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Heat release modeling

Heat release modeling. FPVA-based model V. Terrapon and H. Pitsch. Why is turbulent combustion challenging?. QUALITATIVE. A large range of scales is involved!. Typical engineering application. 10 -9. 10 -6. 10 -3. 10 0. 10 3. [ m ] [ s ]. Reaction time scale. Chemistry.

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Heat release modeling

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  1. Heat release modeling FPVA-based model V. Terraponand H. Pitsch Stanford PSAAP Center - Working draft

  2. Why is turbulent combustion challenging? QUALITATIVE A large range of scales is involved! Typical engineering application 10-9 10-6 10-3 100 103 [m] [s] Reaction time scale Chemistry Reaction zone thickness Turbulent flow Integral length scale Kolmogorov length scale • Equations are very stiff • DNS is usually not possible (LES/RANS) Stanford PSAAP Center - Working draft

  3. Closure is required Source term is highly non-linear Decaying isotropic turbulence Average species transport equation: Average species transport equation simplifies: The source term: Species mass fraction Flamelets DNS with From mean quantities Diffusive and convective terms can usually be treated like for the NS equations From M. Ihme Stanford PSAAP Center - Working draft

  4. Tabulated chemistry as a potential solution Transformation and asymptotic approximation leads to equations for the flame micro-structure similar to the flamelet equations Steady diffusion flame solution for H2/air flame at χst =1 Diffusion flame regime Auto-ignition regime Mixture fraction Flame strain is measured by the scalar dissipation rate Zst Scale separation allows us to pre-compute and tabulate chemistry as function of Z and χ Stanford PSAAP Center - Working draft

  5. Combustion model for high-speed flows based on tabulated chemistry + - Assumptions Current combustion model • Species mass fractions independent of compressibility effects • Flame micro-structure • Based on FlameletProgress Variable Approach (FPVA)* • Tabulated chemistry • Temperature computed from species mass fractions and energy (not from chemistry table) • 3 additional transport equations for the mean and variance of the mixture fraction and for the progress variable Pros Cons • Complex chemistry mechanism • Only few additional scalars to solve • Turbulence – chemistry interaction • Compressibility effects on chemistry not accounted for • Accuracy of ignition dynamics * Pierce & Moin, 2004; Ihme et al., 2005 Stanford PSAAP Center - Working draft

  6. Model algorithm All other quantities Transported variables • EOS • Mixing rules NSE Temperature • Newton iteration • Not looked up from table Turbulence Tabulated chemistry Combustion • Table lookup • Pre-computed chemistry Chemistry does not account for compressibility effects and viscous heating Stanford PSAAP Center - Working draft

  7. Source term of progress variable C has a strong pressure dependence • Dynamics of flame strongly dependent on pressure • Quadratic dependence (mostly 2 body interactions) • Rescaling of source term for progress variable • Sc(P) = Sc(Pref) P2/P2ref Stanford PSAAP Center - Working draft

  8. Rescaled source term as function of the progress variable Z = Zst = 0.028 • Dynamics of flame strongly dependent on pressure • Quadratic dependence (mostly 2 body interactions) • Rescaling of source term for progress variable • Sc(P) = Sc(Pref) P2/P2ref P Stanford PSAAP Center - Working draft

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