A Modeling Study of Ice Accretion on a NACA 4412 Airfoil
by
Daniel Shields
A Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
April 2011
i
© Copyright 2011
by
Daniel Shields
All Rights Reserved
ii
CONTENTS
A Modeling Study of Ice Accretion on a NACA 4412 Airfoil........................................... i
LIST OF TABLES ............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
List of Symbols ................................................................................................................ vii
Keywords .......................................................................................................................... ix
ACKNOWLEDGMENT ................................................................................................... x
ABSTRACT ..................................................................................................................... xi
1. Introduction.................................................................................................................. 1
1.1
1.2
1.3
Atmospheric Conditions – Cloud Formation ..................................................... 3
1.1.1
Stratiform Clouds ................................................................................... 3
1.1.2
Cumuliform Clouds................................................................................ 5
Cloud Properties ................................................................................................. 7
1.2.1
Cloud drop size distribution ................................................................... 7
1.2.2
Cloud liquid water content ..................................................................... 7
Aircraft design criteria for icing environments .................................................. 7
1.3.1
FAA guidelines for continuous maximum icing conditions .................. 7
1.3.2
FAA guidelines for intermittent maximum icing conditions ................. 8
1.4
Ice Formation ..................................................................................................... 8
1.5
Methods of protection ........................................................................................ 9
2. Methodology .............................................................................................................. 11
2.1
Water drop trajectory ....................................................................................... 11
2.1.1
Drop trajectory calculations ................................................................. 11
2.1.2
Supercooled drop heat balance............................................................. 12
2.2
Ice Accretion Parameter ................................................................................... 13
2.3
Model Development ......................................................................................... 14
3. Results........................................................................................................................ 17
iii
3.1
Ice Accretion Parameter ................................................................................... 17
3.2
LEWICE Solutions .......................................................................................... 18
4. Conclusions................................................................................................................ 21
5. References.................................................................................................................. 22
6. Appendices ................................................................................................................ 23
6.1
Appendix A – Test Data Correlation ............................................................... 24
6.2
Appendix B – Input Files and Raw Data ......................................................... 26
6.2.1
Run 1
27
6.2.2
Run 2
30
6.2.3
Run 3
33
6.2.4
Run 4
36
6.2.5
Run 5
39
6.2.6
Run 6
42
6.2.7
Run 7
45
6.2.8
Run 8
48
6.2.9
Run 9
51
6.2.10 Run 10 54
6.2.11 Run 11 57
6.2.12 Run 12 60
6.2.13 Run 13 63
6.2.14 Run 14 66
6.2.15 Run 15 69
iv
LIST OF TABLES
Table 1: Table of Runs .................................................................................................... 15
v
LIST OF FIGURES
Figure 1: Captain Pawlik is lowered to safety during the first external hoist helicopter
rescue. [1] .......................................................................................................................... 1
Figure 2: Stratiform Clouds [7] ......................................................................................... 3
Figure 4: Cumuliform Clouds [7] ...................................................................................... 6
Figure 5: Cumulus cloud water distribution [10] .............................................................. 6
Figure 6: Rime ice accretion [8] ........................................................................................ 9
Figure 7: Glaze ice accretion [9] ....................................................................................... 9
Figure 8: Particle force balance x-direction [2] ............................................................... 12
Figure 9: Energy balance at airfoil surface. [3] ............................................................... 13
Figure 10: Atmospheric icing conditions – Continuous maximum (Stratiform Clouds)
[10]................................................................................................................................... 15
Figure 11: Liquid water content vs. cloud horizontal distance [10] ................................ 16
Figure 12: Ice accretion parameter as a function of temperature and airspeed ............... 17
Figure 13: Ice shape predictions - 15μm MVD, 155 knots, varying temperature and
LWC. ............................................................................................................................... 18
Figure 14: Comparison of ice accretion parameter and volume of ice thickness - 15μm
MVD, 155 knots. ............................................................................................................. 18
Figure 15: LEWICE results - 15μm MVD, 77 knots, varying temperature and LWC. ... 19
Figure 16: Comparison of ice accretion parameter and volume of ice thickness - 15μm
MVD, 155 knots .............................................................................................................. 19
Figure 17: LEWICE Results - 25μm MVD, 155 knots, varying temperature and LWC. 20
Figure 18: Comparison of ice accretion parameter and volume of ice thickness - 25μm
MVD, 155 knots. ............................................................................................................. 20
vi
List of Symbols
Symbol
Description
Units
Q
Total Energy
BTU/hr
qin
Heat transferred out
BTU/hr
qout
Heat transferred in
BTU/hr
qc
Heat transferred due to convection
BTU/hr
qe
Heat transferred due to evaporation
BTU/hr
qw
Heat transferred due to sensible heat
BTU/hr
qf
Heat transferred due to heat of fusion
BTU/hr
qv
Heat transferred due to viscous heating
BTU/hr
qk
Heat transferred due to kinetic energy
BTU/hr
Aice
MVD
Kts
LWC
Ice accretion parameter
dimensionless
Mean drop diameter
μm
Airspeed
kts
g/m3
Liquid water content
V
Aircraft velocity
ft/s
t
Time
min
Fx
Sum of forces in the x-direction
lbf
Fax
Sum of aerodynamic forces in the x-direction
lbf
Fgx
Sum of gravitational forces in the x-direction
lbf
md
Mass of supercooled drop
Cd
Drop coefficient of drag
ρa
Density of air
g/m3
ρd
Density of supercooled drop
g/m3
Ad
Drop surface area
in2
D
Drop diameter
in
Vres
Resultant velocity
ft/s
urel
x-direction velocity
ft/s
fc
Convective heat transfer coefficient
g
dimensionless
vii
BTU/hr-ft2-°F
°F
t∞
Ambient temperature
Le
Latent heat of vaporization of water
BTU/lb
Psi
Ambient pressure
in of Hg
Psw
Vapor pressure over water
in of Hg
Rw
Rate of water catch
lb/hr-ft2
n
Freezing fraction
As
Surface area
dimensionless
in2
r
“recovery” factor applying to kinetic heating
g
Acceleration due to gravity
J
Mechanical equivalent of heat
Cp
Specific heat
ρice
Density of accreted ice
dimensionless
ft/s2
778ft-lbs per BTU
BTU/lb-°F
g/m3
c
Chord length
in
B
Absolute ambient pressure
in of Hg
α
Angle of attack
degrees
viii
Keywords
Ice Accretion
Build-up of ice on an aircraft surface.
