Large Eddy Simulations of Large Eddy Simulations of Turbulent Spray CombustionTurbulent Spray Combustion

in Internal Combustion in Internal Combustion Engines Engines

Farhad JaberiDepartment of Mechanical Engineering

Michigan State UniversityEast Lansing, Michigan

In-Cylinder Flow: Combination of highly unsteady turbulent flow, separated boundary and shear layers, pressure waves, spray, mixing and combustion in complex geometrical configurations with moving pistons and valves.

CFD & IC Engines: The solver should be able to handle complex geometries with dynamic mesh. LES needs high order numerical method and accurate subgrid turbulence models. For spray, advanced primary and secondary break-up models and fully coupled gas-droplet flow solvers with multi-component droplet evaporation models are needed. Turbulent combustion models with appropriate chemical kinetics mechanisms are also needed.

Previous Works: Mostly based on RANS or low-order LES.

Our Model: LES/FMDF, based on a new Lagrangian-Eulerian-Lagrangian mathematical/numerical methodology.

BackgroundBackground

3

LES/FMDF of Single-Phase Turbulent Reacting LES/FMDF of Single-Phase Turbulent Reacting Flows Flows

Scalar FMDF - A Hybrid Eulerian-Lagrangian Methodology Scalar FMDF - A Hybrid Eulerian-Lagrangian Methodology

Eulerian: Conventional LES equations for velocity, pressure, density and temperature fields

- Deterministic simulations

Lagrangian: Transport equation for FMDF (PDF of SGS temperature and species mass fractions

- Monte Carlo simulations

Coupling of Eulerian and Lagrangian fields: A certain degree of “redundancy” (e.g. for filtered temperature)

COCO22 andand CC77HH1616 Mass FractionsMass Fractions

Pressure IsolevelsPressure Isolevels

Nozzle

Wall

Vorticity Contours & Monte Vorticity Contours & Monte Carlo ParticlesCarlo Particles

Monte Carlo Particles

Kinetics: (I ) reduced kinetics schemes with direct ODE or I SAT solvers, and (I I ) flamelet library with detailed mechanisms or complex reduced schemes.Fuels: methane, propane, decane, kerosene, heptane, J P-10

Filtered continuity and momentum equations via a generalized multi-block high-order finite difference EulerianEulerianscheme for high Reynolds number turbulent flows in complex geometries

Various closures for subgrid stresses

GasdynamicGasdynamicFieldField

Scalar Field Scalar Field (mass fractions(mass fractionsand temperature)and temperature)

Filtered Mass Density Function (FMDF) equation via LagrangianLagrangianMonte Carlo method - I to Eq. for convection, diffusion & reaction

ChemistryChemistry

COCO22 andand CC77HH1616 Mass FractionsMass Fractions

Pressure IsolevelsPressure Isolevels

Nozzle

Wall

Vorticity Contours & Monte Vorticity Contours & Monte Carlo ParticlesCarlo Particles

Monte Carlo Particles

Kinetics: (I ) reduced kinetics schemes with direct ODE or I SAT solvers, and (I I ) flamelet library with detailed mechanisms or complex reduced schemes.Fuels: methane, propane, decane, kerosene, heptane, J P-10

Filtered continuity and momentum equations via a generalized multi-block high-order finite difference EulerianEulerianscheme for high Reynolds number turbulent flows in complex geometries

Various closures for subgrid stresses

GasdynamicGasdynamicFieldField

Scalar Field Scalar Field (mass fractions(mass fractionsand temperature)and temperature)

Filtered Mass Density Function (FMDF) equation via LagrangianLagrangianMonte Carlo method - I to Eq. for convection, diffusion & reaction

ChemistryChemistry

LES/FMDF of a Dump Combustor

Lagrangian Monte Carlo Monte Carlo

ParticlesParticles

Eulerian GridEulerian Grid

Kinetics: (I) global or reduced kinetics models with direct ODE or ISAT solvers, and (II) flamelet

library with detailed mechanisms or complex reduced mechanisms

Fuels considered so far: methane, propane, heptane, octane, decane, kerosene, gasoline,

JP-10 and ethanol

LES of Two-Phase Turbulent Reacting LES of Two-Phase Turbulent Reacting Flows Flows

