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ME 475/675 Introduction to Combustion

ME 475/675 Introduction to Combustion. Lecture 12. Announcements. Midterm 1 September 29, 2014 Review Friday, September 26 HW 5 Due Friday, September 26, 2014. Spherical Droplet Evaporation. A is evaporating, find and B is stagnant. Transfer Number, (based on mass fraction Y). ;

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ME 475/675 Introduction to Combustion

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  1. ME 475/675 Introduction to Combustion Lecture 12

  2. Announcements • Midterm 1 • September 29, 2014 • Review Friday, September 26 • HW 5 Due Friday, September 26, 2014

  3. Spherical Droplet Evaporation • A is evaporating, find and • B is stagnant

  4. Transfer Number, (based on mass fraction Y) • ; • is driving potential for mass transfer • If then and • If and do not change with time • Then decreases as decreases

  5. Droplet Diameter versus time • Mass Conservation • , • Evaporation Const. • Constant slope for versus • Confirmed by experiment • Droplet life

  6. If • Same shape as Stefan Problem (Cartesian, last lecture) • Increases rapidly as

  7. Stefan Problem Mass Flux of evaporating liquid A • For • (dimensionless) • increases slowly for small • Then very rapidly for > 0.95

  8. versus r profiles (for ) • : • But: • Ratio: • For

  9. Stefan Problem =0.99 • but • Ratio: ; • For • Large profiles exhibit a boundary layer near exit (large advection near interface) =0.9 =0.5 =0.1 =0.05

  10. Example 3.2 (page 99) Turn in next time for EC • In mass-diffusion-controlled evaporation of a fuel droplet, the droplet surface temperature is an important parameter. Estimate the droplet lifetime of a 100-mm-diameter n-dodecane droplet evaporating in dry nitrogen at 1 atm if the droplet temperature is 10 K below the dodecane boiling point. • Repeat the calculation for a temperature 20 K below the boiling point, and compare the results. • For simplicity, assume that, in both cases, the mean gas density is that of nitrogen at a mean temperature of 800 K. Use this same temperature to estimate the fuel vapor diffusivity. The density of liquid dodecane is 749 kg/m3. • Find:___ • Given:___

  11. Liquid-Vapor Interface Boundary Condition • At interface need • So • Saturation pressure at temperature T • For water, tables in thermodynamics textbook • Or use Clausius-Slapeyron Equation (page 18 eqn. 2.19) A+B Vapor Liquid A

  12. Clausius-Clapeyron Equation (page 18) • Relates saturation pressure at a given temperature to the saturation conditions at another temperature and pressure • Let and (tabulated for fuels on page 701) • Let that we are tying to find at temperature • If given , we can use this to find • Page 701, Table B: , at

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