Accretion parameter
Theoretical value for predicting ice severity.
LEWICE
Computer code for predicting ice growth on an aircraft surface.
NACA 4412
Airfoil shape developed by the National Advisory Committee for
Aeronautics.
Stratiform Clouds
Thinner atmospheric cloud sometime spanning thousands of
miles.
Cumuliform Clouds
Severe weather cloud.
ix
ACKNOWLEDGMENT
To my wife Dawn, thank you for your love and understanding during the pursuit of my
degree. I could not have completed this without you.
For Colton.
x
ABSTRACT
This report describes result of the study designed to investigate the phenomenon of ice
accretion in a standard airfoil at different conditions defined by the FAA 14CFR Part 29
Appendix C. This is an important problem in the aerospace industry because many
rotorcraft accidents occur due to the formation of ice on aircraft control surfaces,
fuselage, and engine inlets.
The continued flight safety of a rotorcraft in all
environments (all weather aircraft) is a primary goal for rotorcraft manufacturers and
owners alike. In this study, the LEWICE code was used to model ice accretion on a
NACA4412 airfoil subjected to an icing environment. The objective was to determine
the effect of varying different atmospheric conditions on the shape and thickness of the
ice. The LEWICE results are compared to a simplified ice accretion parameter based on
the classical icing accretion parameter. The purpose of the accretion parameter in this
application was to identify the severity of different atmospheric icing conditions using
the basic atmospheric parameters governing the FAA certification testing guidelines. It
will be shown that the accretion parameter is a good indicator of icing environment
severity for certification; however, it has limited value in predicting ice accretion
thickness at temperatures approaching the freezing point.
xi
1. Introduction
Helicopters have been used for military and civilian lifesaving missions since the mid
1940’s. In January 1944 a helicopter flew plasma to injured crewmen of the USS Turner
after an explosion ripped through the destroyer off the coast of Sandy Hook NJ. Later
that year, a helicopter rescued a boy stranded on a sandbar in Jamaica Bay, NY. About
the same time in Burma, helicopters were being used in the first combat rescue missions.
The first rotorcraft external hoist rescue off the coast of Fairfield, CT, in inclement
weather, in November 1945, the modern rotorcraft has been the most desirable tool in
conducting search and rescue operations around the globe.
Aviation pioneer Igor
Sikorsky was quoted as saying “If a man is in need of rescue, an airplane can come and
throw flowers on him, and that’s just about all. But a direct lift aircraft could come in
and save his life.”[1] Since that first rescue 65 years ago, the expanding role of the
rotorcraft for search and rescue operations in new and expanding world markets expose
the vehicle to extremely adverse weather conditions.
Figure 1: Captain Pawlik is lowered to safety during the first external hoist
helicopter rescue. [1]
The certification of rotorcraft still depends on experimental wind tunnel and flight
testing; however, the increasing capability of computer processing speed has allowed for
1
more detailed analysis using computational fluid dynamics (CFD) with particle tracking
analysis. It is this type of computational analysis that will be discussed herein.
The formation of ice on aircraft is the most critical natural hazard affecting the safe
operation of aircraft and it has been a concern since the early days of aviation. Even
today,, aircraft accidents continue to occur due to the formation of ice on aircraft control
surfaces, fuselage, and engine inlets. The resulting ice formations on the airframe
decreases lift and engine capability and increases weight, drag and stalling speed.
Accretion of ice on aircraft surfaces is the result of a tendency for water drops in
atmospheric clouds to stay in a liquid state even at temperatures as low as -40°C.
