Large Eddy Simulations of
Two-Phase Turbulent
Reacting Flows
Zahouri Li and Farhad Jaberi
Department of Mechanical Engineering
Michigan State University
East Lansing, Michigan
Multiphase Flows
Single Component
Multi-Component
Phase Change
liquid in gas
solid-gas
solid-liquid
gas bubble in liquid
evaporation/condensation
solidification/melting
with/without
phase change
chemical reactions
Our focus is on turbulent sprays with
droplet evaporation and combustion
Modeling and Simulations of Spray Combustion
 Liquid Atomization
 Dense spray (primary breakup)
 Characteristics: large liquid structures/volume fraction, complex interface topology and small total
interface surface area
 Our Approach: MSU’s hybrid Lagrangian-Eulerian particle-level set method for two-fluid turbulent flows
 Intermediate and dilute spray (secondary breakup)
 Characteristics: small liquid structures/volume fraction, simpler droplet geometry, large total interface
surface area and with droplets’ evaporation, breakup, collision, mixing and reaction.
 Our Approach: MSU’s Lagrangian-Eulerian-Lagrangian LES/FMDF methodology for two-phase
turbulent reacting flows
 Modeling and Computational Challenges







Jump in fluid properties (e.g. ρ) across interface, ρf/ρg=O(1000)
Discontinuity in the interface, physics of interface, surface tension
Rapid and complex topology changes, formation and breakup of ligaments and droplets
Turbulence in one or both phases
Large range of scales: from µm to cm
Interactions between interface and turbulence
Evaporation, mixing and reaction
Mathematical and Numerical Approaches
to Two-Phase Turbulent Flows
 Eulerian-Eulerian Models
Mathematical
Model
 Eulerian-Lagrangian Models
 Lagrangian-Lagrangian Models
 Direct Numerical Simulation
Computational
Approach
 Large Eddy Simulation (LES)
 Reynolds-Averaged Simulation
 Eulerian: Transport equations
for the SGS moments
- Deterministic simulations
 Lagrangian: Transport equation
for the FMDF
- Monte Carlo simulations
 Lagrangian: Spray (droplet)
equations
- Point particle simulations
 Coupling of Eulerian &
Lagrangian fields and a certain
degree of “redundancy”
Filtered Equations
Eulerian
f
 


l
l
t
 
  f x, t Gx  x dx and f

 
ui
l

L
H
l
L
t
 

l
t
L
 


ui
l
L
l
H
uj
L
L
ui

L
xi
 
1
Pl

 rMr2
l
l
 L ui
xi
RT
L
 f
l
/ 
l
dm p
l
x j
 
L
Droplet terms
 S
L
xi
t
 
ui
l
Droplet Equations
Lagrangian
dvi
f
V
 1 ui*  vi   di
dt  p
p
dX i
 vi
dt
 P
xi


L
1


 rMr2
FMDF Equation
Lagrangian
l
q

l
xi
 J i

1   ij l 1

 l ni  ij
Re x j
Fr
x j
N
 i  SH
xi
l
R
L
 Sui
l
M i

 S l  S 
xi
l
xi
T
dt
dTp
NS
0

l
dt
l

f3
p
ln 1  BM  ,
f 2 *
L dm p

T  Tp   v
p
m pCL dt
Re 0  p d p2
CD Re p
Nu
sh
, f3 
18 
24
3 Pr  2
3Sc
 mP f 3

1
dmP 
1

S  
ln( 1  BM ) S ui  
 Fi  vi




V   P
V 
dt 

p 
SH  

MW

1
 m p

1
V
, f1 
, f2 
 m C  f

P P 2 2
T *  TP  Fi (vi  ui* )
2

 r  1) M r  p

h
vi vi  ui*ui*
1
dm 
v,s

(

 ui*vi ) P 


2
V  ( r  1) M r
2
dt 
  (
Two-phase subgrid FL (; x, t )    ( x, t ) (, ( x, t ))G( x  x)d x

scalar FMDF:


Reaction terms
 PL /  l  
PL 
 

S () PL 

ui L PL  ~  ~t 
 m    L PL 

t xi
xi 
xi  


  S   PL    S    PL 




  S   PL /  ()
Droplet terms
   ()     () 




 
 


