Surrogate Fuel Modeling And Uncertainty Quantification - NIST
Surrogate Fuel Modeling andUncertainty QuantificationPerrine Pepiot-Desjardins, Supreet Bhaga,Guillaume BlanquartHeinz PitschStanford University
Outline Component Library Approach for transportationfuel surrogates– Chemistry reduction techniques– Component library approach– Application: Jet fuel surrogate Chemical mechanism for aliphatic species Uncertainty quantification in chemical systems
Reduction StrategiesDRGEP1:Directed Relation Graph with Error Propagation Removes as many species and reactions as possible while retaining the accuracy ofdetailed mechanism Automatic, fast and efficient Generates skeletal mechanisms with consistent chemical pathwaysChemical Lumping2 Replaces chemical isomers by one single representative species Very efficient for large hydrocarbons oxidation Rate coefficients of the lumped reactions estimated accurately through statisticalanalysis of the detailed resultsQuasi-steady state assumptions Replaces differential equations by algebraic expressions12P. Pepiot-Desjardins, H. Pitsch, Combust. Flame, 2008.P. Pepiot-Desjardins, H. Pitsch, Combust. Th. Model., 2008.
Integrated Approach Highest reduction ratio obtained by combining all techniquesExample: Iso-octane oxidation mechanism– Initial size: 850 species, 7212 reactions– Reduced size: 57 species, 504 reactionsPlug Flow ReactorVery lean I-C8H18/airT0 945KAtmospheric laminarburning velocitiesT0 298KI-C8H18/air ignition delay times
Component Library ApproachTransportation fuel:kerosene, diesel,gasoline Existing detailed kinetic mechanisms forpure componentsApplicationsDRGEP, LumpingSurrogate compositionSkeletal mechanisms for purecomponentsComponent libraryCombination: Skeletalmechanism for mixtureInteraction modules,Feature modulesIncremental modulesQSSAReduced chemical model
Individual Components and DetailedKinetic ch: 174 species, Wang et al.,2008Exp: ST, flamesIso-octaneC8H18Mech: 850 species, LLNL, 2002Exp: ST, PFR, flamesMethylcyclohexaneC7H14Mech: 998 species, LLNL, 2005Exp: ST, PFRTolueneC 7H 8ParaffinsNaphthenesStructureAromaticsBenzeneMech: Blanquart et al., 2008Exp: ST, PFR, flamesC 6H 6Base chemistry (C0-C4) developed for PAH and soot formation– Extensively validated– 151 species, Blanquart et al., 2008.
Possible Jet Fuel Surrogate Compositions Automatic composition optimization for any given targetsbased on group additivity theoryAverage JetFuel**DodecaneNeatDodecaneSurrogate 1*Surrogate .1Toluene1028.9Benzene1H/C C9.3H17.7Paraffins 601008862Naphthenes 2006.420Aromatics 1805.618Cetane Number 42.78073.458Treshold Sooting Index 155.29.316.3Hydrocarboncomposition[%vol]*Violi et al., Comb. Sci. Tech. 174:11, 2002** Edwards et al., J. Prop. Pow., 17:2, 2001
Validation ProcedurePyrolysis of MCH in plug flow reactor Reduction done for various configurationsand over a wide range of pressures,equivalence ratios, and temperatures 900 K Validation performed at each stage ofreduction and combination, for each edSurrogateNSNRBase thyl-cyclohexane998882090 91QSS1197Multi-component surrogate
Comparison with Jet Fuel ExperimentsO2Kerosene Premixed Flame2Experiments5 components3 componentsCO2Jet fuel auto-ignition1Jet fuel laminar burning velocitiy3P 20 barP 50 bar5 components3 components1 S.S. Vasu, D. F. Davidson, R. K. Hanson - Combust. Flame, 20082 Doute et al, Combust. Sci. Tech. 106, 19953 Eberius et al., 2001
