PHYSICAL AND OPERATIONAL ASPECTS OF AIRCRAFT ICING 
Where the flow degenerates to a turbulent condition, 
such as at regions 2 (Fig. 1), the temperature of the 
gas particles is substantially equal to that of the fluid 
LLL LLL LLL LLL LLL 
Fic. 1.—Flow through a partially closed carburetor; 0— 
ambient region, 1—laminar flow at high velocity and low 
pressure, 2—separated turbulent flow, 3—solid boundary. 
in the moving free stream at region 1. The relations 
between pressure, temperature, and the liquid water 
precipitated because of expansion along the stream tube 
are given in a practical and usable form in the pseudo- 
adiabatic chart as developed by the U. S. Weather 
Bureau. Because of the velocity of the stream in re- 
gion 1 and the time interval required for a droplet to 
grow to a significant size, visible condensation may not 
occur near the throttle in the moving stream but may 
be seen at some distance downstream. Droplets may 
reach sufficient size to cause an icing problem, how- 
ever, in the separated turbulent regions 2 because of 
the comparatively stagnant movement through these 
regions and the greater time interval consequently 
available for droplet growth. Under certain conditions, 
vorticity may develop in the standing regions. This 
will be conducive to the precipitation of more water 
because of the reduced stream temperature within a 
vortex. It can be assumed that the temperature of the 
droplets so formed conforms closely to the stream tem- 
perature and that in most cases, including the example 
of the engine carburetor, the contents of the air-borne 
droplet do not undergo the phase change to ice until 
mechanically disturbed as when the droplet strikes the 
walls of the carburetor. 
The expanding flow of clear saturated atmospheric 
air over an airfoil such as illustrated in Fig. 2 will result 
Fria. 2—Flow over an airfoil; 0—ambient region, 1—low- 
pressure region, 2—turbulent flow, 3—solid boundary. 
in a supersaturated condition in region 2 for the same 
reasons as those given in the discussion of the carbure- 
tor; however, the comparatively high velocity in the 
turbulent regions over exterior aerodynamic forms pre- 
1191 
vents droplet growth to a significant size. In wing and 
propeller tip vortices, visible condensation does form, 
however, because of the length of time a gas particle 
remains in the vortex and because of the low tempera- 
ture which probably exists at the vortex core. 
It is therefore evident that supercooled water drop- 
lets from which ice may form are found in nature and 
may also be generated by the aerodynamic and ther- 
modynamic processes of stream flow over the airplane 
components. Ice is also formed from cloud droplets 
at temperatures above 32F, although under a combina- 
tion of operating and weather conditions not often en- 
countered. Snowflakes also are intercepted by airplane 
surfaces to a very limited extent, and ice formations 
are thereby accumulated. These special cases of icing 
and the precipitation of moisture on airplane surfaces 
from the gaseous state and the subsequent formation 
of frost are briefly discussed below. 
Water Impingement. As an airfoil moves through a 
cloud, some of the droplets in the volume of space 
swept through by the airfoil are intercepted by the 
moving body. The analysis and explanation of the 
droplet impingement on an airfoil are made for the 
hypothetical condition in which air passes over a sta- 
tionary airfoil. In such a flow pattern (Fig. 2), gas 
particles of the atmosphere follow streamlines past the 
airfoil. Those passing near the forward stagnation re- 
gion of the body have small radii of curvature. The 
inertial effect tending to keep the droplet moving 
straight in such a curving flow field will provide the 
force necessary to overcome the viscous forces which 
tend to hold the droplet motion to that of the air 
streamlines. The result is that droplets will cross stream- 
lines in the direction of the solid boundary of the air- 
foil and some will actually strike the surface in the 
vicinity of the leading edge. In the preceding descrip- 
tion of cloud droplets it was noted that the average 
droplet size is very small, that is, of the order of 8 p to 
20 ». Furthermore, the velocity of the droplets across 
the streamlines is small. It follows that the Reynolds 
number of the droplet motion in the air will be small 
and that the droplet path can therefore be analyzed by 
the equations of Stokes’ flow, from which it follows 
that the resistance to motion is proportional to the 
velocity across the streamlines. 
The development of the theory of cloud-droplet in- 
terception by airfoils is given in [7, 10], from which 
quantitative impingement rates and area of catch for 
particular conditions may be calculated. A method of 
determining the rate of droplet impingement on an 
airplane windshield is given in [6]. A discussion of the 
ingestion of water droplets into the carburetor of an 
engine is discussed in [9]; however, no attempt has 
been made to analyze the efficiency or the location at 
which ingested water comes in contact with the walls 
or throttle plate of a carburetor. 
The area over a component on which the droplets 
impinge is determined by the liquid-water content of 
the atmosphere, the range of droplet sizes in the cloud, 
the velocity, and the shape and size of the airplane 
component. As the radius of curvature of the entering 
