[PPT] - Characterization of differential diffusion effects during the PowerPoint Presentation

SLIDE 1

Characterization of differential diffusion effects during the constant volume ignition of a temperature stratified lean premixed hydrogen/air mixture subject to decaying turbulence

F. Bisetti1, J.-Y. Chen1, J. H. Chen2 and E. R. Hawkes3
1Dept. Mechanical Engineering, University of California at Berkeley

2Combustion Research Facility, Sandia National Laboratory 3School of Photovoltaic and Renewable Energy Engineering,

University of New South Wales, Australia fbisetti@me.berkeley.edu http://firebrand.me.berkeley.edu October 16, 2007

Fabrizio Bisetti (UC Berkeley) Differential diffusion

October 16, 2007

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SLIDE 2

Outline

1

Hydrogen and HCCI ignition

2

Basic definitions of differential diffusion Transport equation

3

Differential diffusion characteristics Effect of differential diffusion on macro combustion characteristics The mechanisms of differential diffusion Statistics

Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 3

Outline

1

Hydrogen and HCCI ignition

2

Basic definitions of differential diffusion Transport equation

3

Differential diffusion characteristics Effect of differential diffusion on macro combustion characteristics The mechanisms of differential diffusion Statistics

Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 4

Hydrogen combustion

Environmentally friendly. CO2 free nature and excellent combustion characteristics

Combustion. Low minimum ignition energy, high laminar flame

speed and wide flammability limits

HCCI. Used as primary fuel (0.1 < Φ < 0.3) or as stabilizing additive

(to natural gas, alcohols, etc.) from onboard reforming.

but...

✞ ✝ ☎ ✆

H2 displays high diffusivity ⇒ differential diffusion

Effect on macro characteristics? E.g. heat release rate, turbulent flame speed and burning rate

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SLIDE 5

Temperature stratification and differential diffusion

Effects of temperature stratification on HCCI ignition

Chen et al., 2006

Stratification promotes a smooth pressure rise High stratification (TRMS = 30 K) promotes deflagrations alongside with spontaneous ignition Differential diffusion effects in HCCI ignition Effects on burn. How does differential diffusion influence heat release rate? Controlling parameters. How is differential diffusion affected by (temperature) inhomogenities?

Mechanism. How do the flow conditions promote differential

diffusion?

Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 6

Outline

1

Hydrogen and HCCI ignition

2

Basic definitions of differential diffusion Transport equation

3

Differential diffusion characteristics Effect of differential diffusion on macro combustion characteristics The mechanisms of differential diffusion Statistics

Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 7

Transport equation for ξH

H-atom mixture fraction ξH =YH2 + YH + βOHYOH + βH2OYH2O + βHO2YHO2 + βH2O2YH2O2 Transport equation DξH Dt = Dth LeH2 ∇2ξH + DthδH2O∇2YH2O +Dth

δH∇2YH + δOH∇2YOH
+DthδH2O2∇2YH2O2 + DthδHO2∇2YHO2

= (Dth/LeH2)∇2ξH

Term I

+ Ωp + Ωr

Term II

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SLIDE 8

Outline

1

Hydrogen and HCCI ignition

2

Basic definitions of differential diffusion Transport equation

3

Differential diffusion characteristics Effect of differential diffusion on macro combustion characteristics The mechanisms of differential diffusion Statistics

Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 9

Effect on heat release rate

0.5 1 1.5 1 1.1 1.2 1.3 1.4 t/!0 "H,max/"0 3.75 K 15 K 30 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 t/τ0 Q/Qmax 15 K 15 K, Le = 1 30 K 30 K, Le = 1

✞ ✝ ☎ ✆

Differential diffusion increases with temperature stratification

✞ ✝ ☎ ✆

Heat release rate is mildly affected by differential diffusion

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SLIDE 10

Tr.m.s. = 30 K temperature stratification

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SLIDE 11

Profiles across igniting kernels (Tr.m.s. = 30 K)

x/δF

T (K) ξH/ξ0

0.2 0.4 0.6 0.8 1 1.2 1.4 1050 1100 1150 1200 1250 1300 1350 1400 0.95 1 1.05 1.1 1.15 1.2 T ξH/ξ0

x/δF

Term I, Term II (1/s) ξH/ξ0

0.2 0.4 0.6 0.8 1 1.2 1.4

15
10
5

5 10 15 20 0.95 1 1.05 1.1 1.15 1.2 ξH/ξ0 Term I Term II

DξH Dt = (Dth/LeH2)∇2ξH

Term I

+ Ωp + Ωr

Term II

✞ ✝ ☎ ✆

Igniting kernels draw excess ξH due to reactions

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SLIDE 12

Temperature and ξH (Tr.m.s. = 30 K)

Snapshot at 50% H.R.