Component Library Infrastructure Fully automatic, multi-stage reduction strategy Development of an interactive framework for chemicalmodeling of transportation fuel surrogates– Modular and flexible Future:– Incorporate JetSurF into Component Library– Validate multi-component surrogates with experimental data
Chemical Mechanism Development Objective:– Integrate our recent developments for PAHchemical mechanism into JetSurFmechanism
PAH Thermodynamics Thermodynamic Properties– Describe how stable each species are– Required for accurate modeling of combustion Heat capacity Entropy Heat of formation Polycyclic Aromatic Hydrocarbons (PAH)– Formed in rich premixed and diffusion flames– Intermediates to soot formation New Database of Thermodynamic Properties– Ab-initio quantum calculations G3MP2//B3– Internal degree of rotation Hindered rotors– Group Corrections (GC) Blanquart, G., Pitsch, H. « Thermochemical properties of Polycyclic Aromatic Hydrocarbons (PAH) from G3MP2B3calculations » Journal of Physical Chemistry A (2007)
Chemical Mechanism Based Blanquart et al. mechanism PAH part starts from Wang, Frenklachmechanism Updated with newrates and pathways Blanquart, G., Pepiot-Desjardins, P., Pitsch, H. « Chemical mechanism for high temperature combustion of enginerelevant fuels with emphasis on soot precursors » Combustion and Flame (2008) submitted
PAH Growth
Chemical Mechanism Small Hydrocarbon Chemistry C3 & C4 Chemistry Aromatic Chemistry Chemistry of Alkanes PAH ChemistryResults––––1 Detailed chemical mechanism13 fuels149 species1651 reactions Blanquart, G., Pepiot-Desjardins, P., Pitsch, H. « Chemical mechanism for high temperature combustion of enginerelevant fuels with emphasis on soot precursors » Combustion and Flame (2008) submitted
Validation Results Entire mechanism validated with large databaseof experimental data– Ignition delay times Lean Stoichiometric Rich– Laminar Burning Velocities Atmospheric Moderate pressure (3bar - 5bar) High pressure (up to 25bar) Soot precursors in flames– Premixed flames n-heptane iso-octane– Counterflow diffusion flames acetylene n-heptane
Soot PrecursorsLaminar Premixed FlamesLaminar Diffusion FlamesIso-Octane / Air flameRich mixture (φ 1.9)AtmosphericAcetylene counterflow flamePartially premixed (φ 0.63)Atmospheric
Fuel ComponentsBenzeneφ 1.80, P 1barφ 1.93, P 1bar Tolueneφ 1.88, P 1barφ 1.75, P 3barn-heptaneiso-octaneφ 2.08, P 1barφ 2.08, P 1barφ 2.18, P 1barφ 2.18, P 1barResults Analysis– Accurate prediction of soot concentration in premixed flames– Soot volume fraction increases with equivalence ratio (φ)
Uncertainty Quantification forReactive Flow Simulations Uncertainty in numerical solution can be classified into Aleatory: Uncertainty due to randomness in system, e.g.uncertainty in operating conditions of system or physicalproperties Epistemic: Uncertainty due to lack of knowledge Monte Carlo (MC) simulations can be used forpropagation of parametric uncertainty MC simulations for complex models are very inefficient No information about sensitivity of model to parametricuncertainty Polynomial chaos (PC) expansions can be used forstochastic representation of uncertainty
Polynomial Chaos Expansion Approach Uncertain model parameter ( ) can be represented as spectralexpansion given its PDFSpectral expansions called Polynomial Chaos expansions canbe constructed using Orthogonal polynomials (Hermite, Legendre, Laguerre etc.) Weights associated with PDF If Hermite polynomials are used then ª0 1, ª1 », ª2 »2-1 etc.
