OCR Text |
Show computed. The solutions would show the fuel efficiency decreasing from its initial concentration to become negative, then increasing to converge to its positive steady state solution. This then meant, from the definition of llf, that Cf > C/ which of course cannot happen. As llr approaches zero, which means no burning then dllr /d't -+ 0, and then the two terms: Rate of destruction and the net fuel concentration into the system should balance each other out. Equation development The development of our PSR equations follow the same balances mentioned in the Baker and Essenhigh paper. The overall reaction is: Fuel + (x. /4»02 + (79X. /21 $ )N2 ~ products of combustion where 4> is the fuel to air ratio, and XI is the stoichiometric fuel to air ratio. The choice of fuel is the methane, and thus the overall rate equation for the fuel concentration with a temperature factor, can be written as: dY Ratefuel = __I = leo (Yi t (Yox)b exp{EIRT) dt Eq.l with overall order, n = a + b = 2. We used the same PSR assumptions, which are: 1. Constituents of the flow inside the combustion chamber are uniformly and instantaneously mixed. This means there are no spatial dimensions that have to be considered. 2. Pressure remains constant 3. Heat loss through the walls is negligible. 4. The entering flow is constant. 5. Cp = constant. The balances that were considered were an energy or thermal balance and two species balances. The factors considered in the energy balance was the net energy in the flow and the amount of energy released by the reaction, which gave the total energy rate. 4 |