Modeling and Large-Scale
Simulations of Turbulent Reacting
Flows
Farhad Jaberi
Department of Mechanical Engineering
Michigan State University
East Lansing, Michigan
Objectives:
 Develop a validated high-fidelity numerical model for high speed
turbulent reacting flows
 Study the effects of various flow, combustion and spray parameters
for “laboratory combustors'' - Numerical experiments
 Integrated simulation of a model combustion/propulsion system
Approach:
 A new high-order, multi-block Eulerian-Lagrangian-Lagrangian
LES/FMDF methodology is developed for simulations of two-phase
subsonic turbulent reacting flows in complex configurations
 LES/FMDF is being improved and extended for application to high
speed (supersonic and hypersonic) turbulent reacting flows
 DNS and experimental data are used for improvement and
validation of LES/FMDF submodels
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 subgrid
velocity model
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
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
Operator
Monte Carlo
Particles
LES of Two-Phase Turbulent Reacting Flows
A New Lagrangian-Eulerian-Lagrangian Methodology
f

l
  f x, t Gx  x dx, f

L

f

Carrier Gas Equations
l
l
      l ui  L

  S   l
t
xi
   l u j  L
t

   l ui  L u j  L
xi
 p l  ij  l  ij  l

    l g j   S ui  l


xi
x j
xi
   l  E  L    l ui  L  E  L
 qi  l N i



 S e  l
t
xi
xi
xi
   l   L    l ui  L   L
 J i  l M i



  S  l   S   l ,
t
xi
xi
xi
p l   lR
0
N
Y T


1
L
M  
  1,2,..., Ns
l
RT
L
LES of Two-Phase Turbulent Reacting Flows
Two-Phase Subgrid Scalar FMDF
PL  , x, t     x, t   ,  x, t G x  x dx
Ns
  , x, t       x, t        x, t 
Fractions
 , x, t  Mass
and Energy
 1
Fine-Grained Density
Scalar FMDF Transport Equation



 PL  l
PL  u i L PL
 


  L D L  Dl
t
x i
x i 
x i
N s 1
N s 1



 m     L PL 
 
 
 1
 1


 

  
S  Reaction terms
S   Droplet terms






 
 Sˆ

Sˆ PL 
 Sˆ  PL



PL
LES of Two-Phase Turbulent Reacting Flows
dX i
 vi
dt
dvi
f
V
 1 ui*  vi   di
dt  p
p
dTp
dt
dm p
dt

f 2 *
L dm p

T  Tp   v
p
m pCL dt
 m p
1
S  
V
Droplet Equations
f3
p
Np
 m
n 1
ln 1  BM  ,
f3
p
p
ln 1  BM 
p 
Re 0  p d p2
18 
, f1 
C D Re p
24
, f2 
Nu
sh
, f3 
3 Pr  2
3Sc
Droplet Source/Sink Terms
 f1 *
Vdi 
f3

m
u

v


m
ln 1  BM vi

p
i
i
p




n 1
p 
p
 p
N
 f2 *

1 p C p 2
f1 *

  m p Vdi vi  m p f 3 ln 1  BM  hv , s  vi vi 




Se  
m
T

T

u

v
v

p
p
i
i
i

V n 1   1M 2   p
p
p
p
2 


1
Sui  
V
Np


LES of Two-Phase Turbulent Reacting Flows
Subgrid-Scale Closures for Carrier Gas
Subgrid Stresses in Momentum Eq. : Tij  
Subgrid Convection in FMDF Eq. :
u
i

L
l
 ui
uu
i
L
P
L
j
L
 ui
  t
L
uj

 PL 
L
l


xi
Subgrid Mixing in FMDF Eq. (LMSE/IEM model) :
2
   
 a 

 

x

x

i
i


PL    
 m    a



a
L
 
L
P 
L
Subgrid Reaction: No model is needed in FMDF methodology!
LES of Two-Phase Turbulent Reacting Flows
Subgrid-Scale Closures for Droplet Field
Subgrid Velocity Field (via a stochastic model) :
2


