPM reference system and one from the National Research Council Canada, respectively labelled DMS 1 and DMS 2 from here on), a loaned TSI EEPS (model 3090) measuring from 5.6 to 560 nm, and the TSI SMPS (model 3938) from the CH nvPM reference system.
The three instrument technologies are based on the same principle of particle charge to drag ratio with all instruments reporting particle size distributions in equivalent electrical mobility space.The DMS500 and EEPS are fast scanning analysers (up to 10 Hz), allowing for transient measurements.They require a mathematical model (i.e., a calibration matrix) to correct for their unipolar charging efficiency and to convert the measured electric current from charged particles hitting their electrometers into a PSD.The SMPS also requires a complex data inversion to determine the PSD, but unlike the fast analysers, it employs bipolar charging and the PSD is based on the CPC-counted monodisperse aerosol downstream of the DMA ("ISO 15900:2009("ISO 15900: " 2014)).The SMPS scans were typically 30-45 s, including retrace and purge time.
The two DMS500s were processed using the monomodal aggregate inversion matrix generated with mini-CAST soot, while the EEPS was processed using the compact inversion matrix generated using spherical particles, as there is no soot calibration matrix representative of gas turbine soot provided by TSI for this instrument.A diesel soot inversion matrix was available for the EEPS, but it was deemed less representative of aviation nvPM than spherical particles given diesel soot is relatively larger and more aggregated E. Durand et al. than aviation PM (Baron et al., 2011;Dastanpour & Rogak, 2014).The SMPS was processed using the multiple charge and diffusion corrections.Additionally, to allow a direct comparison of the total number concentration, the SMPS and the EEPS were corrected to Standard Temperature and Pressure (STP).It is noted that some of the particle size data (DMS 1 and EEPS) used in this research was taken outside of the 12-month service and calibration period recommended by the respective instrument manufacturers.
A schematic representation of the particle size intercomparison experiment is depicted in Fig. 1.The DMS500s, EEPS and SMPS sampled exhaust from Cardiff University's Gas Turbine Research Centre's high pressure RQL combustor rig, described in detail elsewhere (Harper et al., 2022), operating at different air-to-fuel-ratios (AFR) with two fuels, namely: a high sooting conventional Jet-A and a low sooting Fischer Tropsch (FT) Gas-To-Liquid (GTL) JET-A (75:25) blend.The exhaust sample was first diluted by a PALAS VKL-10ED to provide the required flow, suppress condensation, and ensure good mixing before being split using a flow splitter (Grimm model 5483) used without the critical orifice to minimise the pressure drop.The flow splitter was connected to the size instruments using 3/8 ′′ inner diameter electrically conductive silicone tubing made as short as practicable (<1 m), with particle losses to the different instruments virtually identical.A total of six 1-min-long test points (each equivalent to two SMPS scans) at a stable condition were performed, with measured GMD between 24 and 42 nm and including one repeat point at a given condition to showcase rig stability and repeatability, as discussed in section 3.1.
Following the assessment of the relative agreement of the size instruments, previously collected data by the EUR and CH regulatory sampling and measurement systems were re-assessed to specifically look at the applicability of measured-PSD-based system loss correction compared to the currently defined methodology.A schematic representation highlighting the general layout of the compliant sampling systems when deployed independently at certification-like engine tests is shown in Fig. 2a.As shown, additional PSD measurement was made on an ancillary sampling port near the nvPM number Aerosol Particle Counter (AVL APC) and mass (AVL MSS or Artium Technologies LII300) instruments.
Finally, to assess the uncertainty associated with PSD instrument model and sampling location, data obtained during parallel testing of the EUR and CH nvPM reference systems was assessed, with details of the experimental setup and locations of PSD instruments highlighted in Fig. 2b.Again, the high pressure RQL combustor rig was utilised, operating at different AFRs on numerous aviation fuels to offer a wide range of particle GMDs and concentrations, as discussed in detail elsewhere (Harper et al., 2022).As can be seen, the DMS 2 was located either near the inlet-probe (position L1), sampling undiluted exhaust, or at the vent of the diluter (position L2) on the EUR nvPM reference system, while the SMPS was either sampling from the diluter vent (position L2) or near the nvPM instruments (position L3) on the CH nvPM reference system.This setup afforded real-time measurement of particle loss in the full sampling system by comparing the PSDs of DMS 1 and DMS 2 as discussed in the Supplementary Information.It is noted that only the DMS500 was used to sample near the probe inlet, as the SMPS and EEPS could not handle the harsh conditions of the hot undiluted sample.Results detailing the impact of instrument type and location on system loss uncertainty are presented in section 3.3.

