Spark Ignition Engine Combustion

Spark Ignition Engine Combustion MAK 652E Reduced Mechanisms and Autoignition Prof.Dr. Cem Soruşbay Istanbul Technical University - Automotive Laboratories Contents Problem statement Methods of reducing mechanisms Autoignition Physical and kinetic model Engine application 1

Background - Problem Statement with Detailed Chemistry The calculation of spatially homogeneous systems is straightforward using generally available hardware. Calculation of two-dimensional laminar flames requires several hundred hours of supercomputer time. The simulation of the three-dimensional turbulent flames is very time demanding.* * Turanyi, T., 25th Symposium on Combustion, The Combustion Institute, 949-955, 1994. Background - Problem Statement Conflict between chemical and physical complexity 3D flow calculation: ~10 6 computational cells Turbulent flow: ~10 1 differential equations Detailed Chemistry: ~10 2 extra differential equations Great span between high/low values, slow/fast processes: stiffness additional numerical problems 2

Background - Problem Statement Detailed Mechanism Reduced Mechanism Homogeneous model ~1000 reactions Practical fuel mixtures 3D flow model Multi-component fuel mixtures Combustion Calculations Mechanisms for ignition characteristics need to be compact for integration with complex fluid flow calculations Construct reduced chemical mechanisms for: Variable multi-component fuel mixtures, e.g. gasoline and diesel Varying conditions. We need a flexible method for repeated reduction 3

Goals - Requirements Goals: Automate the systematic reduction procedure to generate mechanisms for complex chemical processes given variation in: Fuel mixtures Physically Relevant Conditions Requirements: Extensive reduction capability A measure of the impact of a species on selected variables Reproduction of complex chemical processes Construction of mechanisms using simplified physics models Application SI Engine Knock It is generally accepted that engine knock is initiated by autoignition of unburned gas. Autoignition is defined as spontaneous ignition of some part of the charge in the cylinder.* * Maly and Ziegler, 1982, Li et al., 1996. 4

Knock Abnormal Combustion It causes mechanical damage of engine The simplest way to avoid knock is lower compression ratio but it reduces thermal efficiency Algorithm for Reduced Mechanisms Removal of redundant reactions Quasi steady-state approximations (QSSA) Detailed mechanism (data) Skeletal mechanism (data) Reduced mechanism (code) Source terms Range of test calculations (simplified model) Reaction flow and sensitivity analysis (Soyhan et al., 2000) Range of test calculations (simplified model) Chemical and physical lifetime plus sensitivity analysis State variables and major concentrations CFD code (PDF, RIF) 5

4 4 Skeletal Mechanism The Detailed Mechanism Flow Chart - Reduction procedure Reaction Sensitivity Sensitive Redundant 4 4 Species 4 Flow 4 Species 4 4 Analysis Analysis End of Parameter Loop? Removal of Redundant Species Loop Over Parameter Range 4 Skeletal Mechanisms The Skeletal Mechanism 4 Validation of Skeletal Mechanisms Reduced Mechanism The Skeletal Mechanism Species Maximum 4 Lifetime 4 Species 4 4 Analysis Lifetimes End of parameter loop? Q.S.S.A Reduction Loop over parameter range Reduced Mechanisms Final Reduced Mechanism 4 Validation of Reduced Mechanisms 6

Reduction Methods Skeletal Mechanism Removal of redundant reaction paths A measure of redundance: Reaction flow - transfer rate of atomic species between molecules CH 3 NH 2 CH 2 NH 2 NH 3 CH 2 NH HNO NH 2 N 2 H CHNH NO NO N 2 HCN NO NH NO NO N 2 CN HNCO NO N 2 O NCO N NO Reduction Methods Skeletal Mechanism Sensitivity analysis Redundant species: species that are considered unimportant for the mechanism, due to the very small amounts of formation and destruction A species with low reaction flow is not necessarily redundant. Influence on important combustion parameters has to be measured Non-redundant species: sensitive species, fuel, oxidizer and products Species with high sensitivities are non-redundant, independent of the reaction flows 7

