Unit 1: Fundamentals of Gas Turbine

I. Orientation — Gas-Turbine Propulsion

A gas-turbine engine is a continuous-flow heat engine that converts the chemical energy of fuel into kinetic energy and useful thrust. Its ideal operation is represented by the Brayton cycle: isentropic compression, constant-pressure heat addition, isentropic expansion, and heat rejection through exhaust to the atmosphere.

• Governing principle: Thrust follows Newton’s second and third laws—the engine accelerates a mass of air and exhaust rearward, producing an equal and opposite forward force.
• Continuous-flow operation: Air passes continuously through the inlet, compressor, combustor, turbine, and exhaust system rather than undergoing intermittent combustion.
• Open cycle: Atmospheric air enters the engine, fuel adds energy, and combustion products discharge back to the atmosphere.
• Core components:
  • Inlet or diffuser: Delivers air to the compressor with minimum total-pressure loss.
  • Compressor: Raises air pressure and temperature.
  • Combustion chamber: Adds fuel and releases heat at approximately constant pressure.
  • Turbine: Extracts enough gas power to drive the compressor and accessories.
  • Nozzle: Converts remaining pressure and thermal energy into exhaust velocity.
• Station convention: Total pressure (P_t) and total temperature (T_t) describe stagnation conditions; static pressure (p), static temperature (T), and velocity (V) describe the local flow.
• Performance measures: Important quantities include net thrust in newtons, specific thrust in N·s/kg, thrust-specific fuel consumption, propulsive efficiency, and thermal efficiency.

II. Gas-Turbine Engine Operation — Energy Conversion Through the Core

A. Illustration of working of gas turbine engine

A gas-turbine engine produces thrust by compressing atmospheric air, adding heat through combustion, extracting turbine work, and accelerating the remaining gas through a nozzle.

• Flow sequence:

  1. Intake: The inlet captures free-stream air moving at aircraft velocity (V_0). A diffuser reduces relative velocity and raises static pressure before the compressor face.
  2. Compression: Axial or centrifugal compressor stages increase total pressure. Compression also raises total temperature and requires shaft work.
  3. Combustion: Fuel is sprayed, atomized, and burned in high-pressure air. The combustor raises gas temperature sharply while total pressure falls slightly because of friction and mixing.
  4. Expansion through turbine: Hot gas expands across turbine stages. The turbine drives the compressor through a shaft; turboprops and some turbofans also extract power for a propeller or fan.
  5. Exhaust acceleration: Gas expands through the nozzle, converting enthalpy into kinetic energy and producing a jet velocity (V_e) greater than flight velocity (V_0).

• Ideal Brayton-cycle processes:

1–2: Isentropic compression
2–3: Constant-pressure heat addition
3–4: Isentropic expansion
4–1: Constant-pressure heat rejection

• Power balance: In a basic turbojet, turbine power approximately equals compressor and accessory power.

Ẇt ηm = Ẇc + Ẇaccessories

• (\dot W_t): turbine power, W.
• (\eta_m): shaft mechanical efficiency.
• (\dot W_c): compressor power, W.
• (\dot W_{\text{accessories}}): power for pumps, generators, and other equipment, W.

• Real-engine losses: Inlet pressure loss, non-isentropic compression and expansion, combustor pressure loss, incomplete combustion, mechanical friction, and nozzle inefficiency all reduce available thrust.

III. Propulsive Force — Momentum and Pressure Contributions

A. The thrust equation

The thrust equation expresses the net axial force as the change in fluid momentum plus any force caused by unequal nozzle-exit and ambient pressures.

• Single-stream equation:

F = ṁeVe − ṁaV0 + (pe − p0)Ae

• (F): net uninstalled thrust, N.
• (\dot m_e): exhaust mass-flow rate, kg/s.
• (V_e): exhaust velocity relative to the engine, m/s.
• (\dot m_a): inlet-air mass-flow rate, kg/s.
• (V_0): aircraft flight velocity, m/s.
• (p_e): nozzle-exit static pressure, Pa.
• (p_0): ambient static pressure, Pa.
• (A_e): nozzle-exit area, m².

