Ice Protection Sizing

Ice Protection Sizing (vehicle-design/sizing/ice-protection-sizing)

Use when the task is sizing the steady thermal ice protection system of an aircraft surface: choosing evaporative anti-icing, running-wet anti-icing or cyclic de-icing, computing the two-sided protected area of the band, estimating the droplet catch efficiency from the median volume diameter (MVD) and airspeed, computing the evaporative heat flux, the running-wet surface temperature and the freezing fraction, and converting the heat flux and area into the required electrothermal power or bleed air mass flow, closed by a protect or not protect verdict against the available power margin. This leaf implements the steady thermal sizing model in pure Python, stdlib only, with the FAR/CS 25 Appendix C continuous maximum icing condition as the reference context. It pairs with engine-sizing and nacelle-sizing (surfaces that need the protection), fuselage-sizing for the windshield area context, and vehicle-design/conceptual/constraint-analysis for the power offtake margin around the verdict.

Domain quick reference

• Free-stream total temperature: T_tot = T_inf * (1 + 0.2 * M^2). The adiabatic wall temperature equals T_tot under a turbulent recovery factor of about 1 (assumption stated in the module); the kinetic heating rise is T_kin = T_tot - T_inf.
• Catch efficiency, preliminary reference-only correlation (module constants ETA_K1 = 0.55, MVD_REF = 20 micron, V_REF = 100 m/s, CHORD_REF = 0.5 m): eta = min(1, 0.55 * (mvd / 20)^0.6 * (v / 100)^0.4
  • (0.5 / chord)^0.5). Eta rises with the MVD and airspeed and falls with the chord, capped at 1.
• Water catch rate per unit span: m_wdot = eta * LWC * v * chord (kg/s per m span), with LWC the liquid water content (kg/m3) and chord the surface chord (m). The total catch over the protected segment is m_wdot * span.
• Protected area: A = 2 * band_fraction * chord * span (m2), the two sides of the leading edge band, band length chord fraction times chord times span.
• Freezing fraction (simplified running-wet form, T_frz = 273.15 K, cp_water = 4186 J/(kg K), L_f = 3.34e5 J/kg): n = min(1, max(0, cp_water * (T_frz - T_surf) / L_f)). Evaporative anti-ice runs n = 0; running wet holds part frozen for 0 < n < 1 and n = 0 at or above the freeze temperature.
• Convective coefficient (flat plate turbulent, reference-only): h_c = 0.0296 * k * Re^0.8 * Pr^(1/3) / chord with Re = rho * v * chord / mu, Pr = 0.72, and k, mu power-law fits in temperature (k = 0.0244 * (T / 273.15)^0.85, mu = 1.716e-5 * (T / 273.15)^0.75 W/(m K), Pa s). Convective loss: q_conv = h_c * (T_surf - T_inf).
• Evaporative loss: q_evap = m_evap_dot * L_e / A (W/m2), L_e = 2.501e6 J/kg. Evaporative anti-icing required flux: q_req = q_conv + q_evap + sensible heating of the catch to T_surf, evaluated at the module operating skin temperature T_EVAP = 303.15 K (about 30 C).
• Running-wet anti-icing required flux at the protected limit: q_req = q_conv - kinetic heating contribution = h_c * (T_surf - T_inf
  • T_kin), with T_surf = T_frz (273.15 K) at the limit where the freeze fraction reaches zero; the sustained surface temperature for a flux q is T_surf = T_inf + T_kin + q / h_c.
• Cyclic de-icing: q_req = q_conv at the shed temperature T_SHED = 276.15 K (273.15 K plus 3 K margin); no shedding dynamics.
• Required power: P_req = q_req * A (W), electrical for electrothermal; bleed mass flow m_dot = P_req / (cp_air * (T_bleed - T_inf)) for a pneumatic system, cp_air = 1005 J/(kg K).
• Verdict: protect the surface when it is on the icing-critical list and P_req sits within the available power margin; otherwise flag.
• Units are SI throughout: K, m, m/s, kg/m3, micron for MVD, W, W/m2, kg/s.

