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Transcript of Farhad Jaberi Department of Mechanical Engineering Michigan State University East Lansing, Michigan...
Farhad JaberiDepartment of Mechanical Engineering
Michigan State UniversityEast Lansing, Michigan
A High Fidelity Model for Numerical A High Fidelity Model for Numerical Simulations of Complex Simulations of Complex
Combustion/Propulsion SystemsCombustion/Propulsion Systems
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
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.
Impact 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
DNS of Supersonic Mixing Layer
LES of Supersonic Co-Annular Jet
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.
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”
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 Complex Turbulent Reacting Flows LES/FMDF of Complex Turbulent Reacting Flows A Hybrid Eulerian-Lagrangian Mathematical/Computational MethodologyA Hybrid Eulerian-Lagrangian Mathematical/Computational Methodology
Filtered LES Equations -> Eulerian
0ˆ
i
iu
t
J
tJ
j
ie
jj
je
iij
jii
i uuPuu
t
Ju
t
uJ
ˆˆˆˆˆ
ˆ
/ˆ and ,ˆ_____
ffxdxxGtxff
NS
MWRTRTP
1
0^
ˆ)(
FMDF Equation -> Lagrangian
xdxxGtxtxtxPL
)()),(,(),(),;( Subgrid scalar
FMDF:
LLLmi
lLt
iLLi
i
L PSPx
P
xPu
xt
P)(
/~~
Reaction termReaction term
Reaction termReaction term
SJ
quuPuE
t
JE
t
EJ
ij
i
i
i
i
i
ˆˆˆˆˆˆ
ˆ
)(/ LPS Dt
DP
1Added to FMDF
equation as a source/sink term
Dt
Dp
1
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
Total derivative of pressure in enthalpy equation
LES of High Speed Turbulent Reacting LES of High Speed Turbulent Reacting FlowsFlows• 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 (hydrogen-air) 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
In-CylinderIn-Cylinder
pistonpiston
Piston groovePiston groove
TemperatureTemperatureContoursContours
Hydraulic Chamber Driver ChamberMain Ignition Chamber
Spark Plug
Fuel Injector
Optical Access
piston
piston
piston
Non-Reacting RCM Simulations
Temperature
Pressure
FD: finite-difference (LES) MC: Monte Carlo (FMDF)
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 (LES-FD) and Monte Carlo (FMDF-MC) values of Temperature and Mass Fractions
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 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.
Particle Number Particle Number DensityDensity
Particle Number Particle Number DensityDensity
Particle Number Particle Number DensityDensity
63.5 mm
diam
cen
ter jet
CARS/ Rayleighbeams
M=2 vitiated air jet
Burner/ nozzle
CARS/ Rayleighbeams
M=2 vitiated air jet
Burner/ nozzle
Coflownozzle
Facility flange
M=2 setup M=1 setup
SiC liner
Watercooled shell
Small-scale facilityNozzle (SiC)
Water-cooled combustion chamber
Spark plug
H2 fuel tube
Air+O2
passage
Coflownozzle
Water-cooled injector
10 mm
diam
eter C
enter jet
Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by NASA’s Hypersonic Program
LES/FMDF of Co-Annular JetMixing and combustion
Grid System for LES Grid System for LES
