1 © 2018 Convergent Science. All Rights Reserved

O. Colin, C. Mehl, B. Julien IFP Energies Nouvelles

LES Prediction of Cycle-to-Cycle Variation in a GDI Engine Using G-Equation, Thickened Flame Model, and ECFM

D. Probst, S. Liu, M. Wang, E. Pomraning Convergent Science, Inc.

R. Scarcelli Argonne National Laboratory

2

Motivation • Cycle-to-cycle variation (CCV) can be important to

internal combustion engines - Requires capturing multiple cycles of data

• Large eddy simulation (LES) provides a good framework for investigating CCV

• Obtaining statistically meaningful CCV results may require hundreds of simulated cycles

- Simulating hundreds of consecutive cycles can be very expensive, which is not practical for engineering solutions

- Clearly, it would be advantageous to run multiple cycles concurrently instead of consecutively

• We will investigate the sensitivity of combustion models to CCV in the context of LES

3

Engine and Operating Point

• We investigate a single-cylinder gasoline direct injection (GDI) engine from Argonne National Laboratory

Displacement (L) 0.626

Bore (mm) 89.04

Stroke (mm) 100.6

Compression Ratio 12.1:1

Intake Valve Opening 334° dATDC

Exhaust Valve Opening 135° dATDC

GDI Injector 6 hole, solenoid

Injection Pressure (bar) 150

Spark System Coil-based, 0.7 mm gap

Fuel EPA Tier II EEE

Test Case Non-Dilute Dilute Engine Speed (RPM) 2000 2000 IMEP (bar) 6 6 EGR (%) 0 18 Relative AFR (l) 1 1 Start of Injection (SOI, °aTDC)

-300 -300

Equivalence Ratio 1 1 Spark Advance (SA, °aTDC) -24 -40 Experimental COV of Peak Pressure (%) 8.65 13.88

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CFD Methodology

• CONVERGE 2.4 CFD solver

• Simulate intake, combustion, and exhaust

• Turbulence model: LES Dynamic Structure model - One-equation non-viscosity dynamic model

• Fuel spray model: Conventional Eulerian-Lagrangian discrete droplet method

• Combustion model: G-Equation, thickened flame model (TFM), and Extended Coherent Flame Model (ECFM)

• Discretization: second-order (central) spatial scheme, implicit first-order temporal scheme

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Modified Cartesian Cut-Cell Mesh

• Base cylinder mesh: 1 mm

- 0.5 mm fixed embedding at valve seats

- 0.125 mm fixed embedding at spark gap

• Adaptive Mesh Refinement (AMR) - 0.5 mm for velocity (TFM, ECFM, G-equation)

- 0.25 mm for temperature (TFM)

- 0.25 mm for progress variable (ECFM)

- No temperature or progress variable AMR for G-Equation

• Maximum cell count: 2.5 million AMR

Embedding

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Parallel Perturbation Method (PPM)

• Proposed by Richards et al., (Proceeding of Internal Combustion Engine Division, ICEF2014-5605)

• Implemented and tested by Ameen, et al. on a port fuel injection spark-ignited engine (International Journal of Engine Research, 2016)

• The PPM method (right) is used for the TFM and G-Equation cases

- Ran 10 cases in parallel

• Used a slightly modified approach for ECFM

One or more consecutive LES cycles to wash out initial conditions

Flow field at IVO

Add isotropic velocity perturbations to the restart file or map file

Statistics are collected after the second cycle for each parallel case. Data analysis is based on about 100 cycles

Case 1 Case 2 Case 3 Case N …

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SPARK

IVC SOI IVO EVO

Acceptable

Proceedings of ASME 2018, ICEFM2018-9722

Perturbation Timing

• Must allow sufficient time for the flow field to develop into a valid, distinct realization

• Timings before or during the intake stroke were acceptable

• In this study, we add perturbation at intake valve opening (IVO) and discard the first cycle

EVO Exhaust valve open

IVO Intake valve open

SOI Start of injection

IVC Intake valve close

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Isotropic Velocity Perturbation

