A High Fidelity Model for Numerical
Simulations of Complex
Combustion/Propulsion Systems
Farhad Jaberi
Department of Mechanical Engineering
Michigan State University
East Lansing, Michigan
Objectives



Develop a high-fidelity numerical model for
high-speed turbulent reacting flows
Study “laboratory combustors'' of interest to
NASA for various flow and combustion
parameters with the new model
Improve basic understanding of turbulent
combustion in supersonic and hypersonic flows
Technical Approach


LES/FMDF: A hybrid (Eulerian-Langranian)
model, applicable to subsonic and supersonic
turbulent combustion in complex configurations
DNS data are used together with experimental data
for validation and improvement of LES/FMDF
submodels
Impact
Progress





New high-order numerical schemes are
developed/validated for supersonic turbulent
flows,
Compressible subgrid stress and energy flux
models are implemented and tested,
Scalar FMDF model is extended and applied to
compressible (supersonic) reacting flows,
LES/FMDF predictions are compared with
experimental data,
DNS data for supersonic mixing-layer are
generated. LES results are compared with the
DNS data.




Numerical Simulations of a scramjet combustor
is now possible but reliability and accuracy of
predictions are dependent on compressible
models
Numerical experimental: A systematic and
detailed study of various flow/reaction
parameters on combustion stability and
efficiency
Better understanding of supersonic combustion
Feedback to experimentalists and designers
Publications: (1) Z. Li, A. Banaeizadeh, F. Jaberi, Large
Eddy Simulation of High Speed Turbulent Reacting
Flows, International Symposium on Recent Advances in
Combustion., 2008. (2) A. Banaeizadeh, F. Jaberi, LES
of Supersonic Turbulent Flows with the Scalar FMDF,
APS-DFD, 2009, (3) Li and F. Jaberi, Numerical
Investigations of Shock-Turbulence Interactions in
Planar Mixing Layer, AIAA Annual Meeting, 2010.
LES of Supersonic
Co-Annular Jet
DNS of Supersonic Mixing Layer
LES/FMDF of Complex Turbulent Reacting Flows
A Hybrid Eulerian-Lagrangian Mathematical/Computational Methodology
Monte Carlo
Particles
Vorticity Contours & Monte
Carlo Particles
dx
dz
G
dy
p2
p1
d2
d1
Gasdynamic
Field
Wall
Filtered continuity and
momentum equations via a
generalized multi-block highorder finite difference Eulerian
scheme for high Reynolds
number turbulent flows in
complex geometries
Various closures for subgrid
stresses
Nozzle
Scalar Field
(mass fractions
and temperature)
Pressure Isolevels
Chemistry
CO2 and C7H16 Mass Fractions

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”
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
Filtered LES Equations -> Eulerian
Total derivative of pressure
in enthalpy equation
_____

fˆ   f x, t Gx  xdx and fˆ  f / 

J
J

J uˆi


0
t
t i
 uˆi
J  uˆi uˆ j
P
  uˆ j
  uˆi



e
t
t
 j
 i  i   j
P uˆi
 Eˆ
J  Eˆ uˆi
ˆ
J
 E 

t
t
i
i

 

 
j

 uˆi
 e
 
j





 ˆ uˆi  q
   J S

   
i
 j 
NS

0
ˆ
P   ( RT )   TR  
 1 MW
Reaction term
Subgrid scalar
FMDF:

 PL / 
PL 
 

ui L PL  ~  ~t 
t xi
xi 
xi



For non-reacting flows:
internal energy/enthalpy
equation obtained from
FMDF-MC is consistent with
LES-FD equation
For reacting flows: reaction
terms are closed in FMDF
^
FMDF Equation
-> Lagrangian
1 Dp

 Dt
 S   PL /  (  )

l
 

PL (; x, t )    ( x, t ) (, ( x, t ))G( x  x)d x

Reaction term
 
 


