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
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 2
Combustion Dynamics Augmentor Flameholding Combustion Instability Harvazinski, 2012 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 4
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? 5
Conservation Laws Continuity: Momentum: @ @t ( eu i)+ @ @t + @ @x j ( eu j eu i )= @ @x i ( eu i )=0 @p @x i + @ @x j ( ji ( gu i u j eu i eu j )) Energy: @ @t e h 0 + @ @x j eu j e h0 = @p @t + @ u i ij q @x i (]u j h 0 eu j e h0 ) j 6
LES Resolution Modeled E(k) Resolved Modeled Coarse- Grid LES k c k Fine-Grid LES Coarse-Grid LES Influence of sub-grid model is more significant 7
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 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 in LES grid 1D reaction-diffusion in LEM grid All regimes (low-mach?) 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. 9
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 2 Turbulent Combustion, N. Peters. @ 2 i @Z 2 +ẇ i =0 Flamelet Equation 10
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 11
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. 12
LEM Solution Sub-grid Solution: Y m+1 k Y m k = Z tm + t LEM t m 1 m F k,stir + @@s ( V ky k ) m ẇ k dt Sub-grid stirring Explicit ODE solver Large-scale advection: Y n+1 k k = t LES ũ j +(u 0 j) R @Y k n @x j Y Figure from: Echeki, 2010. 13
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
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 h i @ f @t + h iv j @ f @x j @hpi @x j @ f @V j + @ @ h is k f = @ j @V j h @ ij @x i + @p0 @x j (V, )i f + @ @ k @J i h @x i (V, ) i f All LHS terms are closed Turbulent Combustion Closure All RHS terms must be modeled Z S k = S k ( ) fd 15
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 16
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. 17
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 18
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? 19
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 20