Level 1 — RecognitionCombustion Chemistry (Propulsion Bridge)

Combustion Chemistry (Propulsion Bridge)

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Time limit: 20 minutes
Total marks: 30
Instructions: Answer all questions. For True/False items, a correct justification is required for full marks. Use $...$ notation where needed.

Section A — Multiple Choice (1 mark each) — 10 marks

Q1. For a stoichiometric mixture, the equivalence ratio $\phi$ equals:

(a) $\phi < 1$ (b) $\phi = 1$ (c) $\phi > 1$ (d) $\phi = 0$

Q2. A fuel-rich combustion mixture is characterized by:

(a) excess oxidizer (b) excess fuel (c) exactly balanced reactants (d) no fuel

Q3. The adiabatic flame temperature is highest when the mixture is:

(a) very fuel-lean (b) very fuel-rich (c) near stoichiometric (slightly rich) (d) inert-diluted

Q4. At high temperatures, dissociation reactions such as $H_2O \rightleftharpoons OH + H$ cause the actual flame temperature to be:

(a) higher than the ideal value (b) lower than the ideal value (c) unchanged (d) infinite

Q5. A detonation differs from a deflagration primarily because it:

(a) propagates subsonically (b) propagates supersonically via a shock wave (c) requires no fuel (d) has lower pressure

Q6. In a diffusion flame, fuel and oxidizer are:

(a) premixed before combustion (b) mixed only at the reaction zone (c) never in contact (d) both inert

Q7. A common hypergolic propellant combination is:

(a) $H_2$ + $O_2$ (b) RP-1 + LOX (c) $N_2O_4$ + UDMH/MMH (d) methane + air

Q8. Vieille's law for solid propellant burn rate is written as:

(a) $r = a P^n$ (b) $r = aP + n$ (c) $r = a/P^n$ (d) $r = n P^a$

Q9. In an AP/HTPB/Al composite solid propellant, HTPB acts as the:

(a) oxidizer (b) metal fuel additive (c) polymeric binder/fuel (d) catalyst only

Q10. Thermal $NO_x$ formation (Zeldovich mechanism) is favoured by:

(a) low temperatures (b) high temperatures (c) absence of nitrogen (d) fuel-rich soot zones only

Section B — Matching (1 mark each) — 8 marks

Q11. Match Column A to Column B.

Column A	Column B
(i) RP-1	(P) Cryogenic gaseous fuel, no carbon
(ii) Hydrogen	(Q) Refined kerosene hydrocarbon
(iii) Ammonium perchlorate	(R) Solid oxidizer
(iv) Aluminium	(S) Metal fuel raising flame temperature

Q12. Match the pollutant/species to its origin.

Column A	Column B
(i) Soot	(P) High-T reaction of $N_2$ and $O_2$
(ii) $NO_x$	(Q) Rich-zone carbon particulates
(iii) Unburned hydrocarbons	(R) Incomplete/quenched combustion
(iv) $CO$	(S) Product of $CO_2$ dissociation at high T

Section C — True/False with Justification (2 marks each) — 12 marks

(1 mark answer + 1 mark justification)

Q13. "The NASA-CEA tool computes equilibrium products, chamber temperature $T_c$ , and $I_{sp}$ assuming chemical equilibrium." — True/False? Justify.

Q14. "A fuel-lean mixture always produces more soot than a fuel-rich mixture." — True/False? Justify.

Q15. "Ignition delay of a hypergolic propellant is the time between contact of fuel and oxidizer and the onset of combustion." — True/False? Justify.

Q16. "Premixed flames generally have a well-defined propagation (flame) speed, whereas diffusion flames are limited by mixing rate." — True/False? Justify.

Q17. "Increasing chamber pressure always decreases the burn rate of a solid propellant." — True/False? Justify.

Q18. "Chapman–Jouguet condition corresponds to the detonation wave moving at exactly sonic velocity relative to the burned gases behind it." — True/False? Justify.