A New Lagrangian-Eulerian-Lagrangian MethodologyA New Lagrangian-Eulerian-Lagrangian Methodology Filtered continuity and momentum equations via a generalized multi-block high-order finite difference EulerianEulerian scheme for high Reynolds

number turbulent flows in complex geometries

Various closures for subgrid stresses

Gasdynamics FieldGasdynamics Field

Scalar Field Scalar Field (mass fractions(mass fractions

and temperature)and temperature)

Filtered Mass Density Function (FMDF) equation via LagrangianLagrangian Monte Carlo method -

Ito Eq. for convection, diffusion & reaction

ChemistryChemistry

Droplet Field Droplet Field (spray)(spray)

LagrangianLagrangian model for droplet equations with full mass, momentum and energy couplings between phases and a stochastic sub grid

velocity model

• Liquid Fuel Droplets

LES of Two-Phase Turbulent Reacting LES of Two-Phase Turbulent Reacting FlowsFlows

A New Lagrangian-Eulerian-Lagrangian MethodologyA New Lagrangian-Eulerian-Lagrangian Methodology

FMDF Solver

Spray-Controlled Spray-Controlled Dump CombustorDump Combustor

Fuel Injector

Wall

Wall

• Monte Carlo Particles- Eulerian Grid

Eulerian Cell

Mass,Momentum,Scalar Terms from Droplets

LES Solver

Eulerian Finite Difference Grid

Interpolation /Favre Filter

Monte Carlo Particles

FMDF Solver

Filtered Equations - Eulerian

SJu

t

J

tJ

i

i

ˆ

uij

ie

jj

je

iij

jii

i SJuuPuu

t

Ju

t

uJ

ˆˆˆˆ

ˆˆ

/ˆ and ,ˆ_____

ffxdxxGtxff

NS

MWRTRTP

1

0^

ˆ)(

Droplet termsDroplet terms

dt

dm

VS p

1

dt

vdm

VS iPui

1

Droplet Equations Lagrangian

FMDF Equation

Lagrangian

xdxxGtxtxtxPL

)()),(,(),(),;( Two-phase subgrid

scalar FMDF:

LLLmi

lLt

iLLi

i

L PSPx

P

xPu

xt

P)(

/~~

dt

dm

Cm

LTT

f

dt

dT p

Lp

vp

p

p *2

Sc

shf

Nuf

Cf

d pDppp 3

,Pr3

,24

Re,

18 32

21

2

1ln3M

pp

p Bf

mdt

dm

ii v

dt

dX

dt

dv

dt

dvmLvh

dt

dm

dt

dmCT

dt

dTCm

VS ii

PPP

PPP

LPE )())1

0

Reaction termReaction term

Droplet termsDroplet terms

Reaction termsReaction terms

Eij

i

i

i

i

i SJSJquuPuE

t

JE

t

EJ

ˆˆˆˆˆ

ˆˆ

ˆˆ

ˆˆ

SJSJx

MJu

t

J

tJ

i

i

i

i

i

i

)( *1ii

d

i vuf

dt

dv

)(/)()(

L

LLPS

PSPS

KHKH RTRT

KH/RT Break-upKH/RT Break-up

Main Features of LES/FMDFMain Features of LES/FMDF Large scale, unsteady, non-universal, geometry- depended quantities are explicitly computed in LES/FMDF

FMDF accounts for the effects of chemical reactions in an exact manner and may be used for various types of chemical reactions (premixed, nonpremixed, slow,fast, endothermic, exothermic, etc.).

LES/FMDF can be implemented via complex chemical kinetics models and is applicable to 3D simulations of hydrocarbon flames in complex geometries.

FMDF contains high order information on sub-grid or small scale fluctuations.

The Lagrangian Monte Carlo solution of the FMDF is free of artificial (diffusion) numerical errors. This is very important in IC engine simulations as overprediction of temperature could cause numerical ignition!

