The example provided outlines an afterburning turbojet engine and provides key parameters for various engine properties. Here's a breakdown of how to approach the calculations requested:

Given Parameters:

• $M_0 = 2.0$ (Mach number)
• $p_0 = 10 \, \text{kPa}$ (ambient pressure)
• $T_0 = -45^\circ C$ or $T_0 = 228.15 \, \text{K}$ (ambient temperature)
• $\gamma_c = 1.4$ (specific heat ratio in the compressor)
• c_p_c = 1004 \, \text{J/kgK} (specific heat capacity of air through the compressor)
• $\pi_d = 0.88$ (diffuser efficiency)
• $\pi_c = 12$ (compressor pressure ratio)
• $\eta_c = 0.90$ (compressor efficiency)
• $\tau_t = 8.0$ (turbine pressure ratio)
• $Q_R = 42,000 \, \text{kJ/kg}$ (fuel heating value)
• $\eta_b = 0.98$ (combustion efficiency)
• $\pi_b = 0.95$ (burner pressure ratio)
• $\gamma_t = 1.33$ (specific heat ratio in the turbine)
• c_p_t = 1156 \, \text{J/kgK} (specific heat capacity of air in the turbine)
• $\eta_m = 0.995$ (mechanical efficiency)
• $\eta_AB = 0.98$ (afterburner efficiency)
• $\pi_AB = 0.93$ (afterburner pressure ratio)
• $\gamma_AB = 1.30$ (specific heat ratio in the afterburner)
• c_p_AB = 1243 \, \text{J/kgK}
• $\tau_{AB} = 11$
• $Q_{RAB} = 42,000 \, \text{kJ/kg}$
• $\pi_n = 0.93$ (nozzle pressure ratio)
• $p_9 = p_0$ (exit pressure equal to ambient pressure)

Tasks:

1. Calculate total pressure and temperature throughout the engine, fuel-to-air ratios $f$ and $f_{AB}$:

   • You need to compute the pressure and temperature at each stage of the engine. This involves the isentropic relationships and efficiencies across the compressor, combustor, turbine, and afterburner.

2. Non-dimensional specific thrust $F_n / \dot{m}_a$:

   • Specific thrust can be calculated using the momentum equation for jet engines.

3. Thrust specific fuel consumption (TSFC):

   • TSFC is given by the ratio of fuel consumption rate to thrust. In SI units, it's often expressed in $\text{mg/Ns}$.

4. Thermal and propulsive efficiencies $\eta_t$ and $\eta_p$:

   • Thermal efficiency relates to how efficiently the energy from fuel is converted into useful work.
   • Propulsive efficiency relates to how effectively the jet converts this work into thrust.

Would you like me to begin with a step-by-step calculation for one of these parts or all together?

Here are some follow-up questions:

1. Would you like to see the detailed equations for calculating pressures and temperatures across the engine?
2. Should I go into more detail about how to compute fuel-to-air ratios $f$ and $f_{AB}$?
3. Do you want to understand how specific thrust is derived from jet engine principles?
4. Should I explain the process to calculate TSFC for this specific afterburning turbojet?
5. Would you like to focus on either the thermal or propulsive efficiency in more detail?

Tip: When solving these problems, always remember the role of isentropic relationships and efficiencies when moving through different engine components!