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/m 3 to 0.8g/m 3 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 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. Predicted Ice Shapes at Varying Temperature and LWC – 155kts, 15 μm Predicted Ice Shapes at Varying Temperature and LWC – 77kts, 15 μm Predicted Ice Shapes at Varying Temperature and LWC – 155kts, 25 μm

10. Accretion Parameter Comparison 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. 155kts, 15 μm MVD – Comparison of Ice Accretion Parameter, and predicted thickness at varying temperatures.

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