Description of system loss correction methodologies 2.2.1. General description of system loss correction calculation
Four system loss corrections methodologies calculating the nvPM number and mass correction factors (k SL_num and k SL_mass ), required to predict EEP-representative concentrations from those measured using a regulatory nvPM sampling system, are discussed in this study.Firstly, the currently prescribed method as defined in ARP 6481 (SAE International, 2019) and labelled in this work as method R N/M as described in section 2.2.3, and three measured-PSD-based methodologies, labelled PSD L1 , PSD L2 and PSD B which are further discussed in section 2.2.4.
For all four methods, k SL_num and k SL_mass are calculated in three steps as follows: (a) the penetration efficiency to the nvPM number and mass instruments is calculated using the particle transport model as described in section 2.2.2;(b) a PSD is predicted at the EEP differently depending on the method; (c) k SL_num and k SL_mass are calculated by dividing the EEP PSD to the PSD at the instrument between 10 and 242 nm using equation (1).To calculate k SL_mass , the PSDs are converted into mass-space using equation (2).It is noted that for all particle-size-measurement methods, the particle effective density term cancels itself when calculating k SL and therefore isn't required.
The lower 10 nm size bound was selected for k SL_num in line with the regulatory method measurement given that the number counter must have a minimum 50% counting efficiency at 10 nm and that uncertainty increases significantly for particles <10 nm (SAE International, 2019) as highlighted by the near-zero penetration efficiency <10 nm in Fig. 3.The 242 nm upper size bound was selected to ensure comparability between the different size instruments, given the upper size limit of the SMPS of 242 nm used in this With D p the particle size (i.e., size bin from the distribution) and ρ eff the particle effective density (mass/volume of a sphere with same mobility diameter as fractal nvPM particle).

Penetration efficiency calculation
All system loss correction methodologies discussed in this study use the United Technologies Research Center (UTRC) particle transport model, published with the SAE E− 31 Aerospace Information Report AIR6241 (SAE International, 2020) and described in the AIR6504 (SAE International, 2022), to calculate the penetration efficiency from the sampling system inlet (i.e., EEP) to a given instrument.The UTRC model predicts particle penetration efficiency by combining gas and particle properties to flow characteristics through user-defined sampling system segments.Particle loss is modelled using equations derived from the literature describing the main deposition mechanisms of ultrafine aircraft nvPM, namely in order of importance diffusional, thermophoretic, inertial, electrostatic and bend loss.Further details of the model and loss mechanisms are discussed in depth elsewhere (Baron et al., 2011;Durand et al., 2020;Hinds, 1998).Experimental validation of the UTRC model on a regulatory-compliant system has been previously demonstrated (D.B. Kittelson, Khalek, et al., 2022;Durand et al., 2020), but only for parts of the system and specific loss mechanisms.Further validation of the UTRC model for a full nvPM regulatory system is provided in the supplementary information.Additional volatile particle remover (VPR) loss corrections are required for the nvPM number instrument penetration due to thermophoresis and diffusion and CPC counting efficiency, as discussed further in ARP6481 (SAE International, 2019).
Typical penetration efficiencies to the nvPM number, mass, and size instruments in a regulatory nvPM sampling system are shown in Fig. 3 for visual aid, with losses <100 nm dominated by diffusion, losses >500 nm caused by the 1 μm cyclone (used to remove large particles shed from the walls).The higher losses witnessed for the nvPM number instrument are due to the additional thermophoretic loss in the prescribed VPR.Some assumptions were required for the penetration efficiency calculation in this analysis: the penetration efficiency to the number instruments used for k SL_num were calculated using averaged annual calibration data performed by the manufacturer (AVL) post 2018 (three calibrations for the Swiss APC and one calibration for the EUR APC).The AVL calibration certification procedure was updated in 2019, the date from which an additional catalytic stripper after the CAST aerosol source was employed for the VPR penetration efficiency test.It is thought this resulted in higher reported penetration of the smallest particles after this modification, as the semivolatile soot that would have previously shrunk in the VPR was being removed by the additional catalytic stripper instead.Additionally, since 2019 the calibration of the CPC embedded in the APC has been performed by AVL rather than being performed by TSI, which resulted in slightly different reported counting efficiency at 10 nm due to the different setups and procedures being used by the two calibration laboratories.Additionally, the penetration efficiency in the collection section (i.e., probe inlet to diluter inlet in Fig. 2) used for k SL_num and k SL_mass was calculated for the worst-case scenario corresponding to when the pressure at the inlet of diluter is below ambient and the spill is shut (i.e., flowrate in collection section of ~15 slpm).In practice, the flowrate in the collection section is often higher when sampling high thrust/pressure conditions, however it is noted this has a small impact on the full system penetration efficiency (<2%).

