PhD Comprehensive sum_{i} n_i
int_{T_0}^{T_c} c_{p,i}(T) dT = - m_dot_fuel *
Delta_H_comb,ref – Advanced Rocket
Propulsion
Duration: 60 minutes Total Marks: 25
This examination assesses advanced understanding of thermodynamics, gas
dynamics, propulsion chemistry, and nozzle design in high-performance
liquid rocket systems. Answer all questions clearly, showing full derivations
and reasoning.
1.
Section A — (6 points)
1. A single-stage liquid rocket engine burns RP-1 (C₁₂H₂₆) with liquid oxygen
(LOX) as oxidizer. Given the chamber pressure Pc = 10 MPa, mixture ratio
O/F = 2.6 (by mass), and desired thrust F = 800 kN. Expansion ratio ε = 25,
propellant inlet temperature T₀ = 298 K. Assume ideal gas behavior and
products CO₂, H₂O, CO, H₂, O₂, N₂.
(a) Derive the general symbolic relation for the mass flow rate of fuel and
oxidizer required to achieve the specified thrust (based on later nozzle
analysis).
(b) Using the stoichiometric reaction of C₁₂H₂₆ with O₂, estimate the molar
composition of combustion products. Explain briefly (2–3 sentences) why
incomplete combustion (CO, H₂) may occur.
2.
Section B — (8 points)
2. Assuming all chemical energy converts into thermal energy of the
products (adiabatic, constant-pressure combustion), use the given reaction
enthalpy ΔH_comb,ref = –44,000 kJ/kg_fuel and polynomial Cp(T) relations
(provided in the data table) to numerically determine the adiabatic flame
temperature Tc from:
Type equation here .
Compute Tc, the mean γ = Cp/Cv, and molecular weight M
M of the product
mixture. Report all results clearly with assumptions and iteration method
used.
