classification of ignition regimes in thermally stratified

Classification of ignition regimes in thermally stratified Classification of ignition regimes in thermally stratified nn--heptaneheptane--air mixtures using computational singular air mixtures using computational singular pp g p gg p gperturbation perturbation

Saurabh Gupta, Hong G. ImDepartment of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125

Mauro ValoraniDipartimento di Meccanica e Aeronautica, University of Rome La Sapienza, Via Eudossiana 18, 00184 Rome, ItalyLa Sapienza, Via Eudossiana 18, 00184 Rome, Italy

Sponsored by DOEUniversity Consortium on HPLB Engine Research

MotivationMotivation

DOE University Consortium of Advanced IC EnginesHCCI (Homogeneous Charge Compression Ignition) Engines

https://www-pls.llnl.gov/

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

Workshop on Validation and Verification in Computational Science, 2011 2

• Thermal inhomogeneities can be utilized to control ignition and extend combustion duration• Need fundamental understanding of ignition in stratified mixtures

Ignition RegimesIgnition Regimes

Classification of Ignition Regimes• Homogeneous/Spontaneous Ignition• Front Propagation

- Spontaneous Ignition Front Propagation

Experimental Observations in Spark-Assisted HCCI Engines (Zigler, Wooldridge et al., 2007)

HIGH LOAD ( 0 62); LOW Tint (271C)

- Spontaneous Ignition Front Propagation- Deflagration Front Propagation

HIGH LOAD (=0.62); LOW Tint (271C)

Spark assist with high load (~0.6) and low T is dominated by flame (deflagration) type behavior.

LOW LOAD (=0.40); HIGH Tint (321C)

(de ag at o ) type be a o

Spark assist with low load (~0.4) and high T shows mixed modeand high T shows mixed-mode (front/homogeneous) ignition.

Need for Classification: Development of ignition sub-models for large scale multi-dimensional sim lations of HCCI comb stion


dimensional simulations of HCCI combustion

Validation and identification of physical and chemical Validation and identification of physical and chemical processes in processes in autoignitionautoignition problemsproblems

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 quasi-steady state approximations

2) Insights into chemical pathways

Heat release rate isocontoursi h t i 2D DNS

• Reliable computational methods needed to enable feature detection and automate data reduction for analysis of intermittent combustion phenomena

3) Feature tracking in n-heptane-air 2D DNS(Yoo et al, Combustion & Flame, 2011)

• Development of predictive combustion models for modern engines need fundamental insights into ignition regime detection

3) Feature-tracking

4) Ignition regime detection


detection 4) Ignition regime detection

CSP : Basic conceptsCSP : Basic concepts

Ignition problems are closely linked to singularly perturbed problems, i.e. they have solutions that vary on disparate time scales.

CSP : Computational Singular Perturbation

100sChemical Time

ScalesPhysical Time

Scales

Sl ti lTake advantage of this separation of time

scales to obtain reduced problems that are simpler than the original full problem

10-2s

Slow time scales(NO formation)

Time scales of flow transport

Intermediate time scales

Decouple the fast time scales from the slow time scales

10-4s

10-6s

flow, transport and turbulence

time scales(Radical-molecule

reactions)

10 s

10-8s

Fast time scales(Radical-radical

reactions)


CSP : Finding Slow Invariant Manifold (SIM)CSP : Finding Slow Invariant Manifold (SIM)

Geometrical Representation of Chemical Kinetics

Consider homogeneous ignition systemg g yy(t) = [ y1, y2, ….. , yN, T ] : solution vectorg(y): chemical reaction source

dy g(y)dtdy

g

Pg

(I-P) g Trajectory

Pg


Optimal Projector P = ? Manifold

CSP : Optimal projector and CSP : Optimal projector and eigenvalueseigenvalues

g(y)dtdy

df Λf, f Bgdt

...…..(1)

Differentiating (1) once w r t time: diagonalΛ

……..(5)

Jgdtdg

dydgJ

1

Differentiating (1) once w.r.t. time:

……..(2)for individual modes

g

therefore, mode decoupling is achieved

rSrSrSg

t)exp(λff i0i i

i

τλ

Mode amplitude Mode timescale

Optimal Projector (P)-Leads to complete mode decoupling

Consider basis vectors as the eigenvectors

.g)(ba......g)(ba.g)(bag NN2211 N21

RR2211 rS.....rSrSg

IBA Physical Representation

dB

J = AΛB

of the Jacobian, J

……..(3)

NN

22

11 fa.....fafag

)fa.....f(a)fa.....f(ag NN

1M1M

MM

11

Optimal Representation

0dtdB

d(Bg) BAΛ(Bg)

from (2), (3), and realizing

in the neighborhood of the fixed point)J const(

……..(4)


(I-P)g : gfast Pg : gslowBAΛ(Bg)

dt……..(4)

CSP : Extension to convective/diffusive systemsCSP : Extension to convective/diffusive systems

y

Extension of CSP from ODEs to PDEs(Goussis, Valorani, Creta, Najm (2005), Progress Comput. Fluid Dynamics, 5(6):316-326)

(y)L(y)Lg(y)ty

dc

Transport terms are projected on the SIM through the “chemical” projector, P

(I-P) {g+Lc+Ld}

P b b

ygJ

BAJ

)LL.(gbf dcii

P{g+Lc+Ld} P = aM+1bM+1 + …. + aNbN(same as before)

(includes transport contribution)

Diffusion and Convection of all species are considered as separate processes in the


p p pcalculation of Importance and Participation Indices

CSP : Mode separation (M) and Importance IndexCSP : Mode separation (M) and Importance Index

