Level 2 — RecallCombustion Chemistry (Propulsion Bridge)

Combustion Chemistry (Propulsion Bridge)

40 marksprintable — key stays hidden on paper

Level: 2 (Recall — definitions, standard problems, short derivations) Time: 30 minutes Total Marks: 40

Q1. Define the equivalence ratio $\phi$ and state the value/range of $\phi$ for stoichiometric, fuel-rich, and fuel-lean mixtures. (3 marks)

Q2. Write the balanced stoichiometric combustion reaction of methane ( $\text{CH}_4$ ) with air, and calculate the stoichiometric air–fuel mass ratio (AFR). Take air as 21% $\text{O}_2$ and 79% $\text{N}_2$ by mole; molar masses: C = 12, H = 1, O = 16, N = 14. (5 marks)

Q3. Distinguish between a deflagration and a detonation using at least three physical characteristics (wave speed, pressure behaviour, propagation mechanism). (4 marks)

Q4. State Vieille's law for solid propellant burn rate and define each symbol. For a propellant with $a = 3.0\ \text{mm/s}$ (at $p$ in MPa) and pressure exponent $n = 0.35$ , compute the burn rate at a chamber pressure of $7\ \text{MPa}$ . (4 marks)

Q5. Briefly explain the difference between a premixed flame and a diffusion flame, giving one example of each. (4 marks)

Q6. For the dissociation equilibrium $\text{CO}_2 \rightleftharpoons \text{CO} + \tfrac{1}{2}\text{O}_2$ , explain qualitatively (using Le Chatelier's principle) how the extent of dissociation changes with (a) increasing temperature and (b) increasing pressure. State the effect of dissociation on the adiabatic flame temperature. (4 marks)

Q7. A hypergolic bipropellant uses $\text{N}_2\text{O}_4$ (oxidiser) with MMH ( $\text{CH}_3\text{NHNH}_2$ ). (a) State what "hypergolic" means and define ignition delay. (2 marks) (b) Write the balanced overall combustion reaction of MMH with $\text{N}_2\text{O}_4$ assuming products are $\text{CO}_2$ , $\text{H}_2\text{O}$ , and $\text{N}_2$ . (3 marks)

Q8. Estimate the adiabatic flame temperature (constant pressure) for burning 1 mol of $\text{H}_2$ with $\tfrac12$ mol $\text{O}_2$ to give $\text{H}_2\text{O}(g)$ , given: $\Delta H_f^\circ[\text{H}_2\text{O}(g)] = -242\ \text{kJ/mol}$ ; mean $C_p[\text{H}_2\text{O}(g)] = 42\ \text{J/mol·K}$ ; reactants start at $298\ \text{K}$ ; neglect dissociation and assume all heat goes to the single product. (5 marks)

Q9. List three major pollutants formed in hydrocarbon combustion and state one formation cause for each. (3 marks)

Q10. Name the NASA CEA tool's purpose and list any three output quantities it computes for a rocket combustion problem. (3 marks)

End of paper

Answer keyMark scheme & solutions

Q1. (3 marks) $\phi = \frac{(F/A)_{\text{actual}}}{(F/A)_{\text{stoichiometric}}}$ where $F/A$ is the fuel-to-oxidiser ratio. (1)

$\phi = 1$ : stoichiometric (exact O₂ for complete combustion) (⅔)
$\phi > 1$ : fuel-rich (excess fuel) (⅔)
$\phi < 1$ : fuel-lean (excess oxidiser/air) (⅔)

Q2. (5 marks) Balanced reaction: $\text{CH}_4 + 2\,\text{O}_2 \rightarrow \text{CO}_2 + 2\,\text{H}_2\text{O}$ (1) With air, per mole O₂ there are $79/21 = 3.76$ mol N₂: $\text{CH}_4 + 2(\text{O}_2 + 3.76\,\text{N}_2) \rightarrow \text{CO}_2 + 2\,\text{H}_2\text{O} + 7.52\,\text{N}_2$ (1)

Mass of fuel = $16\ \text{g/mol}$ (½)
Mass of air = $2\times(32 + 3.76\times28) = 2\times(32+105.28)=2\times137.28 = 274.56\ \text{g}$ (1½) $\text{AFR} = \frac{274.56}{16} \approx 17.2$ (1)

Q3. (4 marks) (1 mark each, any 3–4 valid points)

Deflagration	Detonation
Subsonic (m/s scale)	Supersonic (km/s, > sound speed of unburnt gas)
Pressure ≈ constant / slight drop	Sharp pressure rise (shock-coupled)
Heat/mass diffusion drives propagation	Shock wave compresses/ignites mixture
Flame moves into unburnt gas subsonically	Coupled shock + reaction zone (CJ condition)

