Calculate and plot as a function of mixture fraction the

Question

Problem 1

For the global reaction v'_FC_mH_n + v'_{O_2} O₂ = v''_{CO_2} CO₂ + v''_{H_2O} H₂O calculate the stoichiometric mixture fraction and the adiabatic flame temperature for the following fuels, if both fuel and oxygen are pure (no N₂) and in the unburned at T = 298.16K: CH₄, C₂H₄, and C₃H₈. Use c_p = 1.2kEka . Document all your solution steps.

For bonus points, use NASA polynomials and solve numerically if the oxidizer stream contains 50% mass-fraction of N₂.

Problem 2

Consider the global reaction

H₂ + 1/2O₂ = H₂O                 (1)

in a stoichiometric hydrogen/oxygen system. Document all your solution steps.

a) Calculate the unburned mass fractions of oxygen and hydrogen, Y_{O_2,u} and Y_{H_2O}.

b) Calculate the element mass fractions of H and 0 in the system.

c) For T = 2000K, T = 3000K, and T = 4000K at p = lbar and p = 10bar, calculate the chemical equilibrium compositions of H₂, O₂, and H₂O. Compare these values to those for complete combustion. (Hint: you can find a closed solution for this by expressing, for example, YH₂O as a function of the element mass fractions, the equilibrium constant, and pressure.)

d) Discuss the observed trends of c) for increasing temperate and increasing pressure.

Problem 3

Consider an adiabatic two feed system at p = lbar, where the fuel stream consists of pure H₂O at T = 298.16K and the oxidizer stream is pure O₂ at T = 298.16K. The global reaction is

H₂ + 1/2O₂ = H₂O       (2)

Calculate and plot as a function of mixture fraction the temperature and the mass fractions of H₂, O₂, and H₂O in the burnt for

a) complete combustion,
b) chemical equilibrium.

Document all your solution steps. Upload any code you used to solve this problem to the Homework Blackboard link. No credit will be given if the code is not uploaded.