Gas-Turbine Engine Inlets (Exam Notes)

Sections of a Gas Turbine Engine

  • Cold Section
    • Air-intake (Inlet)
    • Compressor
    • Diffuser passage
  • Hot Section
    • Combustion chamber
    • Turbine
    • After-burner (where fitted)
    • Exhaust nozzle

Air-Inlet (General)

  • Located upstream of the compressor; integral part of the airframe.
  • Adds no shaft work to the flow; its only “work” is aerodynamic diffusion.
  • Directly influences engine net thrust— poor total-pressure recovery immediately erodes thrust.

Functional Requirements

  • Supply the compressor with the required mass-flow at the correct Mach number & highest possible total pressure.
  • Minimise stall / surge tendencies of the downstream compressor.
  • Tolerate wide aircraft incidence (angle-of-attack, yaw) without flow separation.
  • Interior should be straight and smooth to suppress boundary-layer growth; deliver uniform pressure distribution to the fan face.
  • Convert kinetic energy of free-stream air into static (ram) pressure – i.e. act as an aerodynamic diffuser.
  • Subsonic application: must avoid strong shocks & shock-induced separation when {0.8 < M < 1.0}.
  • Military/stealth: geometry often tailored for low radar cross-section (deep S-ducts, bifurcated walls, RAM coatings).

Visual Examples of Subsonic Inlets

  • Turbojet nacelles (classic round pitot)
  • Large turbofan nacelles (mixed-flow, translating cowl, O-duct lips)
  • Turboprop scoops / conical spinners
  • Turboshaft bell-mouth inlets (helicopters, test stands)

Taxonomy by Flight Regime

  • Subsonic inlets
    • Designed for M<1; typically a simple fixed-geometry divergent diffuser.
    • Employed on airline transports (A320, B737), turboprops, bizjets, etc.
  • Supersonic inlets
    • Serve M>1 vehicles; employ convergent–divergent shapes with shock-systems.
    • Often variable-geometry (ramps, cones, spikes) to align shocks.
    • Examples: F-15, MiG-29, Kfir, Concorde.

Thermodynamics of Aircraft Inlets

Station Nomenclature

  • 0 – Free-stream (undisturbed)
  • 1 – Inlet entrance / lip
  • 2 – Inlet exit (compressor face)

Ideal (Isentropic) Diffusion

  • 0 \rightarrow 2 : adiabatic, reversible; s0=s2 and no total-pressure loss.

Actual Diffusion

  • 0 \rightarrow 2 : adiabatic but irreversible; s2>s0 due to boundary-layer and shock losses (if present).
  • Total-pressure drop expressed via recovery ratio (\pid) and adiabatic efficiency (\etad).

Perfect-Gas, Calorically Perfect Assumptions

  • R=287\ \text{J kg}^{-1}\text{K}^{-1}, \gamma=1.4 (piece-wise constant by component).

Useful Relations (Calorically Perfect Gas)

  • Stagnation temperature: T_t = T\,[1+\frac{\gamma-1}{2}M^2]
  • Stagnation pressure: P_t = P\,[1+\frac{\gamma-1}{2}M^2]^{\gamma/(\gamma-1)}
  • Stagnation density: \rho_t = \rho\,[1+\frac{\gamma-1}{2}M^2]^{1/(\gamma-1)}
  • Total enthalpy: h_t = h + V^2/2.

Inlet Performance Metrics (Sub- & Supersonic)

  • Inlet adiabatic efficiency
    \etad = \frac{T{02s}-T0}{T{02}-T0} = \frac{(P{02}/P0)^{(\gamma-1)/\gamma}-1}{(\gamma-1)M0^2/2}
  • Total-pressure recovery \pid = \frac{P{02}}{P_{0}} (subscripts as above).
    • For subsonic ducts: only friction losses.
    • For supersonic ducts: friction + shock losses.
  • Non-dimensional entropy rise
    \frac{\Delta sd}{R}=\ln\Big(\frac{P0}{P_{02}}\Big) (adiabatic assumption).
  • Static-pressure recovery coefficient (compressible flow)
    C{pr}=\frac{P1-P0}{\tfrac12\rho0 V0^{2}}=\Big[1+\tfrac{\gamma-1}{2}M0^2\Big]^{-\gamma/(\gamma-1)}-1.

