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 release; Distribution Unlimited
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 Distribution A – Approved for public release; Distribution Unlimited 2
Combustion Dynamics Cocks et al., 2014 Augmentor Flameholding Harvazinski, 2012 Combustion Instability Hassan et al., 2014 3 Distribution A – Approved for public release; Distribution Unlimited Distribution A – Approved for public release; Distribution Unlimited
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 Distribution A – Approved for public release; Distribution Unlimited 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? Distribution A – Approved for public release; Distribution Unlimited 5
Conservation Laws Continuity: ∂ρ ∂ t + ∂ ( ρ e u i ) = 0 ∂ x i Momentum: ∂ ∂ u i ) = − ∂ p ∂ ∂ t ( ρ e u i ) + ( ρ e u j e + ( τ ji − ρ ( g u i u j − e u i e u j )) ∂ x j ∂ x i ∂ x j Energy: ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ∂ ∂ = ∂ p ∂ u i τ ij − q i − ρ ( ] ρ e u j e u j e + ρ e ∂ t + u j h 0 − e h 0 ) h 0 h 0 ∂ t ∂ x j ∂ x j 6 Distribution A – Approved for public release; Distribution Unlimited
LES Resolution Modeled E(k) Resolved Modeled Coarse- k c Grid LES k Fine-Grid LES • Coarse-Grid LES – Influence of sub-grid model is more significant Distribution A – Approved for public release; Distribution Unlimited 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 Distribution A – Approved for public release; Distribution Unlimited 8
Turbulent Combustion Models Model Key Assumptions Solution Process Validity • Low Mach • 1D, Steady, laminar • Solves Z, Z’’ eqns velocity field • Reaction progress • High Da Flamelets variable • Equal diffusion • Low Re (Non-premixed) coefficients • Tabulated reactive G-Equation • Presumed-PDF scalars (premixed) • Low Mach • Derived filtered quantities • Sub-grid transport • Species convection • All regimes Linear Eddy Model • 1D const pressure in in LES grid (low-Mach?) Premixed/Non- sub-grid • 1D reaction-diffusion premixed * Exact combustion in LEM grid • Scalar-mixing • Solves for PDF- • Low Mach PDF-Transport transport assumptions transport using • All Da Premixed/Non- • Treats combustion Langevin eqn and • All Re premixed source exactly Langragian method 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 Distribution A – Approved for public release; Distribution Unlimited
Flamelet Model • Basic Assumptions – Represent large- dimensional manifold by a low-dimensional manifold – Pressure assumed to be constant, i.e., low Mach Turbulent Combustion, N. Peters. – Assumption of equal diffusion coefficients 2 χ∂ 2 ψ i ρ w i = 0 ∂ Z 2 + ˙ – Velocity field is specified from a canonical (but Flamelet Equation unrelated) problem – Presumed PDF model Distribution A – Approved for public release; Distribution Unlimited 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 Distribution A – Approved for public release; Distribution Unlimited 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. Distribution A – Approved for public release; Distribution Unlimited 12
LEM Solution Sub-grid Solution: Z t m + ∆ t LEM − 1 ✓ ◆ F k,stir + ∂ ∂ s ( ρ V k Y k ) m − ˙ Y m +1 − Y m = w k dt k k ρ m t m Sub-grid stirring Explicit ODE solver Large-scale advection: j ) R � ∂ Y n Y n +1 k � − Y ⇤ u j + ( u 0 k = − ∆ t LES ˜ k ∂ x j Figure from: Echeki, 2010. Distribution A – Approved for public release; Distribution Unlimited 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 Distribution A – Approved for public release; Distribution Unlimited 14
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 PDF Transport Equation h ρ i ∂ ˜ ∂ ˜ ∂ ˜ � ∂ h p i + ∂ p 0 f f f ∂ ∂ h� ∂τ ij ∂ ∂ J α h ρ i S k ˜ ( V, ψ ) i ˜ ∂ x i ( V, ψ ) i ˜ i � � � � � � ∂ t + h ρ i V j + f = f + h f ∂ x j ∂ x j ∂ V j ∂ψ j ∂ V j ∂ x i ∂ x j ∂ψ k All LHS terms are closed All RHS terms must be modeled Z S k ( ψ ) ˜ ˜ S k = Turbulent Combustion Closure fd ψ Distribution A – Approved for public release; Distribution Unlimited 15
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 Distribution A – Approved for public release; Distribution Unlimited 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. Distribution A – Approved for public release; Distribution Unlimited 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 Distribution A – Approved for public release; Distribution Unlimited 18
Recommend
More recommend