• Fuel contribution: Since (\dot m_e=\dot m_a+\dot m_f), fuel flow (\dot m_f) contributes to exhaust momentum, although it is often small compared with airflow.
• Momentum thrust: The term (\dot m_eV_e-\dot m_aV_0) measures the net rate of axial momentum increase.
• Pressure thrust: The term ((p_e-p_0)A_e) is positive when the exhaust is underexpanded, zero when (p_e=p_0), and negative when sufficiently overexpanded.
• Static thrust: During a stationary ground test, (V_0=0), so ram drag disappears.
• Specific thrust:

Fs = F / ṁa

• (F_s): thrust per unit inlet airflow, N·s/kg.
  • Multi-stream engines: For a turbofan, momentum and pressure terms are calculated separately for the core and bypass streams, then added.
  • Installed thrust: Actual aircraft thrust is lower than uninstalled thrust because inlet spillage, nacelle drag, bleed-air extraction, and power offtake introduce installation losses.

IV. Thrust Sensitivity — Engine, Flight, and Atmospheric Influences

A. Factors affecting thrust

Gas-turbine thrust depends on mass flow, jet acceleration, nozzle pressure balance, engine condition, and the surrounding flight environment.

• Air mass flow: From (\dot m=\rho AV), thrust increases when inlet density (\rho), capture area (A), or through-flow velocity (V) increases.
• Turbine inlet temperature: A higher allowable turbine-entry temperature raises available specific work and nozzle energy, but blade temperature and creep limits constrain it.
• Compressor pressure ratio: Increasing pressure ratio generally improves thermal efficiency and available expansion, but excessive ratio raises compressor work and discharge temperature.
• Fuel flow: Additional fuel raises combustor-exit temperature and thrust until turbine-temperature, compressor-stability, smoke, or nozzle-flow limits are reached.
• Flight speed: Increasing (V_0) increases inlet ram pressure but also increases the negative ram-drag term (\dot m_aV_0). Turbojet net thrust commonly decreases moderately with subsonic speed.
• Altitude: Ambient density and pressure fall with altitude, reducing mass flow and thrust. Lower temperature partly offsets this loss by increasing corrected compressor performance.
• Humidity: Water vapour displaces denser dry air and slightly reduces air mass flow and thrust at a given volume flow.
• Component efficiency: Fouled compressor blades, damaged seals, combustor losses, and turbine deterioration reduce pressure ratio or increase the work needed to sustain it.
• Bleed and shaft extraction: Compressor bleed for cabin systems and shaft power for accessories reduce the energy available to the propulsive stream.
• Nozzle matching: Exit area determines nozzle pressure ratio, choking, mass flow, and pressure thrust; a variable-area nozzle maintains matching over a wider operating range.

V. Compressor-Inlet Conditions — Ram Effect and Atmospheric Variation

A. Effect of pressure, velocity and temperature changes of air entering compressor

Compressor inlet conditions determine captured mass flow, corrected rotational speed, pressure ratio, surge margin, and ultimately engine thrust.

• Pressure change: Higher inlet total pressure (P_{t2}) increases air density and mass flow, so gross thrust generally rises. Intake pressure losses have the opposite effect and cannot be recovered downstream.
• Velocity change: Forward speed creates ram compression in the inlet; for an ideal adiabatic flow:

Tt = T[1 + (γ − 1)M²/2]
Pt = p[1 + (γ − 1)M²/2]^(γ/(γ − 1))

• (T_t, P_t): total temperature and pressure.
• (T, p): static temperature and pressure.
• (M): Mach number.

• (\gamma): ratio of specific heats, approximately 1.4 for air.

  Ram compression raises compressor-entry total pressure and mass-flow capability, but increasing flight velocity also raises ram drag.