ξH/ξ0 T (K)

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1000 1100 1200 1300 1400 1500

(b) (a) (c)

Along combustion fronts

0.7 0.8 0.9 1 1.1 1200 1250 1300 1350 1400 ξH/ξ0 T (K) Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

✞ ✝ ☎ ✆

Temperature correlates with mixture fraction

✞ ✝ ☎ ✆

Stronger correlation holds along fronts

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SLIDE 13

Curvature effects (Tr.m.s. = 30 K)

H.R.R. along fronts (Le = 1)

−10 −5 5 10 10 20 30 40 50 60 δF ∇ ⋅ n − H.R.R. 109 (W/m3) Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

H.R.R. along fronts (Le = 1)

−10 −5 5 10 10 20 30 40 50 60 δF ∇ ⋅ n − H.R.R. 109 (W/m3) Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

div(n) < 0 n

burnt unburnt

n div(n) > 0

κ = div(n) = ∇ · n Sd = − ˙ ωi ρ|∇Yi|−∇ · (ρDi∇Yi) ρ|∇Yi|

☛ ✡ ✟ ✠

Diff-diff increases H.R.R. in regions of ∇ · n < 0

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SLIDE 14

Summary

1 Diff-diff is most prevalent for large temperature

stratification

2 It develops early in the combustion process at

igniting kernels

3 Diff-diff enhances H.R.R. at negatively curved

deflagration fronts

4 Diff-diff doesn’t have an effect on spontaneous

ignition fronts

5 Overall the heat release rate is mildly affected

(≈ 10%)

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SLIDE 15

Thanks for your attention! Any questions?

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SLIDE 16

Homogeneous Charge Compression Ignition (HCCI)

Homogeneous Charge Compression Ignition engine technology

Thermodynamic efficiency higher then spark ignited (high compression ratios) Ultra-low NOx: 2-25 ppm and 0.04 g/kWh (compare to 8-18 g/kWh for Diesel) Virtually non-existent particulate matter

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SLIDE 17

How do we conceptualize (model) HCCI ignition?

Lumped model Charge is homogeneous Reaction rates control heat release rate, not transport In reality. . . Composition and temperature fields are inhomogeneous Level of turbulence mixing affects ignition

T < Tc T > Tc t

t+

Tc low reaction rate high reaction rate T(x) x, position t

✞ ✝ ☎ ✆

Coupling between transport and chemistry?

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SLIDE 18

Inhomogeneities and modeling

Two regimes. Spontaneous ignition and deflagration fronts (dependin on level of stratification) Engine regimes. thin reaction zones and corrugated flamelets ⇒ turbulence effects on the preheat zone Hydrogen combustion. Lewis number effects and differential diffusion ⇒ area increase vs. flame speed effects

✞ ✝ ☎ ✆

Accounting for inhomogenities is challenging

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SLIDE 19

DNS captured the effect of temperature stratification

Major conclusions

1 Temperature inhomogeneities (stratification)

create a smooth pressure rise

2 High stratification (TRMS = 30 K) promotes

deflagrations alongside with spontaneous ignition

3 Stratification can locally switch the regime

from spontaneous ignition to flame propagation

Figures from: Chen, Hawkes, Sankaran, Mason, Im, in Combustion and Flame (145) 2006 pp. 128-144 Fabrizio Bisetti (UC Berkeley) Differential diffusion

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SLIDE 20

Direct Numerical Simulation to understand ignition

Fuel H2 Oxidizer Air Φ 0.1 Compression Ratio 15:1 Initial pressure, atm 1:41 Initial temperature, K 400:1070 ∆xDNS , mm 4.1 L, mm 1.0 U, m/s 0.5 ReL O(100) TRMS , K 3.75, 15, 30

Direct Numerical Simulation (2D) performed by J. Chen, E. Hawkes and

thers (Sandia NL).

