Insights into Model Assumptions and Road to Model ...ccas.seas.ucla.edu/AFRL presentation...

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Insights into Model Assumptions and Road to Model Validation for Turbulent Combustion

2015 AFRL/RQR Basic Research Review UCLA

Jan 20, 2015

Venke Sankaran AFRL/RQR

AFTC PA Release# 15011, 16 Jan 2015


Goals

2

• 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


Combustion Instability

Augmentor Flameholding Cocks et al., 2014

Hassan et al., 2014Harvazinski, 2012


Approach

4

• 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


Questions

5

• 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?


Conservation Laws

6

Energy:

Momentum:

Continuity:@⇢

@t

+@

@xi(⇢eui) = 0

@

@t

(⇢eui) +@

@xj(⇢eujeui) = � @p

@xi+

@

@xj(⌧ ji � ⇢(guiuj � euieuj))

@

@t

⇣⇢

eh0

⌘+

@

@xj

⇣⇢euj

eh0

⌘=

@p

@t

+@

@xj

⇣ui⌧ij � qi � ⇢(]ujh0 � euj

eh0)

⌘


LES Resolution

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• Coarse-Grid LES – Influence of sub-grid model is more significant

k

E(k)

Modeled Resolved

kc

Fine-Grid LES

Coarse-Grid LES

Modeled


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

8


Turbulent Combustion Models

9

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/Non-premixed

• Sub-grid transport • 1D const pressure in sub-grid * Exact combustion

• Species convection in LES grid • 1D reaction-diffusion in LEM grid

• All regimes (low-Mach?)

PDF-Transport Premixed/Non-premixed

• Scalar-mixing transport assumptions • Treats combustion source exactly

• Solves for PDF-transport 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.


Flamelet Model

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Turbulent Combustion, N. Peters.

Flamelet Equation

⇢

2�@2 i

@Z2+ wi = 0

• Basic Assumptions – Represent large-

dimensional 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


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

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Figure from: Kerstein, 2013.


LEM Solution

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Y m+1k � Y m

k =

Z tm+�tLEM

tm

� 1

⇢m

✓Fk,stir +

@

@s(⇢VkYk)

m � wk

◆dt

Sub-grid Solution:

Sub-grid stirring Explicit ODE solver

Figure from: Echeki, 2010.

Y

n+1k � Y

⇤k = ��tLES

�uj + (u0

j)R�@Y

nk

@xj

Large-scale advection:


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

14


Sk =

ZSk( )fd

PDF Models

• PDF-Transport Equation – Joint PDF equation can be written for velocity-composition-

turbulent frequency, or for velocity-composition, or just for composition

– Turbulent combustion closure treated exactly – Scalar-mixing must be modeled

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Turbulent Combustion Closure

h⇢i@f@t

+ h⇢iVj@f

@xj� @hpi@xj

@f

@Vj+

@

@ j

�h⇢iSkf

�=

@

@Vj

�h�@⌧ij

@xi+@p

0

@xj(V, )if

�+

@

@ k

�h @J

↵i

@xi(V, )if�

PDF Transport Equation

All LHS terms are closed All RHS terms must be modeled


Comments

• Low Mach assumption commonly applied – Compressible version with joint-PDF of velocity-

composition-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

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This approach provides a clear basis for the evaluation of the turbulent combustion closure models and is DNS consistent.


Road to Model Validation

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• 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


Road to Model Validation

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• 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?


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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