ui L

P
1
*
du  

 Gij u i*  u i
 xi Re 0 x j x j

L

 dt  C0 dWi


dX i  Ai X dt  Bij X dW j
1 3 
Gij     C0  ij ,
2 4 
  C k 2 3  f ,
  k
Subgrid Energy or Temperature Field : No model is needed!
Subgrid Mass Fractions Fields : No model is needed!
LES of Turbulent Reacting Flows
Velocity-Scalar FMDF
FL V , , x; t  

  x, t  V ,U x, t , ,  x, t Gx  x dx

 V ,U x, t , , x, t    V  U x, t     x, t 
Fine-Grained Density
Velocity-Scalar FMDF Transport Equation
F
1  p
FL
L
v
 
i x
t
ˆ xi
i 
l



 FL  Sˆ  FL
   ij


| V , FL / ˆ 
 
 v 
 
vi  x j

 i
 
  J i

| V , FL / ˆ  

   xi
 vi
Turbulent convection and chemical
reaction terms are closed
 p
| V ,


 xi
l

 pl


FL / ˆ 

xi 

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
Application and Validation of LES/FMDF
Double
Swirl
Spray
Burner
Axisymmetric
Combustor
Spray Controlled Lean Premixed
Square Dump Combustor
Homogeneous
Compressible
Turbulent
Combustion
Round and
Planar
Singleand
Two-Phase
Reacting
Jets
Direct Injection
Gasoline Engine
With Moving
Valves and
complex Piston
& Cylinder Head
Validation of LES Models and
Numerical Schemes
 Jet and bluff body flame
Comparison with
experiment
 Two-phase turbulent jet
 Dump combustor
 Swirl-stabilized burner
 Turbulent mixing layer
Comparison with
DNS
Comparison
between different
LES methods
 Planar turbulent Jet
 Homogeneous turbulent flow
 A generalized high-order
finite difference vs. finite
volume and spectral schemes
Consistency of Eulerian and
Lagrangian fields
Performance of Various Numerical
Methods in Isotropic Turbulence
High-order finite difference vs. second-order finite volume
Consistency of Eulerian-Lagrangian Methodology
 Eulerian: Transport
equations for the SGS
moments
– Deterministic simulations
 Lagrangian: Transport
equation for the FMDF
– Monte Carlo simulations
 Coupling of Eulerian &
Lagrangian fields and a
certain degree of
“redundancy”
Lagrangian Monte
Carlo Particle
Eulerian Grid Point
LES/FMDF of a Dump Combustor
Monte
Carlo
Particles
Vorticity Contours and
Monte Carlo Particles
Spray-Controlled Lean Premixed
Square-Section Dump Combustor
(O. Hsu, B. Pang & K. Yu, 2001)
Wall
Nozzle
Nozzle
Consistency for Non-Isothermal Flows without Reaction & Spray
x/D = 2
x/D = 4
x/D = 4
LES/FMDF of a
Dump Combustor
Consistency for Reacting
Flows without Spray
Nozzle
Centerline
Centerline
Pressure Isolevels
x/D = 2
CO2 and C7H16 Mass Fractions
x/D = 2
Finite Difference
Cold
x/D = 4
Filtered Temperature Contours
x/D = 4
Cold
Monte Carlo
Vorticity Isolevels
and Spray
LES/FMDF of a
Dump Combustor
C7H16 and CO2
Mass Fractions
Consistency for Reacting
Flows with Spray
x/D = 2
x/D = 2
Cold
Finite Difference
Filtered Temperature Contours
Cold
x/D = 4
Monte Carlo
x/D = 4
LES/FMDF of a Double-Swirl Spray Burner
Consistency for Reacting Flow with Spray