Supercooled drops are observed when the liquid temperature gradient at the drop surface
is larger than the air temperature gradient at the surface of the drop [2].
These
supercooled drops will crystallize in the presence of a seed such as another ice crystal,
snow flake, dust or dirt. In the absence of any seeds, the water drops can remain in the
liquid phase until they come in contact with something that will promote freezing such
as an aircraft surface.
There are several approaches to protecting aircraft from excessive ice accretion. The
first method has been employed since the 1930’s and involves allowing a small amount
of ice to form on a surface and then locally deforming that surface to break the ice away.
In the early days this usually involved a pneumatically inflated rubber bladder on the
leading edge of the wing. With today’s technology, the method remains the same but in
place of a rubber bladder, carbon fiber composites can be used along with an electrical
expulsive device. The second method involves heating the surface to either prevent ice
from forming or to heat the surface at specific intervals to shed ice that has formed on
the surface. Several rotorcrafts are certified for operation in forecast icing conditions
and while the method of protection may differ greatly, the design and development of
such technologies depends upon knowledge of atmospheric conditions, icing properties,
water drop kinematics, heat transfer and fluid mechanics.
2
1.1 Atmospheric Conditions – Cloud Formation
Clouds develop when air cools adiabatically as it ascends and expands. The water vapor
undergoes a change of state from gas to liquid as it condenses at lower temperatures and
pressures.
There are two types of clouds generally associated with aircraft icing:
stratiform (layer type clouds) and cumuliform (vertical development cloud).
1.1.1
Stratiform Clouds
Stratiform clouds (Figure 2) are a horizontal layering of clouds consisting of three
separate levels with a generally uniform base. The horizontal base of these clouds can
span for a thousand square miles. Icing in stratiform clouds normally occurs in the
lower two levels, at altitudes below 20,000 feet.
Figure 2: Stratiform Clouds [7]
The lower level stratiform clouds (<6,500 feet) known as stratocumulus, stratus and
nimbostratus are generally the most important to the icing environment because of the
higher cloud liquid water content and the extensive cloud coverage. These lower clouds
are characterized by the white to gray appearance with repetitive masses or rolls, low
ragged dark clouds or uniform gray sheet like clouds resembling fog.
3
High level stratiform clouds (>20,000 feet), do not contain liquid water because water
that precipitates out of solution freezes instantly forming ice crystals regardless of drop
size or lack of seed crystals. Ice crystals at these conditions do not contribute to aircraft
icing in any way. It should be noted that ice crystallization is an extremely important
atmospheric condition for the aerospace industry but it is outside the scope of this paper
and therefore will not be addressed.
Cloud properties such as liquid water, drop size and temperature vary greatly in
stratiform clouds as indicated by the temperature, liquid water and drop diameter plots in
Figure 3. For example, lower stratiform cloud temperature in the cloud decreases with
altitude while liquid water content however, will increase. The liquid water content and
drop size in the low level stratiform clouds will generally reach its maximum at or near
the top of the cloud due to adiabatic lifting. Adiabatic lifting predicts an increase in the
liquid water as cloud temperature decreases due to the air’s decreased ability to hold
water in vapor form [10].
Figure
Stratiform
Cloud
Properties
[9]
Figure
3:3:
Stratiform
Cloud
Properties
[10]
4
At higher levels there is less dependence of liquid water content and drop size on
temperature. The non-uniform changes between temperature and other cloud properties
with altitude results in many levels of icing severity at different altitudes. Stratiform
clouds can result in prolonged icing exposure and form the criteria used for design points
of ice protection systems.
1.1.2
Cumuliform Clouds
Cumuliform clouds (Figure 4) are clouds which form rapidly and generally in a vertical
direction. Characterized by their flat bases, and vertical formation, these types of clouds
are 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. Cumuliform clouds are not as stable as
stratiform clouds and because of their vertical formation have a much smaller footprint,
generally about 4 to 6 square miles. The only type of cumuliform cloud that contains the
proper conditions for icing is the cumulonimbus cloud. Icing conditions in these clouds
can vary greatly and depend largely on the stage of development of the cloud. Figure 5
is a diagram of drop distribution in cumulus clouds. In the lower levels of the cumulus
cloud, Zone I, newly formed drops begin to precipitate out of the air. As the air and
drops in the cloud rises due to adiabatic lifting, more water precipitates out and
coalesces, Zone II. Zone III in the center top of the cloud contains the largest drops due
mainly to coalescence. The upper outer edges of the cloud, Zone IV, the drops shrink in
size due to evaporation. [9]
5
Figure 4: Cumuliform Clouds [7]
Figure 5: Cumulus cloud water distribution [10]
6
1.2 Cloud Properties
NASA is constantly collecting atmospheric and cloud data with the intent of defining
and bounding the internal structure and water distribution of atmospheric clouds.
Variations in cloud properties are dependent on many things including time of the year,
seasons, and geography.