Q4. (4 marks) Vieille's (Saint-Robert's) law: $r = a\,p^{\,n}$ (1) where $r$ = linear burn rate, $p$ = chamber pressure, $a$ = burn-rate coefficient (temperature dependent), $n$ = pressure exponent. (1) Compute: $r = 3.0 \times 7^{0.35}$ . $7^{0.35} = e^{0.35\ln 7}=e^{0.35\times1.9459}=e^{0.6811}=1.976$ (1) $r = 3.0 \times 1.976 \approx 5.93\ \text{mm/s}$ (1)

Q5. (4 marks)

Premixed flame: fuel and oxidiser mixed before reaching the flame front; reaction rate limited by chemical kinetics; example: Bunsen burner (air hole open), SI engine. (2)
Diffusion flame: fuel and oxidiser initially separate and burn where they meet by diffusion; mixing-controlled; example: candle flame, diesel spray, most rocket injectors. (2)

Q6. (4 marks) (a) Dissociation is endothermic ⇒ increasing $T$ shifts equilibrium right (more dissociation). (1) (b) Reaction increases moles (1 → 1.5) ⇒ increasing $p$ shifts equilibrium left (less dissociation). (1½) Effect: dissociation absorbs energy, so it lowers the adiabatic flame temperature below the ideal (no-dissociation) value. (1½)

Q7. (5 marks) (a) Hypergolic = propellants that ignite spontaneously on contact without an external ignition source. (1) Ignition delay = time between contact of fuel and oxidiser and the onset of combustion/pressure rise. (1) (b) MMH = $\text{CH}_3\text{NHNH}_2$ = $\text{CH}_6\text{N}_2$ ; oxidiser $\text{N}_2\text{O}_4$ . Balance C, H, N, O: $\text{CH}_6\text{N}_2 + \tfrac{5}{4}\,\text{N}_2\text{O}_4 \rightarrow \text{CO}_2 + 3\,\text{H}_2\text{O} + \tfrac{7}{2}\,\text{N}_2$ Check O: LHS $=\tfrac{5}{4}\times4=5$ ; RHS $=2+3=5$ ✓. N: $2 + 2\times\tfrac54=4.5$ ; RHS $=7$ ? Recompute N: LHS N $= 2 + \tfrac52 = 4.5$ → RHS N $= 2\times3.5=7$ . Mismatch — correct N₂ coefficient: N balance: $2 + 2(\tfrac54)=2+2.5=4.5$ atoms N → $4.5/2 = 2.25\,\text{N}_2$ . $\boxed{\text{CH}_6\text{N}_2 + \tfrac{5}{4}\,\text{N}_2\text{O}_4 \rightarrow \text{CO}_2 + 3\,\text{H}_2\text{O} + \tfrac{9}{4}\,\text{N}_2}$ (3) (Award marks for correct O and C/H balance; N₂ coefficient $= 2.25$ .)

Q8. (5 marks) Energy released = $-\Delta H_f^\circ = 242\ \text{kJ} = 242000\ \text{J}$ (elements at 298 K start) (1) This heats the 1 mol product from 298 K to $T$ : (1) $q = n\,C_p\,(T - 298)$ $242000 = 1\times 42\times(T-298)$ (1) $T - 298 = \frac{242000}{42} = 5762\ \text{K}$ (1) $T \approx 6060\ \text{K}$ (1) (Note: unrealistically high because dissociation & multi-species heat capacity are neglected — real ~3100 K; this is expected for the idealised problem.)

Q9. (3 marks) (1 each)

NOₓ: thermal (Zeldovich) fixation of N₂ + O₂ at high flame temperatures.
Soot (particulate carbon): incomplete combustion in fuel-rich zones / poor mixing.
Unburned hydrocarbons (UHC): flame quenching at walls, incomplete oxidation, over-lean/over-rich regions.

Q10. (3 marks) CEA computes chemical equilibrium composition and thermodynamic properties of combustion/rocket systems. (1) (½ each, any 3 outputs)

Chamber temperature $T_c$ / adiabatic flame temperature
Specific impulse $I_{sp}$
Equilibrium product mole fractions
Characteristic velocity $c^*$ , thrust coefficient, molecular weight, $\gamma$

[
  {"claim":"Methane-air AFR ≈ 17.2", "code":"m_fuel=16; m_air=2*(32+3.76*28); AFR=m_air/m_fuel; result = abs(AFR-17.16)<0.1"},
  {"claim":"Burn rate r = 3.0 * 7**0.35 ≈ 5.93 mm/s", "code":"r=3.0*Float(7)**Float(0.35); result = abs(float(r)-5.93)<0.02"},
  {"claim":"H2 idealized flame temp ≈ 6060 K", "code":"T=298+242000/42; result = abs(T-6060)<15"},
  {"claim":"MMH+N2O4 N2 coefficient = 9/4", "code":"N_from=2+2*Rational(5,4); n2=N_from/2; result = n2==Rational(9,4)"}
]