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 → 2 0 \rightarrow 2 0 → 2 s < e m > 0 = s < / e m > 2 s<em>0=s</em>2 s < e m > 0 = s < / e m > 2 Actual Diffusion 0 → 2 0 \rightarrow 2 0 → 2 s < e m > 2 > s < / e m > 0 s<em>2>s</em>0 s < e m > 2 > s < / e m > 0 Total-pressure drop expressed via recovery ratio ( π < e m > d ) (\pi<em>d) ( π < e m > d ) ( η < / e m > d ) (\eta</em>d) ( η < / e m > d ) Perfect-Gas, Calorically Perfect Assumptions R = 287 J kg − 1 K − 1 R=287\ \text{J kg}^{-1}\text{K}^{-1} R = 287 J kg − 1 K − 1 γ = 1.4 \gamma=1.4 γ = 1.4 Useful Relations (Calorically Perfect Gas) Stagnation temperature: T t = T [ 1 + γ − 1 2 M 2 ] T_t = T\,[1+\frac{\gamma-1}{2}M^2] T t = T [ 1 + 2 γ − 1 M 2 ] Stagnation pressure: P t = P [ 1 + γ − 1 2 M 2 ] γ / ( γ − 1 ) P_t = P\,[1+\frac{\gamma-1}{2}M^2]^{\gamma/(\gamma-1)} P t = P [ 1 + 2 γ − 1 M 2 ] γ / ( γ − 1 ) Stagnation density: ρ t = ρ [ 1 + γ − 1 2 M 2 ] 1 / ( γ − 1 ) \rho_t = \rho\,[1+\frac{\gamma-1}{2}M^2]^{1/(\gamma-1)} ρ t = ρ [ 1 + 2 γ − 1 M 2 ] 1/ ( γ − 1 ) Total enthalpy: h t = h + V 2 / 2 h_t = h + V^2/2 h t = h + V 2 /2 Inlet adiabatic efficiency η < e m > d = T < / e m > 02 s − T < e m > 0 T < / e m > 02 − T < e m > 0 = ( P < / e m > 02 / P < e m > 0 ) ( γ − 1 ) / γ − 1 ( γ − 1 ) M < / e m > 0 2 / 2 \eta<em>d = \frac{T</em>{02s}-T<em>0}{T</em>{02}-T<em>0} = \frac{(P</em>{02}/P<em>0)^{(\gamma-1)/\gamma}-1}{(\gamma-1)M</em>0^2/2} η < e m > d = T < / e m > 02 − T < e m > 0 T < / e m > 02 s − T < e m > 0 = ( γ − 1 ) M < / e m > 0 2 /2 ( P < / e m > 02 / P < e m > 0 ) ( γ − 1 ) / γ − 1 Total-pressure recovery
π < e m > d = P < / e m > 02 P 0 \pi<em>d = \frac{P</em>{02}}{P_{0}} π < e m > d = P 0 P < / e m > 02 For subsonic ducts: only friction losses. For supersonic ducts: friction + shock losses. Non-dimensional entropy rise Δ s < e m > d R = ln ( P < / e m > 0 P 02 ) \frac{\Delta s<em>d}{R}=\ln\Big(\frac{P</em>0}{P_{02}}\Big) R Δ s < e m > d = ln ( P 02 P < / e m > 0 ) Static-pressure recovery coefficient (compressible flow) C < e m > p r = P < / e m > 1 − P < e m > 0 1 2 ρ < / e m > 0 V < e m > 0 2 = [ 1 + γ − 1 2 M < / e m > 0 2 ] − γ / ( γ − 1 ) − 1 C<em>{pr}=\frac{P</em>1-P<em>0}{\tfrac12\rho</em>0 V<em>0^{2}}=\Big[1+\tfrac{\gamma-1}{2}M</em>0^2\Big]^{-\gamma/(\gamma-1)}-1 C < e m > p r = 2 1 ρ < / e m > 0 V < e m > 0 2 P < / e m > 1 − P < e m > 0 = [ 1 + 2 γ − 1 M < / e m > 0 2 ] − γ / ( γ − 1 ) − 1 Subsonic Inlet Aerodynamics Geometry Variables θ \theta θ N N N L L L W , R W,R W , R Increasing θ \theta θ N N N Flow Separation Map Small θ , N / W \theta,\ N/W θ , N / W Moderate θ \theta θ Large θ \theta θ 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 (m ˙ \dot m m ˙ A < e m > 0 A < / e m > 1 = M < e m > 1 M < / e m > 0 [ 1 + γ − 1 2 M < e m > 0 2 1 + γ − 1 2 M < / e m > 1 2 ] ( γ + 1 ) / [ 2 ( γ − 1 ) ] \frac{A<em>0}{A</em>1}=\frac{M<em>1}{M</em>0}\Bigg[\frac{1+\tfrac{\gamma-1}{2}M<em>0^2}{1+\tfrac{\gamma-1}{2}M</em>1^2}\Bigg]^{(\gamma+1)/[2(\gamma-1)]} A < / e m > 1 A < e m > 0 = M < / e m > 0 M < e m > 1 [ 1 + 2 γ − 1 M < / e m > 1 2 1 + 2 γ − 1 M < e m > 0 2 ] ( γ + 1 ) / [ 2 ( γ − 1 )] Designer chooses M 1 M_1 M 1 Critical (Choked) Area A < e m > A^<em> A < e m > M = 1 M=1 M = 1 A A < / e m > = 1 M [ 2 γ + 1 ( 1 + γ − 1 2 M 2 ) ] ( γ + 1 ) / [ 2 ( γ − 1 ) ] \frac{A}{A^</em>}=\frac{1}{M}\Bigg[\frac{2}{\gamma+1}(1+\tfrac{\gamma-1}{2}M^2)\Bigg]^{(\gamma+1)/[2(\gamma-1)]} A < / e m > A = M 1 [ γ + 1 2 ( 1 + 2 γ − 1 M 2 ) ] ( γ + 1 ) / [ 2 ( γ − 1 )] For a given m ˙ \dot m m ˙ A ∗ A^* A ∗ Additive (Pre-Entry) Drag Due to pressure on external stream-tube: D < e m > a d d = A < / e m > 1 [ P < e m > 1 ( 1 + γ M < / e m > 1 2 / 2 ) − P < e m > 0 ( 1 + γ M < / e m > 0 2 / 2 ) ] − A < e m > 0 P < / e m > 0 ( 1 − M 0 2 ) D<em>{add}=A</em>1\Big[P<em>1(1+\gamma M</em>1^2/2)-P<em>0(1+\gamma M</em>0^2/2)\Big]-A<em>0P</em>0(1-M_0^2) D < e m > a dd = A < / e m > 1 [ P < e m > 1 ( 1 + γ M < / e m > 1 2 /2 ) − P < e m > 0 ( 1 + γ M < / e m > 0 2 /2 ) ] − A < e m > 0 P < / e m > 0 ( 1 − M 0 2 ) Non-dimensional form: C < e m > D , a d d = D < / e m > a d d A < e m > 0 P < / e m > 0 C<em>{D,add}=\dfrac{D</em>{add}}{A<em>0P</em>0} C < e m > D , a dd = A < e m > 0 P < / e m > 0 D < / e m > a dd Increases sharply at low flight Mach when A0/A 1>1 (“spillage drag”). Worked Subsonic Examples (condensed answers) Example 1 (diffuser, isentropic): P 2 = ? ? P_2=?? P 2 = ?? Example 3 (capture area): for M < e m > 0 = 0.78 , M < / e m > 1 = 0.66 M<em>0=0.78,\ M</em>1=0.66 M < e m > 0 = 0.78 , M < / e m > 1 = 0.66 A < e m > 0 / A < / e m > 1 = 0.92 A<em>0/A</em>1=0.92 A < e m > 0/ A < / e m > 1 = 0.92 Example 4 (area to choke): A = 1.493 m 2 A=1.493\ \text{m}^2 A = 1.493 m 2 M = 0.5 M=0.5 M = 0.5 M = 1.0 M=1.0 M = 1.0 Example 5 (flow at sea level): A < e m > 0 = 4.33 m 2 , P < / e m > 1 = 112.4 kPa A<em>0=4.33\ \text{m}^2,\ P</em>1=112.4\ \text{kPa} A < e m > 0 = 4.33 m 2 , P < / e m > 1 = 112.4 kPa Example 6 (additive drag): D < e m > a d d ( M = 0 ) = 110 kN ; D < / e m > a d d ( M = 0.9 ) = 0.79 kN D<em>{add}(M=0)=\,110\ \text{kN};\ D</em>{add}(M=0.9)=0.79\ \text{kN} D < e m > a dd ( M = 0 ) = 110 kN ; D < / e m > a dd ( M = 0.9 ) = 0.79 kN Example 7 (throat Mach): solve A < e m > 0 / A < / e m > t h = 0.7 / 1.15 A<em>0/A</em>{th}=0.7/1.15 A < e m > 0/ A < / e m > t h = 0.7/1.15 M t h ≈ 0.75 M_{th}\approx0.75 M t h ≈ 0.75 Example 8 (multi-section design): (a) M 1 = 0.66 M_1=0.66 M 1 = 0.66 (b) A < e m > 1 / A < / e m > t h = 1.12 A<em>1/A</em>{th}=1.12 A < e m > 1/ A < / e m > t h = 1.12 (c) A < e m > 2 / A < / e m > t h = 1.46 A<em>2/A</em>{th}=1.46 A < e m > 2/ A < / e m > t h = 1.46 Supersonic Inlets – Purpose & Challenges Must decelerate wide-range supersonic free-stream to subsonic M < 0.5 M\lt0.5 M < 0.5 P t P_t P t Confront multiple interacting shocks and boundary layers. Basic