1.2.1
Cloud drop size distribution
The distribution of cloud water drop sizes is never uniform across the cloud. The total
liquid water content of the cloud can be calculated if the concentration of drops is
grouped by drop sizes. However, in most cases the entire distribution can be adequately
represented by the median volume drop diameter (MVD). MVD is expressed in μm and
typically ranges from 2-50μm in diameter.
1.2.2
Cloud liquid water content
The liquid water content (LWC) is the most important factor in icing. LWC represents
the amount of liquid water and is expressed in grams of liquid water per cubic meter of
air.
LWC includes water in supercooled form only.
Water in vapor form is not
considered until it condenses in to liquid form with decreasing temperature or pressure.
LWC can range between 0.1 to 2.5 g/m3.
1.3 Aircraft design criteria for icing environments
The Federal Aviation Administration (FAA) sets regulatory requirements based on
atmospheric criteria which aircraft must comply with to certify any aircraft for
inadvertent flight into un-forecast icing (30minute limit) and additional requirements to
certify as an “all weather” aircraft to include flight into known icing conditions.
1.3.1
FAA guidelines for continuous maximum icing conditions
The continuous maximum icing conditions set forth by the FAA are based on the
stratiform cloud icing conditions described in Section 1.1.1. As mentioned above, the
stratiform clouds can have a very large footprint in which icing may occur. The FAA
uses statistical analysis of atmospheric data to determine a standard distance of 17.4
7
nautical miles.
This distance should be the basis for designing any design of
experiments; however, it should not be the only case. For cloud distances other than the
standard distance determined by the FAA, a liquid water content scaler can be applied to
simulate a larger cloud base. Applying the scaler quantity to the liquid water content
parameter is intended to simulate the extended supercooled drop exposure from a larger
cloud without increasing the test time.
1.3.2
FAA guidelines for intermittent maximum icing conditions
The intermittent maximum icing conditions set forth by the FAA are based on the
cumuliform clouds described above in Section 1.1.2. The horizontal footprint of the
cumuliform cloud is much smaller than the stratiform cloud due to its inherent instability
and vertical growth. As a result the standard distance for the intermittent maximum
icing conditions is only 2.6 nautical miles. A similar scaler quantity for the intermittent
maximum conditions can be applied to the liquid water content to simulate longer
exposure times due to a larger cloud.
1.4 Ice Formation
Upon contact of the supercooled drops on a surface, the drop will freeze and begin to
form an ice accretion. The two major types of ice accretion considered are rime ice and
glaze ice. Rime ice (Figure 6), occurring at very cold temperatures (-9°C and below), is
where the water freezes almost instantaneously resulting in smaller ice accretions in the
general vicinity of the impact. Rime ice is generally has a milky or white appearance
due to the large amount of air trapped in the crystalline structure. The trapped air in the
ice structure results in ice formations with feathered edges and lower densities.
Glaze icing (Figure 7) generally occurs at warmer temperatures. Glaze ice accretions are
generally clear smooth ice deposits. The supercooled drops do not freeze instantly
therefore some of the water will flow along the airfoil surface forming a larger icing
ridge or a double horn or mushroom shapes. Due to the variation in temperatures and
8
icing conditions is the atmosphere mixtures of glaze and rime ice are possible and
actually quite common.
Figure 6: Rime ice accretion [8]
Figure 7: Glaze ice accretion [9]
1.5 Methods of protection
Protection of airframe surfaces are briefly discussed, although protection methods are
out of the scope of this paper. The detailed physics of how accreted ice adheres to an
aircraft surface is not well understood. There is however, some experimental data
available which helps describe the measurements of the adhesive (ice-to-surface bond)
9
and cohesive (ice-to-ice bond) properties of ice. The measurements include the shear
force required to break the bond between the ice and surface [6].
The accretion is mainly governed by the heat transfer, which includes kinetic heating,
convective cooling, evaporative cooling, and latent heat of freezing, from the aircraft
surface, the supercooled water drops and the surrounding environment.
One typical method of protection is quite simply heating the surface to maintain the
surface above the freezing point. Heating a critical surface allows no ice to accrete
locally. However, once the impinging water drops migrate to a location that is not
heated, the water would freeze. By design, unheated regions of the aircraft structure do
not affect the continued airworthiness of the aircraft.
A different approach is to allow the ice to accrete to some small amount and only heat
the surface over a short time span. The heat addition would be just enough to melt the
water on a microscopic level breaking the ice’s adhesive bond with the aircraft structure.
Lastly, allow ice to accrete over a short time span on a surface that would deform such
that the adhesive bond between the airframe surface and the cohesive bond of the ice
structure would fracture. Older technologies have been around since the early days of
aviation involve using elastomeric air filled bladders and electromotive leading edge
structures to break the ice from the airframe. Modern technologies involve light weight
composite structures with electro-expulsive devices to locally shock the composite and
break the ice bonds or actuated control surfaces to break the surface bond.
There are advantages and disadvantages to each approach, power management, material
selection and component criticality to name a few, and require system engineered
solutions to achieve a certifiable aircraft.