Vorticity
Isolevels
8
Finite Difference
T/Tref
x/D=0.0
x/D=2.0
x/D=4.0
x/D=0.0
x/D=2.0
x/D=4.0
Inner
Swirler
Outer
Swirler
33 mm
19 mm
Fuel
Air, Outer
Annulus
Air Inner
Annulus
mization
el
62 mm
40 mm
Atomization
gas
Inner Air Flow
Outer Air
Flow
A Schematic of
Double SwirlStabilized Spray
Burner
Filtered Temperature
7
6
FD
FD
FD
MC
MC
MC
5
4
3
2
Monte Carlo
1
0
0
1
r/D
2
3
Temperature Contours
LES/FMDF of Piloted Turbulent CH4/Air Jet Flames
(R. S. Barlow and J. H. Frank)
x
 Main Jet : 25%CH4 +
q
75%Air
r
 Pilot Flame : equilibrium
composition of methane
and air
 Coflow : air
Pilot
Coflow
 ReD=22400 (flame D)
44800 (flame F)
Fuel
 Nozzle diameter
= 7.2mm
LES/FMDF Predictions of Turbulent Jet Flames
Experimental Assessment of Two-Phase
LES Models
Dispersed Gas-Particle
Turbulent Jet
(Gillandt et al. , 2001)
Jet Diameter : 12mm
Reynolds Number : 5700
Particles : glass beads
Mean Particle Diameter :
0.11mm
Mass Loading Ratio : 1
Volume Fraction: 0.4 %
Experimental Assessment of Two-Phase LES
Experimental Assessment of LES/FMDF
An Axisymmetric Dump Combustor
0.914 m
0.676
0.762 m
Honeycomb Flow
Strighteners
Vorticity Contours
DOP Seeder
Quarts Test Section
5:1 Contraction
Extension Duct
L=596.9 mm
 Lean premixed
propane-air dump
combustor , ER=0.5
Air
 High Reynolds
number, Re=115,000
r=38.1 mm
R=76.2 mm
H=38.1 mm
Axisymmetric Dump Combustor
(Gould et al. 1994)
Multi-Block grid
system
LES/FMDF of a Dump
Combustor
Mean Flow Streamlines
O-H and H-H grid
Axial Velocity
mean axial velocity - Cold flow
LES/FMDF of a Dump Combustor
consistency check and comparison with experiment
Consistency for non-isothermal flows
Finite difference
Finite difference
Hot Gas
Instantaneous Temperature
“Mean” Temperature
Nonreacting Flow
- mixing of
temperature and
passive scalars
Hot Gas
Monte Carlo
Monte Carlo
Reacting
flow
Fuel Contours
Fuel and oxygen isolevels
Heat Release Contours
LES/FMDF of Dump Combustor
Vorticity Isolevels and
Monte Carlo Particles
Low Inflow Turbulence
Low Inflow
Turbulence
Moderate
Inflow
Turbulence
High Inflow
Turbulence
Reacting Flows
Numerical Experiments
Effects of Flow, Combustion and Spray Parameters
 Inflow Turbulence
 Inlet/Outlet Nozzles and Diffusers
 Inlet Premixed Gas Equivalence Ratio
 Inlet Gas Preheated Temperature
 Fuel Type
 Operating Pressure
 Spray (Nozzle) Angle
 Spray Injection Angle or Direction
 Average Droplet Size of Injected Fuel
 Type of Droplet Size Distribution
 Spray Injection Frequency and Duty Cycle
 Liquid Fuel/Gas Mass Loading Ratio
Effects of Inlet/Outlet Nozzles and Diffusers
Inflow
Vorticity
Isolevels
Nozzle
Outflow
Centerline
Temperature
Centerline
Velocity
Vorticity
Isolevels and
Monte Carlo
Particles
ym
m
ry
et
A
s
xi
Effects of
Injection
Angle
rS
to
ua
ct
≈0o
A
LES/FMDF of a
Dump Combustor