Subsonic Inlet Aerodynamics

Geometry Variables

  • \theta – included divergence angle.
  • N – diffuser axial length.
  • L – wall length.
  • W,R – rectangular width or conical radius.
  • Increasing \theta or reducing N promotes boundary-layer growth → separation → stall patches.

Flow Separation Map

  • Small \theta,\ N/W ⇒ attached flow.
  • Moderate \theta ⇒ transient separation; unsteady but overall attached.
  • Large \theta ⇒ fully separated stall flow, high total-pressure loss.

External vs. Internal Compression

  • External (state 0 → 1): isentropic diffusion ahead of lip (stream-tube divergence).
  • Internal (state 1 → 2): adiabatic, non-isentropic diffusion inside duct.
  • Excessive external compression → boundary-layer thickening & separation around lip.

Subsonic Cruise Analysis (0 → 2)

Capture-area Ratio

  • Continuity (\dot m constant, isentropic 0→1) gives
    \frac{A0}{A1}=\frac{M1}{M0}\Bigg[\frac{1+\tfrac{\gamma-1}{2}M0^2}{1+\tfrac{\gamma-1}{2}M1^2}\Bigg]^{(\gamma+1)/[2(\gamma-1)]}.
  • Designer chooses M_1 (lip) to balance external compression & cowl drag.

Critical (Choked) Area

  • A^ satisfies M=1 in isentropic flow: \frac{A}{A^}=\frac{1}{M}\Bigg[\frac{2}{\gamma+1}(1+\tfrac{\gamma-1}{2}M^2)\Bigg]^{(\gamma+1)/[2(\gamma-1)]}.
  • For a given \dot m, A^* is unique; remains constant through isentropic sections 1 ↔ 2.

Additive (Pre-Entry) Drag

  • Due to pressure on external stream-tube:
    D{add}=A1\Big[P1(1+\gamma M1^2/2)-P0(1+\gamma M0^2/2)\Big]-A0P0(1-M_0^2).
  • Non-dimensional form: C{D,add}=\dfrac{D{add}}{A0P0}.
  • Increases sharply at low flight Mach when A0/A1>1 (“spillage drag”).

Worked Subsonic Examples (condensed answers)

  • Example 1 (diffuser, isentropic): P_2=?? (students compute via isentropic tables).
  • Example 3 (capture area): for M0=0.78,\ M1=0.66 → A0/A1=0.92.
  • Example 4 (area to choke): A=1.493\ \text{m}^2 required to go from M=0.5 to M=1.0.
  • Example 5 (flow at sea level): A0=4.33\ \text{m}^2,\ P1=112.4\ \text{kPa}.
  • Example 6 (additive drag): D{add}(M=0)=\,110\ \text{kN};\ D{add}(M=0.9)=0.79\ \text{kN}.
  • Example 7 (throat Mach): solve A0/A{th}=0.7/1.15 & isentropic ratios → M_{th}\approx0.75 (shock risk low).
  • Example 8 (multi-section design):
    • (a) M_1=0.66
    • (b) A1/A{th}=1.12
    • (c) A2/A{th}=1.46.

Supersonic Inlets – Purpose & Challenges

  • Must decelerate wide-range supersonic free-stream to subsonic M\lt0.5 for compressor, with maximal P_t.
  • Confront multiple interacting shocks and boundary layers.

Basic Shock Diffuser Arrangement

  1. External oblique shocks (ramps / cones) perform initial compression.
  2. Normal shock (or final oblique) located near throat gives final jump to subsonic.
  3. Subsonic divergent duct completes diffusion to compressor face.

