A Modeling Study of Ice Accretion
on a NACA 4412 Airfoil
Daniel Shields
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.
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.
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.
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
Particle Trajectory
F
x
 Fa  Fg
Aerodynamic Forces
1
2
Fax  C D  a AdVres
2
Gravitational Forces
 a
Fgx  md g 1 
 d

 sin    

Equations for y-direction are identical and are not shown.
Energy Balance at the Airfoil
Surface
Q  qin  qout
qin  qk  qv  q f
2
V
qk  Rw A(  )
2 gJC p
Kinetic Energy
2
rV
qv  f c A
2 gJC p
q f  144nRw A
Viscous heating
Latent heat
qout  qc  qe  qw
qc  f c A32  t 
Convection
 P  P  
qe  2.90 Le f c A sw  
B


qw  Rw ACw 32  t 
Evaporation
Droplet warming
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)
0.9
32deg
Liquid Water Content (g/m 3)
0.8
14deg
-4deg
0.7
-22deg
0.6
Data Points
0.5
0.4
0.3
0.2
0.1
0
10
15
20
25
Mean Effective Drop Diam eter (μm )
30
35
40
LEWICE Results
Predicted Ice Shapes at Varying Temperature
and LWC – 155kts, 15μm
Predicted Ice Shapes at Varying Temperature
and LWC – 77kts, 15μm
0.060
0.060
0.040
0.040
0.020
0.020
0.000
-1C
-5.5C
-10C
-20C
-30C
y/c
y/c
-1C
-5.5C
-10C
-20C
-30C
0.000
-0.020
-0.020
-0.040
-0.040
-0.060
-0.060
-0.050
-0.050
0.000
0.050
0.100
0.150
0.000
0.050
0.200
x/c
0.100
0.150
0.200
x/c
0.060
0.040
-1C
-5.5C
-10C
-20C
-30C
0.020
y/c
•Increase in airspeed, and liquid water
content results in an increase amount of
water impinging on the surface over the
same time span.
Predicted Ice Shapes at Varying Temperature
and LWC – 155kts, 25μm
0.000
•Ice thickness increases with increasing
temperature until -5.5C. At -5.5C the ice
thickness decreases rapidly due to
incomplete freezing upon contact.
-0.020
-0.040
-0.060
-0.050
0.000
0.050
0.100
x/c
0.150
0.200
Accretion Parameter Comparison
155kts, 15μm MVD – Comparison of Ice Accretion Parameter, and
15um MVD; 155 Kts - Comparison of Ice Accretion and Thickness vs. Temperature
predicted thickness at varying temperatures.
4000
0.05
3000
0.04
2500
2000
0.03
1500
Accretion Parameter
0.02
LEWICE Data
1000
0.01
500
•Accretion parameter is
adequate for predicting icing
severity up to -10°C.
0
0
-30
-20
-10
Temperature (C)
0
Ice Thickness
•LEWICE shows less ice
thickness at higher accretion
parameters for test case shown.
3500
Accretion Parameter
•Accretion parameter is a nondimensional mass flux term and
can be thought of as the ice
thickness that would form on an
imaginary flat plate.
0.06
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