Description of the regulatory method (method R N/M )
The currently prescribed system loss correction method labelled R N/M (regulatory number to mass ratio) uses the measured nvPM number and mass concentration as inputs to predict a PSD at the EEP and system loss correction factors.It generates a PSD at the EEP by minimising the square of the relative difference (δ method R N/M ) between the measured and calculated particle number to mass concentration (N/M) ratio, as shown in equations ( 3) and ( 4) and described in detail in the ARP 6481 1 (SAE International, 2019) and the AIR 6504 1 (SAE International, 2022).It requires several assumptions, the main ones being a particle effective density of 1 g/cm 3 , mono-modality and lognormality at the EEP, and a GSD of 1.8.
Where η num/mass is the penetration efficiency to the number/mass instruments, k thermo is the size-independent thermophoretic loss correction factor in the collection section of a regulatory system, DF 1 is the dilution factor in diluter, DF 2 is the second stage (VPR) dilution factor in the number instrument, and nvPM num/mass STP is the measured nvPM number and mass at STP conditions (0 • C and 101.325 kPa).
It is noted that while there is no fundamental basis for aerosols to have a lognormal distribution, the various stochastic aspects to condensational growth and coagulation in single-source particle formation processes typically result in a distribution close to lognormal (Seinfeld & Pandis, 2016).Furthermore, the mathematical form of a lognormal distribution is mathematically convenient for describing aerosols (Baron et al., 2011).However, some deviations from lognormality can be observed in traditional RQL aircraft engines (Durand, 2019), where soot is produced and grown in the combustor rich zone, followed by consumption in the mixing and lean zones.

Description of size-measurement-based methods (methods PSD L1 , PSD L2 and PSD B )
Three system loss correction methodologies requiring a PSD measurement as an input were developed and are presented, with the Matlab® script detailing these available with the supplementary information.The first method PSD L1 (particle size distribution one lognormal) minimises the square of the relative difference between the measured PSD and a mono-modal lognormal PSD at the EEP scaled to the penetration efficiency to the size instrument, as per equation (5).A limitation with methods R N/M and PSD L1 is that they only use one lognormal mode at the EEP, making them both unsuitable to deal with bi-modal distributions and monomodal distributions significantly deviating from a lognormal shape.Therefore, a second method PSD L2 was designed to operate similarly to method PSD L1 ; however, it fits the measured PSD with two lognormal distributions at the EEP, allowing it to effectively predict EEP PSDs in the case of bi-modal and non-lognormal monomodal distributions (see illustrative example in Fig. S6 in supplementary information).Fig. 3. Example of penetration efficiency to the nvPM number (η nvPM number ), mass (η nvPM mass ) and size (η size ) instruments in a typical regulatory standard sampling and measurement system estimated using the UTRC model.
1 An Excel® spreadsheet system loss tool is supplied with ARP 6481 while both the Excel® and a Matlab® system loss tools are provided with AIR 6504.

E. Durand et al.
Finally, a third method PSD B (particle size distribution bin-by-bin) was developed which doesn't require any fitting.Instead, it directly uses the measured PSD and divides the concentrations in each non-zero size bin by the penetration to the size instrument, as per equation (6).A similar method is used by Cambustion Ltd to correct for particle loss in their catalytic stripper (Cambustion Ltd, 2016, p. Appendix A).
Where N tot (total number concentration), GMD and GSD are the three variables of a lognormal distribution, and η size is the penetration efficiency to the size instruments.
Finally, once the EEP PSD is generated, the three measured-PSD-based methods calculate k SL_num and k SL_mass similarly to method R N/M by dividing the sum of the EEP PSD by the sum of the PSD at the nvPM number or mass instrument, as per equation (1).

