Insights into Model Assumptions and Road to
Model Validation for Turbulent Combustion
Venke Sankaran
AFRL/RQR
2015 AFRL/RQR Basic Research Review
UCLA
Jan 20, 2015
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AFTC PA Release# 15011, 16 Jan 2015
Goals
• Air Force relevant problems
– Air breathing, rockets and scramjets
• Target Physical Phenomena
– High-speeds
– High pressures
– Compressible physics - shocks, dilatation, baroclinic
– Acoustics-combustion-turbulence interactions
• Off-design operation
– Combustion stability
– Flame blowout
– Ignition
• Focus on LES models
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Combustion Dynamics
Augmentor Flameholding
Combustion Instability
Harvazinski, 2012
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Cocks et al., 2014
Hassan et al., 2014
3
Approach
• Evaluate fundamental model assumptions
– LES sub-grid models
– Turbulent combustion models
• Road to validation
– Define criteria for model validation
– Maintain traceability to model assumptions
• Model improvements
– Based on observed model deficiencies
– Use validation metrics to demonstrate enhancements
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Questions
• Backscatter
– What is the importance of back-scatter in non-reacting
and reacting turbulence?
• LES Numerics
– Can we distinguish between physical and numerical
errors in LES sub-grid models?
• Physical Models
– What are the best models for turbulence, combustion
& turbulent combustion for comp flow in the presence
of high pressures, high speeds, shocks & acoustics?
• Validation
– Can we establish definite validation criteria?
– What expts/diagnostics are needed for validation?
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Conservation Laws
Continuity:
@⇢
@
+
(⇢e
ui ) = 0
@t
@xi
Momentum:
@
@
(⇢e
ui ) +
(⇢e
uj u
ei ) =
@t
@xj
@p
@
+
(⌧ ji
@xi
@xj
Energy:
@ ⇣ e ⌘
@ ⇣ e ⌘ @p
@ ⇣
⇢h 0 +
⇢e
u j h0 =
+
ui ⌧ij
@t
@xj
@t
@xj
⇢(ug
i uj
qi
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u
ei u
ej ))
]
⇢(u
j h0
u
ej e
h0 )
⌘
6
LES Resolution
Modeled
E(k)
Resolved
Modeled
CoarseGridcLES
k
k
Fine-Grid
LES
• Coarse-Grid LES
– Influence of sub-grid model is more significant
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LES Challenges
• Implicit vs. explicit filtering
• Effects of numerical dissipation on sub-grid model
– Validity of SGS model definition
• Ability to capture back-scatter
– Combustion adds energy in the smallest scales
• Gradient diffusion models for scalar transport
– Validity for reacting turbulence
• Near-wall LES treatment
• Hybrid RANS/LES
– Consistency of TKE defn in RANS and LES regions
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Turbulent Combustion Models
Model
Key Assumptions
Solution Process
Validity
Flamelets
(Non-premixed)
G-Equation
(premixed)
• 1D, Steady, laminar
velocity field
• Equal diffusion
coefficients
• Presumed-PDF
• Low Mach
• Solves Z, Z’’ eqns
• Reaction progress
variable
• Tabulated reactive
scalars
• Derived filtered
quantities
• Low Mach
• High Da
• Low Re
Linear Eddy Model
Premixed/Nonpremixed
• Sub-grid transport
• 1D const pressure in
sub-grid
* Exact combustion
• Species convection • All regimes
in LES grid
(low-Mach?)
• 1D reaction-diffusion
in LEM grid
PDF-Transport
Premixed/Nonpremixed
• Scalar-mixing
transport assumptions
• Treats combustion
source exactly
• Solves for PDFtransport using
Langevin eqn and
Langragian method
• Low Mach
• All Da
• All Re
Sankaran, V. and Merkle, C. Fundamental Physics and Model Assumptions in Turbulent Combustion Models for
Aerospace Propulsion, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 2014.
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Flamelet Model
• Basic Assumptions
– Represent largedimensional manifold by a
low-dimensional manifold
– Pressure assumed to be
constant, i.e., low Mach
– Assumption of equal
diffusion coefficients
– Velocity field is specified
from a canonical (but
unrelated) problem
– Presumed PDF model
Turbulent Combustion, N. Peters.
⇢ @2 i
+ ẇi = 0
2 @Z 2
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Flamelet Equation
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Other Assumptions
• Other Assumptions
– Flame location at stoichiometric line
– Inconsistency between premixed and non-premixed
formulations
– Distributed combustion zones challenged by laminar
flamelets
– Unsteady effects are represented qualitatively
– Neglects effects of neighboring flamelets, walls, radical
species, temperature and pressure effects
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Linear Eddy Model
• Key Element - Triplet Maps
– Inserts a “1D” eddy in sub-grid
• compresses the original profile in
a given length interval (eddy size)
into one-third of the length
• triplicates the profile and reverses
middle section for continuity
• eddy location, size and frequency
are determined stochastically
– Provides effect of 3D eddy
along line-of-sight
Figure from: Kerstein, 2013.
