Unit 2: Inlets

I. Orientation — Governing Principles of Inlet Flow

An aircraft-engine inlet captures atmospheric air, delivers the required mass flow to the compressor or combustor, and converts part of the incoming kinetic energy into static pressure. Its operation follows conservation of mass, momentum, and energy, with performance limited principally by boundary-layer separation and shock losses.

• Defining functions:
  • Capture: Supply the engine mass-flow demand, (\dot m).
  • Diffusion: Reduce velocity while increasing static pressure.
  • Flow conditioning: Deliver a nearly uniform, low-distortion velocity and pressure field.
• Continuity principle:

ṁ = ρAV

Here, (\dot m) is mass flow rate in kg/s, (\rho) is density in kg/m³, (A) is streamtube area in m², and (V) is mean axial velocity in m/s.

• Adiabatic-flow energy equation:

h₀ = h + V²/2

Here, (h_0) is stagnation enthalpy, (h) is static enthalpy, and (V^2/2) is kinetic energy per unit mass. An ideal diffuser raises static enthalpy without changing (h_0).

• Mach-number distinction:
  • Subsonic inlet: Diffusion normally requires increasing streamtube area.
  • Supersonic inlet: Deceleration requires compression waves or shocks before subsonic diffusion.
• Principal losses: Wall friction, separated flow, shock waves, flow spillage, nonuniformity, and unsteady interactions reduce stagnation pressure.

II. Subsonic Inlet Flow — Diffusion, Separation, and External Capture

A. Internal flow and stall in subsonic inlets

Internal flow in a subsonic inlet is decelerated through an expanding passage, but excessive diffusion can cause inlet or diffuser stall.

• Subsonic area–velocity relation:

dA/A = (M² − 1)dV/V

Here, (A) is local area, (M) is Mach number, and (V) is velocity. For (M<1), a velocity decrease ((dV<0)) requires an area increase ((dA>0)).

• Pressure conversion: In inviscid flow, lower velocity produces higher static pressure according to Bernoulli’s relation:

p + ρV²/2 = constant

Here, (p) is static pressure and (\rho V^2/2) is dynamic pressure.

• Inlet stall: Stall occurs when the adverse pressure gradient becomes too strong for the wall boundary layer to remain attached.
  • Separation reduces the effective flow area.
  • Recirculation creates total-pressure and velocity distortion.
  • Unsteadiness may propagate downstream and threaten compressor stability.
• Controlling factors: Large wall angle, abrupt area change, low Reynolds number, surface roughness, and distorted approach flow increase stall susceptibility.

B. Boundary layer separation

Boundary-layer separation occurs when low-momentum fluid near the wall cannot move against the diffuser’s rising static pressure.

• Adverse pressure gradient: Diffusion produces (dp/dx>0), where (x) is distance downstream; near-wall velocity consequently decreases.
• Separation condition:

τw = μ(∂u/∂y)wall = 0

Here, (\tau_w) is wall shear stress, (\mu) is dynamic viscosity, (u) is streamwise velocity, and (y) is wall-normal distance. Downstream of separation, (\tau_w) may become negative because of reverse flow.

• Consequences:
  • Pressure loss: Mixing of the separated shear layer irreversibly lowers stagnation pressure.
  • Blockage: Displacement thickness and recirculation reduce usable area.
  • Distortion: Circumferential or radial pressure variations enter the compressor face.
• Prevention: Gentle wall curvature, moderate diffusion angle, sufficient inlet length, boundary-layer bleed, vortex generators, and flow-control slots help preserve attachment.

C. Major features of external flow near a subsonic inlet

External inlet flow is governed by the relation between the engine-demanded capture streamtube and the physical inlet opening.

• Capture area:

Ac = ṁ/(ρ∞V∞)

Here, (Ac) is the far-upstream capture area, while (\rho\infty) and (V_\infty) are freestream density and velocity.

• High mass flow: If (A_c) exceeds the inlet frontal area, streamlines converge toward the lip and accelerate around it. Strong lip curvature can create a local suction peak and internal-lip separation.
• Matched flow: When the capture streamtube approximately meets the inlet lip, spillage and external disturbance are small.
• Low mass flow: If (A_c) is smaller than the inlet area, excess approaching air is diverted around the nacelle.
  • A stagnation point moves onto the inner lip.
  • The captured streamtube decelerates externally.
  • Spillage drag increases because uncaptured flow is turned around the inlet.
• Flight-condition influence: Angle of attack, crosswind, and aircraft boundary layers make capture asymmetric and increase compressor-face distortion.

D. Relation between minimum area ratio and eternal deceleration ratio

The limiting inlet-area requirement is related to how much the captured stream is decelerated before entering the internal diffuser.

• External deceleration ratio:

De = V∞/Vi

Here, (De) is external deceleration ratio, (V\infty) is freestream velocity, and (V_i) is velocity at the inlet plane.

• Area relationship: For approximately incompressible flow, continuity gives:

Ai/Ac = V∞/Vi = De

Here, (A_i) is inlet-plane area and (A_c) is upstream capture area. Thus, greater external deceleration requires a larger inlet-to-capture area ratio.

• Compressible correction:

Ai/Ac = (ρ∞V∞)/(ρiVi)

Here, (\rho_i) is inlet-plane density. Density change prevents the area ratio from being determined by velocity ratio alone.

• Minimum-area implication: The minimum physical area must pass the demanded (\dot m) without excessive local acceleration or lip separation. A smaller area raises velocity and reduces static pressure near the lip.
• Design compromise: A large inlet supports low-speed mass flow but increases frontal and spillage drag; a small inlet reduces drag but has less stall margin.

E. Diffuser performance

Diffuser performance measures static-pressure rise, stagnation-pressure retention, and the uniformity of delivered flow.

