GATE Aerospace Engineering Propulsion Syllabus

Define thermal efficiency and overall efficiency of a propulsion engine.

Thermal efficiency converts fuel energy to flow kinetic energy: $$\eta_{th} = \frac{\frac{1}{2}\left(\dot{m}_e V_e^{2} - \dot{m}_a V_\infty^{2}\right)}{\dot{m}_f Q_R}$$ Overall efficiency is $\eta_o = \eta_p\,\eta_{th} = \dfrac{F V_\infty}{\dot{m}_f Q_R}$.

State the Breguet range equation for jet aircraft.

$$R = \frac{V_\infty}{g\,\text{TSFC}}\frac{L}{D}\ln\!\left(\frac{W_i}{W_f}\right)$$ where $\frac{L}{D}$ is lift-to-drag ratio, and $W_i$, $W_f$ are initial and final weights. Range improves with higher $\frac{L}{D}$ and lower TSFC.

List the four ideal processes of the Brayton (Joule) cycle in order.

1. Isentropic compression (compressor). 2. Constant-pressure heat addition (combustor). 3. Isentropic expansion (turbine). 4. Constant-pressure heat rejection. It is the ideal cycle for gas turbines and jet engines.

Give the thermal efficiency of the ideal Brayton cycle in terms of pressure ratio.

$$\eta_{th} = 1 - \frac{1}{r_p^{\frac{\gamma - 1}{\gamma}}}$$ where $r_p = \dfrac{p_2}{p_1}$ is the compressor pressure ratio. Efficiency increases monotonically with pressure ratio.

For an ideal Brayton cycle, at what pressure ratio is the specific net work maximized for fixed $T_{\min}$ and $T_{\max}$?

Maximum specific work occurs when the temperature ratio across the compressor equals the square root of the overall temperature limit ratio: $$r_p^{\frac{\gamma-1}{\gamma}} = \sqrt{\frac{T_{\max}}{T_{\min}}}$$

How does a real (non-ideal) Brayton cycle differ from the ideal cycle?

The compression and expansion are non-isentropic (entropy increases), characterized by isentropic efficiencies $\eta_c < 1$ and $\eta_t < 1$; there are pressure losses in the combustor and ducts, and heat losses. These reduce net work and thermal efficiency.

Describe the working principle of a ramjet and its key limitation.

A ramjet compresses incoming air purely by ram (dynamic) compression in the inlet/diffuser, with no rotating compressor or turbine; fuel is burned and the hot gas accelerated through a nozzle. It produces no static thrust (cannot work at zero speed) and requires supersonic/high-subsonic flight to operate.

What distinguishes a scramjet from a ramjet?

In a ramjet the flow is decelerated to subsonic speed before combustion, whereas in a scramjet (supersonic combustion ramjet) combustion occurs in a supersonic airstream. Scramjets are used for hypersonic flight (typically $M > 5$) where slowing the flow to subsonic would cause excessive temperatures and losses.

List the main components of a turbojet engine in flow order.

Inlet/diffuser, compressor, combustion chamber (burner), turbine, and exhaust nozzle. The turbine extracts just enough work to drive the compressor; remaining energy accelerates the jet to produce thrust.

Why does a turbojet have high TSFC and best suit high-speed flight?

A turbojet ejects a small mass of gas at very high velocity, giving low propulsive efficiency at low/moderate speeds (high specific fuel consumption). Its propulsive efficiency improves as flight speed rises toward the jet velocity, making it best for high subsonic/supersonic flight.

Define the bypass ratio of a turbofan engine.

The bypass ratio is the ratio of mass flow passing through the bypass (fan) duct to the mass flow through the core (gas generator): $$BPR = \frac{\dot{m}_{\text{bypass}}}{\dot{m}_{\text{core}}}$$ High-BPR engines power most modern airliners.

Why is a high-bypass turbofan more fuel efficient than a turbojet at subsonic speeds?

A turbofan accelerates a large mass of air to a moderate velocity (low $V_e/V_\infty$), giving higher propulsive efficiency $\eta_p = \dfrac{2}{1 + V_e/V_\infty}$ and thus lower TSFC and quieter operation than a turbojet, which uses a small mass at very high velocity.

Describe a turboprop engine and its optimal speed regime.

A turboprop uses a gas turbine core to drive a propeller (usually via a reduction gearbox), with most energy extracted by the turbine as shaft power and little thrust from the exhaust jet. It gives very high propulsive efficiency at low to moderate subsonic speeds (roughly up to $M \approx 0.6$–$0.7$).

What is a turboshaft engine and where is it used?

A turboshaft is a gas turbine optimized to deliver essentially all its energy as shaft power (negligible jet thrust), typically through a free/power turbine. It is used in helicopters, tanks, ships, and as auxiliary power units and industrial generators.

What is the function of an afterburner (reheat) and its main drawback?

An afterburner injects and burns additional fuel in the jet pipe downstream of the turbine, using the oxygen remaining in the exhaust to raise temperature and exit velocity, boosting thrust for takeoff/combat. Its drawback is a very large increase in fuel consumption (low efficiency).

Why can extra fuel be burned in an afterburner even after the main combustor?

Gas turbines operate fuel-lean (turbine temperature limits force air-fuel ratios far above stoichiometric), so the exhaust still contains substantial unused oxygen, which the afterburner uses to burn more fuel.

