Mauro Valorani Dipartimento di Meccanica e Aeronautica, University of Rome

Transcription

1 Classification of ignition regimes in thermally stratified n-heptane-air air mixtures using computational singular perturbation Saurabh Gupta, Hong G. Im Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI Mauro Valorani Dipartimento di Meccanica e Aeronautica, University of Rome La Sapienza, Via Eudossiana 18, Rome, Italy Sponsored by DOE University Consortium on HPLB Engine Research

2 Motivation DOE University Consortium of Advanced IC Engines HCCI (Homogeneous Charge Compression Ignition) Engines Promises in low emissions and high efficiencies Challenges in control of ignition and combustion phasing Thermal inhomogeneities can be utilized to control ignition and extend combustion duration Need fundamental understanding of ignition in stratified mixtures Workshop on Validation and Verification in Computational Science,

3 Ignition Regimes Classification of Ignition Regimes Homogeneous/Spontaneous Ignition Front Propagation - Spontaneous Ignition Front Propagation - Deflagration Front Propagation Experimental Observations in Spark-Assisted HCCI Engines (Zigler, Wooldridge et al., 2007) HIGH LOAD (=0.62); LOW Tint (271C) LOW LOAD (=0.40); HIGH Tint (321C) Spark assist with high load (~0.6) and low T is dominated by flame (deflagration) at type behavior. Spark assist with low load (~0.4) and high T shows mixed-mode mode (front/homogeneous) ignition. Need for Classification: Development of ignition sub-models for large scale multi- dimensional simulations of HCCI combustion Workshop on Validation and Verification in Computational Science,

4 Validation and identification of physical and chemical processes in autoignition problems Given temporally and spatially resolved data, computational singular perturbation (CSP) provides an automated method to develop and validate reduced order models. Validation of temporal resolution for implementation of efficient time-integration schemes 1) Temporal resolution and stiffness Validation of reduced chemical mechanisms and quasisteady state approximations 2) Insights into chemical pathways Reliable computational methods needed to enable feature detection and automate data reduction for analysis of intermittent combustion phenomena 3) Feature-tracking Heat release rate isocontours i h t i 2D DNS (Yoo et al, Combustion & Flame, 2011) 3) Feature tracking in n-heptane-air 2D DNS Development of predictive combustion models for modern engines need fundamental insights into ignition regime detection 4) Ignition regime detection Workshop on Validation and Verification in Computational Science,

5 CSP : Basic concepts CSP : Computational Singular Perturbation Ignition problems are closely linked to singularly perturbed problems, i.e. they have solutions that vary on disparate time scales. Chemical Time Scales 10 0 s Physical Time Scales Slow time scales (NO formation) Intermediate time scales (Radical-molecule reactions) 10-2 s 10-4 s 10-6 s Time scales of flow, transport and turbulence Take advantage of this separation of time scales to obtain reduced problems that are simpler than the original full problem Decouple the fast time scales from the slow time scales Fast time scales (Radical-radical reactions) 10-8 s Workshop on Validation and Verification in Computational Science,

6 CSP : Finding Slow Invariant Manifold (SIM) Geometrical Representation of Chemical Kinetics Consider homogeneous ignition system y(t) = [ y 1, y 2,.., y N, T ] : solution vector g(y): chemical reaction source dy g(y) dt g Pg (I-P) g Trajectory Optimal Projector P =? Manifold Workshop on Validation and Verification in Computational Science,

7 CSP : Optimal projector and eigenvalues dy dt g(y).....(1) Differentiating (1) once w.r.t. time: dg dt Jg J dg dy..(2) Optimal Projector (P) -Leads to complete mode decoupling Consider basis vectors as the eigenvectors of the Jacobian, J J = AΛB BA I from (2), (3), and realizing ( J const..(3) db 0 dt in the neighborhood of the fixed point) d(bg) BAΛ(Bg) dt..(4) df Λf, f Bg dt..(5) Λ diagonal therefore, mode decoupling is achieved for individual modes f i f 0 exp(λ i t) Mode amplitude 1 λ g S1 r1 S2 r2... SR rr Physical Representation g a1(b1.g) a 2(b2.g)... a g a g (a τ i Mode timescale N (b i N.g) 1 2 N 1f a 2f... a Nf 1 M M1 1f... a Mf ) (a M1f... Optimal Representation (I-P)g : g fast Pg : g slow a N f N ) Workshop on Validation and Verification in Computational Science,

8 CSP : Extension to convective/diffusive systems Extension of CSP from ODEs to PDEs (Goussis, Valorani, Creta, Najm (2005), Progress Comput. Fluid Dynamics, 5(6): ) y y t g(y) L c (y) L d (y) Transport terms are projected on the SIM through the chemical projector, P (I-P) {g+l c +L d } J g y J AB P{g+L c +L d } P = a M+1 b M a N b N(same as before) f i b.(g L i c L d ) (includes transport contribution) Diffusion and Convection of all species are considered as separate processes in the calculation of Importance and Participation Indices Workshop on Validation and Verification in Computational Science,

9 CSP : Mode separation (M) and Importance Index CSP : Mode separation (M) and Importance Index Mode timescales < < < < < Specify r and a get M Slow modes Fast modes j M i j ε y ε ) f a ( τ Specify r and a g a r 1 i i 1 M ε y ε ) f a ( τ Sl ( f t) I t I d c N N k s i S (b ) Slow (or fast) Importance Index How important is k th process in slow (or fast) dynamics of i th species N p c j N N M s j j s i s M s k k s i s slow i k r S b a r S b a I ). ( ). ( ) ( Workshop on Validation and Verification in Computational Science,

