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lecture_13 - 16.512, Rocket Propulsion Prof. Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 13: Examples of Chemical Equilibrium 13.1 Numerical Iteration Procedure For the Shuttle main engine, we take R = O/F = 6, and P = 210 atm. To get started, we neglect , , and , so that Eqs. (12.2-3) and (12.2-4) reduce to 2 O n O n H n OH n += 22 HO H 8 2n 3 2 n1 = which give , 1/3 and (since all other ’s are taken to be zero, n = 4/3). 2 = 2 H n = i n The enthalpy before reaction was (assuming very cold reactants, i.e. ), 0 i T0 K = () =+ 41 HhO hO 32 = -15,632 J (for the 4 3 moles of , 2 H 1 2 mole of ). 2 O For the products to have the same enthalpy, the temperature must be very high. Using the table in Ref. 12.1 (pp. 692-693) we have the trial values tabulated below: T(K) 3400 4000 4200 2 h (J/mole) -92,973 -58,547 -46,924 2 h (J/mole) 103,738 126,846 134,700 H 1 hh 3 + -58.394 -16,265 -2,024 Since we must obtain an enthalpy of -15,632 J, these values indicate a temperature very close to 4000 K. Linear interpolation between 4000 and 4200 K gives T = 4009 K We can now use this temperature to calculate the four equilibrium constants through . These are given in Table 12 of Ref. 12.1. With some interpolation, we obtain: 1 K 4 K ( ) = 1/2 1 K0 . 9 7 4 a t m ( ) = 2 K2 . 6 1 a t m = 3 K 0.589 atm ( ) = 4 K 2.286 atm 16.512, Rocket Propulsion Lecture 13 Prof. Manuel Martinez-Sanchez Page 1 of 5
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At this point we can obtain our first nonzero estimate of the “minor” species concentrations. From Eqs. (12.2-14) through (12.2-17), == = 2 2 HO OH 1 1/2 H n n1 4 / 3 n K 0.974 0.138 p 200 n 1/3 = 2 H H2 nn 4/3 x1/3 n K x 2.61 0.076 P2 0 0 () ⎛⎞ = ⎜⎟ ⎝⎠ 2 2 2 2 2 2 2 O3 H n 4 / 3 n K 0.589 0.021 n p 200 = 2 O O4 nn 4 /3 x 0.021 n K x 2.286 0.018 P 200 We are now at the end of the first loop of our iteration procedure. We can
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_13 - 16.512, Rocket Propulsion Prof. Manuel...

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