Application of LES/FMDF to Subsonic Flows
Axisymmetric
Combustor
Homogeneous
Compressible
Turbulent
Combustion
Double
Swirl
Spray
Burner
Spray Controlled Lean Premixed
Square Dump Combustor
Round and
Planar
Singleand
Two-Phase
Reacting
Jets
IC Engine With Moving
Valves/Piston and
complex cylinder head
LES of an In-Cylinder Turbulent Flow
Morse et al. (1978)
Comp. ratio 3:1
RPM=200
Re=2000
Dimensions are mm.
4-block moving structured
grid for LES
grid compression
or expansion
Crank angle=36o
5th cycle instantaneous
axial velocity contours
m/s
Piston
Crank angle=144o
LES of an In-Cylinder Turbulent Flow
Smag, Cd=0.01
Exp. Data
CA=36o
Dynamic Smag
CA=144o
Mean Velocity
RMS of Velocity
x
Sandia's Piloted Turbulent CH4/Air Jet Flames
q
r
(Experiments by R. S. Barlow and J. H. Frank)
LES/FMDF + 12-step kinetics Predictions
Pilot
x/D = 15
Coflow
x/D = 7.5
Fuel
Flame D (Re=22400)
Main Jet :
25%CH4 +
75%Air

Flame F (Re=44800)
x/D = 7.5
x/D = 15
 Nozzle
Diameter
= 7.2mm
 Flame D:
ReD=22400
 Flame F:
ReD=44800
x
Sandia's Piloted Turbulent CH4/Air Jet Flames
q
r
(Experiments by R. S. Barlow and J. H. Frank)
LES/FMDF + 12-step kinetics Predictions
Pilot
x/D = 15
Coflow
x/D = 7.5
Fuel
Flame D (Re=22400)
Main Jet :
25%CH4 +
75%Air

Flame F (Re=44800)
x/D = 7.5
x/D = 15
 Nozzle
Diameter
= 7.2mm
 Flame D:
ReD=22400
 Flame F:
ReD=44800
Sandia's Piloted Turbulent CH4/Air Jet Flames
(R. S. Barlow and J. H. Frank)
Flame D (Re=22400)
Experiment
LES/FMDF+12-step Kinetics
Flame F (Re=44800)
Experiment
LES/FMDF+12-step Kinetics
Particle-Laden Turbulent Jet with Two-Way Coupling
Vorticity
Isolevels
Finite Difference (FD)
Temperature
Contours
Consistency for Reacting Flows with Spray
Monte Carlo (MC)
8
8
FD
MC
x/R=2
6
Radial
Variations of
Temperature
4
Temperature
Temperature
6
62 mm
40 mm
0
19 mm
0.4
0
1
2
r/R
3
FD
MC
Inner Air Flow
Outer Air
Flow
Schematic of
Double-Swirl Spray Burner
Prof. Gupta’s experiment
2
r/R
3
4
FD
MC
0.3
Radial
Variations
of
Fuel Mass
Fraction
0.2
0.1
0
1
x/R=4
0.3
Atomization
gas
0
0.4
x/R=2
Fuel
0
4
0
0.5
1
r/R
1.5
2
Fuel Mass Fraction
33 mm
Air, Outer
Annulus
Air Inner
Annulus
Atomization
Gas
Fuel
4
2
2
Inner
Swirler
Outer
Swirler
FD
MC
x/R=4
Fuel Mass Fraction
zz
LES/FMDF of a Double Swirl Spray Burner
0.2
0.1
0
0
0.5
1
r/R
1.5
2
Dump Combustor with Liquid Fuel Spray
 Experimental setup
Reacting flow without spray
0.06
7
FD
MC
Fuel Mass Fraction
6
Temperature
5
4
3
2
0.5
r/D
1
1.5
Fuel Mass Fraction
Temperature
5
4
3
2
0.5
r/D
1
1.5
FD
MC
0.04
x/D=4
0.02
x/D=4
1
0
0
0.06
FD
MC
6
0
0
0.5
r/D
1
1.5
Fuel Mass Fraction
FD
MC
6
5
4
3
2
0.5
r/D
1
1.5
FD
MC
0.04
x/D=6
0.02
x/D=6
1
0
0
0.06
7
Temperature
 Consistency check
x/D=2
0.02
0
0
7
Spray-Controlled Lean Premixed
Square-Section Dump Combustor
(Prof. Yu’s experiment)
0.04
x/D=2
1
0
FD
MC
0
0
0.5
r/D
1
1.5
0
0.5
r/D
1
1.5
Dump Combustor with Liquid Fuel Spray (cont)
Consistency – Instantaneous Centerline
Temperature and Fuel Mass Fraction
Reacting flow with spray
Numerical Experiments
Effects of Flow, Combustion and Spray Parameters
 Spray (Nozzle) Angle
 Spray Injection Angle or Direction
 Average Size of Injected Droplets
 Droplet Injection Velocity
 Droplet Size and Velocity Distribution
 Spray Injection Frequency and Duty Cycle
 Liquid Fuel/Gas Mass Loading Ratio
 Inlet Gas Equivalence Ratio
 Inlet Gas Preheated Temperature
 Inflow Turbulence and Mean Flow Oscillations
 Fuel type
 Pressure
Double Swirl Spray Burner
Enclosed and Unenclosed Flames
Nozzle
x/R=2
Enclosed
Unenclosed
x/R=3.5
Temperature
Vorticity
Vorticity Iso-levels
with fuel droplets
Double Swirl Spray Burner
Effects of Spray Angle ( α )
α=200
α=200
x/R=2
α=200
Vorticity Iso-level
with fuel droplets
α=600
α=600
x/R=4
α=600
Temperature
Vorticity
Double Swirl Spray Burner
Vorticity
Temperature
Effects of Droplet Mass-Loading Ratio (MLR)
MLR=0.04
MLR=0.1
MLR=0.3
A
rS
to
ua
ct
ym
m
ry
et
A
s
xi
Spray Controlled
Lean Premixed
Dump Combustor
y
b
Combustor Symmetry Axis
Effects of
Spray
Injection
Frequency
 = 38 Hz
 = 38 Hz
 = 250 Hz
 = 250 Hz
 = 500 Hz
 = 500 Hz
 = 1 KHz
 = 1 KHz
Pressure Iso-surfaces
Fuel Mass Fraction
Temperature
x/D = 2
x/D = 4
x/D = 6
Effects of Spray Mass Loading
 = 0.01
 = 0.01
 = 0.055
 = 0.055
 = 0.11
 = 0.11
 = 0.22
 = 0.22
 = 0.33
 = 0.33
x/D = 2
x/D = 4
x/D = 6
 = 0.44
Temperature
 = 0.44
Fuel Mass Fraction
SMD=15m
Effects of
Average
Droplet Size or
SMD
SMD=30m
x/D = 3
x/D = 6
x/D = 3
x/D = 6
SMD=45m
SMD=60m
SMD=60m
SMD=90m
SMD=120m
SMD=90m
Temperature Contours
x/D = 6
Effects of
Spray Angle