Contrast axial and centrifugal compressors.

Axial compressors pass flow parallel to the axis through successive rotor-stator stages, giving high mass flow, high efficiency, and easy multi-staging for high pressure ratios (large engines). Centrifugal compressors fling flow radially outward, giving a high pressure ratio per stage in a compact, rugged unit but lower efficiency and frontal-area penalty (small engines/APUs).

What are the two main components of a single axial compressor stage and their roles?

A rotor (rotating blade row) that adds energy to the fluid, increasing its absolute velocity and total enthalpy/pressure, followed by a stator (fixed blade row) that diffuses the flow, converting kinetic energy into a static pressure rise and redirecting flow for the next stage.

State the angular momentum (moment-of-momentum) principle applied to a turbomachine rotor.

The torque on the rotor equals the rate of change of angular momentum of the fluid: $$\tau = \dot{m}\left(r_2 C_{\theta 2} - r_1 C_{\theta 1}\right)$$ where $C_\theta$ is the tangential component of absolute velocity and $r$ the radius.

State Euler's turbomachinery (work) equation for a compressor.

$$w = U_2 C_{\theta 2} - U_1 C_{\theta 1}$$ the specific work input equals the change in the product of blade speed $U = \omega r$ and tangential absolute velocity $C_\theta$. For an axial stage with $U_1 = U_2 = U$: $w = U\,\Delta C_\theta$.

For an axial compressor stage with constant axial velocity and constant mean radius, express the stage work in terms of the change in swirl.

$$w = U\,\Delta C_\theta = U\left(C_{\theta 2} - C_{\theta 1}\right)$$ This equals the stagnation enthalpy rise of the stage, $w = c_p\,\Delta T_0$.

Relate the stage work to the stagnation temperature rise across a compressor stage.

$$w = c_p\,\Delta T_0 = U\,\Delta C_\theta$$ Hence the stage stagnation temperature rise is $$\Delta T_0 = \frac{U\,\Delta C_\theta}{c_p}$$

Define the stage loading (work) coefficient $\psi$ for an axial compressor stage.

$$\psi = \frac{w}{U^{2}} = \frac{\Delta C_\theta}{U} = \frac{c_p\,\Delta T_0}{U^{2}}$$ It is a dimensionless measure of the work done per stage; lower loading generally improves efficiency.

Define the flow coefficient $\phi$ for an axial compressor stage.

$$\phi = \frac{C_a}{U}$$ the ratio of axial velocity $C_a$ to blade speed $U$. Together with the stage loading and reaction it sets the stage velocity triangles.

Define the stage pressure ratio in terms of the stagnation temperature rise and stage (isentropic) efficiency.

$$\frac{p_{03}}{p_{01}} = \left(1 + \frac{\eta_s\,\Delta T_0}{T_{01}}\right)^{\frac{\gamma}{\gamma - 1}}$$ where $\eta_s$ is the stage isentropic efficiency and $\Delta T_0$ the actual stagnation temperature rise.

Define the isentropic efficiency of a compressor.

$$\eta_c = \frac{\text{ideal (isentropic) work}}{\text{actual work}} = \frac{h_{02s} - h_{01}}{h_{02} - h_{01}} = \frac{T_{02s} - T_{01}}{T_{02} - T_{01}}$$ for the same inlet and outlet pressures.

Define the degree of reaction of an axial compressor stage.

The degree of reaction is the fraction of the stage static-enthalpy (static-pressure) rise that occurs in the rotor: $$R = \frac{\text{static enthalpy rise in rotor}}{\text{static enthalpy rise in stage}} \approx \frac{\Delta h_{\text{rotor}}}{\Delta h_{\text{stage}}}$$

Give the degree of reaction for an axial stage in terms of axial velocity, blade speed, and air angles.

For constant axial velocity: $$R = \frac{C_a}{2U}\left(\tan\beta_1 + \tan\beta_2\right)$$ equivalently $R = 1 - \dfrac{C_{\theta 1} + C_{\theta 2}}{2U}$, where $\beta_1,\beta_2$ are relative flow angles.

What is special about a 50% reaction axial compressor stage?

At $R = 0.5$ the rotor and stator share the static enthalpy rise equally and the velocity triangles are symmetric (rotor and stator blade rows are mirror images). This symmetry gives good efficiency and is widely used in axial compressor design.

Why are axial compressors built with multiple stages, and how does the overall pressure ratio combine?

Each stage gives only a modest pressure ratio (typically 1.1–1.4) because the diffusing flow limits how much pressure rise avoids separation, so many stages are stacked to reach high overall pressure ratios. The stage pressure ratios multiply: $$\frac{p_{0,\text{out}}}{p_{0,\text{in}}} = \prod_{i=1}^{n}\left(\frac{p_{0,i+1}}{p_{0,i}}\right)$$

Define polytropic (small-stage) efficiency and explain why multistage compressor isentropic efficiency is lower than the stage efficiency.

Polytropic efficiency $\eta_\infty$ is the isentropic efficiency of an infinitesimal stage, assumed constant through the machine. Because reheat (the divergence of constant-pressure lines on the $T$–$s$ diagram) makes each later stage require more work for the same pressure ratio, the overall isentropic efficiency of a multistage compressor is less than the per-stage efficiency: $\eta_c < \eta_\infty$.