Ignition of extremely lean mixture of H2/Air with temperature stratifications

Goal. Parametric study aimed at

clarifying ignition mechanism

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SLIDE 21

Premixed turbulent combustion scale analysis

lt 1 mm u′ 50 cm/s τt = lt/u′ 2 ms lη 0.024 mm τη 0.166 ms lF 0.47 mm sL 65 cm/s τF = lF/sL 0.72 ms Rel = ltu′/ν 145

u′/sL

0.77

lt/lF

2.12

Da = τt/τF

2.77

Ka = τF/τη

4.35

t

l

F

l ( ) / log ( ) log

t

u /

F

u well−stirred reactor distributed reaction zones this work Da < 1 Ka < 1 Da > 1, Ka > 1 Da = 1 Ka = 1 corrugated flamelets wrinkled flamelets Re = 1

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SLIDE 22

Element-based mixture fraction

ξe = ξe(Ze) = Ze − Ze,2 Ze,1 − Ze,2 ξH = ZH ξO = 1 − ZO ZO,2 where ZH,1 = 1, ZH,2 = 0, while ZO,1 = 0 and ZO,2 = 0.233. The explicit value of the element mass fraction is ZH = YH2 + YH + βOHYOH + βH2OYH2O + βHO2YHO2 + βH2O2YH2O2 (0)

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SLIDE 23

Transport equation for ξH

ZH = YH2 + YH + βOHYOH + βH2OYH2O + βHO2YHO2 + βH2O2YH2O2 (1)

Y Le Nr βi δi H2 0.30 1.0 0.0 O2 1.11 0.0 0.0 O 0.70 0.0 0.0 OH 0.73 0.054

0.116

H2O 0.83 0.1121

0.238

H 0.18 1.0 2.222 HO2 1.10 0.0306

0.074

H2O2 1.12 0.0594

0.145

N2 1.04 0.0 0.0

DξH Dt = Dth LeH2 ∇2ξH +DthδH2O∇2YH2O +Dth

δH∇2YH + δOH∇2YOH
+DthδH2O2∇2YH2O2

+DthδHO2∇2YHO2 = (Dth/LeH2)∇2ξH

I

+ Ωp + Ωr

II

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SLIDE 24

Tr.m.s. = 15 K temperature stratification

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SLIDE 25

Front speed and strain rate

div(n) < 0 n

burnt unburnt

n div(n) > 0

front curvature κ = div(n) = ∇ · n front speed Sd = − ˙ ωi ρ|∇Yi|−∇ · (ρDi∇Yi) ρ|∇Yi| front stretch rate Ka = KaT + KaC KaT ≡ (nn : ∇u + ∇ · u)τF KaC ≡ (Sd/SL)δF∇·n = (Sd/SL)κ

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SLIDE 26

Local heat release rate along fronts

PDF of H.R.R. along fronts

10 20 30 40 0.05 0.1 0.15 0.2 0.25 − H.R.R. 109 (W/m3) pdf 30 K 30 K, Le = 1

Fraction of burnt area

0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 t/τ0 fraction area burn 15 K 15 K, Le = 1 30 K 30 K, Le = 1

✞ ✝ ☎ ✆

Differential diffusion increases H.R.R. spread

✞ ✝ ☎ ✆

Regime make-up is conserved

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SLIDE 27

Curvature effects on H.R.R. and front speed

H.R.R. along fronts (Le = 1)

−10 −5 5 10 10 20 30 40 50 60 δF ∇ ⋅ n − H.R.R. 109 (W/m3) Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

H.R.R. along fronts (Le = 1)

−10 −5 5 10 10 20 30 40 50 60 δF ∇ ⋅ n − H.R.R. 109 (W/m3) Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

Effect on front speed

−10 −5 5 10 1 2 3 4 5 Ka = KaC + KaT Sd/SL Sd/SL < 1.1 Sd/SL > 1.1 Conditional mean

☛ ✡ ✟ ✠

Diff-diff increases H.R.R. in regions of ∇ · n < 0

✓ ✒ ✏ ✑

Wide scatter of Sd with KaT as observed in lean premixed hydrogen/air

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