1. 36th International Symposium on Combustion
Seoul, August 5th, 2016
The role of preferential evaporation on the ignition of multicomponent fuels in a homogeneous spray/air mixture
A. Stagnia,c, L. Esclapezc, P. Govindarajub, A. Cuocia, T. Faravellia, M. Ihmeb,c
a Department of Chemistry, Materials, and Chemical Engineering “G. Natta”, Politecnico di Milano
b Department of Mechanical Engineering, Stanford University
c Center for Turbulence Research, Stanford University

2. Outline 1. Introduction and motivations 2. Mathematical model
Target properties of real fuels
Ignition of multicomponent droplets: state of the art
2. Mathematical model
Model formulation and assumptions
Surrogate formulation
Kinetic model
Thermodynamic/transport properties
3. Results
Preferential evaporation in liquid droplets
Two-phase autoignition
Time-scale analysis
Low temperature chemistry
4. Conclusions and future work

3. Target properties of real fuels
Physical targets
Chemical targets
Density
Ignition propensity
Flash point
Sooting tendency
Freeze point
Flame propagation
Viscosity
Molecular Weight
Pollutants formation
Ignition Quality Tester
Ignition propensity is estimated in standard conditions: T = 833 K; P = 22.1 atm
Derived Cetane Number
(ASTM D6890)
Droplet distribution
Equivalence ratio …
Non-standard conditions
No direct control on operating parameters

4. Preferential evaporation in multicomponent fuels
Huge variety of components constituting real fuels
Spray evaporation models consider homogeneous droplets composition
Jet-A composition
Dooley et al., Comb Flame 157 (2010)
Intradroplet species diffusion is neglected
Objective
Understand the role of liquid diffusion on ignition at gas-turbine relevant conditions: equivalence ratio, droplet diameter

5. Ignition of a multicomponent spray
Chemical Reactivity
Liquid diffusion
Stefan-Maxwell diffusion model
Skeletal mechanism
Spray
Ignition
Turbulence
Gas-phase transport
Homogenous phase
Ambient conditions
Liquid fuel properties
Standard conditions (833 K – 22.1 atm)
Group-contribution model

6. Model formulation r Liquid phase Model representation
Diffusion flux r
Model representation
Mono-dispersed droplet in homogeneous isobaric gas-phase
Model simplifications
Spherical symmetry
No liquid-phase reactions
Finite diffusion (Stefan-Maxwell approach)
Interface
Thermodynamic equilibrium
Peng-Robinson EoS for fugacity evaluation
Evaporation fluxes
Bellan & Harstad, Int J Heat Mass Tran (1987)

7. Threshold Sooting Index
Real fuel vs surrogate
Dooley et al. Comb Flame 157 (2010)
Property
Influence on
n-alkanes
i-alkanes
aromatics
Avg. Molecular weight
Fuel diffusion ↑ = ↓
H/C ratio
Adiabatic Flame Temperature
Derived Cetane Number
Ignition
Threshold Sooting Index
Soot formation
POSF 4658
POSF 4658 surrogate
Dooley et al. Comb Flame 159 (2012)

8. 10% Maximum error on Ignition delay time
Skeletal mechanism
10% Maximum error on Ignition delay time
POLIMI mechanism
352 species reactions
POSF 4658 mechanism
181 species 4089 reactions
DoctorSMOKE++
Dooley et al. Comb Flame 159 (2012)
P = 20 atm
𝚽 = 1
Stagni et al. Comb Flame 163 (2016)

9. Thermodynamic and transport properties
Critical properties (Tc, Pc, ω)
Heat capacity
Heat of vaporization
Liquid viscosity
Liquid conductivity
Group contribution framework for the evaluation of thermodynamic and transport parameters
Corrections for pressure and temperature dependance
Distillation curve
Droplet evaporation
Temperature [K]
Recovered mass fraction [-]
Constantinuou & Gani, AIChE J 10 (1994)
Govindaraju & Ihme, Int J Heat Mass Tran 102 (2016)

10. Autoignition in standard conditions (833 K – 22.1 atm)
Radial composition profile
Center vs interface
d = 20 µm 𝚽 = 1
d = 20 µm 𝚽 = 1
normalized droplet radius [-]
The most volatile species (iso-octane) evaporates first
Radial composition gradients are present inside the droplet
Preferential evaporation affects gas-phase composition
Effects on ignition?