Cutler et al. 2007Cutler et al. 2007
Large-scale facility
3D LES 3D LES
Calculations with Calculations with Compact SchemeCompact Scheme
Iso-Levels of Mach Number
Iso-Levels of Mach Number
Vorticity Magnitude
LES/FMDF of Supersonic Co-Annular Jet Mixing Case – No Combustion
Pressure Temperature
LES of Supersonic Co-Annular Jet Mixing Case – No Combustion
ExperimentSmagorinsky
MKEV 0.02MKEV 0.03
LES/FMDF of Supersonic Co-Annular Jet – Mixing Case
ExperimentSmagorinsky
MKEV 0.02MKEV 0.03
Instantaneous ScalarInstantaneous Scalar
LES-FD
FMDF-MC
Experiment
Instantaneous Scalar Mean Scalar
LES - FD
FMDF - MC
LES/FMDF of Supersonic Co-Annular Jet – Consistency of FD and MC
DNS and DNS and LES of LES of
Supersonic Supersonic Turbulent Turbulent
Mixing LayerMixing Layer
DNS Without Incident Shock DNS Without Incident Shock WaveWave
Vorticity ContoursM2=1.8
M1=4.2
Pressure Contours
-10 0 101
1.5
2
2.5
3
3.5
4
x=222
x=275
x=347U
y
Re=400
-10 0 10
-0.5
0
0.5
x=222
x=275
x=347
(U-U
c)/(
U1
-U2
)
(y-y )/0
-10 0 10
-0.5
0
0.5 Re=300
Re=350
Re=400
Re=500
(U-U
c)/(
U1
-U2
)
(y-yo)/ (x)
amp=0.08
-10 0 10
-0.5
0
0.5
amp=0.04
amp=0.08
(U-U
c)/(
U1
-U2
)
(y-yo)/ (x)
Re=400
Vorticity Contours
Vorticity
LES of Supersonic Turbulent Mixing-Layer - No ShockLES of Supersonic Turbulent Mixing-Layer - No Shock
0 100 200 300 400-0.5
0
0.5
1
1.5
2
2.5
3
DNS
NOMODEL
LES-MKEV
LES-MIXED
LES-Smag
x
0 100 200 300 400-0.5
0
0.5
1
1.5
2
2.5
3
DNS
NOMODEL
LES-MKEV
LES-MIXED
LES-Smag
x
-10 0 10
1.5
2
2.5
3
3.5
DNS
NOMODEL
LES-MKEV
LES-Smag
X=347
y
U
d=2h
-10 0 10
0
0.5
1
DNS
LES-MKEV
LES-Smag
X=275
y
-10 0 10
0
0.5
1
DNS
LES-MKEV
LES-Smag
X=347
y
LES of Supersonic Turbulent Mixing-Layer - No LES of Supersonic Turbulent Mixing-Layer - No ShockShock
-10 0 10
0
0.5
1
DNS
LES-MKEV
LES-Smag
X=347
y
M
ean
Sca
lar
Mea
n A
xial
Vel
ocit
y
-10 0 10
1.5
2
2.5
3
3.5
DNS
NOMODEL
LES-MKEV
LES-Smag
X=275
y
U
-10 0 10
1.5
2
2.5
3
3.5
DNS
NOMODEL
LES-MKEV
LES-Smag
X=347
y
U
d=2h
Vorticity Contours
DNS of Supersonic Turbulent Mixing-Layer with ShockDNS of Supersonic Turbulent Mixing-Layer with Shock
-10 0 100
0.04
0.08
0.12
X=300
ek
-10 0 100
0.04
0.08
0.12
X=340
No-ShockShock-Angle 16o
Shock-Angle 18o
Shock-Angle 20o Shock-Angle 22o
-10 0 100
0.04
0.08
0.12
X=340
-10 0 100
0.1
0.2
0.3
X=380
Imposed Shock
LES of Supersonic Turbulent Mixing-Layer with ShockLES of Supersonic Turbulent Mixing-Layer with Shock
Pressure Scalar
-10 0 101
1.5
2
2.5
3
3.5
U
y
X=340
-10 0 101
1.5
2
2.5
3
3.5
DNS
LESSmag
LESMKEV
U
y
X=380
-10 0 10
0
0.2
0.4
0.6
0.8
1
DNS
LESSmag
LESMKEV
y
x=380
-10 0 10
0
0.2
0.4
0.6
0.8
1
y
x=340
Mea
n A
xial
Vel
ocit
y
Mea
n S
cala
r
LES of High Speed Turbulent Reacting LES of High Speed Turbulent Reacting FlowsFlows• 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 (hydrogen-air) 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.
Future PlansFuture 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
Reliable and accurate subgrid models for turbulence-shock-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
Critical ChallengesCritical Challenges