A Modeling Study of Ice Accretion on a NACA 4412 Airfoil

1. A Modeling Study of Ice Accretion on a NACA 4412 Airfoil Daniel Shields

2. Background • The formation of ice on aircraft surfaces has been a concern since the early days of aviation. • Ice formations on aircraft reduces the amount of lift and increases drag and weight. • Rotorcraft are particularly susceptible due to lower speeds and a limited altitude envelope.

3. Problem Statement • A 2D airfoil shape (NACA4412) will be constructed to analyze the amount of ice that will form on the leading edge. • The airfoil will be subjected to a variety of airspeeds, temperatures and cloud liquid water content (LWC). • Results will be compared to a theoretical maximum ice accretion parameter.

4. Atmospheric Conditions • Stratiform Cloud Layers • Horizontal layering of clouds • Three separate levels • Generally uniform base. • The horizontal base can span for a thousand square miles. • Icing in stratiform clouds normally occurs at altitudes below 20,000 feet. • Cumuliform Cloud Layers • Form rapidly and generally in a vertical direction. • Flat base, and vertical formation, • Most commonly associated with severe weather such as thunderstorms, hail, and tornadoes. • Cumuliform clouds can contain large amounts of liquid water and because of adiabatic lifting can result in supercooled drops and severe icing conditions.

5. Methodology • A brief introduction of the energy balance and potential flow modeling techniques. • A LEWICE 2D model will be created and run varying parameters • Airspeed: 77kts, 155kts • Temperature: -30°C, -20°C, 10°°C, -5.5°C, -1°C • Liquid Water Content (LWC): 0.1g/m3 to 0.8g/m3 • Ice accretion parameter will be developed for comparison to modeling predictions

6. Particle Trajectory Aerodynamic Forces Gravitational Forces Equations for y-direction are identical and are not shown.

7. Energy Balance at the Airfoil Surface Kinetic Energy Viscous heating Latent heat Convection Evaporation Droplet warming

8. Model Development • The data points collected are consistent with the typical rotorcraft continuous maximum icing envelope outlined by 14CFR Part 29, Appendix C. • Data points are taken at the FAA standard cloud distance (17.4NM)

9. LEWICE Results Predicted Ice Shapes at Varying Temperature and LWC – 155kts, 15μm Predicted Ice Shapes at Varying Temperature and LWC – 77kts, 15μm Predicted Ice Shapes at Varying Temperature and LWC – 155kts, 25μm • Increase in airspeed, and liquid water content results in an increase amount of water impinging on the surface over the same time span. • Ice thickness increases with increasing temperature until -5.5C. At -5.5C the ice thickness decreases rapidly due to incomplete freezing upon contact.

10. Accretion Parameter Comparison 155kts, 15μm MVD – Comparison of Ice Accretion Parameter, and predicted thickness at varying temperatures. • Accretion parameter is a non-dimensional mass flux term and can be thought of as the ice thickness that would form on an imaginary flat plate. • LEWICE shows less ice thickness at higher accretion parameters for test case shown. • Accretion parameter is adequate for predicting icing severity up to -10°C.

11. References • Gent, R. W., Aircraft Icing, Mathematical, Physical and Engineering Sciences, 2000, Vol. 358, No. 1776, The Royal Society, pp. 2873-2911 • Messinger, B. L., Equilibrium Temperature of an Unheated Icing Surface As A Function of Airspeed, Journal of the Aeronautical Sciences, 1953, Vol. 20, pp. 29-42 • Myers, T.G., Ice and Water Film Growth From Incoming Supercooled Droplets, International Journal of Heat and Mass Transfer, 1999, Vol. 42, pp. 2233-2242 • FAA Aircraft Icing Handbook, US Department of Transportation, Federal Aviation Administration, March 1991