11. Mapping two-phase autoignition
Non-monotonic behavior as a function of droplet size and equivalence ratio
Highest reactivity region around d = 20 µm - ɸ = 0.8
Competition among:
Evaporation rate
Cooling rate of gas-phase
Ignition delay time (of evaporating mixture)

12. Relevant time scales
Crucial role of gas-phase cooling in ignition delay times: a minimum 𝛕ign,prevap is obtained at small diameters
Overlapping between evaporation and two-phase ignition delay times
Homogeneous ignition
Two-phase ignition
Equivalence ratio [-]
Diameter [µm]
0.001
0.01
0.1 3 1

13. Timescale analysis Identified three ignition regimes:
Regime i: Ignition is driven by chemical kinetics:
Regime ii: non-linear, controlled by preferential evaporation:
Regime iii: ignition is controlled by evaporation and fuel-availability:
≈ 1
>> 1
Equivalence ratio [-]
< 1
Ideal case
Diameter [µm]

14. Sensitivity to preferential evaporation
In region (ii), ignition is determined by the composition of the evaporating mixture
The boundary between (i) and (ii) is very sensitive to preferential evaporation

15. Role of Low Temperature Chemistry
d = 20 µm - 𝚽 = 1
Surrogate components have a different reactivity in standard conditions
n-dodecane is more reactive (LTC behavior)
Pure aromatics are less reactive (40 times)
LTC affects evaporation rate and gas-phase composition
d = 20 µm 𝚽 = 1
d = 20 µm 𝚽 = 1

16. Conclusions Implications Future investigation
A high level of detail was used on critical submodels:
Finite liquid diffusion
Thermodynamic equilibrium
Thermodynamic/transport properties
Preferential evaporation affects ignition delay in a narrow region, relevant for gas-turbine operating conditions and DCN measurements
Implications
Lagrangian spray models (0-diffusion) might need proper integration to account for fuel heterogeneity.
Standard ignition delay measurements (Derived Cetane Number) are carried out in critical conditions for preferential evaporation
Future investigation
Effects of gas-phase transport (1D model)
Effect of slip velocity

17. Thank you for your attention? !

18. Backup slides

19. Decomposition products Steady-state approximation
Alkyl radicals quickly evolve into decomposition products
Weak interactions with smaller molecules at high T
Chemical lumping
Initiation
Product selectivities can be found
Decomposition products
Steady-state approximation
R· +
Continuity equations
4x4 linear system in Ri
j = 1…4
1 lumped alkyl radical
1 lumped reaction
C7H15  C2H C5H C3H C4H C4H C3H C5H C2H C6H CH3

20. From detailed to lumped mechanism
Detailed Scheme 135 Primary reactions
Lumped Scheme 15 Primary lumped reactions
38 Intermediate radicals
4 Intermediate radicals
26 Primary products (retaining nC7 structure)
3 Primary lumped products
3 n-heptenes 8 cyclic-ethers 15 keto-hydroperoxides
1 lumped n-heptene 1 lumped cyclic-ether 1 lumped keto-hydroperoxide

21. Skeletal reduction via flux analysis
Detect and remove species/reactions not important in the operating conditions
Reaction states are sampled in ideal reactors (Batch/Jet Stirred)
Temperature
Pressure
Equivalence ratio
Fuel
Air
Products
Ti – Pi –𝚽i A
Pepiot & Pitsch Comb Flame 154 (2008)
Different criterions to quantify the importance of a species, but common principle
Species with a characterizing index below a threshold can be safely removed
rAB
rAC B C
rCD
rBD
rCE
Directed Relation Graph with Error Propagation: graph algorithm to estimate species interactions
rDE D E

22. Sensitivity analysis Flux analysis Sensitivity analysis
Unimportant species
Marginal species
Important species
Flux analysis
Sensitivity analysis
Error-controlled procedure: ranking species according to the error induced by their removal.
Ignition delay time
Time-consuming
More accurate
Zheng et al. PROCI 31 (2007)

23. Sensitivity analysis on reactions
Model response to the variation of governing parameters (kinetic constants)
One further set of ODE per kinetic constant
Normalized sensitivity coefficients
Cuoci et al. Comp Phys Comm 192 (2015)

24. Numerical implementation
Significant computational load of the reduction procedure. Bottlenecks:
Sensitivity analysis on species
Sensitivity analysis on reactions
Solutions
OpenSMOKE++ framework
Divide-and-conquer algorithm: reduction is carried out separately for each reactor
Parallel libraries (MPI-based)
DoctorSMOKE++
Stagni et al. Comb Flame 163 (2016)

25. n-heptane droplets autoignition
Smaller droplet diameters result in faster convection flow (Stefan flow)
Temperature and mass fraction profiles quickly become homogeneous in the gas phase
Mass fraction
Temperature
d = 20 µm 𝚽 = 1
d = 20 µm 𝚽 = 1
Moriue et al. Proc Comb Inst 30 (2005)