Particle size instrument intercomparison
The PSDs of the two DMS500s, an EEPS, and a SMPS simultaneously sampling RQL rig combustion exhaust are presented in Fig. 4, with shapes appearing to closely overlap, although the magnitude (i.e., total number concentration) differs slightly.A small inflection can be observed at ~30 nm for the DMS 2 for test points 3 to 5, thought to originate from the calibration uncertainty of the DMS at this size where the singly charged to doubly charged particle split occurs.The corresponding mass-space particle size distributions (i.e., MSD) are also discussed with Fig. S3 in the supplementary information.
Analysis of the PSDs highlighted that the GMD agreed within ±2 nm (i.e., ±5% of the average) and the GSD within ±0.08 (i.e., ±5% of the average) across the size ranges measured, as shown in Fig. 5. DMS 2 typically reported the largest GMD and GSD, while DMS 1 reported the smallest GMD and the EEPS reported the smallest GSD.This witnessed uncertainty in reported PSD is in agreement with literature (Corbin et al., 2022;Xue et al., 2015) and better than the certified accuracy provided by the manufacturers for the fast-scanning instruments (±10% of size standard).This is promising for regulatory use, given that each instrument type was calibrated on a different source using a different protocol as discussed in section 2.1.
It is noted that this analysis is limited to only six test points on RQL combustor exhaust with the GMD ranging from 24 to 42 nm; hence wider disagreement may be observed across larger GMDs and on alternative combustion sources.It is suggested that to get even better closure between the size instruments for aviation gas turbine exhaust measurement, standard measurement and calibration procedures should be adopted as is currently prescribed for aircraft engine nvPM number and mass emission measurements.

Aircraft nvPM system loss correction methodologies 3.2.1. Comparison between regulatory and measured-PSD-based system loss correction methods
The nvPM number (k SL_num ) and mass (k SL_mass ) system loss correction factors for certification-like gas turbine emission testing calculated using method R N/M , and methods PSD L1, PSD L2, and PSD B are presented in Fig. 6.Both k SL_num and k SL_mass increased with decreasing GMD due to the larger diffusional loss at small sizes and ranged between 1.6 -7.8 and 1.06-2.5,respectively.As can be seen, the three measured-PSD-based methods closely correlated with one another, while method R N/M was more scattered, particularly <25 nm GMD, corresponding to relatively lower measured nvPM mass ~<10 μg/m 3 .This increased scatter is thought to originate from the uncertainty associated with nvPM mass measurement approaching an estimated LOQ of 3 μg/m 3 (SAE International, 2019) coupled with shedding events of large particles (>250 nm) re-entrained from the collection cup of the 1-μm cyclone ("RAPTOR Project Library" 2022, p. WP4) prescribed in a regulatory measurement system.
The ratio between method PSD B and the other system loss correction methods was subsequently calculated.Method PSD B was chosen as the reference method, given it is the one requiring the least assumption, directly using the measured PSD.The ratio between method R N/M and method PSD B was on average 0.97 ± 0.16 for k SL_num (ranges between 0.33 and 1.30 in Fig. 7a) and 1.04 ± 0.08 for k SL_mass (ranges between 0.67 and 1.49 in Fig. 8a).While the average agreement between the two methods is good, it can again be seen that method R N/M can significantly underpredict k SL_num and either underpredict or overpredict k SL_mass at measured GMD <25 nm (i.e., measured nvPM mass ~<10 μg/m 3 ).Generally, the current regulatory prescribed method (method R N/M ) can be assumed to have an uncertainty of up to 67% for k SL_num and 49% for k SL_mass when compared with method PSD B .This difference is driven by the assumptions required (section 2.2.3) and the uncertainty associated with the input nvPM number and mass parameters (Lobo et al., 2020).
A better agreement is witnessed between measured-PSD-based methods, with a ratio of method PSD L1 to method PSD B of 1.00 ± 0.03 for k SL_num (scatters between 0.95 and 1.25 in Fig. 7b) and 0.99 ± 0.03 for k SL_mass (scatters between 0.81 and 1.19 in Fig. 8b) although two outliers (outside of the ±20% shaded area) are still present, thought to originate due to significant deviations from lognormality.The best agreement is between method PSD L2 and method PSD B with a ratio of 1.00 ± 0.01 for k SL_num (scatters between 0.94 and 1.09 in Fig. 7c) and 1.00 ± 0.02 for k SL_mass (scatters between 0.90 and 1.10 in Fig. 8c) with no outliers observed from the fit.
It is noted that using a consistent particle size range and resolution (e.g., 10-242 nm) was critical to allow meaningful comparison of the different system loss correction methods, given the particle size instruments measured different size ranges and resolutions affecting method PSD B , with artifacts appearing <10 nm and >300 nm for some instruments, as discussed in the supplementary