Reduction Methods Skeletal Mechanism Developed form of the sensitivity analysis Sensitivity of species B on temperature T: N = r ' dt SB, T νb, r dω r= 1 r N r ω r ν B,r : number of reactions : reaction velocity of reaction r : stoichiometric coefficient of species B in reaction r Reduction Methods Skeletal Mechanism Reaction flow analysis Redundant species: species that are considered unimportant for the mechanism, due to the very low rates of formation and consumption Gives the atomic mass flow through the given reactions This is used to detect redundant species in the mechanism, for differently defined levels of mass flow 8

Reduction Methods Skeletal Mechanism Developed form of the reaction flow analysis Relative importance of the species i N s N s Si, r Ii = max I j f ji, I jcji, max( S ) j= 1 j= 1 i, r Nr a N l, i r a ωrνi, r' ν j r'' l, i, a Ns Ns ωrν i, r'' ν j, r' = l r al r = ' j r al j = '' f = r 1, a j, i, ν,, ν j, r al, j N = r= 1 l, r r j= 1 j= 1 cj, i '' Nr ωrν j, r a r= 1 l, r : number of atom l turned over in reaction r ωrν j, r' r= 1 : formation of species j from species i c ji : consumption of species j to species i f ji 0< I i <100 0<(c ji,f ji )<1 ω r = reaction velocity of reaction r [mole/cm 3 s] ν i = stoichiometric coefficient of the reactant i ν i = stoichiometric coefficient of the product i a l,i = number of atom l in species i N r : number of reactions Reduction Methods Skeletal Mechanism Sensitivity and reaction flow in one: species importance N = r d S ' T B, T νb, r dω r= 1 r I i N s N s S i r j c, max I j f ji, I ji, max( S ) j= 1 j= 1 i, r = E D c E, A f E, A A C B 9

Reduction Methods Skeletal mechanism > Reduced mechanism The elimination of redundant species from the detailed mechanisms generally speeds up the calculations. The skeletal mechanisms can be used as starting mechanism for further reduction. In this way, some mathematical difficulties will be eliminated in further reduction procedure. Reduction Methods Fitting to measurements Pros: Compact and reliable Measurement Global mechanism Cons: Restricted range of conditions Equipment intensive Easily measurable species only Detailed mechanism Skeletal mechanism Systematic reduction Reduced mechanism Pros: Versatility of detailed mechanism Standard procedure for recalculation Automation possibility Cons: Expertise and labour intensive for manual calculation 10

Reduction Methods Reduced Mechanism CSP (Computational Singular Perturbation) Demands high computational capacity ILDM (Intrinsic Low Dimensional Manifolds) Usable for simple fuels, needs high memory because of tabulation QSSA (Quasi Steady State Approximation): The evaluation of the rate equations is very fast. Applicable for a wide range of conditions and for complex fuels. Ref: Turanyi, T., 25th Symposium on Combustion, The Combustion Institute, 949-955, 1994. Reduction Methods Reduced Mechanism Lifetime analysis A measure of species lifetimes is taken from the diagonal elements of the Jacobian matrix of the chemical source terms. It is assumed that the species with the lifetime shorter than and mass-fraction less than specified limits are in steady state. For the steady state species, no partial differential equation needs to be solved. 11

Reduction Methods Reduced Mechanism Species lifetime from diagonal elements of thejacobian matrix: τ = i 1 J ii A fast reaction with a short-lived species => reduction by steadystate assumption: N r N s ν ν j r i j [ X j ],, kr r = 1 j = 1 [ X i ] = N r N s ν ν j r i, j [ X j ], kr r = 1 j = 1 j i X i : molefraction of species i, k r : reaction rate of reaction r ν i,j : stoichiometric coefficient of species i in reaction r N s : number of species, N r : number of reactions Reduction Methods Reduced Mechanism Species lifetimes and reduction by QSSA: A fast reversible reaction with a short-lived species CH 3 + OH CH 3 O + H Quasi Steady-State Assumption (QSSA): [ CHO 3 ] = [ CH3 ][ OH] kf [ CHO 3 ][ H] k r = 0 t [ CH k 3 ][ OH ] f [ CH3 O ] = [ H ] k An explicit algebraic expression (which is easily calculated) => the species can be removed from the set of differential equations r 12