S () PL 
 m    L PL 


 
Added to FMDF
1 DP


equation as a
 Dt
source/sink term
LES of High Speed Turbulent Reacting Flows
• In LES, large-scale variables are correctly calculated when reliable and accurate
numerical methods+BC , SGS models and chemical kinetics models are provided.
• For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order
numerical schemes have been developed and tested.
• Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been
employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for
supersonic and hypersonic flows are needed.
• Compressibility effects are included in the scalar FMDF for supersonic turbulent
combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows
with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is
established. Better mixing and SGS convection models for FMDF are desirable.
• DNS data for non-reacting supersonic mixing layer are generated and are being used for
evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogenair) mixing-layer are being generated.
• Comparison of LES results with experimental data for supersonic reacting flows is
essential.
• Reliable and efficient reduced chemistry models and solver are needed. However, no
serious problem is expected in the implementation of chemical reaction in LES/FMDF.
Rapid Compression Machine – LES/FMDF Predictions
Optical Access
Piston groove
Spark Plug
Fuel Injector
In-Cylinder
piston
Main Ignition Chamber
Hydraulic Chamber
Driver Chamber
Non-Reacting RCM Simulations
FD: finite-difference (LES)
MC: Monte Carlo (FMDF)
piston
Temperature
piston
Temperature
Contours
Pressure
Rapid Compression Machine - LES/FMDF Predictions
Reacting Simulations - Consistency between finite-difference (LES-FD) and
Monte Carlo (FMDF-MC) values of Temperature and Mass Fractions
FD
MC
Temperature Contours
FD
MC
Fuel Mass Fraction Contours
3D Shock Tube Problem– LES/FMDF Predictions
3D Shock Tube
p2
p1
Two-Block Grid
p2/p1=15
• Compressibility effects are included in FMDF-MC. Without
Compressible term FMDF-MC results are very erroneous.
• By varying the initial number of MC particles per cell, the
filtered temperature does not noticeably change.
• By increasing the initial particle/cell number, MC particle
number density becomes smoother and nearly the same as
filtered density.
5 MC per cell
Particle Number
Density
20 MC per cell
Particle Number
Density
50 MC per cell
Particle Number
Density
Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by
NASA’s Hypersonic Program
Watercooled
combustion
chamber
Spark
plug
H2 fuel
tube
Air+O2
passage
Watercooled
injector
Small-scale facility
Large-scale facility
M=2
vitiated
air jet
CARS/
Rayleigh
beams
Burner/
nozzle
Cutler et al. 2007
Cutler et al. 2007
63.5 mm diam
center jet
Nozzle
(SiC)
10 mm diameter
Center jet
Coflow
nozzle
M=2 setup
Coflow
nozzle
SiC line
Facility flange
Watercooled shell
LES/FMDF of
Co-Annular Jet
3D LES
Calculations with
Compact Scheme
Mixing and combustion
Iso-Levels of
Mach Number
Grid System for LES
Iso-Levels of
Mach Number
LES/FMDF of Supersonic Co-Annular Jet
Mixing Case – No Combustion
Vorticity Magnitude
Pressure
Temperature
Experiment
Smagorinsky
MKEV 0.02
MKEV 0.03
LES of Supersonic Co-Annular Jet
Mixing Case – No Combustion
LES/FMDF of Supersonic Co-Annular Jet – Mixing Case
Instantaneous Scalar
Experiment
Smagorinsky
MKEV 0.02
MKEV 0.03
Instantaneous Scalar
LES/FMDF of Supersonic Co-Annular Jet – Consistency of FD and MC
LES - FD
Instantaneous Scalar
Mean Scalar
FMDF - MC
Experiment
LES-FD
FMDF-MC
DNS and
LES of
Supersonic
Turbulent
Mixing Layer
Pressure Contours
M1=4.2
Vorticity Contours
M2=1.8
DNS Without Incident Shock
Wave
4
0.5
3.5
(U-Uc)/(U1-U2)
x=222
x=275
3
x=347
U
2.5
x=222
x=275
x=347
0
2
Re=400
1.5
-0.5
-10
0
-10
10
Re=300
0.5
(U-Uc)/(U1-U2)
y
(y-y0 )/ 
0
10
0.5
(U-Uc)/(U1-U2)
1
Re=350
Re=400
Re=500
0
amp=0.04
amp=0.08
0
amp=0.08
Re=400
-0.5
-0.5
-10
0
(y-yo)/  (x)
10
-10
0
(y-yo)/ (x)
10
Vorticity Contours
LES of Supersonic Turbulent Mixing-Layer - No Shock
3
DNS
2.5
NOMODEL
LES-MKEV
2
LES-MIXED
LES-Smag