Shock Diffuser Arrangement External oblique shocks (ramps / cones) perform initial compression. Normal shock (or final oblique) located near throat gives final jump to subsonic. Subsonic divergent duct completes diffusion to compressor face. Classification External-compression (normal shock outside) – simplest, poor P t P_t P t 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 ≈[ ν ( M ) ] [\nu(M)] [ ν ( M )] Designed throat chokes at supersonic design Mach M D M_D M D M ! 2 ≈ 0.3 M!_2≈0.3 M ! 2 ≈ 0.3 Area ratio requirement: A < e m > 1 A < / e m > t h = ( A < e m > 1 A ∗ ) < / e m > M \frac{A<em>1}{A</em>{th}} = \Big(\frac{A<em>1}{A^*}\Big)</em>M A < / e m > t h A < e m > 1 = ( A ∗ A < e m > 1 ) < / e m > M Low-Speed Behaviour M ≪ 1 M\ll1 M ≪ 1 0/A 1>1 (spillage). One unique subsonic Mach yields onset of choking (A < e m > 0 / A < / e m > 1 = 1 A<em>0/A</em>1=1 A < e m > 0/ A < / e m > 1 = 1 Higher M M M 0/A 1<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 P_t P t “Start” = shock system swallowed, stabilises near throat according to back-pressure. Starting Methods Overspeeding: temporarily accelerate above M < e m > D M<em>D M < e m > D M < / e m > D M</em>D M < / e m > D Kantrowitz–Donaldson (K-D) enlarged-throat inlet: self-starts due to extra A < e m > t h A<em>{th} A < e m > t h P < / e m > t P</em>t P < / e m > t Variable-geometry throat: actuator widens throat for start, then closes; offers best P t P_t P t Overspeed Example Isentropic C–D inlet designed for M D = 1.5 M_D=1.5 M D = 1.5 γ = 1.4 \gamma=1.4 γ = 1.4 Use normal-shock tables: minimum overspeed M O S ≈ 1.76 M_{OS}≈1.76 M O S ≈ 1.76 Key Supersonic Equations Mass-flow parameter (choked): MFP = m ˙ P A R T γ = M [ 1 + γ − 1 2 M 2 ] − ( γ + 1 ) / [ 2 ( γ − 1 ) ] \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)]} MFP = P A m ˙ γ R T = M [ 1 + 2 γ − 1 M 2 ] − ( γ + 1 ) / [ 2 ( γ − 1 )] Normal-shock total-pressure ratio: P < e m > t 2 P < / e m > t 1 = [ ( γ + 1 ) M < e m > 1 2 2 ] γ / ( γ − 1 ) [ 1 + γ − 1 2 M < / e m > 1 2 ] γ / ( γ − 1 ) 1 [ ( γ + 1 ) 2 γ M 1 2 − ( γ − 1 ) ] 1 / ( γ − 1 ) \frac{P<em>{t2}}{P</em>{t1}} = \frac{\Big[\tfrac{(\gamma+1)M<em>1^2}{2}\Big]^{\gamma/(\gamma-1)}}{\Big[1+\tfrac{\gamma-1}{2}M</em>1^2\Big]^{\gamma/(\gamma-1)}}\frac{1}{\Big[\tfrac{(\gamma+1)}{2\gamma M_1^2- (\gamma-1)}\Big]^{1/(\gamma-1)}} P < / e m > t 1 P < e m > t 2 = [ 1 + 2 γ − 1 M < / e m > 1 2 ] γ / ( γ − 1 ) [ 2 ( γ + 1 ) M < e m > 1 2 ] γ / ( γ − 1 ) [ 2 γ M 1 2 − ( γ − 1 ) ( γ + 1 ) ] 1/ ( γ − 1 ) 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 π d \pi_d π d Civil subsonic nacelles prioritise acoustic performance, fan/ice spray ingestion, bird-strike tolerance, and minimal drag rather than extreme P t P_t P t 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: η < e m > d \eta<em>d η < e m > d π < / e m > d \pi</em>d π < / e m > d 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.