Physical Model The two-zone model* Flame front Propagation Burned gas Unburned gas Piston 0-dimensional, time-dependent model 2 zones in model burned gas zone unburned gas zone Reaction zone calculated as discontinuity between burned and unburned gas zone * Hajireza et al., COMODIA 98,Kyoto,1998 Equations for Unburned Gas Species balance equation dy j, u Nr ρ u = M j, u ν j, k dt k= 1 ω k Energy balance equation ρ c u p u N s hj J= 1 N r j, u ν j k k= 1, dtu dp = M dt dt A ωk + α V w u ( T T ) w u 13

Equations for Burned Gas Species balance equation: dy ρb dt j, b = M N r j, b k= 1 ν j, k m& ωk + ρb m b b ( Y Y ) j, f j, b Energy balance equation: ρ c b p b 4 ( h h ) σεt N s N r m& N s,, 1,, 1, b hj bm j b ν j kωk + ρb Yj j 1, f j= k= m j f j b b b = dtb dp = dt dt The Pressure History The ideal gas law: p mrt + mrt b b b u u u = Vtotal The Wiebe function*: m total θ θ0 xb = 1 exp b m b θ n+ 1 *Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw Hill, Singapore, 1988. 14

Kinetic Model The chemical kinetic mechanism for primary reference fuels (PRF) is based on a detailed mechanism for C 1 -C * 4 hydrocarbons, extended with a simplified model for C 5 -C * * 8 hydrocarbons. The detailed mechanism involves 510 chemical reactions and 75 species. The RON-number of the fuel is an adjustable input parameter. Skeletal and reduced mechanisms for the oxidation of n-heptane and iso-octane under engine knock conditions will be generated automatically by using the automatic reduction method explained. * Chevalier, C., Ph.D.-Thesis, Universität Stuttgart, Germany, 1993. ** Müller, U.C, Ph.D.-Thesis, RWTH Aachen, Germany, 1993 Engine Specifications Engine parameters -Initial values, Boundary conditions, Fuel Composition* Compression ratio 5.6:1 Engine speed 1500 rpm Timing of ignition -10 CAD BTDC Combustion duration 50 CAD Equivalence ratio 1.0 End-gas temperature 800-1000 K, at 42.3 CAD BTDC Wall temperature 300K Pressure 3.95 bar, 42.3 CAD BTDC Fuel composition 40% n-heptane 60% iso-octane * Research engine in Chalmers University (CTH) in Göteborg 15

Knock Detection and Unburned Gas Temp Measurement Pressure transducer location Occurrence of knock is measured by a pressure transducer End-gas temperature is measured by rotational CARS* Spark plug locations *Bood et al., SAE Paper No: 971669, 1997. Validation of Detailed Mechanism Calculated first ignition delay for n-heptane and iso-octane in comparison with the experimental results, respectively* 10 4 10 1 ignition delay time (ms) 10 3 10 2 10 1 10 0 10-1 10-2 experiments calculations 0.6 0.8 1 1.2 1.4 1.6 1.8 2 1000/T (1/K) ignition delay time (ms) 10 0 10-1 10-2 *Fieweger et al., Combustion and Flame, 109, 599-619, 1997. calculated measured 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1000/T (1/K) 16

Validation of Detailed Mechanism Comparison between calculated temperature in unburned zone with the experimental results* 1000 Temperature (K) 900 800 700 600 Ti = 607 K Ti = 574 K Ti = 527 K 500-50 -40-30 -20-10 0 10 20 30 Crank angle degree (CAD) *Bood et al., SAE Paper No: 971669, 1997. Results Sensitivity of Radicals for Different RON Numbers Skeletal Mechanisms 2500 initial temperature = 900 K, RON number = 60 2500 initial temperature = 900 K, RON number = 78 temperature change [K] 2000 1500 1000 500 OH H 2 O 2 HO 2 CH 3 temperature change [K] 2000 1500 1000 500 OH H 2 O 2 HO 2 CH 3 0 5.962 5.964 5.966 5.968 5.97 5.972 crank angle [CAD] 0 6.504 6.508 6.512 6.516 6.520 crank angle [CAD] 17