• We apply a small isotropic velocity perturbation generated via random Fourier modes to the restart file data just before IVO

• The CCV results are not sensitive to the size of the actual perturbation level

- In this study, we used 0.355 m/s RMS velocity perturbation

- Tests were conducted using 0.0035 m/s RMS velocity perturbation which showed the same results (G-Equation), (Proceedings of ASME 2018, ICEFM2018-9722)

Unperturbed velocity field

0.355 m/s RMS perturbed velocity field

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Parallel Perturbation Method Results (1/2)

Eight distinct velocity magnitude fields 150 CAD after intake valve open

Velocity magnitude field

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Parallel Perturbation Method Results (2/2)

Eight distinct equivalence ratio fields 150 CAD after intake valve open

Equivalence ratio field

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TFM with Detailed Chemistry (1/4)

• Premixed flame front thickness is about 0.01-1 mm

• Generally, it is too computationally expensive to resolve the flame front (need four or more grid points)

• Thickening the flame is an effective way to resolve the turbulence premixed flame in an LES simulation

O. Colin et al., Phys. Fluids A 12 (7) (2000) 1843–1863

Scaling laws:

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TFM with Detailed Chemistry (2/4)

• Only the flame front is thickened

- A transport scalar (flame sensor) is used to determine the

flame front (more details in AIAA Propulsion and Energy

Forum, 2018-4563)

• Efficiency function (Charlette model)

𝑺 = 𝟎 𝑺 = 𝟏

set to 4 in this study

set to 0.69 in this study

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TFM with Detailed Chemistry (3/4)

• 1D validations (flamespeed):

• 2D Validation (decaying turbulence):

Find more 1D testing results in AIAA

Propulsion and Energy Forum, 2018-4563

DNS results

DNS results

flame front resolved

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TFM with Detailed Chemistry (4/4)

• Chemical mechanism: Jia iso-octane 2006, 38 species and 69 reactions (Fuel 85 (2006) 2593–2604)

• Iso-octane is used as a surrogate for gasoline

• Ignition: Energy is sourced in the spark gap directly—initial spark radius is 0.4 mm

- Thickening starts 2 CAD after spark

• The TFM model parameters are identical for the dilute and non-dilute cases!

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Combustion Modeling: G-Equation

• Transport of G:

• Turbulent flamespeed (Pitsch, 2002): - In this study, b1 = 8.0 and b3 = 3.4

• Laminar flamespeed: From 4D (P, T, Phi, EGR) flamespeed table generated

via the Jia iso-octane 2006 mechanism

• Ignition: Source G directly in the spark gap (0.4 mm radius)

• The G-Equation model parameters are the same the for dilute and non-dilute cases!

'it u t

i i i

u GG G GD s

t x x x

22 2 23 3 3

1 1

12 2

tt l

l t t l

u

b s b s b

b us s

b

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Combustion Modeling: ECFM

• Flame surface density transport equation [1]:

• ISSIM spark ignition model [2]:

• Species reaction rate for ECFM (RANS and LES):

• Laminar flamespeed is from the Gulder correlation

lam

[1] Richard et al., PCI, 2007 [2] Colin and Truffin, PCI, 2011

sgsT sgsS sgsC resCPres resS

2(1 ) 1

. . ( ) ( . )3 1

issim

d t T l lam d Tu S N a S S N A St c c

( )i

b u

Y u i i LY Y S

. (1 ) (1 ) issim

res sgs sgs sgs res res ignu P T S C C S S St

α is a transition factor (α = 1 during ignition; α = 0 after ignition); Initial flame kernel and its growth rate are modeled

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G-Equation Results: Non-Dilute Operating Condition

Peak pressure of cycle n vs. peak pressure of cycle n+1

Individual LES cycles Mean pressure

• Simulated CCV is similar to experimental CCV • Simulated mean pressure (red) matches the experimental mean (blue)

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G-Equation Results: Dilute Operating Condition

Peak pressure of cycle n vs. peak pressure of cycle n+1

Individual LES cycles Mean pressure

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TFM Results: Non-Dilute Operating Condition