10
2. Methodology
2.1 Water drop trajectory
Supercooled drop trajectory calculations are used to determine where and how much ice
will accrete on a surface. The volume of water that impacts the aircraft surface and
freezes is a function of the water catch efficiency, the liquid water content of the cloud,
the diameter of the drops, the speed of the body as it moves through the cloud, ambient
pressure and temperature. These terms are some of the inputs used in ice prediction
models to determine ice accretion. LEWICE, first developed in the 1980’s, uses the
above parameters along with Lagrangian drop trajectory calculations to determine the
path of the drops as they impact the structure.
2.1.1
Drop trajectory calculations
Using a CFD flow solution the drop trajectory is calculated at the discrete node positions
of the flow solution using Newtonian mechanics. The sum of the forces in the xdirection acting on the particle shown in Figure 8 is
F
 Fax  Fgx  md V
Fax 
1
C D  a Ad V 2 res cos 
2
x
where
or

1
C D  a ADVres u rel
2
with
Ad  
D2
4
represents the aerodynamic force acting on the water drop. In addition to the
aerodynamic force, the gravitational force is given by
  
Fgx  md g 1  a  sin(    )
 d 
11
where the mass of the drop is
md   d
4
D3

3
8
Figure 8: Particle force balance x-direction [2]
The sum of forces in the y-directions would be accomplished in the same manner and are
not shown in this text.
2.1.2
Supercooled drop heat balance
The second part of the icing calculation involves an energy balance at the structure
surface, shown in Figure 9, to determine the rate of freezing and amount of water run
back.
Q  qin  qout
The energy balance at the surface includes heat lost due to convection,
qc  f c As 32  t  
evaporation
 P  Psi 
qe  2.90 Le f c As  sw

 B 
and sensible heat absorbed by the warming of the drop.
q w  Rw AC p (32  t  )
Heat is added to the control surface due to the latent heat of fusion
12
q f  144nRw As
viscous heating
 rV 2 
q v  f c A
 2 gJc
p





and kinetic energy of the impinging liquid.
 V 2
q k  Rw Ad 
 2 gJ



The resulting energy balance accompanied with a mass balance determines the overall
ice shape on the structure. [3]
Figure 9: Energy balance at airfoil surface. [3]
2.2 Ice Accretion Parameter
The ice accretion parameter is a non dimensional mass flux term that can be thought of
as the thickness of ice that would form on a flat plate placed perpendicular to the
freestream flow for a period of time. The accretion parameter is defined as
Aice 
V LWC t
 ice c
13
A simplified accretion parameter using the three readily available parameters, airspeed,
liquid water content, and time to describe the severity of the icing conditions shall be
used herein.
2.3 Model Development
The intent of this project is to model a NACA4412 airfoil which is then subjected to an
icing environment to determine the effect of varying different atmospheric conditions in
accordance with the FAA guidelines outlined in Appendix C of 14CFR Part 29 on the
shape and thickness of the ice. The variables to be analyzed include temperature, liquid
water content (LWC), median volume drop diameter (MVD) and the vehicle airspeed.
Each condition will be varied independently to determine the effect on ice shape and
thickness. The type of ice accretion, rime or glaze, will not be considered. Each set of
independent runs will be compared to a hand calculation using the ice accretion
parameter to verify the validity and severity of the run. A matrix of runs with each
variable and the corresponding accretion parameter is shown in Table 1.
The results of the LEWICE calculations will be a two dimensional ice shape plot which
will be integrated to find the volume of ice per airfoil unit length. The trends of the
results will then be compared to the ice accretion parameter.
The conditions selected are values consistent with the typical rotorcraft continuous
maximum icing envelope as described by 14CFR Part 29 Appendix C (Figures 10 and
11) for a total of 15 runs. The selected runs in this case will assume worst case liquid
water content at that given temperature for a standard cloud distance. For example, from
figure 9 the maximum liquid water content observed at -30°C (-22°F) would be 0.2g/m3
and would have a median drop diameter of 15 μm. The same -30°C point for Run 11
would only have a liquid water content of 0.1g/m3 with a median drop diameter of 25
μm. For this analysis all of the runs are completed assuming the horizontal extent of the
cloud is the standard distance for the continuous maximum. The intermittent maximum
values of LWC and drop size are higher and should result in higher ice accretion values;
however, the continuous maximum envelope outlined in Figures 10 and 11 was used to
14
establish a trend in the thickness data that could be extrapolated to include the
intermittent maximum values.