Results Sensitivity of Combustion Intermediate Species for Different RON Numbers Skeletal Mechanisms temperature change [K] 1500 1000 500 0-500 initial temperature = 900 K, RON number = 60 CH 2 O C H 2 4 C H 3 5 A-C H 8 17 I-C H 4 8 C H 2 6 temperature change [K] 1500 1000 500 0-500 initial temperature = 900 K, RON number = 78 CH O 2 C H 2 4 C 3 H 5 A-C 8 H 17 I-C H 4 8 C 2 H 6-1000 5.955 5.960 5.965 5.970 5.975 crank angle [CAD] -1000 6.504 6.508 6.512 6.516 6.52 6.524 6.528 crank angle [CAD] Results Skeletal Mechanisms Species reduced for different levels of relative importance I Species 5.0% 10.0% 12.0% 15.0% 20% Skel. CH 3O 2H R R R R R R C 2H R R R R R R CH 2CO R R R R R R OCHCHO R R R R R R C 3H 6O R R R R R R CH 2OH R R R R R CH 3O 2 R R R R R CH 2CHO R R R R R C 3H 8 R R R R R CH 3OH R R R R 1C 7H 15O 2 R R R R 1HEOOH-2 R R R R Neo-C 5H 11 R R 1-C 7H 15 R Different pre-defined levels of relative importance, between 5% and 20.0%. Reactions, and the species occurring only in these reactions, were removed from the mechanism according to the table. The mechanism with 12.0% of relative importance is chosen as skeletal mechanism after validation procedure. 18

Results Skeletal Mechanisms Calculated molefraction profiles for hydroxyl and hydroperoxyl radicals OH molefraction 2 10-2 1.5 10-2 1 10-2 5 10-3 0 10 0 initial temperature = 800 K detailed 5% 10% 12% 15% 20% HO 2 molefraction 5 10-4 4 10-4 3 10-4 2 10-4 1 10-4 0 10 0 initial temperature = 800 K detailed 5% 10% 12% 15% 20% 27 27.5 28 28.5 29 29.5 30 crank angle (CAD) 27 27.5 28 28.5 29 29.5 crank angle (CAD) Results Skeletal Mechanisms Calculated molefraction profiles for iso-octane and n-heptane showing the fuel decomposition i-c8h18 molefraction 1.2 10-2 1 10-2 8 10-3 6 10-3 4 10-3 2 10-3 0 10 0 initial temperature = 800 K detailed 5% 10% 12% 15% 20% 0 5 10 15 20 25 30 35 crank angle (cad) n-c7h16 molefraction 8 10-3 6 10-3 4 10-3 2 10-3 0 10 0 initial temperature = 800 K detailed 5% 10% 12% 15% 20% 5 10 15 20 25 crank angle (CAD) 19