x/D = 3
 ≈ 0°
 ≈ 20°
 ≈ 40°
 ≈ 80°
Temperature Contours
Effects of Injected Droplet Velocity
up = 60 m/s
up = 15 m/s
up = 30 m/s
up = 60 m/s
Fuel Mass Fraction
up = 30 m/s
Temperature Contours
up = 15 m/s
Effects of Inlet Turbulence Intensity
s
4×
s
s
2×
s
4×
Fuel Mass Fraction
s
2×
Temperature Contours
s
x/D = 6
x/D = 6
Effects of Gas Preheating
Tin = 375 K
Tin = 475 K
Tin = 375 K
Tin = 475 K
Tin = 575 K
Tin = 575 K
Tin = 675 K
Tin = 675 K
Tin = 775 K
Tin = 775 K
Tin = 1100 K
Tin = 1100 K
Temperature
Fuel Mass Fraction
x/D = 6
Hybrid Particle-Level Set (PLS) Method for Dense Spray
 Non-dimensional incompressible two-fluid Navier-Stokes equations

 U  0


 1   (2 ( ) D) 1 k ( )H ( ) 1 y
U
p
    (U  )U 



t
 ( )
Re
 ( )
We
 ( )
Fr y
Level set function:

 0, x  1



 ( x , t )   0, x  
 0, x  
2

and
0

H  ( )  (1     1  sin(   )) / 2
1

  
 
 
 Density and viscosity are modeled as continuous functions of level set function
 ( )    (1   ) H  ( ),  ( )    (1   ) H  ( ) where    2 / 1 and    2 / 1
 Interface transport equations



 (U  )
t
Level set equation

 Particle-based re-initialization procedure
(i,j)
L
TwoDimensional
i
Flu
1
IP-
IP
i
Flu
(i,j-2)
dt
 