Table 1: Table of Runs
Run Temperature MVD
(°C)
LWC
Time
Velocity
(microns) (g/m3) (min) (knots)
1
-30
15
0.2
30
155
2
-20
15
0.3
30
155
3
-10
15
0.6
30
155
4
-5
15
0.7
30
155
5
0
15
0.8
30
155
6
-30
15
0.2
30
77
7
-20
15
0.3
30
77
8
-10
15
0.6
30
77
9
-5
15
0.7
30
77
10
0
15
0.8
30
77
11
-30
25
0.1
30
155
12
-20
25
0.15
30
155
13
-10
25
0.32
30
155
14
-5
25
0.41
30
155
15
0
25
0.5
30
155
15
0.9
32deg
14deg
-4deg
-22deg
Data Points
0.8
Liquid Water Content (g/m3)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
10
15
20
25
30
35
Mean Effective Drop Diameter (μm)
Figure 10: Atmospheric icing conditions – Continuous maximum (Stratiform Clouds) [10]
15
40
1.6
1.34
1.4
Liquid Water Content Factor
1.2
1
0.8
0.6
0.4
310
0.2
0
1
10
100
17.4
Cloud Horizontal Extent (NM)
Figure 11: Liquid water content vs. cloud horizontal distance [10]
16
1000
3. Results
3.1 Ice Accretion Parameter
The results of the ice accretion parameter, simulating a “worst case” flat plate accreting
ice with one hundred percent catch efficiency, are shown in Figure 12 derived from the
FAA guidelines outlined in 14CFR Part 29 Appendix C - Continuous Maximum Icing
Conditions at Standard Distance. The ice accretion parameter, a function of liquid water
content, airspeed and time show an increasing trend as temperature increases from -30°C
to 0°C. This is largely due to two of the three independent variables of the accretion
parameter increasing resulting in the mass fraction of water available in the atmosphere
and liquid water content increasing with increasing temperature shown in the FAA
guidelines (Figures 10 and 11). The ice accretion parameter however does not account
for the heat flux at the airfoil surface and assumes that 100% of the water freezes
instantaneously (no runback). With increasing airspeed, the mass flux, amount of water
impinging on the surface of the airfoil increases.
Secondary effects of the higher
velocities include the increased convection heat transfer coefficient and viscous heating
of the aircraft surface.
4000
15MVD 155 Kts
15MVD 77 Kts
25MVD 155 Kts
3000
3
Accretion Parameter (Kts-Min-g/m )
3500
2500
2000
1500
1000
500
0
-30
-20
-10
0
Temperature (C)
Figure 12: Ice accretion parameter as a function of temperature and airspeed
17
3.2 LEWICE Solutions
The results of the LEWICE solutions, shown in Figure 13 through Figure 18, show the
overlays of the ice shapes as a function of increasing temperature and liquid water
content. Also shown are plots of ice thickness as a function of temperature along with
the theoretical ice accretion parameter for the same conditions. Conditions 1 through 4,
from matrix in Table 1, show that the formation of ice increases with increasing
temperature up to approximately -5°C.
Above -5°C, the amount of ice accreting
decreases rapidly reaching zero at 0°C.
0.060
0.040
-1C
-5.5C
-10C
-20C
-30C
y/c
0.020
0.000
-0.020
-0.040
-0.060
-0.050
0.000
0.050
0.100
0.150
0.200
x/c
Figure 13: Ice shape predictions - 15μm MVD, 155 knots, varying temperature and
LWC.
4000
0.06
3500
0.05
3000
0.03
2000
Ice Thickness
Accretion Parameter
0.04
2500
1500
Accretion Parameter
LEWICE Data
0.02
1000
0.01
500
0
0
-30
-20
-10
0
Temperature (C)
Figure 14: Comparison of ice accretion parameter and volume of ice thickness 15μm MVD, 155 knots.
18
The test matrix conditions 5 through 8 repeat the points at a slower airspeed. Similar to
runs 1 through 4, the volume of ice will increase with increasing temperature, although
at a much lower rate due to the decreased volume of water impingement, until
approximately the same temperature before decreasing to zero.
0.060
0.040
y/c
0.020
-1C
-5.5C
-10C
-20C
-30C
0.000
-0.020
-0.040
-0.060
-0.050
0.000
0.050
0.100
0.150
0.200
x/c
Figure 15: LEWICE results - 15μm MVD, 77 knots, varying temperature and
LWC.
2000
0.025
1800
1600
0.02
1200
0.015
1000
800
0.01
Ice Thickness (in)
Accretion Parameter
1400
Accretion Parameter
LEWICE Data
600
400
0.005
200
0
0
-30
-20
-10
0
Temperature (C)
Figure 16: Comparison of ice accretion parameter and volume of ice thickness 15μm MVD, 155 knots
19
The final conditions from the test matrix, runs 9 through 12, repeat the same airspeed
and temperatures as runs 1 through 4 with an increased drop size (25 µm). Again similar
to the two other batch runs, the ice accretion increases, again at a much lower rate, up to
approximately -5°C before decreasing rapidly.
0.060
0.040
-1C
-5.5C
-10C
-20C
-30C
y/c
0.020
0.000
-0.020
-0.040
-0.060
-0.050
0.000
0.050
0.100
0.150
0.200
x/c
Figure 17: LEWICE Results - 25μm MVD, 155 knots, varying temperature and
LWC.
2500
0.045
0.04
2000
0.035
0.025
0.02
Ice Thickness
Accretion Parameter
0.03
1500
1000
Accretion Parameter
LEWICE Thickness Results
0.015
0.01
500
0.005
0
0
-30
-20
-10
0
Temperature (C)
Figure 18: Comparison of ice accretion parameter and volume of ice thickness 25μm MVD, 155 knots.