Results Skeletal Mechanismsh Calculated temperature profiles for autoignition in the end-gas temperature [K] 3500 3000 2500 2000 1500 initial temperature = 1100 K detailed 5% 10% 12% 15% 20% 1000-25.5-25 -24.5-24 -23.5-23 crank angle [CAD] Calculated difference in the occurrence of maximum heat release change in autoignition time (CAD) 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 5% 10% 12% 15% 20% 0 700 800 900 1000 1100 1200 initial temperature (K) 1300 Results Species Lifetimes species OC8H15O HOOC8OOH OOC8OOH AOEOOH-2 AC8H17O2 C-C8H17 A-C8H17 OC7H13O HOOC7OOH OOC7OOH 2HEOOH-1 1HEOOH-2 2C7H15O2 1C7H15O2 2-C7H15 1-C7H15 T-C4H9 I-C4H9 I-C3H7 N-C3H7 C3H3 C2H5 CH3CO OCH2CHO C2H3 C2H CH2OH CH3O CH3 3-CH2 1-CH2 HCO CH OH O 10-12 10-10 10-8 10-6 10-4 10-2 H 10 0 lifetime Reduced mechanisms Red-36 Red-24 Red-20 Red-19 Red-17 Reduced Mechanisms Species in the reduced mechanisms Species H, O, OH, HO2, H2O2, CH2O, CH3, CH4, HCCO, C2H2, C2H3, CH2CHOO, C2H4, CH3CHO, C2H6, C3H3, C3H4, C3H4P, C3H5, C3H6, i-c4h7, i-c4h8, n-c4h9, neo-c5h11, 1-C5H11, i-c6h13, n-c7h16, OC7OOH, i-c8h18, OC8OOH, CO, CO2, H2, H2O, O2; N2 OH, H2O2, CH2O, CH4, HCCO, C2H2, C2H4, CH3CHO, C2H6, C3H4, C3H4P, C3H6, i-c4h7, i-c4h8, n-c7h16, OC7OOH, i-c8h18, OC8OOH, CO, CO2, H2, H2O, O2, N2 CH2O, CH4, HCCO, C2H2, C2H4, CH3CHO, C2H6, C3H4, C3H4P, C3H6, i-c4h7, i-c4h8, n-c7h16, i-c8h18, CO, CO2, H2, H2O, O2, N2 CH2O, CH4, C2H2, C2H4, CH3CHO, C2H6, C3H4, C3H4P, C3H6, i-c4h7, i-c4h8, n-c7h16, i-c8h18, CO, CO2, H2, H2O, O2, N2 CH2O, CH4, C2H2, C2H4, C2H6, C3H4, C3H4P, C3H6, i-c4h8, n-c7h16, i-c8h18, CO, CO2, H2, H2O, O2, N2 20

Results Reduced Mechanisms Molefraction profiles for CO and CH 2 O calculated by QSSA-reduced mechanisms CO molefraction 1 10-1 8 10-2 6 10-2 4 10-2 2 10-2 0 10 0 det-74 skl-62 red-36 red-24 red-20 red-19 red-17-38 -37-36 -35-34 -33-32 crank angle (cad) CH 2 O molefraction 1.2 10-2 1 10-2 8 10-3 6 10-3 4 10-3 2 10-3 0 10 0 det-74 skl-62 red-36 red-24 red-20 red-19 red-17-42 -40-38 -36-34 -32 crank angle (cad) Results Reduced Mechanisms Fuel decomposition calculated by QSSA-reduced mechanisms 1.2 10-2 8 10-3 i-c 8 H 18 molefraction 1 10-2 8 10-3 6 10-3 4 10-3 2 10-3 0 10 0 det-74 skl-62 red-36 red-24 red-20 red-19 red-17 n-c 7 H 16 molefraction 6 10-3 4 10-3 2 10-3 0 10 0 det-74 skl-62 red-36 red-24 red-20 red-19 red-17-2 10-3 -40-20 0 20 40 60 80 crank angle (cad) -2 10-3 -40-20 0 20 40 60 80 crank angle (cad) 21

Results Reduced Mechanisms Calculated temperature profiles for autoignition in the end-gas Calculated difference in the occurrence of maximum heat release temperature [K] 3500 3000 2500 2000 1500 det-74 skl-62 red-36 red-24 red-20 red-19 red-17 1000-37 -36.5-36 -35.5-35 -34.5-34 -33.5-33 crank angle (cad) change in autoignition time (CAD) 1.2 1.0 0.8 0.6 0.4 0.2 0 62 36 24 20 19 17 number of species Conclusions: Method An automatic reduction method for detailed chemical mechanisms proposed combines species sensitivity analysis with reaction flow analysis and lifetime analysis Sensitivity analysis finds important species in the chain reactions Reaction flow analysis gives an quantitative measure for the atomic mass flows Lifetime analysis identifies the species the Quasi Steady State Approximation is valid for 22

Conclusions: Mechanism Skeletal mechanism chosen: 12 of 74 species are found as redundant for an ignition process Reduced mechanism chosen: 41 of the remaning 62 species are found to be in steady state over the full parameter range Further work required to use reduced mechanisms with CFD web.itu.edu.tr /sorusbay/si/si.htm 23