10 Feature-tracking tracking & ignition regime detection Ignition regime identification using the importance index of transport processes I T I T (TDiffusion) slow I T (TConvection) slow The importance of diffusive and convective transport of heat (sensible enthalpy) on the slow dynamics of Temperature field Identify a reaction zone / ignition front by M profile Look for the distribution of I T in the region just upstream of the front I T 1 Reaction zone propagates by virtue of diffusion & convection Deflagration I T 0 Reaction zone propagates by virtue of chemical reactions Spontaneous Ignition 0 I T 1 Gives the relative strength of deflagrative behavior Workshop on Validation and Verification in Computational Science,

11 Ignition regimes in 2D turbulent H 2 /air mixture** Initial conditions: 2D homogeneous isotropic turbulence turbulence with thermal inhomogeneities (p=41atm, =0.1) H 2 /air detailed chemistry Mueller et al (21 reactions, 9 species) **DNS data obtained from G. Bansal, H.G. Im, Combustion & Flame (2011) Workshop on Validation and Verification in Computational Science,

12 Ignition regimes in turbulent mixture 2D Analysis 50% heat release point (ε r =10-3, ε a =10-7 ) Fronts tracked by M profile Front propagation Cyan Highly Active Reaction Region Red Gives the direction of front propagation Workshop on Validation and Verification in Computational Science,

13 Ignition regimes in turbulent mixture 2D analysis (Import. Index) I T Mixed-mode propagation p for a closely connected front contour I T I I T T (TDiffusion) slow (TConvection) slow Workshop on Validation and Verification in Computational Science,

14 2D analysis Classification of ignition regimes I T HS H: Homogeneous kernel F: Front S: Spontaneous Ignition FS D: Deflagration HD Workshop on Validation and Verification in Computational Science,

15 2D analysis Classification of ignition regimes I T HS H: Homogeneous kernel F: Front FD S: Spontaneous Ignition FS D: Deflagration HD Workshop on Validation and Verification in Computational Science,

16 Autoignition of n-heptane heptane/air mixture Negative Temperature Coefficient (NTC) Two-stage ignition behavior Workshop on Validation and Verification in Computational Science,

17 Temporal resolution and stiffness 850K, 40atm, =0.3 Homogeneous autoignition of n-heptane-air mixture 58 species mechanism (Yoo et al., Combustion & Flame, 2011) (ε =10-3 ε =10-9 r, a ) Δt integration < τ 1 Driving time-scale 1 st stage Small stiffness Large stiffness 2 nd stage Workshop on Validation and Verification in Computational Science,

18 Insights into chemical pathways Fastest active mode: #15 CSP radical: HCO Importance Index for HCO CH 2 O+OH=HCO+H 2 O (0.321) HCCO+O 2 =CO 2 +HCO (0.202) HCO+O 2 =CO+HO 2 (-0.319) 14 exhausted modes. Quasi-steady state species: C 3 H 2, C 4 H 7 O, nc 3 H 7 CO, C 2 H 5 CO, CH 2 (s), C 7 H 14 OOH4-2, C 4 H 8 OOH1-3, C 7 H 14 OOH2-4, C 7 H 14 OOH3-5, C 7 H 14 OOH1-3, C 7 H 15-3, C 7 H 15-4, C 7 H 15-2, CH 3 Workshop on Validation and Verification in Computational Science,

19 Feature-tracking tracking & ignition regime detection Constant volume 1D n-heptane-air autoignition, P init =40atm, φ init =0.3 (ε r =10-3, ε a =10-7 ) 0.4ms 1 st stage ignition front propagating in deflagration mode Workshop on Validation and Verification in Computational Science,

20 Feature-tracking tracking & ignition regime detection 0.8ms Ignition fronts have reached the walls. M dips at the center implying reactions have started cooking up beyond the 1 st stage of ignition Workshop on Validation and Verification in Computational Science,

21 Feature-tracking tracking & ignition regime detection 1.0ms M dips down further throughout the domain. The entire mixture is now undergoing homogeneous autoignition Workshop on Validation and Verification in Computational Science,

22 Feature-tracking tracking & ignition regime detection 1 st stage front 2 nd stage front 1.4ms Spontaneous ignition fronts have now appeared; pertaining to both 1 st and 2 nd ignition stages Workshop on Validation and Verification in Computational Science,

23 Feature-tracking tracking & ignition regime detection 1.8ms Spontaneous ignition fronts have reached the walls. M starts to increase at the center implying the system moving towards near-equilibrium equilibrium Workshop on Validation and Verification in Computational Science,

24 Feature-tracking tracking & ignition regime detection 2.2ms M dips at the walls, suggesting end gas consumption Workshop on Validation and Verification in Computational Science,

25 Effect of different initial mixture composition a) Uniform b) Positively correlated c) Negatively correlated a) Spontaneous ignition front b) Fronts propagating due to both transport and reactions c) Homogeneous autoignition Workshop on Validation and Verification in Computational Science,

26 Summary CSP analysis has been used as a tool in homogeneous & 1D laminar (n-heptane-air), and 2D turbulent (H 2 -air) constant volume problems for: Validation of temporal resolution requirements and stiffness τ M+1 : driving time scale, τ 1 : fastest time scale (among M exhausted modes) More gap between the two means higher stiffness Validation of chemical pathways Identification of QSS species, rate-limiting reactions, reactions responsible for heat release, through relevant importance indices Feature tracking Number of exhausted modes (M) profile allows for automated detection of pre-ignition, ignition and post-ignition zones Ignition regime detection ti I T I T (TDiffusion) In the region just upstream of the ignition front T I 1 Deflagration T I 0 slow I T (TConvection) Spontaneous ignition slow Workshop on Validation and Verification in Computational Science,