1.5
1
0.5
0
-0.5
0
100
200
x
300
400
3
DNS
2.5
NOMODEL
LES-MKEV
2
LES-MIXED

LES-Smag
1.5
1
0.5
0
-0.5
0
100
200
x
300
400
Vorticity
0
1.5
LES of Supersonic Turbulent
Mixing-Layer - No Shock
y
-10
X=222
0
3.5
X=275
3.5
-10
10
X=222
X=347 1
1
X=275
0
y
1
DNS
DNS
DNS
NOMODEL
LES-MKEV
LES-MKEV
LES-Smag
LES-Smag
DNS
NOMODEL
3
3
LES-MKEV
LES-MKEV
LES-Smag
LES-Smag
0.5
2.5
2.5
-10
Mean Axial Velocity
U

U
2
2
0
1.5
0
1.5
y
-10
-10
10
y
0
DNS
DNS
NOMODEL
3
LES-MKEV
LES-Smag
0.5

d=2h
0
0
0
yy
0
X=275
X=3471
3.5
-10
10
DNS
0.5
Mean Scalar
NOMODEL
10
10
-10
y
10
y
10
X=347
1
DNS
LES-MKEV
LES-MKEV
LES-MKEV
0
LES-Smag
LES-Smag
LES-Smag
0.5
2.5
U
0.5


2
d=2h
0
0
1.5
10
-10
0
y
-10
10
0
y
10
-10
0

DNS of Supersonic Turbulent Mixing-Layer with Shock
X=300
0.12
0.08
0.3
X=340
X=380
0.12
0.2
ek
0.08
0.1
0.04
0.04
Imposed Shock
0
-10
0
10
0
-10
0
10
0
-10
0
10
No-Shock
Shock-Angle 16o
Shock-Angle 18o
Shock-Angle 20o
Shock-Angle 22o
0.3
X=380
0.2
0.1
Vorticity Contours
0
-10
0
10
LES of Supersonic Turbulent Mixing-Layer with Shock
X=340
3


2.5
U
2
1.5
1
-10
0
y
10
Scalar
3.5
X=380
x=340
1
3
0.8
2.5
0.6
U
DNS
2
LESSmag
0.8

0.6

0.4

1
-10
0
y
10

DNS
0.4
0.2
LESSmag
0.2
1.5
LESMKEV
x=380
1
Mean Scalar
3.5
Mean Axial Velocity
Pressure
LESMKEV
0
0
-10
0
y
10
-10
0
y
10
LES of High Speed Turbulent Reacting Flows
• In LES, large-scale variables are correctly calculated when reliable and accurate
numerical methods+BC , SGS models and chemical kinetics models are provided.
• For LES and DNS of non-reacting supersonic/hypersonic turbulent flows, high-order
numerical schemes have been developed and tested.
• Compressible (Dynamic) Gradient, Similarity, Mixed and MKEV models have been
employed for subgrid stresses and scalar fluxes. Better subgrid turbulence models for
supersonic and hypersonic flows are needed.
• Compressibility effects are included in the scalar FMDF for supersonic turbulent
combustion. Efficient Lagrangian Monte Carlo methods have been developed for flows
with shock waves in complex geometries. Consistency/accuracy of LES/FMDF is
established. Better mixing and SGS convection models for FMDF are desirable.
• DNS data for non-reacting supersonic mixing layer are generated and are being used for
evaluation/improvement of subgrid models. DNS data for supersonic reacting (hydrogenair) mixing-layer are being generated.
• Comparison of LES results with experimental data for supersonic reacting flows is
essential.
• Reliable and efficient reduced chemistry models and solver are needed. However, no
serious problem is expected in the implementation of chemical reaction in LES/FMDF.
Critical Challenges
 Reliable and accurate subgrid models for turbulenceshock-combustion interactions in strongly compressible
reacting flows
 ‘Correct’ implementation of boundary/initial conditions
 Efficient kinetics solver
 Limited well-defined, detailed experimental data and
DNS data for supersonic turbulent combustion
Future Plans
 Further improvement and validation of LES/FMDF:
-
DNS of supersonic turbulent reacting (H2) mixing layer
LES/FMDF of co-annular reacting (H2) jet
Improved SGS turbulence models for supersonic flows
Implementation/testing of reduced kinetics models