 U * (x p )
(i+1,j)
 IP+1
h
(i,j-1)
d1
Particle transport equation

dx p
are density and viscosity ratios
(i+1,j-1)
d2
(i+1,j-2)
Three-Dimensional
Hybrid Particle-Level Set Method ( Numerical Examples )
1
( b )( a )
(a)
60
60
0.6
0.6
Y
Y
Y
40
0.4
t=0.0
t=628.0
(20a )
1
60
X
0.8
Y Y
t=0.0
(b)
0
0.2
0.2
0
0
Y
100
0
0
Interface at t=0
Interface
at
0.2
0.4t=360
40
ParticelsXat t=0X
Particels at t=3
0
0
0.8
20
20
0
20
0.2
40
0.4
X
0.6
X
60
0
0
80
0.8 100
( c( )c )
20
80
80
0.8 100
0
1
X
0
0.2
60
80
0.8
(c)
0.4
4
0.6
2
2
0.8
1
1
2
3
4
0
0
1
2
Y
Interface at t=0
X
Particels at t=0 X
0.6
0.8
0
100
0
4
0
0
1
2
3
4
0
0
1
X/R
8
2
3
4
3
4
X/R
8
8
t=5.0
t=6.0
t=7.0
Interface at t=0
Interface at t=3
Particels at t=0
Particels at t=3
Interface at
0.2
0.4t=3
0
3
X/R
t=4.0
0.4
1
X
8
0.6
0.2 Particels at t=3
1
40
1
0.6
4
X/R
0.2
0
4
(c)
t=0.0
Interface at t=0
t=0.0
Interface
at t=3
Particels at t=0
Particels
at t=3
0.2
t=628.0
6
2
0.6
0.6
t=628.0
6
(b)
Y t=628.0
t=0.0
60
20
0.4
2
0.4
80
0
0
1
6
Interface at t=0
Interface at t=3
Particels at t=0
Particels at t=3
0.4
0.2
0
0
100
(c)
Y
40
100
0.8 100
(b)
1
80
0.4
60
0.6 80
(b)
0.6
628.0
X
X 0.4 60X
0.4
40
Y Y t=628.0
20
0.2 40
0.8
0.6
40
20
0.6
60
60
( b )( a )
0
0.8
0.8
80
0
0
( b () a )
100
0.0
0
100
1
80
(a)
80
4
1
( c()c )
0.2
6
0.8
1
Interface at t=0
Interface at t=3
Particels at t=0
Particels at t=3
Y/R
100
40
0.2
Interface at t=0
Interface at t=3
Particels at t=0
Particels at t=3
1
t=3.0
0.4
4
X
0.6
0.8
6
6
6
Y/R
100
0
0.2
1
8
t=2.0
Y/R
20
20
6
0.4
t=628.0
8
t=1.0
Y/R
t=0.0
8
t=0.0
0.8
Y
40
40
8
0.8
80
Y/R
(a)
80
Y/R
(a)
Y/R
1
100
100
0
Rising Bubble Simulations with
Particle-Level Set Method
(b)
Vortex Stretching
Y/R
Zalesak Disk
4
4
4
2
2
2
1
(c)
0.8
0.6
60
Y
2
Y
t=0.0
0.6
0.4
40
Y t=628.0
t=0.0
0
0
0.4
20
0.2
t=628.0
0.2
0
20
40
X
0
20
60
40
X
60
80
0
100
Interface at t=0
Interface at
0.2
0.4t=3
0
Particels at t=0X
Particels at t=3
0.6
0.8
( a ) Level set method without
reinitialization,
X
( b ) Level set method with reinitialization
( c ) Hybrid particle-level set method
80
100
0
0
0.2
0.4
0.6
0.8
1
1
2
3
4
X/R
Interface at t=0
Interface at t=3
Particels at t=0
Particels at t=3
1
Re  100
0
0
1
2
3
X/R
4
0
0
1
2
3
X/R
4
0
0
1
2
X/R
We  200   1 : 100   1 : 200
Re=Reynolds number We=Weber Number
   2 / 1 and    2 / 1
Application of PLS to Two-Fluid Isotropic Turbulence
  1 and We  
  20 and We  10
  1 and We  10
  10 and We  2
   2 / 1 and 
We=Weber
2 / 1 number
  10 and We  10
  10 and We  20
Application of PLS to Two-Fluid Isotropic Turbulence
0
0
1
2
3
4
X
5
0
6
0
1
2
3
X
4
5
6
(b)
66
6
Comparison of PLS with ZMA
5
for
low density-ratio
two14
phase isotropic
turbulence
4
(a)
12
100
(a)
Y
(a)
55
44
2
10-2
8
4
(b)
YY
(b)
Energy spectrum
10
5
100
10-2
3
d)
We  (20
6
(c
b ))