Mode timescales

< < < < <

……… ………

Specify r and a get M

Slow modesFast modes

jM

iji1M εyε)fa(τ Specify r and a g

ar1i

i1M εyε)fa(τ

Sl ( f t) I t I d cNN

ksi Sb )(Slow (or fast) Importance IndexHow important is kth process in slow (or fast) dynamics of ith species

p cN

j

NN

Ms

jj

sis

Ms

kk

sis

slowik

rSba

rSbaI

1 1

1

).(

).()(


FeatureFeature--tracking & ignition regime detectiontracking & ignition regime detection

Ignition regime identification using the importance index of transport processes

T)Convection(T

TDiffusion)(T

Tslowslow

III 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 IT in the region just upstream of the frontLook for the distribution of I in the region just upstream of the front

1IT Reaction zone propagates by virtue of diffusion & convection – Deflagration

0IT Reaction zone propagates by virtue of chemical reactions – Spontaneous Ignition

1I0 T Gives the relative strength of deflagrative behavior


g g

Ignition regimes in 2D turbulent HIgnition regimes in 2D turbulent H22/air mixture**/air mixture**

Initial conditions: 2D homogeneous isotropic turbulence turbulence with thermal inhomogeneities (p=41atm, =0.1)

• H2/air detailed chemistry – Mueller et al (21 reactions, 9 species)


**DNS data obtained from G. Bansal, H.G. Im, Combustion & Flame (2011)

Ignition regimes in turbulent mixture Ignition regimes in turbulent mixture –– 2D Analysis2D Analysis

50% heat release point

Fronts tracked by M profile 2 23

1

(εr=10-3, εa=10-7 )

Front propagation

Cyan – Highly Active Reaction RegionRed – Gives the direction of front propagation

Workshop on Validation and Verification in Computational Science, 2011

Red Gives the direction of front propagation

12

Ignition regimes in turbulent mixture Ignition regimes in turbulent mixture –– 2D analysis2D analysis (Import. Index)(Import. Index)

ITIT

Mixed-mode propagation for

TTT III

p p ga closely connected front contour

Workshop on Validation and Verification in Computational Science, 2011

)Convection(TDiffusion)(T slowslowIII

13

IT

2D analysis2D analysis –– Classification of ignition regimesClassification of ignition regimes

HS

IT

H: Homogeneous kernel

F: FrontF: Front

S: Spontaneous Ignition

FSFS D: Deflagration

HD


IT

2D analysis2D analysis –– Classification of ignition regimesClassification of ignition regimes

HS

IT

H: Homogeneous kernel

F: Front

FDFD

F: Front

S: Spontaneous Ignition

FS D: Deflagration

HD


AutoignitionAutoignition of nof n--heptaneheptane/air mixture/air mixture

Negative Temperature Coefficient (NTC)

Two-stage ignition behavior


http://www.reactiondesign.com/products/open/documents/CHEMKIN-PRO%20n-heptane%20Shock%20Tube.pdf

Temporal resolution and stiffnessTemporal resolution and stiffness

850K, 40atm, =0.3

Homogeneous autoignition of n-heptane-air mixture58 species mechanism (Yoo et al., Combustion & Flame, 2011)

(εr=10-3, εa=10-9 ) Δtintegration < τ1

( r , a )

Driving time-scale

1st stage1st stage

Large stiffnessSmall stiffness

2nd stage


Insights into chemical pathwaysInsights into chemical pathways

Fastest active mode: #15CSP radical: HCO

Importance Index for HCO

CH2O+OH=HCO+H2O (0.321)HCCO+O2=CO2+HCO (0.202)HCO+O2=CO+HO2 (-0.319)

14 exhausted modes. Quasi-steady state species:

C3H2, C4H7O, nC3H7CO, C2H5CO, CH2(s), C7H14OOH4-2, C4H8OOH1-3, C7H14OOH2-4, C7H14OOH3-5, C7H14OOH1-3,


C7H15-3, C7H15-4, C7H15-2, CH3


Constant volume 1D n-heptane-air autoignition, Pinit=40atm, φinit=0.3 (εr=10-3, εa=10-7 )

0.4ms

1st stage ignition front propagating in deflagration mode



0.8ms

Ignition fronts have reached the walls. M dips at the center implying reactions have started cooking up beyond the 1st stage of ignition


reactions have started cooking up beyond the 1st stage of ignition


1.0ms

M dips down further throughout the domain. The entire mixture is now undergoing homogeneous autoignition


undergoing homogeneous autoignition


2nd f1st stage front

2nd stage front

1.4ms

Spontaneous ignition fronts have now appeared; pertaining to both 1st and 2nd ignition stages


1 and 2 ignition stages


1.8ms

Spontaneous ignition fronts have reached the walls. M starts to increase at the center implying the system moving towards near-equilibrium


center implying the system moving towards near equilibrium


2.2ms

M dips at the walls, suggesting end gas consumption


Effect of different initial mixture compositionEffect 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

SummarySummary

CSP analysis has been used as a tool in homogeneous & 1D laminar (n-heptane-air), and 2D turbulent (H2-air) constant volume problems for:

V lid ti f t l l ti i t d tiffValidation of temporal resolution requirements and stiffnessτM+1: driving time scale, τ1: fastest time scale (among M exhausted modes) More gap between the two means higher stiffness

V lid ti f h i l thValidation of chemical pathwaysIdentification of QSS species, rate-limiting reactions, reactions responsible for heat release, through relevant importance indices

F t t kiFeature trackingNumber of exhausted modes (M) profile allows for automated detection of pre-ignition, ignition and post-ignition zones

I iti i d t ti TTT IIIIgnition regime detection T)Convection(T

TDiffusion)(T

Tslowslow

III

TI 1 TI 0In the region just upstream of the ignition front

Deflagration Spontaneous ignition


classification of ignition regimes in thermally stratified

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