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Lecture 22: Review for Examination 2

Lecture 22: Review for Examination 2. https://engineering.purdue.edu/ME525/ME525SP2012Exam2.pdf. https://engineering.purdue.edu/ME525/Homework6Solutions.pdf. https://engineering.purdue.edu/ME525/Homework7Solutions.pdf.

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Lecture 22: Review for Examination 2

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  1. Lecture 22: Review for Examination 2 https://engineering.purdue.edu/ME525/ME525SP2012Exam2.pdf https://engineering.purdue.edu/ME525/Homework6Solutions.pdf https://engineering.purdue.edu/ME525/Homework7Solutions.pdf https://engineering.purdue.edu/ME525/ME%20525%202013Homework8_Solution.docx

  2. L11: Momentum Equation The x-component of the momentum equation is: For steady 1-D flow, neglecting friction

  3. L11: Momentum Equation: Cylindrical Coordinates for Jets The x-component of the momentum equation is: A B C D E A: x momentum flow by axial convection per unit volume B: x momentum flow by radial convection per unit volume C: Viscous forces per unit volume D: Approximate pressure gradient in the x direction E: Body force in the x direction

  4. ME 525: CombustionLecture 14: 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.

  5. Conserved Scalars

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

  7. L15: Structure of Premixed Hydrocarbon Flames Mass conservation equation

  8. Analysis of Premixed Hydrocarbon Flames • Species Conservation: Dassumed same for all species.

  9. Burning Rate and Flame Speed Eigen Values • Substitute and rearrange: • The laminar flame speed:

  10. Rewriting the expressions for the laminar flame speed and laminar flame thickness

  11. Structure of Premixed Ф = 1.0 Methane/Air Flames Speed ~ 39 cm/s T, K O2 CH4 CO2 H2O CO H2 OH H HO2 H2O2

  12. Structure of Premixed Ф = 0.6 Methane/Air Flames Speed ~ 13 cm/s O2 T, K CH4 H2O CO2 CO H2 OH H HO2 H2O2

  13. Minimum Ignition Energy for Spark Ignition • Assume that a spherical volume of premixed gases is heated to Tb by a spark. There is a critical radius Rcrit below which heat losses to the surrounding gas will be too high for the flame to propagate.

  14. Minimum Ignition Energy for Spark Ignition • Equate energy liberated by reaction (same as energy supplied by spark) to heat lost to surrounding gases to determine Rcrit:

  15. Minimum Ignition Energy for Spark Ignition • From solution of heat conduction equation for an infinite hollow sphere (see Incropera and Dewitt): • Using:

  16. Minimum Ignition Energy for Spark Ignition • We obtain:

  17. Rayleigh Line: Pressure versus Specific Volume P= 300 kPa P= 200 kPa Physically inaccessible region B P= 100 kPa Physically Inaccessible region A 0.215 0.86 m3/kg 0.43

  18. Detonations and Deflagrations: Comparison • Typical values for detonations and deflagrations are shown above (Turns, Table 16.1, p. 617). Ma1 is prescribed to be 5.0 for normal shock. For normal shock and deflagration for each P2/P1 a unique normal Ma1 exists based on combined conservation of mass and momentum. For detonation, a range exists based on the heat release rate.

  19. Definition of Detonation Velocity • The speed at which the unburned mixture enters the detonation wave approximated as one dimensional for an observed riding with the one dimensional detonation wave By definition:and velocity of burned gases = nx,2 Burned Unburned nx,1 • nx,2 = c2 = r2, P2, T2, c2, Ma2 r1, P1, T1,c1, Ma1

  20. P2

  21. • Zeldovich, von Neumann, and Döring in the early 1940's independently formulated similar theories of the structure of detonation waves. The structure is shown in the diagram below: Induction Zone Normal Shock Reaction Zone 20 P/P1 10 T/T1 r /r1 1 1 1' 2 1"

  22. Laminar Jet Diffusion Flames (Non-premixedJet Flames)

  23. Simplified Theoretical Description of Laminar Jet Diffusion Flame • Assume: 1. Laminar, steady, axisymmetric flow, vertical flame axis, axial diffusion is neglected 2. Equal diffusivity, unity Lewis number, conserved scalar approximation 3. Radiation heat transfer treated using radiation heat loss fraction 4. Pressure gradient assumed to be hydrostatic

  24. Conservation Equations: Cylindrical Coordinates, Thin Flame Conservation of Mass Conservation of Axial Momentum Conservation of Species Mass Fractions Conservation of Energy Constitutive Relationships: Ideal Gas Law, Lewis Number etc.

  25. Conserved Scalar Equations for Laminar Jet Flame • Boundary Conditions At the jet exit plane Count Unknowns:

  26. Tuesday April 2nd Guest Lecture Dr. Charles Baukal from John Zink http://www.purdue.edu/discoverypark/sustainability/events/view.php?id=751 http://books.google.com/books?hl=en&lr=&id=HjurZJYGyuQC&oi=fnd&pg=PR43&dq=Charles+Baukal+John+Zink&ots=wA7kWEEfT_&sig=D3XXtEEW37XSC1IGzulHxmdzu5I

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