Potential improvements of the regulatory method
Given the limitations associated with the required assumptions, in an attempt to reduce the uncertainty associated with method R N/ M, k sl outputs were predicted by replacing the fixed GSD (1.8) and density (ρ eff = 1 g/cm 3 ) assumptions with more representative correlations.The GSD was correlated to the input nvPM N/M using the gas turbine certification-like dataset as shown in Fig. S5 in the supplementary information, and a size-dependent particle effective density derived from the literature (ρ eff = 0.51 × (GMD/100) − 0.52 ) (Olfert & Rogak, 2019).The impact of the improved assumptions was assessed by comparing k SL_num from the improved method R N/M with the reference method PSD B , as presented in Fig. 9.It was found when comparing Fig. 9 with Fig. 8a that better GSD and particle effective density assumptions did not appear to improve k SL_num correlations between method R N/M "improved" and method PSD B , with an average ratio of 0.87 ± 0.14 (range from 0.3 to 1.23) observed.This further supports the hypothesis that method R N/M uncertainty is highly influenced by the nvPM number and mass measurement uncertainty ~<10 μg/m 3 , and that a single particle effective density assumption is not suitable, given particle density is engine type and power dependent (Durdina et al., 2014).

Impact of particle size measurement uncertainty on novel system loss corrections
To better understand the potential benefits of the measured-PSD-based system loss correction methods (PSD L1 , PSD L2 and PSD B ), the uncertainty associated with PSD measurement introduced by different instruments and sampling locations was investigated on k SL .As shown in Fig. 2b, the SMPS, EEPS and DMS500s were positioned at different locations of the EUR and CH regulatory sampling systems during RQL combustor rig testing.

Particle size instrument model uncertainty on measured-PSD-based k SL
The uncertainty arising from the particle size instrument model (DMS 1, DMS 2, SMPS and EEPS) on the k SL_num and k SL_mass derived from method PSD L1 , PSD L2 and PSD B was assessed using the size instrument comparison data (section 3.1), with the results shown in Figs. 10 and 11.To ensure comparability, the same system dimensions to the nvPM number and mass instruments were used to calculate k SL with the various PSD input from the different instruments used to predict the EEP PSD as discussed in section 2.2.1.It was seen that the bias introduced by the size instrument model on reported k SL was dependent on the specific method being used, with k SL_num differences constrained within ±4% for method PSD L1 (Fig. 10a) and PSD L2 (Fig. 10b), and mostly constrained within ±5% for method PSD B (Fig. 10c).Generally, DMS 1 reported the largest k SL_num , whilst the SMPS reported the smallest.This is thought to stem from the fact that DMS 1 measured the highest concentration of particle <20 nm where losses are the highest, in contrast to the SMPS (see Fig. 4).For k SL_mass , the agreement was generally better, with differences constrained within ±4% for method PSD L1 (Fig. 11a), ±3% for PSD L2 (Fig. 11b) and ±2% witnessed for method PSD B (Fig. 11c).It is noted that the quoted differences are defined as the difference between maximum and minimum k SL divided by the average.

Particle size instrument location uncertainty on measured-PSD-based k SL
The impact of the particle size instrument location on system loss correction was assessed by placing the same size measurement instruments at various locations along the respective reference nvPM sampling systems during RQL rig emission testing.Positioning the size instrument nearer to the probe inlet results in lower particle loss to the instrument, meaning more particles are counted by the instrument, and hence less corrections are required to predict an EEP PSD.DMS 2 and SMPS were alternatively located near the probe, at the diluter vent, and near the nvPM number/mass instruments (respectively (L1), (L2) and (L3) in Fig. 2b).Again, to ensure comparability, the same system dimensions to the nvPM number and mass instruments were used to calculate k SL with the various PSD input measured at different locations used to predict the EEP PSD as discussed in section 2.2.1.
The results are presented in Fig. 12 using PSD B , where both k SL_num and k SL_mass follow the same trend regardless of the size instrument location, with similar results observed with methods PSD L1 and PSD L2 .This result suggests that the particle size instrument location in a regulatory system does not significantly impact measured-PSD derived k SL uncertainty, further validating the UTRC model as adequate to correct for theoretical sampling loss.