• Temperature change: Hot inlet air has lower density and therefore reduces mass flow. It also raises compressor work because the ideal specific work is proportional to inlet temperature.
• Corrected quantities:

ṁcorr = ṁ√(Tt/Tref)/(Pt/Pref)
Ncorr = N/√(Tt/Tref)

• (\dot m_{\text{corr}}): corrected mass flow.
• (N_{\text{corr}}): corrected shaft speed.
• (N): actual shaft speed.
• (T{\text{ref}},P{\text{ref}}): reference temperature and pressure.

• Cold-day operation: Greater density raises mass flow and thrust, although mechanical speed, pressure, and turbine-temperature limits may prevent full exploitation.
• Inlet distortion: Nonuniform pressure or swirl at the compressor face reduces surge margin and can cause rotating stall or compressor surge.

VI. Temporary Thrust Increase — Adding Energy or Mass Flow

A. Methods of thrust augmentation

Thrust augmentation temporarily increases exhaust momentum or mass flow when take-off, combat, or hot-and-high operation requires more force.

• Afterburning or reheat: Fuel burns downstream of the turbine, raising exhaust temperature and nozzle velocity. It gives a large thrust increase but sharply increases fuel consumption and requires a variable-area nozzle.
• Water or water–methanol injection: Fluid injected at the compressor inlet or combustor lowers compressor-inlet temperature or increases turbine mass flow. Methanol also supplies energy and prevents freezing.
• Compressor overspeeding: A controlled temporary increase in shaft speed raises pressure ratio and airflow, but rotor stress and turbine-temperature limits restrict duration.
• Fuel-flow increase: Raising turbine inlet temperature increases specific thrust within thermal and surge-margin limits; modern control systems prevent overtemperature.
• Ejector augmentation: A high-speed primary jet entrains secondary ambient air, increasing total accelerated mass. Added duct weight and mixing losses limit aircraft use.
• Thrust-vectoring or lift nozzles: These redirect rather than create thrust, but improve the useful vertical or manoeuvring component. Turning losses make resultant thrust lower than the ideal value.

VII. Engine Configurations — Distribution of Propulsive Power

A. Characteristics of turboprop, turbofan and turbojet

These engines use the same gas-turbine core but differ in how turbine power and exhaust energy are converted into propulsive force.

1. Turboprop:

   • Power distribution: A power turbine and reduction gearbox drive a large propeller; only a small fraction of thrust comes directly from the exhaust.
   • Performance: Accelerating a large airflow through a small velocity change gives high propulsive efficiency at low and medium speeds.
   • Operating range: Best suited approximately below Mach 0.6–0.7, where propeller-tip compressibility and noise remain manageable.
   • Applications and limitations: Ideal for regional transport, patrol, and short runways; disadvantages include gearbox complexity, vibration, and reduced high-speed efficiency.

2. Turbofan:

   • Power distribution: A fan accelerates bypass air around the core. Bypass ratio is the bypass mass flow divided by core mass flow.
   • Performance: High-bypass engines provide high subsonic propulsive efficiency, lower specific fuel consumption, and less jet noise than turbojets.
   • Operating range: High-bypass turbofans dominate subsonic transport; low-bypass versions offer greater specific thrust for high-speed military aircraft.
   • Limitations: Large fan diameter increases frontal area, nacelle drag, weight, and ground-clearance requirements.

3. Turbojet:

   • Power distribution: Nearly all useful propulsive energy remains in the hot core exhaust; the turbine extracts only enough power to drive the compressor and accessories.
   • Performance: High jet velocity gives high specific thrust and a small frontal area, but poor propulsive efficiency at low subsonic speed.
   • Operating range: Suitable for high-speed or compact installations, especially where low drag and afterburning capability are important.
   • Limitations: High fuel consumption and intense exhaust noise make the pure turbojet unsuitable for most modern subsonic transport aircraft.