20
4. Conclusions
Overall the analytical predictions from the LEWICE software show an increasing ice
accretion with increasing airspeed, and liquid water content, similar to the derived ice
accretion parameter. This trend has been verified experimentally in numerous papers.[2]
It should be noted that the airspeeds evaluated herein are relatively low with respect to
fixed wing aircraft or the rotating blade of a rotorcraft. The scope of this paper is
focused on the accretion of the airframe structure. The ice accretion parameter however
assumes all drops impinging on a surface freezes (a water catch efficiency of 1) and does
not account for the heat flux term at the surface of the airfoil at warmer temperatures.
As a result, the accretion parameter will over predict the severity of the icing results at
temperatures above -6°C. At colder temperatures, the ice accretions, rime icing, are
smaller and more compact due to the instantaneous freezing from the higher heat flux of
the supercooled drops. This quick freezing allows for more air to become trapped in the
ice and the resulting density of ice is much lower than the warmer temperature results.
Also, at colder temperatures the lower mass fraction of water in the air results in lower
accretion values. Warmer temperatures and lower heat flux values result in a slower
freezing rate and less air being trapped in the ice formations.
21
5. References
[1] Sikorsky Archives, n.d, http://www.sikorskyarchives.com/first.html November 2010
[2] Gent, R.W., Dart, N.P., Cansdale, J.T., “Aircraft Icing,” Philosophical Transactions:
Mathematical, Physical and Engineering Sciences, Vol. 358, No. 1776, November 2000,
pp. 2873-2911.
[3] Messinger, B.L., “Equilibrium Temperature of an Unheated Icing Surface as a
Function of Air Speed,” Journal of The Aeronautical Sciences, Vol. 20, No. 1, January
1953, pp. 29-42.
[4] Naterer, G.F., “Energy Balances at the Air/Liquid and Liquid/Solid Interfaces with
Incoming Droplets at a Moving Ice Boundary,” International. Journal of. Heat and Mass
Transfer, Vol. 29, No. 1, 2002, pp. 57-66.
[5] Myers, T.G., Hammond, D.W., “Ice and Water Film Growth from Incoming
Supercooled Droplets,” International Journal of Heat and Mass Transfer, Vol. 42, 1999,
pp2233-2242.
[6] Raraty, L.E., Tabor, D., “The Adhesion and Strength Properties of Ice,” Proceedings
of the Royal Society, Vol. XXA245, No. 1241, June 1958, pp. 184-201.
[7] Dutch, Steven. “Clouds.” Steven Dutch, Natural and Applied Sciences. n.d.
November 2010. http://www.uwgb.edu/dutchs/EarthSC102Notes/102Clouds.htm
[8]
C3VP,
Canadian
CloudSat/CALIPSO
Validation.
n.d,
November
2010,
http://c3vp.org.field/avisa/avisa.html
[9] http://www.onera.fr.omph-en/icing/index.php November 2010
[10] FAA Aircraft Icing Handbook, US Department of Transportation, Federal Aviation
Administration, March 1991
22
6. Appendices
23
6.1 Appendix A – Test Data Correlation
A large portion of this project was used attempting to match the analytical results from
the LEWICE code to experimental icing test results further validating NASA’s code for
use in future engine icing certification applications. Although some of the data points
produced similar shapes, overall the results were unsuccessful. This was due to a
number of limitations of the 2-dimensional representation of the geometry tested. The
biggest factor was that some of the profiles selected for analysis were not a good
representation of the actual 3-dimensional geometry. For some of the profiles selected,
the leading edge of the duct was not perpendicular to the flow The simplification from
3D to 2D ignored the leading edge rake angle. The test results generally showed a larger
less dense rime ice accretions even at warmer temperatures where glaze ice was
expected.
24
Test Data vs. Lewice Predictions
1.50
1.00
Lewice Angle of Attack = 2deg
y (in)
0.50
Wind Tunnel Test Data
0.00
Lewice Angle of Attack = 0deg
-0.50
-1.00
-1.50
-2.00
-1.00
0.00
1.00
x (in)
25
2.00
3.00
4.00
6.2 Appendix B – Input Files and Raw Data
Code for the LEWICE input files and data outputs are contained in Appendix B. The
code within can be copied and pasted into an input file to recreate the results shown in
Section 4.
