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ME 525: Combustion Lecture 13: Conserved Scalars and Mixture Fraction

ME 525: Combustion Lecture 13: Conserved Scalars and Mixture Fraction. Schwab Zeldovich variable as conserved scalars. Consider species equations to define conserved scalars Atomic mass is conserved so species equations can be multiplied by a fraction representing mass of an

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ME 525: Combustion Lecture 13: Conserved Scalars and Mixture Fraction

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  1. ME 525: CombustionLecture 13: Conserved Scalars and Mixture Fraction • Schwab Zeldovich variable as conserved scalars. • Consider species equations to define conserved scalars • Atomic mass is conserved so species equations can • be multiplied by a fraction representing mass of an • atomic species and summed over all to provide an • atomic mass balance equation which will not have • source or sink terms and will represent a conserved • scalar. • Mixture fraction • Energy as a conserved scalar.

  2. Conserved Scalars

  3. Example Problem: Mixture Fraction Advection-Diffusion Small velocity, large K Large velocity, small K

  4. Consider Lean Combustion of Biodiesel fuel represented by C11H22O2

  5. Example Problem: Flame Structure Mixture Fraction: Conserved Scalar Other Scalars written as a function of Mixture Fraction T YF YN2 YO2 Solid Lines: Low stretch, high residence time limit. Dashed lines: High stretch, low residence time limit. Time available for reaction is considered to be long enough in both cases, that is reaction is assumed to be fast enough to yield the above major species and temperature profiles.

  6. Sensible + Chemical Energy as a Conserved Scalar

  7. Conserved Scalar form of the Energy Equation

  8. Conserved Scalar form of the Energy Equation T YF YN2 YO2 Solid Lines: Low stretch, high residence time limit. Dashed lines: High stretch, low residence time limit. Enthalpy as a conserved scalar varies from its value equal to the heat of formation of fuel to its value corresponding to the stoichiometric burnt mixture which involves heat of formation and sensible energy of product species and sensible energy of nitrogen at product temperature.

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