Mixture Specific Conventions

Conversions at a Glance

Let $W_{\mathrm{ox}}$ and $W_{\mathrm{fuel}}$ be molecular weights of the delivered streams (e.g., $\mathrm{O}{}_2$, $\mathrm{N}{}_2\mathrm{O}{}_4$, RP-1, $\mathrm{CH}{}_4$).

• Mass $\leftrightarrow$ mole:

$$\left(\frac{O}{F}\right)=\left(\frac{N_{\mathrm{ox}}}{N_{\mathrm{fuel}}}\right)\frac{W_{\mathrm{ox}}}{W_{\mathrm{fuel}}},\left(\frac{N_{\mathrm{ox}}}{N_{\mathrm{fuel}}}\right)=\left(\frac{O}{F}\right)\frac{W_{\mathrm{fuel}}}{W_{\mathrm{ox}}}.$$

• Equivalence ratio:

$$\varphi =\frac{(F/O{)}_{\text{act}}}{(F/O{)}_{\mathrm{sto}}}=\frac{(O/F{)}_{\mathrm{sto}}}{(O/F{)}_{\text{act}}}=\frac{(N_{\mathrm{ox}}/N_{\mathrm{fuel}}{)}_{\mathrm{sto}}{W}_{\mathrm{ox}}/W_{\mathrm{fuel}}}{(N_{\mathrm{ox}}/N_{\mathrm{fuel}}{)}_{\text{act}}{W}_{\mathrm{ox}}/W_{\mathrm{fuel}}}=\frac{(N_{\mathrm{ox}}/N_{\mathrm{fuel}}{)}_{\mathrm{sto}}}{(N_{\mathrm{ox}}/N_{\mathrm{fuel}}{)}_{\text{act}}}.$$

So $\varphi$ is basis-independent (mass vs mole give the same number).

Reading Ambiguous Specs

• If someone says ”$O/F=3.2$ by moles,” convert to mass with $W$‘s before comparing to a mass-based spec.
• If a spec says “Mixture = $60\%$ stoichiometric oxidizer,” that means $r=0.60$ and $\varphi =\frac{1}{0.60}\approx 1.667$ (rich).
• For air-breathing contexts (ram/scram), ”% excess oxidizer” is often quoted relative to air composition assumptions (e.g., $21\%\mathrm{O}{}_2$, $79\%\mathrm{N}{}_2$).