Combustor Symmetry Axis
 = 0°
 = 45 o
 = 45°
 = 60 o
 = 60°
Density Contours
Temperature Contours
A
rS
to
ua
ct
ym
m
A
s
xi
Effects of
Injection Angle
ry
et
LES/FMDF of a
Dump Combustor

Combustor Symmetry Axis
x/D = 2
x/D = 2
x/D = 2
x/D = 6
x/D = 6
x/D = 6
Temperature
Fuel Mass Fraction
Pressure
Effects of
Spray Angle

LES/FMDF of a
Dump Combustor
≈0o
 ≈ 0°
 ≈ 20 o
 ≈ 20°
 ≈ 40°
 ≈ 60 o
 ≈ 60°
Density Isolevels
Temperature Contours
Effects of
Spray Angle
x/D = 6
x/D = 2
x/D = 4
x/D = 6
Fuel Mass Fraction
x/D = 4
Temperature
x/D = 2

LES/FMDF of a
Dump Combustor
LES/FMDF of a
Dump Combustor
Effects of
Average
Droplet Size
or SMD
SMD=30m
SMD=30m
SMD=45m
SMD=45m
SMD=60m
SMD=60m
SMD=90m
SMD=90m
Fuel Mass Fraction Contours
Temperature Contours
LES/FMDF of a
Dump Combustor
x/D = 4
x/D = 6
x/D = 6
Fuel Mass Fraction
x/D = 2
x/D = 4
Temperature
x/D = 2
Effects of
Average
Droplet Size
or SMD
LES/FMDF of a Dump Combustor
A
rS
to
ua
ct
A
s
xi
T
( D  50 % )
ry
et

m
Duty cycle D 
Effects of
Injection
Frequency
ym
Effects of
Injection
Duty Cycle
(  = 38 Hz )


Combustor Symmetry Axis
D  25 %

= 38 Hz
D  50 %

= 250 Hz
D  75 %

= 500 Hz
Fuel Mass Fraction Contours
Temperature Contours
A
Effects of
Injection
Frequency and
Duty Cycle
rS
to
ua
ct
m
ry
et
A
s
xi
(x/D=6)
ym
LES/FMDF of a
Dump Combustor

Combustor Symmetry Axis
Frequency
Frequency
Frequency
Duty Cycle
Duty Cycle
Duty Cycle
Temperature
Fuel Mass Fraction
Pressure
A
rS
to
ua
ct
Effects of Injection
Frequency and Duty
Cycle
ym
m
ry
et
A
s
xi
LES/FMDF of a
Dump Combustor

Combustor Symmetry Axis
Pressure Isolevels
 =38 Hz
D=25%
 =250 Hz
D=50%
 =500 Hz
D=75%
Duty Cycle 50%
Frequency 38 Hz
LES/FMDF of a
Dump Combustor
Effects of Inlet Gas
Equivalence Ratio, Preheated
Temperature and Droplet/Gas
Mass Loading Ratio
Temperature
Fuel Mass Fraction
Mass Loading Ratio
Preheated Temperature
Equivalence Ratio
Wall
Nozzle
LES/FMDF of a DoubleSwirl Spray Burner
Effects of Wall and Nozzle
Temperature
Vorticity
Unenclosed
7
T/Tref
x/D=2
x/D=5
x/D=2
x/D=5
6
Unenclosed
Enclosed
Unenclosed
Enclosed
Enclosed
Unenclosed
Unenclosed
5
4
3
2
1
Enclosed
Enclosed
0
0
1
2 r/D
3
4
LES/FMDF of a DoubleSwirl Spray Burner
Open
Effects of Mass Loading
Ratio (MLR)
MLR=0.3
MLR=0.03
MLR=0.1
MLR=0.3
Vorticity
MLR=0.1
Temperature
MLR=0.03
LES/FMDF of a DoubleSwirl Spray Burner
Open
Effects of Spray Angle (  )
Temperature
Vorticity
 ≈ 20°
9
 ≈ 60°
T/Tref
x/D=5 Sprayangle=20
x/D=5 Sprayangle=60
8
 ≈ 20°
 ≈ 20°
7
6
5
4
3
2
1
 ≈ 60°
 ≈ 60°
0
0
1
2 r/D
3
4
Conclusions and Future Research
 In its present form, LES/FMDF is a robust and efficient
mathematical/numerical methodology for single- and twophase subsonic turbulent reacting flows in complex
geometries
 Further development and validation of LES/FMDF –
Improved mixing model, radiation model, spray model, etc.
 Numerical simulations of new combustion systems under
various operating conditions
 Extension and validation of LES/FMDF for high speed
single-phase combustion/propulsion systems
 Integrated simulations of high speed propulsion systems
Extension and Application of
LES/FMDF to High Speed Flows
 Large-scale compressibility effects are explicitly
calculated
 High-order Eulerian (e.g. finite difference) methods for
LES of high speed turbulent flows
 Development and testing of WENO type and other types
of numerical schemes for LES of high speed flows
 Improved SGS velocity models and wall DES methods for
supersonic and hypersonic flows
 Addition of SGS compressibility effects to scalar FMDF
 Addition of SGS compressibility effects to velocity-scalar
FMDF