26
6.2.1
Run 1
Run 1 – -30C, 15MVD, 0.2g/m^3, 155kts, 30min
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.2
TINF = 243.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
27
Run 1: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
28
0.150
0.200
Run 1: Thickness
0.025
0.020
Thickness
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
29
0.020
0.040
0.060
0.080
0.100
6.2.2
Run 2
Run 2 -20C, 15MVD, 0.3g/m^3, 155kts
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.3
TINF = 253.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
30
Run 2: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
31
0.150
0.200
Run 2: Thickness
0.030
0.025
Thickness
0.020
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
32
0.020
0.040
0.060
0.080
0.100
6.2.3
Run 3
Run 3 - -20C, 15MVD, 0.6g/m^3, 155kts, 30min
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.6
TINF = 263.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
33
Run 3: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
34
0.150
0.200
Run 3: Thickness
0.060
0.050
Thickness
0.040
0.030
0.020
0.010
0.000
-0.010
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
35
0.020
0.040
0.060
0.080
0.100
6.2.4
Run 4
Run 3.5 - -5.5C, 15MVD, 0.7g/m^3, 155kts
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.7
TINF = 267.65
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
36
Run 4: Ice Shape
0.060
0.040
y/c
0.020
0.000
-0.020
-0.040
-0.060
-0.050
0.000
0.050
0.100
x/c
37
0.150
0.200
Run 4: Thickness
0.060
0.050
Thickness
0.040
0.030
0.020
0.010
0.000
-0.010
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
38
0.020
0.040
0.060
0.080
0.100
6.2.5
Run 5
Run 4
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.8
TINF = 272.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
39
Run 5: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
40
0.150
0.200
Run 5: Thickness
1.000
0.900
0.800
0.700
No accretion present for
Thickness
0.600
0.500
this temperature
0.400
0.300
0.200
0.100
0.000
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
41
0.020
0.040
0.060
0.080
0.100
6.2.6
Run 6
Run 5
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 39.612
LWC = 0.2
TINF = 243.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
42
Run 6: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
43
0.150
0.200
Run 6: Thickness
0.009
0.008
0.007
0.006
Thickness
0.005
0.004
0.003
0.002
0.001
0.000
-0.001
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
44
0.020
0.040
0.060
0.080
0.100
6.2.7
Run 7
Run 6
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 39.612
LWC = 0.3
TINF = 253.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
45
Run 7: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
46
0.150
0.200
Run 7: Thickness
0.014
0.012
0.010
Thickness
0.008
0.006
0.004
0.002
0.000
-0.002
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
47
0.020
0.040
0.060
0.080
0.100
6.2.8
Run 8
Run 7
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 39.612
LWC = 0.6
TINF = 263.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
48
Run 8: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
49
0.150
0.200
Run 8: Thickness
0.025
0.020
Thickness
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
50
0.020
0.040
0.060
0.080
0.100
6.2.9
Run 9
Run 8.5
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 39.612
LWC = 0.8
TINF = 267.65
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
51
Run 9: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
52
0.150
0.200
Run 9: Thickness
0.025
0.020
Thickness
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
53
0.020
0.040
0.060
0.080
0.100
6.2.10 Run 10
Run 8
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 15.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 39.612
LWC = 0.8
TINF = 272.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
54
Run 10: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
55
0.150
0.200
Run 10: Thickness
0.0045
0.0040
0.0035
0.0030
Thickness
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
-0.0005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
56
0.020
0.040
0.060
0.080
0.100
6.2.11 Run 11
Run 9
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 25.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.1
TINF = 243.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
57
Run 11: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
58
0.150
0.200
Run 11: Thickness
0.014
0.012
0.010
Thickness
0.008
0.006
0.004
0.002
0.000
-0.002
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
59
0.020
0.040
0.060
0.080
0.100
6.2.12 Run 12
Run 10
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 25.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.15
TINF = 253.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
60
Run 12: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
61
0.150
0.200
Run 12: Thickness
0.016
0.014
0.012
Thickness
0.010
0.008
0.006
0.004
0.002
0.000
-0.002
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
62
0.020
0.040
0.060
0.080
0.100
6.2.13 Run 13
Run 11
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 25.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.32
TINF = 263.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
63
Run 13: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
64
0.150
0.200
Run 13: Thickness
0.035
0.030
0.025
Thickness
0.020
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
65
0.020
0.040
0.060
0.080
0.100
6.2.14 Run 14
Run 11.5
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 25.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.32
TINF = 267.65
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
66
Run 14: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
67
0.150
0.200
Run 14: Thickness
0.045
0.040
0.035
0.030
Thickness
0.025
0.020
0.015
0.010
0.005
0.000
-0.005
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
68
0.020
0.040
0.060
0.080
0.100
6.2.15 Run 15
Run 12
&LEW20
TSTOP = 1800.
IBOD = 1
IFLO = 15
DSMN = 4.0D-4
NPL = 24
&END
&DIST
FLWC = 1.0
DPD = 25.
&END
&ICE1
CHORD = 0.9144
AOA = 0
VINF = 79.738
LWC = 0.5
TINF = 272.15
PINF = 101325.00
RH = 100.0
&END
&LPRNT
FPRT = 1
HPRT = 1
BPRT = 1
TPRT = 0
&END
&RDATA
&END
&BOOT
&END
69
Run 15: Ice Shape
0.040
0.030
0.020
y/c
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
0.000
0.050
0.100
x/c
70
0.150
0.200
Run 15: Thickness
1.000
0.900
0.800
0.700
No accretion present for
Thickness
0.600
0.500
this temperature
0.400
0.300
0.200
0.100
0.000
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
s/c
71
0.020
0.040
0.060
0.080
0.100