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A Methodology to Relate Black CarbonParticle Number and Mass Emissions fromVarious Combustion SourcesRoger Teoh1, Marc Stettler1, Arnab Majumdar1 & Ulrich Schumann21Centre for Transport Studies, Department of Civil and Environmental Engineering, Imperial CollegeLondon, London, UK2Deutsches Zentrum für Luft- und Raumfahrt, Institute of Atmospheric Physics, 82234Oberpfaffenhofen, Germany2018 Cambridge Particle Meeting15th June 20181

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Further Work2

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Further Work3

Why is BC PN Emissions Important? Health Effects: Ultrafine particles have a higher probability of being deposited into the respiratorysystem, and translocated towards the circulatory system and internal organs. Climate Effects: During cruise, Black Carbon (BC) Particle Number (PN) emissions from aircraft enginesact as a condensation nuclei for contrail formation. No. of contrail ice particles No. of aircraft BC particle emissions per kg-fuel burnt (EIn in kg-1) Different young contrail characteristics influenced by BC EIn.𝜏 Optical depth Existing BC EIn models for aviation emission assumes that BC particlemorphologies remain constant irrespective of engine thrust settings. BC mass measurements and estimates remain more commonlyavailable than the number metric.Source: [1]4

Research Objectives1) Develop a new model to estimate BC particle number emissions from mass based onthe theory of fractal aggregates.2) Validate the new model using BC measurements from three different emission sources.3) Perform an uncertainty and sensitivity analysis to understand the accuracy anduncertainty bounds of the newly developed model.5

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Further Work6

Development of a New BC PN Predictive Model Mass of one BC aggregate (m) is the summation of primaryparticle masses:𝑚 𝑛pp 𝜌0where𝜋𝑑pp 36𝑛pp Number of primary particles in an aggregate𝜌0 BC material density (1770 kg/m3)𝑑pp Primary particle diameter The total mass of aggregates (M) is calculated using theintegrated product of the aggregate mass and numberweighted distribution: 𝑀 0where𝑚 𝑑m 𝑛 𝑑m d𝑙𝑛𝑑m𝑛 𝑑m 𝑁 𝑝(𝑑𝑚 )Source: [11]7

𝑚 𝑛pp 𝜌0𝜋𝑑pp 36Development of a New BC PN Predictive Model In the free-molecular regime, the number of primary particles in an aggregate (npp) [6]:𝑑m 2𝐷) α𝑑pp𝑛pp 𝑘a (where 𝑑m 𝐷) fm𝑑pp𝑛pp (or𝑑m Aggregate mobility diameter𝑘a Scaling pre-factor𝐷α Projected area exponentDfm Mass-mobility exponentEggersdorfer et al. (2012) [7] suggested universal values of 𝑘a 0.998 and 𝐷𝛼 1.069 foraggregates formed of polydisperse primary particles, irrespective of the state of sintering. The Knudsen Number (Kn) is a dimensionlessnumber equal to the ratio of the mean freepath (𝜆) to the particle radius:𝐾𝑛 Free-molecular regime7% F/F00Continuum regime65% F/F00100% F/F002𝜆𝑑 Free-molecular regime: Kn 1 Continuum regime:Kn 1 Transition regime:0.1 Kn 108

𝑚 𝑛pp 𝜌0𝜋𝑑pp 36Development of a New BC PN Predictive Model Relationship between primary particle (dpp) and aggregate mobility diameter (dm) [9]:𝑑pp 𝑘TEM 𝑑m 𝐷TEMwhere prefactor-exponent coefficient pairs 𝑘TEM & 𝐷TEM are fitted with Transmission Electron Microscopy (TEM)GDI engine:Aviation gas turbine:𝑘TEM 2.616 10 6𝑘TEM 1.621 10 5𝐷TEM 0.30𝐷TEM 0.39HPDI engine:Inverted burner:𝑘TEM 2.644 10 6𝑘TEM 2.465 10 6𝐷TEM 0.29𝐷TEM 0.29dm (nm)dm (nm)Source: [9]9

Development of a New BC PN Predictive Model The total mass of aggregates (M) for a given particle size distribution:𝑑m 2𝐷) α𝑑pp𝑛pp 𝑘a (𝑚 𝑛pp 𝜌0𝑑pp 𝑘TEM 𝑑m 𝐷TEM𝜋𝑑pp 36𝑛 𝑑m 𝑁 𝑝(𝑑𝑚 ) 𝑀 0𝑚 𝑑m 𝑛 𝑑m d𝑙𝑛𝑑m𝜋𝑀 𝑁𝑘a 𝜌0 ( )(𝑘TEM )3 2𝐷𝛼6 0𝑑m 𝜑 p 𝑑m d𝑙𝑛𝑑mwhere 𝜑 3𝐷TEM 1 𝐷TEM 2𝐷𝛼Source: [11]10

Development of a new BC PN Predictive Model The remaining integral is the φth moment of a log-normal distribution:𝜋𝑀 𝑁𝑘a 𝜌0 ( ) 𝑘TEM6whereGMDGSD Rearrange for N:𝑁 𝜋𝑘a 𝜌0 ( ) 𝑘TEM63 2𝐷𝛼𝜑2 ln GSD 2GMD exp()2𝜑Geometric Mean DiameterGeometric Standard Deviation𝑀3 2𝐷𝛼 GMD𝜑 exp(𝜑2 lnGSD 2)2New N or EIn PredictiveModel, called the FractalAggregates (FA) Model. Advantages: New FA model relates BC mass, number and Particle Size Distribution (PSD) in one equation. Captures the change in particle morphology for different combustion conditions11