Workflow

1. Fix the icing design point: T_inf, Mach, airspeed v, density rho, liquid water content LWC and median volume diameter MVD; get the total and kinetic temperatures with total_temperature and kinetic_temperature_rise.
2. Decide the surface: if it is icing critical, set the protected band geometry (chord, span, band fraction) and compute the two-sided area with protected_area.
3. Compute the catch efficiency with catch_efficiency (mvd, v, chord) and the catch rate per unit span with water_catch_rate; multiply by the span for the total catch over the segment.
4. Evaluate the running-wet limit: convective_heat_transfer_coefficient at the film temperature, convective_heat_loss at T_frz, then running_wet_heat_flux at T_frz; confirm running_wet_surface_temperature returns T_frz and freezing_fraction is zero at the limit.
5. For evaporative anti-icing, sum the convective, evaporative and sensible terms with anti_ice_evaporative_heat_flux (all catch evaporates, surface above freezing); for cyclic de-icing use de_ice_heat_flux at the shed temperature.
6. Convert to the system demand: required_power for the electrothermal case, bleed_mass_flow for the bleed air case at the bleed supply temperature.
7. Close with protect_verdict against the available power; if the evaporative mode exceeds the margin, rerun the running-wet and de-ice modes at the lower flux and re-check the freeze fraction.
8. Confirm the deterministic checks with the contract test scripts/test_ice_protection_sizing.py.

Worked example

Transport wing leading edge protected band: chord c = 0.45 m, protected segment span 12 m, band chord fraction 0.08, so A_protected = 2 * 0.08 * 0.45 * 12 = 0.864 m2. Flight M = 0.78 at T_inf = 218 K (v ~ 235 m/s, rho ~ 0.365 kg/m3), LWC = 0.44 g/m3 (0.44e-3 kg/m3), MVD = 20 micron.

• Total temperature 218 * (1 + 0.2 * 0.78^2) = 244.53 K; kinetic rise 26.53 K.
• Catch efficiency: eta = 0.55 * (20/20)^0.6 * (235/100)^0.4 * (0.5/0.45)^0.5 = 0.816, in the expected 0.5 to 0.9 band.
• Water catch rate: 0.816 * 0.44e-3 * 235 * 0.45 = 0.03797 kg/s per m span, 0.4556 kg/s over the 12 m segment.
• Film temperature (T_frz + T_inf) / 2 = 245.6 K gives h_c = 169.0 W/m2K from the flat plate correlation; q_conv at 273.15 K is 169.0 * 55.15 = 9322.9 W/m2.
• Evaporative anti-icing at the 303.15 K operating skin: evaporating the full catch over the band costs q_evap = 0.4556 * 2.501e6 / 0.864 = 1.319e6 W/m2, so q_req = q_conv + q_evap + sensible heating = 1.521e6 W/m2 and P_req = 1.314e6 W (about 1.31 MW) for the segment. This is the physics of full-catch evaporation: evaporative anti-icing is only practical on small, high-flux surfaces such as inlet lips, and the mode decision below lands on running wet for the wing band.
• Running-wet limit: q_req = h_c * (273.15 - 218 - 26.53) = 4838.7 W/m2, P_req = 4.18 kW for the segment, T_surf = 273.15 K exactly and the freezing fraction is zero at the protected limit.
• Cyclic de-ice at the shed temperature 276.15 K: q_req = 9830.0 W/m2, P_req = 8.49 kW.
• Verdict: against a 100 kW anti-ice power budget the evaporative mode is flagged (1.31 MW exceeds the margin), while the running-wet mode at 4.18 kW protects the surface; the freeze-fraction check at the limit is zero. The running-wet bleed demand is 4180.7 / (1005 * (450 - 218)) = 0.0179 kg/s at a 450 K bleed supply.

All of these numbers are reproduced exactly by the contract test.

