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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 AFTC PA Release# 15011, 16 Jan 2015 Distribution A Approved for public

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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

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Goals

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  • 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

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Combustion Instability Augmentor Flameholding

Cocks et al., 2014 Hassan et al., 2014 Harvazinski, 2012

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Approach

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  • 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

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  • 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

  • f 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

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Energy: Momentum: Continuity:

∂ρ ∂t + ∂ ∂xi (ρe ui) = 0 ∂ ∂t(ρe ui) + ∂ ∂xj (ρe uje ui) = − ∂p ∂xi + ∂ ∂xj (τ ji − ρ( g uiuj − e uie uj)) ∂ ∂t ⇣ ρe h0 ⌘ + ∂ ∂xj ⇣ ρe uje h0 ⌘ = ∂p ∂t + ∂ ∂xj ⇣ uiτij − qi − ρ(] ujh0 − e uje h0) ⌘

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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

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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

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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.

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Flamelet Model

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Turbulent Combustion, N. Peters.

Flamelet Equation

ρ 2χ∂2ψi ∂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

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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

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Figure from: Kerstein, 2013.

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LEM Solution

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Y m+1

k

− Y m

k

= Z tm+∆tLEM

tm

− 1 ρm ✓ Fk,stir + ∂ ∂s (ρVkYk)m − ˙ wk ◆ dt

Sub-grid Solution:

Sub-grid stirring Explicit ODE solver Figure from: Echeki, 2010.

Y n+1

k

− Y ⇤

k = −∆tLES

  • ˜

uj + (u0

j)R ∂Y n k

∂xj

Large-scale advection:

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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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˜ Sk = Z Sk(ψ) ˜ fdψ

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

hρi∂ ˜ f ∂t + hρiVj ∂ ˜ f ∂xj ∂hpi ∂xj ∂ ˜ f ∂Vj + ∂ ∂ψj

  • hρiSk ˜

f

  • =

∂ ∂Vj

  • h∂τij

∂xi + ∂p0 ∂xj (V, ψ)i ˜ f

  • +

∂ ∂ψk

  • h

∂Jα

i

∂xi(V, ψ)i ˜ f

  • PDF Transport Equation

All LHS terms are closed All RHS terms must be modeled

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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.

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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
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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?
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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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