Cumulated particle size measurement uncertainty on measured-PSD-based k SL
The cumulated impact of the particle size instrument model (DMS500, EEPS or SMPS), the particle size measurement location (L1, Fig. 10.Ratio of nvPM number system loss correction factor calculated using method PSD L1 (a), PSD L2 (b) and PSD B (c) to the average plotted against the correspoding system loss correction factor using PSD data from the particle size instrument intercomparison experiment.
E. Durand et al.L2, L3 in Fig. 2b) and the sampling system used (CH, EUR) was subsequently assessed for PSD B using a large dataset collected during RQL rig emission testing, with the results presented in Fig. 13.Again, to ensure system loss correction factor comparability, the same system dimensions to the nvPM number and mass instruments were used to calculate k SL with the various PSD input measured using different instruments at different locations used to predict the EEP PSD as discussed in section 2.2.1.Both k SL_num and k SL_mass were seen to follow the same decreasing trend with increasing GMD regardless of the PSD measurement, brought about as diffusional losses reduce for larger particles.However, a vertical scatter is observed corresponding to the PSD measurement uncertainty on k SL .For a given test point (i.e., GMD), differences of up to 19% were reported for k SL_num (9.5% average difference) and up to 7.7% for k SL_mass (2.4% average difference).The SMPS again generally reported the smallest k SL_num while the EEPS typically reported the largest k SL_num and k SL_mass , suggesting the EEPS measured more of the smaller (<15 nm) and larger (>100 nm) particles when compared with the other size instruments.
In comparison, the difference for the different regulatory systems (CH or EUR) using method R N/M was up to 20.3% for k SL_num (4.2% average difference) and up to 9.1% for k SL_mass (0.6% average difference) for the same dataset.This finding suggests that the impact of current PSD measurement uncertainty on the measured-PSD-based system loss correction methods is marginally smaller than current nvPM number and mass measurement uncertainties.