Application of LES/FMDF to Various FlowsApplication of LES/FMDF to Various Flows

Axisymmetric Dump Combustor

Spray Controlled Lean Premixed Square Dump Combustor

IC Engines with Moving Valves/Piston complex cylinder head/piston, spray and combustion

24 Block grid for a 4-valve

Diesel Engine

10 d

eg

ree A

fter

TD

C

Pressure Iso-Levels

Temperature Contours

Wall

Double Swirl Spray Burner

Fuel Injector

62 mm

40 mm

33 mm

19 mm

Inner Air Flow

Outer Air Flow

Atomization gas

Fuel

20mm 70mm

Dyn. Smag-filtered Dyn. Smag-Averaged Smag Cd=0.01 Exp. Data

Axial Velocity Contours

LES of Cold Flow Around a Poppet Valve

Mean axial velocity RMS of axial velocity

x

yGraftieux et al. 2001

Reynolds No = 30,000Mass rate = 0.015 kg/s Dimensions in mm

y

z

5-block LES grid

PistonPiston

5th cycle instantaneousaxial velocity contours m/s

Grid compression or expansion

4-block moving structured grid for LES

Morse et al. (1978)Comp. ratio 3:1 , RPM=200 , Re=2000

Crank angle=144oCrank angle=36o

LES of Flow in a Piston-Cylinder Assembly

Dynamic Smag Smag, Cd=0.01Exp. Data

Mean VelocityMean Velocity RMS of Velocity

CA

=36

oC

A=

144o

Mean values computed by doing both azimuthal and ensemble averaging over cycles

LES of Flow in a Piston-Cylinder Assembly

Rapid Compression Machine – LES/FMDF Predictions

In-CylinderIn-Cylinder

PistonPiston

Simple Piston GrooveSimple Piston Groove

TemperatureTemperatureContoursContours

Hydraulic Chamber Driver ChamberMain Ignition Chamber

Spark Plug

Fuel Injector

Optical Access

piston

piston

piston

Non-Reacting RCM Simulations

Temperature

Pressure

FDFD

MCMC

MCMC

FDFD

Temperature ContoursTemperature Contours

Fuel Mass Fraction ContoursFuel Mass Fraction Contours

Rapid Compression Machine - LES/FMDF Predictions

Reacting Simulations - Consistency between Finite-Difference (FD) and Monte Carlo (MC) values of Temperature and Fuel Mass Fraction

Rapid Compression Machine - LES/FMDF Predictions

Non-Reacting FlowsTemperature Contours

Flat Piston

Non-Reacting FlowsTemperature Contours

Creviced Piston

Reacting Flows without SprayCreviced Piston at 5msec

Reacting Flows with Ethanol Spray

Temperature Ethanol CO2Pisto

nP

iston

Pisto

nP

iston

Pisto

nP

iston

3D Shock Tube Problem – LES/FMDF Predictions3D Shock Tube Problem – LES/FMDF Predictions

3D Shock Tube3D Shock Tube

pp22/p/p11=15=15

pp11

pp22

Two-Block GridTwo-Block Grid

5 MC per cell5 MC per cell 20 MC per cell20 MC per cell 50 MC per cell50 MC per cell

Compressibility effect is included in FMDF-MC . Without Compressible term FMDF-MC results are very erroneous. Number of MC particles per cell is varied but particle number density does not affect the temperature. By increasing the particle number per cell MC densitybecomes smoother but temperature is the same for all cases.

Modeling of Engine Modeling of Engine ConfigurationConfiguration

Spark Plug Exhaust PortInjector

Cylinder Pistonfuel spray

MSU 3-Valve Direct-Injection Spark-Ignition Single-Cylinder Engine

Bore 90 mmStroke 104 mmCompression Ratio 9.8/11Engine Speed 2500 rpm

Intake valves 2 tilted with 5.1o D = 33 mm

Exhaust valve 1 tilted with 5.8o D = 37 mm

MSU 3-Valve DISI Engine:Bore=90mm Stroke=106mm

Direct-Injection Spark-Ignition Engine – LES Direct-Injection Spark-Ignition Engine – LES PredictionsPredictions

18-block Grid

2D Cross Section of 2D Cross Section of 18-block LES Grid18-block LES Grid

Pressure Pressure contourscontours

Valve lift= 11mmPiston velocity=13m/sCrank angle=100o

Valve lift= 5mmPiston velocity=1.5m/sCrank angle=175o

Axial VelocityAxial Velocity

piston

Direct-Injection Spark-Ignition Engine – LES Direct-Injection Spark-Ignition Engine – LES PredictionsPredictions

CA=90 CA=270CA=140

CA=100o CA=220o

piston piston piston

CA=340o

Contours of Evaporated Fuel Mass Fraction

LES/FMDF ofLES/FMDF of 3-Valve DISI Engine with Spray and Combustion 3-Valve DISI Engine with Spray and Combustion

