GATE Aerospace Engineering Propulsion Syllabus

Propulsion syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Propulsion in GATE Aerospace Engineering, not a summary of it.

1. 1

   Basics

   4 topics

   • Thermodynamics
   • Boundary Layers
   • Heat Transfer
   • Combustion and Thermochemistry
2. 2

   Aerothermodynamics of Aircraft Engines

   2 topics

   • Thrust, efficiency, range
   • Brayton Cycle
3. 3

   Engine Performance

   6 topics

   • Ramjet
   • Turbojet
   • Turbofan
   • Turboprop
   • Turboshaft Engines
   • Afterburners
4. 4

   Turbomachinery

   3 topics

   • Axial Compressors
     • Angular Momentum
     • Work and Compression
     • Characteristic Performance of a Single Axial Compressor Stage
     • Efficiency of the Compressor and Degree of Reaction
     • Multi-staging
   • Centrifugal Compressor
     • Stage Dynamics
     • Inducer
     • Impeller
     • Diffuser
   • Axial Turbines
     • Stage Performance
5. 5

   Rockets

   5 topics

   • Thrust Equation and Specific Impulse
   • Rocket Performance
   • Multi-staging
   • Chemical Rockets
   • Performance of Solid and Liquid Propellant Rockets
6. 6

   Special Topics

   4 topics

   • Aerothermodynamics of Non-rotating Propulsion Components
     • Intakes
     • Combustor
     • Nozzle
   • Turbine Blade Cooling
   • Compressor-Turbine Matching
   • Surge and Stall

Propulsion flashcards for GATE Aerospace Engineering

18 of 51 cards from the Propulsion deck — real questions with worked answers.

1. State the first law of thermodynamics for a control mass (closed system) and define each term.

   $$dU = \delta Q - \delta W$$ where $dU$ is the change in internal energy, $\delta Q$ is heat added to the system, and $\delta W$ is work done by the system. For a quasi-static process $\delta W = p\,dV$.

2. Write the steady-flow energy equation (SFEE) per unit mass for an open system with one inlet and one outlet.

   $$q - w_s = \left(h_2 - h_1\right) + \frac{V_2^{2} - V_1^{2}}{2} + g\left(z_2 - z_1\right)$$ where $q$ is heat added, $w_s$ is shaft work, $h$ is specific enthalpy, $V$ is velocity, and $z$ is elevation.

3. Define stagnation (total) temperature for a perfect gas in terms of static temperature and Mach number.

   $$T_0 = T\left(1 + \frac{\gamma - 1}{2}M^{2}\right)$$ where $T$ is static temperature, $M$ is Mach number, and $\gamma$ is the ratio of specific heats.

4. Give the isentropic stagnation pressure ratio as a function of Mach number for a perfect gas.

   $$\frac{p_0}{p} = \left(1 + \frac{\gamma - 1}{2}M^{2}\right)^{\frac{\gamma}{\gamma - 1}}$$

5. How are the specific gas constant $R$, $c_p$, and $c_v$ related for a perfect gas?

   $$R = c_p - c_v, \qquad \gamma = \frac{c_p}{c_v}, \qquad c_p = \frac{\gamma R}{\gamma - 1}$$

6. Define the boundary layer and state what characterizes its outer edge.

   The boundary layer is the thin region adjacent to a solid surface where viscous effects are significant and velocity rises from zero (no-slip) at the wall to the free-stream value. Its edge is conventionally taken where the local velocity reaches $0.99\,U_\infty$.

7. Define the displacement thickness $\delta^{*}$ of a boundary layer and give its integral expression.

   The displacement thickness is the distance by which the wall would be displaced to give the same mass-flow deficit as the boundary layer: $$\delta^{*} = \int_0^{\infty}\left(1 - \frac{u}{U_\infty}\right)dy$$

8. Define the momentum thickness $\theta$ of a boundary layer.

   $$\theta = \int_0^{\infty}\frac{u}{U_\infty}\left(1 - \frac{u}{U_\infty}\right)dy$$ It represents the loss of momentum flux due to the boundary layer, and relates to wall drag.

9. What parameter governs transition from laminar to turbulent flow in a boundary layer, and give the typical critical value for a flat plate.

   The Reynolds number $Re_x = \dfrac{\rho U_\infty x}{\mu}$. Transition on a smooth flat plate typically begins near $Re_x \approx 5\times 10^{5}$.

10. What causes boundary-layer separation?

    Separation occurs when an adverse pressure gradient $\left(\frac{dp}{dx} > 0\right)$ decelerates the near-wall flow until the wall shear vanishes $\left(\left.\frac{\partial u}{\partial y}\right|_{y=0} = 0\right)$ and reverse flow begins, detaching the boundary layer from the surface.

11. State the three modes of heat transfer and the basic law governing each.

    Conduction (Fourier's law $q = -k\,\frac{dT}{dx}$), convection (Newton's law of cooling $q = h\,A\,\Delta T$), and radiation (Stefan-Boltzmann law $q = \varepsilon\sigma A\,T^{4}$).

12. Write Fourier's law of heat conduction in one dimension.

    $$q = -k\,A\,\frac{dT}{dx}$$ where $k$ is thermal conductivity, $A$ is area, and the negative sign indicates heat flows down the temperature gradient.

13. Define the Nusselt, Prandtl, and Reynolds numbers used in convective heat transfer.

    $$Nu = \frac{hL}{k}, \qquad Pr = \frac{\mu c_p}{k} = \frac{\nu}{\alpha}, \qquad Re = \frac{\rho V L}{\mu}$$ Nu is dimensionless heat-transfer coefficient, Pr relates momentum to thermal diffusivity, Re relates inertial to viscous forces.

14. Define the heating value of a fuel and distinguish higher (HHV) from lower (LHV) heating value.

    The heating value is the heat released per unit mass of fuel burned completely. HHV assumes the product water is condensed to liquid (latent heat recovered); LHV assumes water remains vapor: $$\text{LHV} = \text{HHV} - m_{H_2O}\,h_{fg}$$

15. Define the stoichiometric air-fuel ratio and the equivalence ratio $\phi$.

    The stoichiometric air-fuel ratio is the exact mass of air to completely burn unit mass of fuel. The equivalence ratio is $$\phi = \frac{(F/A)_{\text{actual}}}{(F/A)_{\text{stoich}}}$$ with $\phi > 1$ rich, $\phi < 1$ lean, $\phi = 1$ stoichiometric.

16. Define the adiabatic flame temperature.

    The adiabatic flame temperature is the temperature of combustion products when fuel burns completely in an adiabatic (no heat loss), constant-pressure (or constant-volume) process, so all released chemical energy goes into raising the product temperature. It is maximum near stoichiometric mixtures.

17. Write the complete (stoichiometric) combustion reaction of a hydrocarbon $\ce{C_xH_y}$ in oxygen.

    $$\ce{C_xH_y + \left(x + \frac{y}{4}\right)O2 -> x\,CO2 + \frac{y}{2}\,H2O}$$ For methane specifically: $\ce{CH4 + 2O2 -> CO2 + 2H2O}$.

18. Write the general thrust equation for an air-breathing engine.

    $$F = \dot{m}_e V_e - \dot{m}_a V_\infty + (p_e - p_\infty)A_e$$ where $\dot{m}_a$ is inlet air mass flow, $\dot{m}_e$ is exit mass flow, $V_e$ and $V_\infty$ are exit and flight velocities, and the last term is the pressure thrust.

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