Summary and conclusions
Four methodologies to correct for particle loss in an ICAO regulatory nvPM system were assessed to predict emissions representative of those at engine exit (EEP), namely the current regulatory method (R N/M ) and three measured-PSD-based methods (PSD L1 , PSD L2 and PSD B ). Data collected by the EUR and CH nvPM systems, including additional PSD measurement, and covering thirty-two gas turbine engines representative of the current commercial fleet, were used for this analysis.
To first provide confidence in using measured PSD for system loss correction, four particle size measurement instruments (two Cambustion DMS500s, one TSI EEPS and one TSI SMPS) were compared on nvPM from a generic aero engine RQL combustor.The Fig. 11.Ratio of nvPM mass system loss correction factor calculated using method PSD L1 (a), PSD L2 (b) and PSD B (c) to the average plotted against the correspoding system loss correction factor using PSD data from the particle size instrument intercomparison experiment.measured GMD for the different instruments was found to agree within ±2 nm and the GSD within ±0.08 (i.e., ±5%) for particle size distributions typical of aircraft nvPM, demonstrating that these instruments were suitable for measuring aircraft nvPM in a regulatory system.
In the absence of prescribed PSD measurement, method R N/M has been shown to perform relatively well in predicting k SL_num and k SL_mass (i.e., ±20% of measured-PSD-based method) at GMD >25 nm, corresponding to measured nvPM mass >10 μg/m 3 .However, k SL uncertainty with method R N/M increased for measured GMD <25 nm when the prescribed nvPM mass measurement approached LOQ, with k SL_num underpredicted by up to 67% and k SL_mass overpredicted by up to 49% when compared with the reference method PSD B .This is particularly relevant as modern engine technologies and sustainable aviation fuel (SAF) with higher hydrogen content will drive nvPM emissions to be lower in mass and number concentrations and smaller in size, increasing the need for a measured PSD.Also, it was found that method R N/M could not be meaningfully improved with more representative GSD and particle effective density.The three measured-PSD-based methods agreed to within ±10% for both k SL_num and k SL_mass , with each method having specific advantages and disadvantages.Method PSD L1 assumes a single lognormal mode and therefore is not suitable for non-lognormal and multimodal distributions.However, assuming a lognormal distribution minimises the uncertainty associated with the measured PSD shape which can be impacted by the calibration matrix for fast-scanning instruments.Also, given that method PSD L1 fits the measured PSD, it can calculate system loss correction factors for any given particle size range and resolution.Method PSD L2 has the same advantages as method PSD L1 (i.e., user-defined size range and resolution) and can also resolve non-lognormal and multimodal distributions with greater accuracy, and has better closure with method PSD B , as it can fit two lognormal modes.It is noted that this method could easily be adjusted to include more than two lognormal modes should they be required in the future.Method PSD B is more straightforward than methods PSD L1 and PSD L2 as it does not fit the measured PSD and does not assume lognormality.Instead, the measured PSD scaled by the system penetration function is directly used.Both the main advantage and inconvenience of this method is therefore that it solely relies on the measured PSD and that the size range and resolution is fixed by the input PSD.If the PSD measurement is highly accurate and performed at the full relevant size range, then method PSD B may be considered the best available system loss correction methodology.However, PSD measurement uncertainty can strongly impact its prediction, particularly at the bounds of the measured PSD given the relatively higher losses for the smallest (<20 nm) and largest (>300 nm) particles in a regulatory system.
Overall, method PSD L2 is recommended for system loss correction given it can resolve multimodal and non-lognormal distributions (unlike method PSD L1 ) and can be calculated for any user-input size range and resolution (unlike method PSD B ).It is noted that measured PSDs from the nvPM datasets used in this analysis were generally monomodal and near lognormal.However, the capability of solving more than one mode will be critical with future technologies (e.g., lean burn), sustainable aviation fuels, and towards total PM regulation (volatile and non-volatile modes).It is also noted that it was critical to use a consistent size range (10-242 nm in this analysis) to permit meaningful comparison of the different system loss correction methods, given the size instruments measured PSDs at different size ranges and resolutions, with artifacts sometimes appearing <10 nm and >300 nm when corrected to the EEP.
Finally, to better understand the potential benefits of the measured-PSD-based loss correction methods, the uncertainty associated with PSD measurement introduced by different size instruments and sampling locations within a regulatory nvPM system was investigated.It was found that the particle size instrument model, the measurement location, and the reference sampling system being used were responsible for a bias of up to ~19% for k SL_num and ~8% for k SL_mass .It is recommended that standard calibration and measurement procedures should be adopted for particle size measurement to further reduce the uncertainty associated with system loss correction.
This study demonstrates that adopting measured-PSD-based system loss correction methods would reduce uncertainty for engineexit-representative nvPM number and mass emissions of aircraft gas turbine engines, resulting in improved modelling and characterisation potential to assess the impact of nvPM emissions on the environment and local air quality.The particle loss correction methodologies discussed in this manuscript can also be applied to any sampling system equipped with PSD measurement.

Fig. 4 .
Fig. 4. Measured PSDs (in number counting space) from different instruments for different test points (a-f) during the particle size instrument intercomparison experiment.

Fig. 5 .
Fig. 5. Ratio of statistical GMD (a) and GSD (b) to the average plotted against measured GMD/GSD for the six test points taken during the particle size instrument intercomparison experiment.

Fig. 6 .
Fig. 6. nvPM number (a) and mass (b) system loss correction factors plotted against measured statistical GMD using different methods (squares represent EUR data, circles represent CH data, filled symbols represent data with measured nvPM mass >10 μg/m 3 and open symbols represent data with measured nvPM mass <10 μg/m 3 ).

Fig. 7 .Fig. 8 .
Fig. 7. nvPM number system loss correction factor for method R N/M (a), method PSD L1 (b) and method PSD L2 plotted against the reference method PSD B with measured nvPM mass colour mapping.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 12 .
Fig. 12. nvPM number and mass calculated using method PSD B with (a) DMS 2 at locations L1 and L2, and (b) SMPS at locations L2 and L3 plotted against measured statistical GMD.

Fig. 13 .
Fig. 13.nvPM number (a) and mass (b) system loss correction factors calculated using method PSD B with various PSD measurements (different models, locations and sampling systems) during the RQL testing plotted against statistical GMD of the measured PSD (Red edges symbols = EUR system data; Black edges symbols = CH system data; symbols with dots in the centre = PSD measurement position L1/raw; symbols with crosses in the centre = PSD measurement position L2/vent).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)