Pitfalls

• Choosing evaporative anti-icing for a wing band: full-catch evaporation costs q_evap ~ 1.3 MW per m2 of catch (1.31 MW in the worked example) and is only practical on small, high-flux surfaces like inlet lips; the mode decision must fall back to running wet (4.18 kW) or cyclic de-ice for large bands.
• Forgetting the kinetic heating credit: the running-wet flux is q_req = h_c * (T_surf - T_inf - T_kin) with the kinetic rise (26.53 K in the worked example) reducing the required heat; an adiabatic-wall calculation without the recovery credit over-sizes the anti-ice demand.
• Reading the freeze fraction sign: n is min(1, max(0, cp_water * (T_frz - T_surf) / L_f)), so it is 0 at and above 273.15 K and 1 only for a very cold surface; a running-wet surface at the limit has zero freeze fraction by construction.
• Sizing the catch on the wrong chord or span: the catch rate is per unit span (eta * LWC * v * chord) and the protected area is TWO-sided (2 * band_fraction * chord * span); mixing per-meter with total values mis-sizes both the catch and the power.
• Quoting the electrothermal power for a bleed-air system: the required power converts to bleed mass flow through the bleed supply temperature (0.0179 kg/s at 450 K in the worked example), and a bleed supply at or below the free-stream temperature raises ValueError.
• Verdict without the power margin: protect_verdict compares the mode's P_req against the AVAILABLE power (the 100 kW budget rejects the 1.31 MW evaporative mode), so the mode and the margin are one decision.

Verification

• Confirm total_temperature(218, 0.78) = 244.53 K and the kinetic rise is 26.53 K.
• Confirm catch_efficiency(20, 235, 0.45) = 0.816, inside the 0.5 to 0.9 band, rising with MVD and airspeed and falling with chord, capped at 1.
• Confirm water_catch_rate returns 0.03797 kg/s per m span and scales linearly in eta, LWC, v and chord.
• Confirm freezing_fraction is 0 at and above 273.15 K, between 0 and 1 just below freezing, and 1 for a very cold surface.
• Confirm the running-wet round trip: running_wet_surface_temperature of running_wet_heat_flux at any surface temperature returns that temperature, and at the protected limit it returns 273.15 K with zero freeze fraction.
• Confirm required_power reproduces 4.18 kW (running wet) and 1.314 MW (evaporative) for the worked example band, and bleed_mass_flow the 0.0179 kg/s running-wet bleed demand.
• Confirm every non-physical input raises ValueError: negative airspeed, non-positive chord, negative LWC, non-positive MVD, non-positive temperatures, negative heat flux, non-positive area, out-of-range band fraction or catch efficiency, bleed supply at or below the free stream temperature, and negative available power.
• Run the contract test offline: python3 scripts/test_ice_protection_sizing.py (35 tests, deterministic).

Related leaves

• vehicle-design/sizing/engine-sizing: the engine is the bleed source for a pneumatic anti-ice system; the bleed mass flow demand feeds back into the engine sizing offtake.
• vehicle-design/sizing/nacelle-sizing: the nacelle lip is a protected surface; its geometry sets the protected area for the inlet anti-ice calculation.
• vehicle-design/sizing/fuselage-sizing: fuselage windshield area context for the surfaces that need protection against ice.
• vehicle-design/conceptual/constraint-analysis: the power offtake margin against which the protect verdict is drawn.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_ice_protection_sizing.py

The test covers the worked example values (total and kinetic temperature, catch efficiency in the 0.5 to 0.9 band, catch rate, protected area, convective coefficient and loss, evaporative loss and flux decomposition, the running-wet limit flux and the round-trip identity of the surface temperature, de-ice flux, required power for both modes and the bleed mass flow), the correlation trends, the freezing fraction limits, and ValueError rejection of non-physical inputs, 35 test methods in total.

Compliance

• Standards referenced, not reproduced: far-25 and cs-25 resolve in standards-map.yaml, both reference-only; the FAR/CS 25 Appendix C continuous maximum icing condition is named and paraphrased (typical LWC and MVD orders), with no reproduced tables or text.
• compliance: STANDARDS-REF, gated: false.