Peak pressure of cycle n vs. peak pressure of cycle n+1

Individual LES cycles Mean pressure

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TFM Results: Dilute Operating Condition

Peak pressure of cycle n vs. peak pressure of cycle n+1

Individual LES cycles Mean pressure

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ECFM: Non-Dilute Operating Condition

Individual LES cycles Mean pressure

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ECFM: Dilute Operating Condition • Concurrent cycles vs. consecutive cycles

24 concurrent (PPM) cycles 27 consecutive cycles Mean pressure

• CCV from concurrent cycles is similar to CCV from consecutive cycles • Mean pressure curve from concurrent cycles and consecutive cycles are about the same

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Peak Pressure: Standard Deviation

Uncertainty: With 95% confidence

Standard Deviation of Peak Pressure (bar)

Non-Dilute Dilute

EXP 3.54 6.04

G-EQN 2.92 3.81

TFM 2.61 4.48

ECFM 3.12 3.22

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COV of Peak Pressure

Non-Dilute

Dilute

EXP 8.65% 13.88%

G-EQN 7.29% 8.81%

TFM 6.38% 10.41%

ECFM 7.25% 7.33%

Peak Pressure: COV

Uncertainty: With 95% confidence

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LES TFM Cases In Parallel: Dilute operating Condition (1/2)

• 10 cases in parallel throw away first cycle (100 sims) vs. 90 cases in parallel keep first cycle (90 sims)

10 cases in parallel (100 sims) 90 cases in parallel (90 sims) Mean pressure

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LES TFM Cases In Parallel: Dilute operating Condition (2/2)

• 10 cases in parallel (100 simulations) vs. 90 cases in parallel (90 simulations)

COV of Peak Pressure (Dilute operating Condition)

EXP 13.88%

TFM (10 cases in Parallel) 10.41%

TFM (90 cases in Parallel) 11.29%

Uncertainty: With 95% confidence

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TFM Fast and Slow Cycle: Dilute Operating Condition

Fast cycle: Peak pressure 52.2 bar Slow cycle: Peak pressure 26.4 bar

High velocity fluctuation and equivalence ratio level close to 1 near the spark results in high peak pressure and vice versa

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G-Equation Fast and Slow Cycle: Non-Dilute Operating Condition

Fast cycle: Peak pressure 53.8 bar Slow cycle: Peak pressure 35.8 bar

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ECFM Fast and Slow Cycle: Non-Dilute Operating Condition

Slo

w c

ycle

Fa

st c

ycle

• Propagation direction from the ignition instant has a large impact on the combustion process • LES is a powerful tool to better understand CCV

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Possible Reasons for CCV Under-Prediction

• Grid resolution too coarse

• LES turbulence model

• Neglecting fluctuations - boundary condition pressure fluctuations

- injected fuel mass

- spark energy

- EGR

• Chemical mechanism or flamespeed data

• Combustion Model

• Other

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Conclusions

• The large eddy simulations in CONVERGE predicted CCV for a GDI engine at two operating points

• G-equation, TFM, and ECFM cases show a reasonable match with experimental measurement at non-dilute and dilute conditions

- The TFM shows better prediction of CCV at the dilute condition

• The concurrent (PPM) run method can greatly reduce wall clock time

- Hundreds of cycles can run in less than a week given enough computing resources

- This methodology is applicable to important engine research topics with high CCV, including predicting COV, knock, emissions, etc.

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Parallel Perturbation Method

Cycle 1

Cycle 1 Cycle 2 Cycle 3 Cycle 5 Cycle 4

Cycle 5*

Cycle 5 Cycle 4*

Cycle 3* Cycle 5 Cycle 4

Cycle 2* Cycle 3 Cycle 5 Cycle 4

Cycle 1* Cycle 2 Cycle 3 Cycle 5 Cycle 4

Velocity fluctuation

Velocity fluctuation

Velocity fluctuation

Velocity fluctuation

Velocity fluctuation

5 ECFM cases are running in

parallel

With coarse mesh