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HW6SolnME525SP2011

# HW6SolnME525SP2011 - 1 ME 525 Homework#6 Due Thursay Prof...

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1 ME 525 Homework #6 Due Thursay, April 28, 2011 Prof. Lucht (E-mail address: [email protected] ) 1. Consider a jet diffusion flame with ethylene (C 2 H 4 ) as the fuel issuing into still air. The nozzle diameter is 10 mm and the initial jet velocity of the ethylene is 5 mm/sec. The pressure is 1 bar and both the ethylene and the surrounding air are initially at 300 K. The viscosity of ethylene is 102.3x10 -7 N-sec/m 2 at 300 K. Assume that the mixture fraction as a function of position in the flame can be determined using the non-reacting jet solution from Turns. Use the adiabatic equilibrium code HPFLAME to determine state functions for temperature and the mole fractions of O 2 , CO 2 , and CO as a function of mixture fraction f . Plot the temperature, the mole fractions, mixture fraction, and axial and radial velocities as a function of radius at the jet half- height L f /2, where L is the axial distance from the nozzle at which the mixture fraction drops to its stoichiometric value.

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6 2. Use Roper's correlation to calculate the laminar flame lengths for the following fuel mixture compositions issuing from a 10-mm diameter circular port: (a) pure H 2 (b) mole fraction H 2 = 0.5, mole fraction N 2 = 0.5 (c) mole fraction H 2 = 0.5, mole fraction He = 0.5 (d) pure C 4 H 10 (n-butane) (e) mole fraction C 4 H 10 = 0.5, mole fraction N 2 = 0.5 (f) mole fraction C 4 H 10 = 0.5, mole fraction H 2 = 0.5 For each case assume that the velocity profile at the jet exit is uniform, the jet exit velocity is 1.0 m/sec, and that the jet issues into quiescent air.
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8 3. Consider a burning n-heptane droplet (C 7 H 16 , MW = 100 kg/kmol). The burning rate of the 0.1-mm-diameter droplet is given by   0, 4/ ln 1 , g sc p g s Fq q pg fg kr h c T T mB w h e r e B ch    Assume that the burning process is quasi-steady and use the following properties: 0.1 /( ) g kW m K  , ( ) pg ck J k g K , r f 1 mm , 370 s TT K , 00 0 1 40,000 / cF O x P r h h h h kJ kg      , and h fg 300 kJ / kg . The quantity is the stoichiometric air/fuel ratio on a mass basis. Assume that the combustion reaction is given by   11 kg fuel kg oxidizer kg products  , and that the oxidizer is air. (a) Calculate the burning rate F m . (b) Consider the mass fluxes at the flame sheet. Calculate ,, a n d FO x P r mm m   at f rr (just inside the flame sheet) and at f (just outside the flame sheet). (Hint: the products are stagnant inside the flame sheet, 0 Pr m at f .) (c) Consider an energy balance at the flame sheet. Assume a flame temperature of 2000 K. Calculate the temperature gradients at f and at f . [Hint: consider first the energy balance for a control volume bounded by the inner surface of the droplet ( s ) and the inner surface of the flame sheet ( f ). Then consider a control volume with f at the outer surface. Draw the control volume boundaries and indicate the energy transport terms into and out of this control volume.) r s r f - r f r f + r s - r s +
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HW6SolnME525SP2011 - 1 ME 525 Homework#6 Due Thursay Prof...

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