• Pressure-recovery coefficient:

σd = p₀e/p₀i

Here, (\sigmad) is diffuser total-pressure recovery, and (p{0i}) and (p_{0e}) are inlet and exit stagnation pressures. An ideal adiabatic diffuser has (\sigma_d=1).

• Static-pressure recovery coefficient:

Cp = (pe − pi)/(p₀i − pi)

Here, (C_p) is static-pressure recovery, while (p_i) and (p_e) are inlet and exit static pressures.

• Ideal incompressible recovery:

Cp,ideal = 1 − (Ai/Ae)²

Here, (A_e) is exit area; the result follows from continuity and Bernoulli’s equation.

• Effectiveness:

ηd = Cp/Cp,ideal

Diffuser effectiveness (\eta_d) compares actual recovery with ideal recovery for the same area ratio.

• Assessment: High recovery alone is insufficient; compressor-face distortion, turbulence, flow angularity, and stability margin must also remain acceptable.

III. Supersonic Inlet Systems — Compression and Starting

A. Supersonic inlets

A supersonic inlet uses shock waves and area variation to reduce supersonic flight velocity to a compressor-compatible subsonic value.

• Compression arrangements:
  1. External compression: Ramps or cones generate oblique shocks outside the cowl; drag and shock-position sensitivity are important.
  2. Internal or mixed compression: Some compression occurs inside the duct, offering higher design-point recovery but greater starting difficulty.
• Shock sequence: Several weak oblique shocks generally retain more stagnation pressure than one strong normal shock producing the same overall compression.
• Terminal normal shock: The final normal shock changes the core flow from supersonic to subsonic; a conventional diffuser then completes deceleration.
• Normal-shock downstream Mach number:

M₂² = [1 + ((γ − 1)/2)M₁²] / [γM₁² − (γ − 1)/2]

Here, (M_1) and (M_2) are upstream and downstream Mach numbers, and (\gamma) is the specific-heat ratio.

• Loss mechanism: Static pressure rises across a shock, but stagnation pressure falls because entropy increases.

B. Starting problem on supersonic inlets

Starting is the process of establishing the intended internal supersonic flow and placing the terminal shock at its stable operating location.

• Unstarted condition: During acceleration, a normal shock may stand ahead of the cowl because the contracted internal passage cannot pass the shock-processed mass flow.
• Area–Mach function:

A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)]^[(γ+1)/(2(γ−1))]

Here, (A^*) is sonic area and the other symbols retain their usual meanings.

• Kantrowitz condition: After a normal shock at the entrance, the throat must be large enough to pass the resulting subsonic stream without choking prematurely. This starting contraction is less severe than the contraction supportable after the inlet has started.
• Symptoms of non-start: A detached shock, large spillage, reduced mass flow, drag increase, poor pressure recovery, and oscillatory “buzz” may occur.
• Starting aids: Variable throat geometry, translating centerbodies, bypass doors, bleed slots, and temporarily reduced back pressure enlarge the stable operating range.

C. Shock swallowing by area variation

Shock swallowing uses temporary geometric variation to move the entrance normal shock through the inlet and establish supersonic internal flow.

• Starting sequence:
  1. Enlarge the throat: Increasing (A_t) lets the duct accept the subsonic flow behind the normal shock.
  2. Move the shock downstream: As mass-flow capacity rises, the shock passes through the contraction.
  3. Reset the geometry: After starting, the throat contracts toward its efficient design position.
• Variable mechanisms: Movable ramps, collapsing or translating centerbodies, variable cowl lips, and auxiliary doors alter the effective contraction ratio (A_c/A_t).
• Hysteresis: The area required to start is larger than that required to remain started; therefore, starting and operating limits do not coincide.
• Practical limitation: Variable geometry adds mass, actuation loads, leakage, control complexity, and thermal-management requirements.

D. External declaration

External deceleration reduces Mach number through compression waves located ahead of the inlet throat, thereby limiting internal contraction and easing starting.

• Oblique-shock compression: A ramp or cone turns the flow toward itself, increasing pressure and reducing the normal component of Mach number.
• Advantages: External compression lowers the Mach number entering the cowl, reduces internal shock strength, and can improve starting tolerance.
• Penalties: Shock waves create wave drag, and flow not captured after compression produces spillage drag.
• Off-design behavior: At Mach numbers or mass flows away from design, shock intersections miss the cowl lip, reducing capture and pressure recovery.
• Boundary-layer interaction: Shock-induced pressure rise can separate the ramp boundary layer; bleed is often placed near shock impingement or throat regions.

IV. Inlet Operating Regimes — Stability and Matching

A. Models of inlet operation

Models of inlet operation classify how shock position, mass-flow demand, throat choking, and downstream back pressure determine inlet behavior.

• Critical operation: The shock system lies near its intended position, captured mass flow matches engine demand, and pressure recovery is near the design value.
• Subcritical operation: Excess back pressure drives the terminal shock upstream.
  • The inlet spills more flow.
  • External drag and distortion increase.
  • Severe upstream movement may cause unstart.
• Supercritical operation: Reduced back pressure draws the terminal shock downstream into the duct.
  • Mass flow may approach a choked limit.
  • Internal shock and boundary-layer losses increase.
  • Compressor-face recovery may deteriorate despite stable capture.
• Quasi-one-dimensional model: Continuity, the area–Mach relation, shock equations, and an imposed back pressure predict mean shock location.
• Dynamic model: Plenum volume, duct inertia, engine demand, and moving shocks are included to represent buzz and inlet–engine interaction.
• Operating map: Practical limits are plotted against Mach number, corrected mass flow, contraction ratio, or back pressure; the usable region must maintain start, recovery, and distortion margins simultaneously.