Consistency between Finite Difference (FD) and Monte Carlo (MC) parts of the hybrid LES/FMDF numerical solver

In-Cylinder Temperature Volume Averaged

Crank angle of 350 5 mm from TDC

Instantaneous Values

LES/FMDF Predictions of MSU’s 4-Valve Diesel EngineLES/FMDF Predictions of MSU’s 4-Valve Diesel Engine

Pressure Contours

Temperature Contours

24 Block grid for a 4-valve Diesel Engine

Pressure Iso-Levels

Beginning of Compression

CA=190

LES/FMDF of MSU’s 4-Valve Diesel EngineLES/FMDF of MSU’s 4-Valve Diesel Engine

14o BeforeTDC

6o BeforeTDC

6o AfterTDC

Contours of Evaporated Fuel Mass Fraction and Fuel Droplets

Temperature Contours

LES/FMDF of LES/FMDF of MSU’s 4-Valve MSU’s 4-Valve Diesel EngineDiesel Engine

10 degree After TDC

Temperature Contours

Numerical Simulations of 3-Valve DISI Engine

Without Sprayair mass via cell volume = air mass via ideal gas

With Spray – Valves Closedmass of liquid fuel+evaporated fuel = injected liquid fuel

Variations of mean Temperature

Overall Validation of the model

Simulations of 3-Valve Engine – Spray

In-cylinder Spray Modeling:Initial droplet size, position and

velocity distributionDroplet breakup and collision

modelsMulti-component non-

equilibrium evaporation models

Wall collision and film models

• Stroke: 105.8 mm• Compression Ratio: 11:1• Eight nozzles with cone angle of 8

degree each. Initial SMD: 30 m• Injection Velocity: 50 m/s

Secondary Break-up ModelsSecondary Break-up Models::1) Taylor Analogy Break-up (TAB) -1) Taylor Analogy Break-up (TAB) -

Spring, mass and damperSpring, mass and damper2) Rayleigh-Taylor Break-up (RTB) -2) Rayleigh-Taylor Break-up (RTB) - RT instable wavesRT instable waves3) Kelvin-Helmond Break-up (KHB) -3) Kelvin-Helmond Break-up (KHB) - KH invisid instable wavesKH invisid instable waves4) KH/RT Break-up model4) KH/RT Break-up model

Primary Break-up ModelPrimary Break-up Model: : Parent Parent droplets injected with specific droplets injected with specific velocities and diameters (bold model)velocities and diameters (bold model)

Simulations of 3-Valve Engine – Chemistry

Ethanol

• Detailed Kinetics: e.g. 372 elementary reactions and 57 species for ethanol • Multi-Step Reactions

• Global Mechanisms

• Ignition delays calculated from detailed Mechanism using CHEMKIN for homogeneous 0-D reactor based on equivalence ratio and temperature conditions prevalent in the cell

• By addition of ignition delay, the unphysical phenomenon of autoignition in numerical simulation of SI engines do not occur.

Simulations of 3-Valve DISI Engine – Effects of Fuel

Operating conditions are the same for both fuels

Mixtures are stoichiometric when all fuel is evaporated and mixed

CombustionNo combustion for ethanol fuel

Vaporization No significant evaporation for ethanol

Summary and ConclusionsSummary and Conclusions A robust and affordable LES model is developed for detailed simulations of

various realistic single-cylinder engines: (i) A multi-block compressible LES solver in generalized coordinate system, (ii) Combustion and spray simulations are via a new Lagrangian-Eulerian-

Lagrangian LES/FMDF methodology

Several test cases are simulated with the newly developed models: (i) flow around a poppet valve, (ii) flow in a piston-cylinder assembly, (iii) flow in a single-cylinder three-valve direct-injection spark engine, (iv) flow in a single-cylinder four-valve diesel engine

LES with high-order numerical methods, dynamic SGS models and two-phase FMDF can predict the complex in-cylinder turbulent flows with spray and combustion in realistic engines

Detailed experimental data, under controlled and well defined flow conditions are needed for complete validation of LES/FMDF

LES/FMDF is used for studying effects of (i) chemistry model, (ii) spray model and (iii) various parameters on turbulence, mixing and combustion,