Large Eddy Simulations of
Turbulent Spray Combustion
in Internal Combustion
Engines
Farhad Jaberi
Department of Mechanical Engineering
Michigan State University
East Lansing, Michigan
Background
 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-EulerianLagrangian mathematical/numerical methodology.
LES/FMDF of Single-Phase Turbulent Reacting Flows
Scalar FMDF - A Hybrid Eulerian-Lagrangian Methodology
Monte Carlo
Particles
Vorticity Contours & Monte
Carlo Particles
dx
dz
G
dy
p2
p1
d1
d2
LES/FMDF of a
Dump Combustor
Gasdynamic
Field
Wall
Various closures for subgrid
stresses
Nozzle
Scalar Field
(mass fractions
and temperature)
Pressure Isolevels
Chemistry
Lagrangian Monte
Carlo Particles
Eulerian Grid
Filtered continuity and
momentum equations via a
generalized multi-block highorder finite difference Eulerian
scheme for high Reynolds
number turbulent flows in
complex geometries
Filtered Mass Density Function
(FMDF) equation via Lagrangian
Monte Carlo method - Ito Eq. for
convection, diffusion & reaction
Kinetics: (I) reduced kinetics
schemes with direct ODE or
ISAT solvers, and (II)
flamelet library with detailed
mechanisms or complex
reduced schemes.
Fuels: methane, propane,
decane, kerosene, heptane,
JP-10
CO2 and C7H16 Mass Fractions

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)
3
LES of Two-Phase Turbulent Reacting Flows
A New Lagrangian-Eulerian-Lagrangian Methodology
Gasdynamics Field
Filtered continuity and momentum equations
via a generalized multi-block high-order finite
difference Eulerian scheme for high Reynolds
number turbulent flows in complex geometries
Various closures for subgrid stresses
Scalar Field
(mass fractions
and temperature)
Droplet Field
(spray)
Chemistry
Filtered Mass Density Function (FMDF)
equation via Lagrangian Monte Carlo method Ito Eq. for convection, diffusion & reaction
Lagrangian model for droplet equations with
full mass, momentum and energy couplings
between phases and a stochastic sub grid
velocity model
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 Flows
A New Lagrangian-Eulerian-Lagrangian Methodology
Spray-Controlled
Dump Combustor
Wall
Fuel
Injector
dx
dz
G
dy
p1
p2
dx
Eulerian Cell
- Eulerian Grid
Mass,Momentum,Scalar
Terms from Droplets
• Monte Carlo Particles
Liquid Fuel Droplets
•
d2
d1
Fuel Droplets
dy
p1
p2
Monte-Carlo particles
Wall
dz
G
FMDF
Solver
d2
d1
FMDF
Solver
LES
Solver
Eulerian Finite
Difference Grid
Interpolation /
Favre Filter
Monte Carlo
Particles
Droplet
Equations
Lagrangian
Filtered Equations - Eulerian
_____
ˆf   f x, t Gx  xdx and fˆ  f / 



J  uˆi
Droplet terms


 JS 
t
t
 i
 uˆi
J  uˆiuˆ j
P   uˆ j    uˆi 
J
  uˆi 
 
e

e
 JSui
t
t
 j
i i   j   j   j 
J
P uˆi
 Eˆ
J  Eˆ uˆi
ˆ
J
 E 

t
t
i
i
 ˆ uˆi  q
   J S  JS E

   
i
 j 
ˆ
J i M i
J ˆ uˆi
ˆ
J
 



 J S  JS 
t
t
i
i
xi
NS

0
ˆ
P   ( RT )   TR  
 1 MW
^
FMDF Equation
Lagrangian
Reaction terms
Two-phase subgrid
scalar FMDF:

 PL / 
PL 
 

ui L PL  ~  ~t 
t xi
xi 
xi

Droplet terms

l
 
dX i
 vi
dt
dvi
f
 1 (ui*  vi )
dt  d
dTp

dt
dmp
 m p
dt
KH
RT
L dmp
f 2 *

T  Tp   v
p
mpCL dt
f3
p
ln1  BM 
 p d p2
CD Re p
Nu
sh
p 
, f1 
, f2 
, f3 
18 
24
3 Pr 2
3Sc
 dm p
 dt
S  
1
V
  
SE  
1
  m C
V

P
L



Sui  
1
V
 dmP vi 

dt 
 
dv dv 
dTP
dmP dmP
)  TPCP
)
(h0  Lv)  mP i i 
dt
dt
dt
dt dt 

PL (; x, t )    ( x, t ) (, ( x, t ))G( x  x)d x

 

 m   

 

  S   PL 




   ()  


KH/RT Break-up
Reaction term
L
P   S ()P 

L
L

 S    PL 

  S   PL /  ()
 () 



