Transcript 2 - Michigan State University
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
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.
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.
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 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 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
dy dz dx G
p
2
Gasdynamic Field Filtered continuity and momentum equations via a generalized multi-block high order finite difference complex geometries Eulerian scheme for high Reynolds number turbulent flows in Various closures for subgrid stresses Scalar Field (mass fractions and temperature) 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 CO 2 C 7 H 16
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”
f
ˆ
J J
t
t u
ˆ
i
Filtered LES Equations -> Eulerian
f
,
x
x
d x
and
f
ˆ
u
ˆ
i
J
t
J
t
u
ˆ
i u i
ˆ
i u
ˆ
j
j
0
P
i
i
_____
f
/
e
u
ˆ
j
j
j
e
u
ˆ
i j J
E
ˆ
t
E
ˆ
J
t
E
ˆ
u
ˆ
i
i
P
i u
ˆ
i
ˆ
u
ˆ
i j
q
i
J
S
Total derivative of pressure in enthalpy equation
1
Dp
Dt
For non-reacting flows: internal energy/enthalpy equation obtained from FMDF-MC is consistent with LES-FD equation
P
^ (
RT
) ˆ
R
0
NS
1
MW
Reaction term For reacting flows: reaction terms are closed in FMDF FMDF Equation -> Lagrangian
P L
t
x i
u i L
Subgrid scalar FMDF:
P L
x i
S
~ ~
t
P L
x i
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P L
/ ( )
l
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) (
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(
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Added to FMDF equation as a source/sink term Reaction term
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DP Dt
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 (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
Piston groove
Optical Access Spark Plug Fuel Injector
In-Cylinder piston
Main Ignition Chamber Hydraulic Chamber
Non-Reacting RCM Simulations
FD: finite-difference (LES) MC: Monte Carlo (FMDF)
Driver Chamber
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 p 2 p 1 Two-Block Grid 5 MC per cell p 2 /p 1 =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.
20 MC per cell 50 MC per cell Particle Number Density Particle Number Density Particle Number Density
Supersonic Mixing and Reaction - Co-Annular Jet Experiments Supported by NASA’s Hypersonic Program
M=2 setup Coflow nozzle M=2 vitiated Small-scale facility Large-scale facility Nozzle (SiC) Water cooled combustion chamber Spark plug H 2 fuel tube Air+O 2 passage Water cooled injector CARS/ Rayleigh Burner/ nozzle
Cutler et al. 2007 Cutler et al. 2007
Facility flange Coflow nozzle SiC liner Watercooled shell M=1 setup
3D LES Calculations with Compact Scheme
LES/FMDF of Co-Annular Jet
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
Instantaneous Scalar Experiment Smagorinsky MKEV 0.02
MKEV 0.03
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
4 3.5
3
U
2.5
2 1.5
1
DNS and LES of Supersonic Turbulent Mixing Layer
x=222 x=275 x=347
0.5
Pressure Contours M1=4.2
Vorticity Contours M2=1.8
DNS Without Incident Shock Wave
x=222 x=275 x=347 Re=400
10 0 -0.5
10 0.5
-10
y
0
Re=300 Re=350 Re=400 Re=500
0.5
-10
0
0
(y-y )/
amp=0.04
amp=0.08
Vorticity Contours
0 0 -0.5
-10
(y-yo)/
0
(x) amp=0.08
10 -0.5
-10
(y-yo)/
0
(x) Re=400
10
LES of Supersonic Turbulent Mixing-Layer - No Shock
3 2.5
2
DNS NOMODEL LES-MKEV LES-MIXED LES-Smag
1.5
1 0.5
0 -0.5
0 3 100 200
x
300 400 2.5
2
DNS NOMODEL LES-MKEV LES-MIXED LES-Smag
1.5
1 0.5
0 -0.5
0 100 200
x
300 400
Vorticity
3.5
3 1
X=222 DNS LES-MKEV LES-Smag
10
0.04
X=300
0.12
0.08
e k
0 -10 0 0.12
X=340
10 0.08
0.04
0 -10 0 0.2
0.04
0.12
DNS of Supersonic Turbulent Mixing-Layer with Shock
X=300 X=340
0.3
X=380
0.12
0.2
0.08
e k
0.08
0.04
-10 0 0.1
Imposed Shock
0 10 -10 0 -10 0.3
X=380
0 10
No-Shock Shock-Angle 16 o Shock-Angle 18 o Shock-Angle 20 o Shock-Angle 22 o
0 0 10 0.1
10 0 -10
Vorticity Contours
0 10
LES of Supersonic Turbulent Mixing-Layer with Shock Pressure
3.5
X=340
3 2.5
U
2 1.5
1 -10 0
y
10
Scalar
2.5
U
2 1.5
1 3.5
X=380
3 -10 0
y DNS LESSmag LESMKEV
10 0.2
0 1 0.8
0.4
0.6
x=340
-10 0
y
10 0.2
1
x=380
0.8
0.4
0.6
0 -10 0
y DNS LESSmag LESMKEV
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 (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.
Critical Challenges
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
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