Question

A gas turbine combustor burns methane with air at equivalence ratio $\phi=0.5$, where $\displaystyle \phi=\frac{(F/A)}{(F/A)_{\text{st}}}$. If the air mass-flow rate is $\dot m_{\text{air}}=20\ \text{kg/s}$, find the methane mass-flow rate (kg/s). (round off to two decimal places)

Hint:

Use $\phi=(F/A)/(F/A)_{\text{st}}$. For methane, $(A/F)_{\text{st}}\approx17.2$ (so $(F/A)_{\text{st}}\approx0.058$).

Answer 1

Step 1: Stoichiometric ratio for methane.
For $\mathrm{CH_4}+2\,\mathrm{O_2}\to\mathrm{CO_2}+2\,\mathrm{H_2O}$, O$_2$ mass needed per 16 kg CH$_4$ is $64$ kg. Taking O$_2$ mass fraction in dry air $\approx 0.232$, stoichiometric air mass is $64/0.232=275.86$ kg. \[ \Rightarrow\ (A/F)_{\text{st}}=275.86/16=17.241, (F/A)_{\text{st}}=\frac1{17.241}=0.058. \]

Step 2: Actual $F/A$ at $\phi=0.5$.
\[ (F/A)=\phi(F/A)_{\text{st}}=0.5\times 0.058=0.029. \]

Step 3: Fuel flow.
\[ \dot m_f = (F/A)\,\dot m_{\text{air}}=0.029\times 20=0.58\ \text{kg/s}. \] \[ \boxed{0.58\ \text{kg/s}} \]