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1. (b) $\phi = 1$ . Equivalence ratio is defined as actual fuel/oxidizer ratio divided by stoichiometric ratio; at stoichiometric it equals 1. ✔

Q2. (b) excess fuel. Fuel-rich means $\phi > 1$ , more fuel than can be fully oxidized. ✔

Q3. (c) near stoichiometric (slightly rich). Maximum heat release per unit mixture with minimal excess diluent; peak often shifts slightly rich because dissociation and product speciation. ✔

Q4. (b) lower. Dissociation is endothermic; it absorbs energy, reducing the actual flame temperature below the ideal (no-dissociation) value. ✔

Q5. (b) supersonic via shock wave. Detonation couples a shock to the reaction zone and travels supersonically; deflagration is subsonic conduction/diffusion-driven. ✔

Q6. (b) mixed only at the reaction zone. In diffusion flames reactants meet by molecular diffusion at the flame surface. ✔

Q7. (c) $N_2O_4$ + UDMH/MMH. Classic hypergolic pair igniting on contact without external ignition. ✔

Q8. (a) $r = aP^n$ . Vieille's (Saint-Robert's) law; $a$ = temperature coefficient, $n$ = pressure exponent. ✔

Q9. (c) polymeric binder/fuel. HTPB (hydroxyl-terminated polybutadiene) binds the composite and serves as fuel. ✔

Q10. (b) high temperatures. Zeldovich thermal $NO_x$ has high activation energy, so it rises steeply with temperature. ✔

Section B (1 mark each; award per correct pair)

Q11. (i)→Q, (ii)→P, (iii)→R, (iv)→S. RP-1 = kerosene; $H_2$ = cryogenic carbon-free fuel; AP = solid oxidizer; Al = metal fuel additive.

Q12. (i)→Q, (ii)→P, (iii)→R, (iv)→S. Soot from rich carbon particulates; $NO_x$ from thermal $N_2+O_2$ ; UHC from quenched combustion; CO from $CO_2$ dissociation / incomplete oxidation.

Section C (2 marks each: 1 answer + 1 justification)

Q13. True. CEA solves for equilibrium composition by minimizing Gibbs free energy and outputs $T_c$ , product mole fractions, and performance parameters including $I_{sp}$ . (1+1)

Q14. False. Soot forms predominantly in fuel-rich zones where excess carbon lacks oxidizer; lean mixtures have excess oxygen and soot little. (1+1)

Q15. True. Ignition delay is exactly the interval from contact/mixing of hypergolic reactants to detectable combustion; short delay is desired for reliable ignition. (1+1)

Q16. True. A premixed flame has a characteristic laminar flame speed $S_L$ ; a diffusion flame's rate is governed by how fast fuel and oxidizer inter-diffuse/mix. (1+1)

Q17. False. Per Vieille's law $r=aP^n$ with $n>0$ , burn rate increases with pressure. (1+1)

Q18. True. At the C–J point the detonation propagates such that the flow velocity of the products relative to the wave equals the local sound speed (Mach 1 in the burned gas frame); this is the stable steady-detonation condition. (1+1)

[
  {"claim":"Vieille's law: at n>0, higher P gives higher r (Q17 False since claim says decrease)","code":"P1,P2,a,n=symbols('P1 P2 a n',positive=True); r1=a*P1**n; r2=a*P2**n; result = bool(simplify((r2-r1).subs({a:1,n:0.35,P1:5,P2:10}))>0)"},
  {"claim":"Stoichiometric equivalence ratio equals 1 (Q1)","code":"phi=Rational(1,1); result = (phi==1)"},
  {"claim":"Vieille exponent example: doubling pressure with n=0.4 multiplies burn rate by 2**0.4","code":"a,P,n=symbols('a P n',positive=True); ratio=(a*(2*P)**n)/(a*P**n); result = bool(simplify(ratio - 2**n).subs(n,Rational(2,5))==0)"}
]