We  100
Y
33
3
22
2
11
1
10-4
1
E(K)
-4
10 6
0
E(K)4
10-6
0
1
2
3
X
4
4
11
22
0
33
X
X
44
55
0
66
t
3
41
10
4
102
K
3
2
102
1
2
3003
3
X
4
5
ZMA with Pr=0.7
ZMA with Pr=60
IPLS with We=100
1500
4
100
0
0
ZMA with Pr=0.7
1ZMA with Pr=60
2
IPLS with We=100
6
250
t
3
4
 l 1 ( /  )2 
 3
t
0
1.5
Case6 We  5
0.5  10
Case3 We
1
2
2
10
1
0
0.5
1
1.5
t
2
0
10 0
0
2.5
0.5
0.5
1
1
tt
1.5
1.5
Case7 We
 20
0
2
2
2.5
2.5
0
10
-5
10
-7
1
10
-11
10
-13
0.5
0
10-2
10
-4
10
-6
Case 1
8
Case 2
Case 3
4
(d)
6
Case 0
2
t
Case 0
Case 1
Case 1
Case 2
Case 3
2
2
15
ZMA
E(K)with Pr=0.7
ZMA with
Pr=60
-9
IPLS10with We=100
150
100
2.5
FIG. 11. Temporal variations of lengths of10interfaces under different conditions. ( a )
010various density ratios, ( b ) various Weber number.
6
10
0
1
2
3
5
(b)
( a )6
X 4
(
c
)
Case
0
10
200
2001
6
Case5 We  2
-3
2502
5
(( ab ))
4
-1
0
4
6
(d)
Case4   20
300
0
X
Case 5
Case 6
Case 3
Case 7
20
3
1
3504
3
4
350
(d)
(C)
2
8
(d)
Y 15
Case3   10
(C)
Enstrophy dissipation rate
4005
Case1   1
1
Case 1
K
5
400
Case1
 5
Y
6
10-10 0
10
0
25
10
(a)
ZMA with Pr=60
IPLS
with We=100 Case 2
6
Case 3
20
Case 4
101
(c)
ZMA with Pr=0.7
1 ZMA with Pr=60
52
IPLS with We=100
-10
100
( bZMA
) with Pr=0.7
10-8
ZMA with Pr=0.7
ZMA with Pr=60
6
IPLS with We=100
2
10
00 0
0
6
25
10-6
10-8
0
5
10-8
Case 4 3
2
4
Case 2
Case 3
4
Case 4
2
10-10
4
10-15 0
10
10
1
K
10
2
10-12 0
10
0
0
0.5
110 t K1.5
1
2
10
2
2.5
0
0
0.5
FIG.8. Temporal variation of mean enstrophy in variou
Concluding Remarks
 Turbulent Spray Combustion - Modeling and
Computational Challenges
 Jump in fluid properties (e.g. ρ) across interface
 Discontinuity in the interface, physics of interface, surface tension
 Rapid and complex topology changes, formation and breakup of
ligaments and droplets
 Turbulence in one or both phases
 Large range of scales: from µm to cm
 Interactions between interface and turbulence
 Evaporation, mixing and reaction
 Reliable subgrid-scale models for LES of dense, intermediate
regimes of turbulent sprays – detailed experimental and DNS data
are needed
Concluding Remarks (cont.)
 For dense spray simulation
 A hybrid Lagrangian-Eulerian particle level set (PLS) model is developed
and validated against standard interface tracking, laminar, and turbulent
2D two-phase problems.
 PLS model is being extended to 3D. LES via PLS is being considered.
 For dilute and intermediate spray simulation
 A Lagrangian-Eulerian-Lagrangian LES/FMDF model is developed.
The model is successfully applied to variety of single- and two-phase
turbulent (non-)reacting flows.
 The LES/FMDF is being further improved, validated and applied to
more complex problems.
 For integrated simulation of turbulent spray combustion
 Coupling of LES/PLS and LES/FMDF model ?????