Main Features of LES/FMDF
 Large scale, unsteady, non-universal, geometrydepended 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 Flows
Axisymmetric
Dump Combustor
Nozz
le
Inner
Swirler
Outer
Swirler
62 mm
40 mm
33 mm
19 mm
Fuel
Air, Outer
Annulus
Double Swirl Spray Burner
Air Inner
Annulus
Atomization
Gas
Fuel
Atomization
gas
Inner Air Flow
Outer Air
Flow
Spray Controlled Lean Premixed
Square Dump Combustor
Fuel
Injector
Wall
10 degree After TDC
IC Engines with Moving Valves/Piston complex
cylinder head/piston, spray and combustion
Temperature
Contours
24 Block grid for
a 4-valve
Diesel Engine
Pressure
Iso-Levels
LES of Cold Flow Around a Poppet Valve
Reynolds No = 30,000
Mass rate = 0.015 kg/s
Dimensions in mm
5-block
LES grid
Graftieux et al. 2001
y
z
Axial
Velocity
Contours
70mm
20mm
Mean axial velocity
Dyn. Smag-filtered
Dyn. Smag-Averaged
x
y
RMS of axial velocity
Smag Cd=0.01
Exp. Data
LES of Flow in a Piston-Cylinder Assembly
4-block moving
structured
grid for LES
Piston
Grid compression
or expansion
Morse et al. (1978)
Comp. ratio 3:1 , RPM=200 , Re=2000
Crank angle=36o
5th cycle instantaneous
axial velocity contours m/s
Crank angle=144o
LES of Flow in a Piston-Cylinder Assembly
Mean values computed by doing both azimuthal and ensemble averaging over cycles
Smag, Cd=0.01
Exp. Data
CA=36o
Dynamic Smag
CA=144o
Mean Velocity
RMS of Velocity
Rapid Compression Machine – LES/FMDF Predictions
Optical Access
Simple Piston Groove
Spark Plug
Fuel Injector
In-Cylinder
Piston
Main Ignition Chamber
Hydraulic Chamber
Driver Chamber
Non-Reacting RCM Simulations
piston
Temperature
piston
Temperature
Contours
Pressure
Rapid Compression Machine - LES/FMDF Predictions
Reacting Simulations - Consistency between Finite-Difference (FD) and
Monte Carlo (MC) values of Temperature and Fuel Mass Fraction
FD
MC
Temperature Contours
FD
MC
Fuel Mass Fraction Contours
Rapid Compression Machine - LES/FMDF Predictions
Piston
Non-Reacting Flows
Temperature Contours
Flat Piston
Piston
Non-Reacting Flows
Temperature Contours
Creviced Piston
Temperature
Ethanol
CO2
Piston
Reacting Flows with
Ethanol Spray
Reacting Flows without Spray
Creviced Piston at 5msec
3D Shock Tube Problem – LES/FMDF Predictions
3D Shock Tube
p1
p2
Two-Block Grid
p2/p1=15
 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 density
becomes smoother but temperature is the same for all cases.
5 MC per cell
20 MC per cell
50 MC per cell
Modeling of Engine Configuration
MSU 3-Valve Direct-Injection Spark-Ignition Single-Cylinder Engine
Bore
Stroke
Compression Ratio
Engine Speed
Intake valves
90 mm
104 mm
9.8/11
2500 rpm
Injector
Spark Plug
Exhaust Port
2 tilted with 5.1o D = 33 mm
Exhaust valve 1 tilted with 5.8o D = 37 mm
Cylinder
fuel spray
Piston
Direct-Injection Spark-Ignition Engine – LES Predictions
MSU 3-Valve DISI Engine:
Bore=90mm Stroke=106mm
Axial Velocity
18-block Grid
2D Cross Section of
18-block LES Grid
Valve lift= 11mm
Piston velocity=13m/s
Crank angle=100o
Pressure
contours
piston
Valve lift= 5mm
Piston velocity=1.5m/s
Crank angle=175o
Direct-Injection Spark-Ignition Engine – LES Predictions
CA=100
o
CA=220o
CA=340o
piston
piston
piston
Contours of Evaporated Fuel Mass Fraction
CA=90
CA=140
CA=270
LES/FMDF of 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
Crank angle of 350
5 mm from TDC
Instantaneous Values
In-Cylinder
Temperature
Volume Averaged
LES/FMDF Predictions of MSU’s 4-Valve Diesel Engine
24 Block grid for a 4-valve
Diesel Engine
Beginning of
Compression
CA=190
Pressure Iso-Levels
Pressure
Contours
Temperature
Contours
LES/FMDF of MSU’s 4-Valve Diesel Engine
14o Before
TDC
6o Before
TDC
6o After
TDC
Temperature Contours
Contours of Evaporated Fuel Mass Fraction and Fuel Droplets
LES/FMDF of
MSU’s 4-Valve
Diesel Engine
Temperature
Contours
10 degree
After TDC
Numerical Simulations of 3-Valve DISI Engine
Overall Validation of
the model
Without Spray
air mass via cell volume = air mass via ideal gas
Variations of mean Temperature
With Spray – Valves Closed
mass of liquid fuel+evaporated fuel = injected liquid fuel
Simulations of 3-Valve Engine – Spray
In-cylinder Spray Modeling:
 Initial droplet size, position and
velocity distribution
 Droplet breakup and collision
models
 Multi-component non-equilibrium
evaporation models
 Wall collision and film models
Primary Break-up Model: Parent
droplets injected with specific
velocities and diameters (bold model)
Secondary Break-up Models:
1) Taylor Analogy Break-up (TAB) Spring, mass and damper
2) Rayleigh-Taylor Break-up (RTB) RT instable waves
3) Kelvin-Helmond Break-up (KHB) KH invisid instable waves
4) KH/RT Break-up model
•
•
•
•
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
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
Vaporization
No significant evaporation for ethanol
Combustion
No combustion for ethanol fuel
Operating conditions are the same for both fuels
Mixtures are stoichiometric when all fuel is evaporated and mixed
Summary 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-EulerianLagrangian 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 singlecylinder 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,