Non-Intrusive Polynomial Chaos MC sampling of stochastic parameters is done tocompute deterministic solution Coefficients of PC expansion are computed by projectingsolutions onto PC basis Advantage: No need to modify trusted deterministiccodes Disadvantage: Expensive for computationally intensiveproblem Intrusive method can be used for efficient solution
Intrusive Polynomial Chaos Variable u(x,t,») is expressed in form of PC expansion The expansion is substituted in the deterministic equation Orthogonality is used to get N 1 equations for uk’s Nonlinear models involve operations on multiple stochasticparameters Pseudospectral approach is used to simplify functionevaluation of stochastic parameters
Uncertainty Quantification Objective:– Uncertainty propagation in LES E.g.: Effect of uncertain rates on NOx emissions fromaircraft engine– Intrusive PC too expensive and complicated New UQ method with greatly reduced cost basedon direct solution of uncertainty PDF equation New method didn’t work! Focus on Intrusive PC in laminar chemistry code Epistemic uncertainty Uncertainty caused by chemistry reduction
Pseudospectral Approach Intrusive PC leads to high order polynomials in non-linearterms Pseudospectral approachMultiplication Product of two PC expansions having order P result in PC expansionof order 2P Expansion of order 2P is projected on PC expansion of order P Thus if w u v thenwhere
Implementation Overloaded mathematical operators and functions wereimplemented in a library Can be used in chemical kinetic calculations to propagateuncertainty in initial conditions, reaction rate parameters,thermodynamic properties etc. E.g. Knowing PC expansions of A, T, Ea, evaluation of reaction ratek ATnexp(-Ea/T) can be done asWhereandare overloaded multiplication anddivision operators
Future Work Incorporation of JetSurF intoComponent Library Validate surrogates based on JetSurF Integration of PAH chemistry intoJetSurF mechanism UQ– Intrusive PC in laminar chemistry code– Model uncertainty caused by chemistryreduction
Uncertain model parameter ( ) can be represented as spectral expansion given its PDF Spectral expansions called Polynomial Chaos expansions can be constructed using Orthogonal polynomials (Hermite, Legendre, Laguerre etc.) Weights associated with PDF If Hermite polynomials are used then ª 0 1, ª 1 », ª 2
1.1 Measurement Uncertainty 2 1.2 Test Uncertainty Ratio (TUR) 3 1.3 Test Uncertainty 4 1.4 Objective of this research 5 CHAPTER 2: MEASUREMENT UNCERTAINTY 7 2.1 Uncertainty Contributors 9 2.2 Definitions 13 2.3 Task Specific Uncertainty 19 CHAPTER 3: TERMS AND DEFINITIONS 21 3.1 Definition of terms 22 CHAPTER 4: CURRENT US AND ISO STANDARDS 33
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fractional uncertainty or, when appropriate, the percent uncertainty. Example 2. In the example above the fractional uncertainty is 12 0.036 3.6% 330 Vml Vml (0.13) Reducing random uncertainty by repeated observation By taking a large number of individual measurements, we can use statistics to reduce the random uncertainty of a quantity.
73.2 cm if you are using a ruler that measures mm? 0.00007 Step 1 : Find Absolute Uncertainty ½ * 1mm 0.5 mm absolute uncertainty Step 2 convert uncertainty to same units as measurement (cm): x 0.05 cm Step 3: Calculate Relative Uncertainty Absolute Uncertainty Measurement Relative Uncertainty 1
Fuel transfer pump (35) is mounted on the back of unit injector hydraulic pump (1). The fuel transfer pump pushes pressurized fuel out of the outlet port and the fuel transfer pump draws new fuel into the inlet port. Fuel is drawn from fuel tank (12) and flows through two micron fuel filter (11) . Fuel flows from fuel filter (11) to the inlet .
Nature of modeling uncertainty in the Earth Sciences Needs to be application tailored Several sources of uncertainty Measurements and their interpretation Geological setting Spatial variation Response uncertainty Uncertainty assessment is subjective Dealing with a high-dimensional / large problem Mathematical challenges
Uncertainty in volume: DVm 001. 3 or 001 668 100 0 1497006 0 1 3 3. %. % .% m m ª Uncertainty in density is the sum of the uncertainty percentage of mass and volume, but the volume is one-tenth that of the mass, so we just keep the resultant uncertainty at 1%. r 186 1.%kgm-3 (for a percentage of uncertainty) Where 1% of the density is .