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Further Work12

Model Validation – CIDI Engine & Inverted Burner𝑁 𝑀𝜋𝒌𝐚 𝜌0 ( )6𝜑2 ln GSD 2𝑘TEM 3 2𝑫𝜶 GMD𝜑 exp()2(a) Experimentally fitted 𝒌𝒂 and 𝑫𝜶 valuesfor each operating mode [14]CIDI Engine Data Source:Inverted Burner Data Source:where 𝜑 3𝐷𝑇𝐸𝑀 1 𝐷𝑇𝐸𝑀 2𝑫𝜶[12][13](b) Constant 𝒌𝒂 𝟎. 𝟗𝟗𝟖 and 𝑫𝜶 𝟏. 𝟎𝟔𝟗 forall operating mode [7]13

Model Validation – Aircraft Gas Turbine EnginesConstant 𝒌𝒂 𝟎. 𝟗𝟗𝟖 and 𝑫𝜶 𝟏. 𝟎𝟔𝟗 for all operating mode [7]EIn EIm𝜋𝜑2 ln GSD 2𝒌𝐚 𝜌0 ( ) 𝑘TEM 3 2𝑫𝜶 GMD𝜑 exp()6where 𝜑 3𝐷𝑇𝐸𝑀 1 𝐷𝑇𝐸𝑀 2𝑫𝜶2(a) GroundValidation(b) CruiseValidation When ka and Dα values of 0.998 and 1.069 [7] are applied to aircraft datasets, on average, we obtainnegative R2 and 100% NMB valuesSource:SAMPLE III.2[10]Source:NASA ACCESS[15]14

Model Validation – Aircraft Gas Turbine EnginesConstant 𝒌𝒂 𝟎. 𝟗𝟗𝟖 and 𝑫𝜶 𝟏. 𝟎𝟔𝟗 for all operating mode [7]EIn EIm𝜋𝜑2 ln GSD 2𝒌𝐚 𝜌0 ( ) 𝑘TEM 3 2𝑫𝜶 GMD𝜑 exp()6where 𝜑 3𝐷𝑇𝐸𝑀 1 𝐷𝑇𝐸𝑀 2𝑫𝜶2(a) GroundValidation(b) CruiseValidationdm (nm)dm (nm)dm (nm) When ka and Dα values of 0.998 and 1.069 are applied to aircraft datasets, on average, we obtainnegative R2 and 100% NMB valuesSource:SAMPLE III.2[10]Source:NASA ACCESS[14]15

Model Validation – Aircraft Gas Turbine EnginesEIn EIm𝜋6𝟏 𝜌0 ( ) 𝑘TEM Recall: 𝒏𝒑𝒑 𝒌𝒂 (𝜑2 ln GSD 23 𝑫𝒇𝒎GMD𝜑 exp()2𝒅𝒎 𝟐𝑫) 𝜶𝒅𝒑𝒑or 𝒏𝒑𝒑 (𝒅𝒎 𝑫𝒇𝒎𝒅𝒑𝒑)where 𝜑 3𝐷𝑇𝐸𝑀 1 𝐷𝑇𝐸𝑀 𝑫𝐟𝐦12. Hence, we assume that 𝑘𝑎 1 and 𝐷𝛼 𝐷fm [7](b) CruiseValidation(a) GroundValidationSource:SAMPLE III.2[10]Source:NASA ACCESS[15]16

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Future Work17

Results: Uncertainty Analysis Uncertainty analysis is performed using the MonteCarlo 1000-member ensembles [16]. The uncertainty of the estimated EIn are asymmetricallydistributed (-37%, 55%) at 1.96σ. The asymmetrical distribution is due to the non-linearityof the FA model. An uncertainty analysis on the estimated EIn was notconducted in previous aviation PN methodologies.18

Results: Sensitivity Analysis A variance-based global sensitivity analysis identifiedthat the uncertainties in GSD contribute to the largestsensitivity in the FA model output.Sensitivity Analysis(Measured Input Parameters) A prioritisation can be recommended for futureresearch to measure certain variables (such as M, Dfm,GMD and GSD) more accurately to reduce theuncertainty bounds of the FA model outputs. Given that ka contributes to the lowest sensitivity to theestimated EIn, the assumption of 𝑘a 1 across allengine types & F/F00 would not significantly affect theFA model outputs.19

Outline1.Introduction & Motivation2.Derivation of a new BC N or EIn Predictive Model3.Model Validation4.Uncertainty & Sensitivity Analysis5.Conclusions & Further Work20

Conclusions A new methodology to relate BC ParticleNumber and Mass emissions is developedbased on the theory of fractal aggregates.𝑁 𝑀𝜋𝑘a 𝜌0 ( 6 ) 𝑘TEM3 2𝐷𝛼 GMD𝜑 exp(𝜑2 lnGSD 2)2 The new FA Model is validated with threedifferent emission sources: An internal combustion engine (CIDI)An inverted burnerTwo aircraft gas turbine engines An uncertainty analysis estimates N or EIn tohave an asymmetrical uncertainty bound(-36%, 54%) at 1.96σ. A sensitivity analysis shows that GSD is themost critical input parameter, followed by the M,Dfm and GMD.21

Future WorkFA Model Application to Aviation Emissions:Is there a net climate benefit in diverting flights to avoid contrail formation?Aircraft Activity Dataset:CARATS Open Data, JapanEmissions:CO2, BC EIn (FA Model) & EIm, Ambient atmospheric conditions:Contrail Model:ECMWF DatasetCoCiPClimateImpactsAir TrafficManagement22

Thank you, [email protected] Postgraduate,Centre for Transport Studies,Department of Civil and Environmental EngineeringImperial College LondonAcknowledgements:This PhD is funded by The Lloyds Register Foundation, and the Skempton Scholarship from the Department ofCivil and Environmental Engineering, Imperial College London.23