Classification

  • External-compression (normal shock outside) – simplest, poor P_t recovery.
  • Internal-compression (series of oblique shocks entirely inside cowl).
  • Mixed-compression (combo, most modern fighters).
  • Geometric installation: nose/pitot, side-mounted, ventral, dorsal/top.

Centre-Body Devices

  • Cones, spikes, translating plugs create controllable oblique shocks.

Ideal Supersonic Convergent–Divergent (C–D) Inlet

  • Uses Prandtl–Meyer (P-M) isentropic compression ramp: flow turned ≈[\nu(M)].
  • Designed throat chokes at supersonic design Mach M_D (e.g. 2.2) with subsonic exit M!_2≈0.3.
  • Area ratio requirement: \frac{A1}{A{th}} = \Big(\frac{A1}{A^*}\Big)M from isentropic tables.

Low-Speed Behaviour

  • M\ll1: throat un-choked, A0/A1>1 (spillage).
  • One unique subsonic Mach yields onset of choking (A0/A1=1).
  • Higher M → throat remains choked, A0/A1<1 and spillage decreases.

Spillage Drag Effects

  • Adds skin-friction and pressure drag on nacelle; can induce separation.

Starting Phenomenon

  • “Unstarted” = normal/bow shock stands ahead of lip, severe P_t loss.
  • “Start” = shock system swallowed, stabilises near throat according to back-pressure.

Starting Methods

  1. Overspeeding: temporarily accelerate above MD – practical only for low MD (≈1.5–1.8).
  2. Kantrowitz–Donaldson (K-D) enlarged-throat inlet: self-starts due to extra A{th} but incurs higher Pt loss.
  3. Variable-geometry throat: actuator widens throat for start, then closes; offers best P_t but heavier/complex.

Overspeed Example

  • Isentropic C–D inlet designed for M_D=1.5, \gamma=1.4.
  • Use normal-shock tables: minimum overspeed M_{OS}≈1.76 to push normal shock just inside cowl.

Key Supersonic Equations

  • Mass-flow parameter (choked): \text{MFP}=\frac{\dot m}{PA}\sqrt{\frac{R T}{\gamma}} = M\Big[1+\tfrac{\gamma-1}{2}M^2\Big]^{-(\gamma+1)/[2(\gamma-1)]}.
  • Normal-shock total-pressure ratio: \frac{P{t2}}{P{t1}} = \frac{\Big[\tfrac{(\gamma+1)M1^2}{2}\Big]^{\gamma/(\gamma-1)}}{\Big[1+\tfrac{\gamma-1}{2}M1^2\Big]^{\gamma/(\gamma-1)}}\frac{1}{\Big[\tfrac{(\gamma+1)}{2\gamma M_1^2- (\gamma-1)}\Big]^{1/(\gamma-1)}}.
  • Oblique-shock & P-M functions used for ramp design.

Practical/Philosophical Notes

  • Efficient inlet design balances thermodynamics, aerodynamics, stealth, structural weight, maintainability.
  • Modern fighters integrate variable-ramp and bleed systems controlled by FADEC to maximise \pi_d through whole flight envelope.
  • Civil subsonic nacelles prioritise acoustic performance, fan/ice spray ingestion, bird-strike tolerance, and minimal drag rather than extreme P_t recovery (already ~98%).

High-Level Summary

  • Inlets are aerodynamic diffusers; their goal is to maximise total-pressure delivered to the compressor across a vast matrix of flight conditions while avoiding separation, stall, or shock instability.
  • Subsonic inlets use purely isentropic diffusion (external+internal) but fight boundary-layer separation; metrics: \etad, \pid, additive drag.
  • Supersonic inlets orchestrate shock-waves; success measured by total-pressure recovery, starting margin, and spillage drag; variable geometry often mandatory.
  • Mastery of gas-dynamic formulas (isentropic tables, normal/oblique shock relations, P-M functions) is essential for inlet sizing and performance prediction.