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LEM Solution
Sub-grid Solution:
Ykm+1
Ykm =
Z
tm + tLEM
tm
1
⇢m
✓
@
m
Fk,stir +
(⇢Vk Yk )
@s
Sub-grid stirring
Explicit
◆
ẇk dt
ODE solver
Large-scale advection:
Ykn+1
Yk⇤ =
tLES ũj + (u0j )R
@Ykn
@xj
Figure from: Echeki, 2010.
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Comments
• DNS Limit
– Inconsistency due to no inter-LES grid species diffusion
• Splicing operation
– Convective transport between LES cells is arbitrary
• Constant pressure assumption in sub-grid solution
• Presence of two temperatures
– From the resolved grid energy equation
– Sub-grid energy equation - approximate form used
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PDF Models
• PDF-Transport Equation
– Joint PDF equation can be written for velocity-compositionturbulent frequency, or for velocity-composition, or just for
composition
– Turbulent combustion closure treated exactly
– Scalar-mixing must be modeled
PDF Transport Equation
@ f˜
@ f˜
h⇢i
+ h⇢iVj
@t
@xj
@hpi @ f˜
@
@
@⌧ij
@p0
@
@Ji↵
˜
˜
+
h⇢iSk f =
h
+
(V, )if +
h
if˜
@xj @Vj
@ j
@Vj
@xi
@xj
@ k @xi (V, )
All LHS terms are closed
Turbulent Combustion Closure
All RHS terms must be modeled
S̃k =
Z
Sk ( )f˜d
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Comments
• Low Mach assumption commonly applied
– Compressible version with joint-PDF of velocitycomposition-frequency-enthalpy-pressure has been
proposed, but not commonly used
• Scalar Mixing Models
– Modeled portion of PDF methods
• DNS Consistency recently pursued for mixing models
– Allows treating differential diffusion correctly
– Reduces to DNS in limit of vanishing filter width
• Co-variance terms
– Represented exactly in PDF, negating use of eddy
viscosity and gradient diffusion models
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Point-of-View
• Conservation laws
– Mass, momentum, energy and species equations
– Reynolds stresses using standard closures
• Turbulent combustion model
– Use flamelets, LEM, PDF, or other source term closure
• Dual species and temperature solutions
– Provide basis for error estimation
This approach provides a clear basis for the evaluation of the
turbulent combustion closure models and is DNS consistent.
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Road to Model Validation
• Establish validation methodologies
– Utilize hierarchy of DNS, fine-LES and coarse-LES
• DNS must resolve flame structure
• Fine-LES is 10 times Kolmogorov scale
• Coarse-LES is at start of inertial sub-range
– Utilize DNS-consistent framework for the large-scales
• All models are restricted to sub-grid closures
• Grid refinement asymptotically approaches DNS
– Design test cases to address phenomena such as
turbulent scales (Re), combustion scales (Da),
compressible phenomena (Ma) and acoustics
• Select combustion kinetics to directly control relevant scales
• Characterize shock/acoustics on flame & turbulence
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Road to Model Validation
• Obtain experimental and diagnostics data
– Design experiments to observe fundamental physics
• Address relevance of back-scatter
– Air Force relevant phenomena
• High speeds, shocks, acoustics, ignition transients
– Off-design operation
• Flame stability, blowout, etc.
• What experiments & data are needed for validation?
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Acknowledgments
•
Chiping Li, AFOSR Program Officer
•
Charles Merkle, Purdue University
•
Jean-Luc Cambier, AFRL/RQR
•
Ez Hassan, AFRL/RQH
•
Dave Peterson, AFRL/RQH
•
Joseph Oefelein, Sandia
•
Guillaume Blanquart, Caltech
•
Suresh Menon, Georgia Tech
•
Ann Karagozian, UCLA
•
Haifeng Wang, Purdue
•
Matthias Ihme, Stanford
•
Richard Miller, Clemson
•
William Calhoun, CRAFT-Tech
•
Alan Kerstein, Sandia
•
Esteban Gonzales, Combustion Science and Engg
•
Justin Foster, Corvid
•
Sophonias Teshome, Aerospace
•
Brock Bobbitt, Caltech
•
Randall McDermott, NIST
•
Vaidya Sankaran, UTRC
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