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NASA Contractor Report 175092
Analytical Determination of PropellerPerformance Degradation Dueto Ice Accretion
(NASA-CR-175Q92) ANALYTICAL DETEEMINATION N86-23577OF PROPELLER PEBFGRHANCE DEGRADATION DUE TOICE ACCRETION Final Eeport (SverdrupTechnology, Inc.) 138 p HC A07/MF A01 Unclas
CSCL 01C G3/03 05976
Thomas L. Miller
Sverdrup Technology, Inc.Lewis Research CenterCleveland, Ohio
April 1986
Prepared forLewis Research CenterUnder Contract NAS 3-24105
NASANational Aeronautics andSpace Administration
https://ntrs.nasa.gov/search.jsp?R=19860014106 2020-05-12T02:48:49+00:00Z
TABLE OF CONTENTS
Pa_ge_
LIST OF SYMBOLS . . . . i i i
CHAPTER 1. INTRODUCTION . . . . 1
CHAPTER 2. SUMMARY OF PREVIOUS WORK 5
A . Early Work
1. Experimental Effort 5
2. Analytical Effort 7
B. Recent Work
1. Experimental Effort 1O
2. Analytical Effort . 12
CHAPTER 3. CODES EMPLOYED 17
A. Theodorsen Transformation 17
B. Droplet Trajectory Code 19
C. Aerodynamic Coefficient Correlations 22
1. Gray Correlation 30
2. Bragg Correlation 32
3- Flemming Correlations 34
4. Miller Correlation 36
D. Propeller Performance Code 37
CHAPTER 4. PERFORMANCE DEGRADATION CODE ASSEMBLY .... 39
CHAPTER 5. RESULTS . . . . . . . 44
A. Bragg 48
B. Gray 49
C. Flemming ..... 51
Page
SUMMARY AND CONCLUSIONS 54
REFERENCES . . 57
FIGURES . . . . . . ....... 62
TABLES OF EXPERIMENTAL & ANALYTICAL DATA . . . . . . . .60
APPENDIX 1. PROGRAM FLOWCHART 85
APPENDIX 2. USER'S GUIDE ... . . . . . . . 88
APPENDIX 3. SAMPLE CASE . 100
ii
LIST OF SYMBOLS
a speed of sound
Ac accumulation parameter
b propeller section chord
B number of propeller blades
BMP propeller power absorption
c airfoil section chord
C . section drag coefficient
C section lift coefficient
C. propeller power coefficient = P_
. 3.5Pn D
CT propeller thrust coefficient =
-P . /,- propeller diameter
E total collection efficiency =
Fr Froude number = U
-PnV
g gravitational constant
h airfoil project height
I airfoil drag constant
J propeller advance ratio =nD
2K inertia parameter•= c & U
18cu
k/c particle roughness height
K modified inertia parameter = K(l +' .O967 (R )°'6397)o u
M, M local Mach number
m
n, N propeller revolutions per minute
r leading edge radius of curvature
R droplet Reynolds number = Plu - DIU&/U
5 airfoil surface arc length
t/c airfoil thickness to chord ratio
T freestream temperature
u local air velocity
U, V freestream velocity
w liquid water content
x propeller radial location in fraction of tip radius
Y initial droplet y-coordinate
of. airfoil section angle of attack
«f. induced angle of attack
6 impingement efficiency = dy /ds; propeller twist
angle
&max maximum local impingement efficiency
& droplet diameter
CD propeller efficiency = J T
CP
T) local droplet velocity vector
p. absolute air viscosity
P air density
Pice ice density ....
ff droplet density
ff section solidity = Bb'P . . ~~
JID
IV
T icing time
+ resultant advance angle
CHAPTER 1
INTRODUCTION
The accretion of ice on the lifting or propulsive
surfaces of an aircraft is a phenomenon which can have severe,
if not diaaatroua, consequences if it is not dealt with
properly, and in a timely fashion. In many cases, this
accretion may produce a serious reduction in lift and increase
in drag, requiring more power than is available and resulting
in a aerious departure from the mission profile. Although
>measures and devices exist which generally prevent this worst-
case scenario from happening, ice accretion on airfoils is
still a common occurrence in certain atmospheric conditions
and aa such merits further study because of the significant
negative effect which it has on airfoil and aircraft
performance. It is the objective of this thesis to provide a
single computer code which will accurately predict the degree
of performance degradation, primarily with respect to drag
increment, which will result from the exposure of an airfoil
to some set of atmospheric and flight conditions conducive to
ice formation.
Two basic types of ice are found to occur as a result of
exposing an airfoil in forward motion to aupercooled water
droplets in a sub-freezing environment (Fig. 1). The type of
ice which will form may be determined by a variety of factors
including freestream velocity, liquid water content of the
cloud, droplet size distribution, and freestream temperature.
Based upon an investigation of the data currently available.
. the two latter factors appear to be the moat influential in
determining the resulting ice type. The first kind of ice,
known as rime ice, occurs at relatively low velocities, low
•- r • • . . « ' . • ' - • •liquid water content values (typically O.5 to l.O grams per
cubic meter), and temperatures well below freezing. Due
primarily to the very cold temperatures associated with rime
ice formation, the droplets tend to freeze on impact to form a
fairly smooth 'addition to the leading edge of the airfoil. At
some point with respect to the combination of flight and
'atmospheric conditions present, ice type transitions from'rime
to glaze ice. Not only is the crystalline structure of these
ice types different, but glaze ice is also produced by higher
'" freestream velocities, higher' liquid water content values (on
the orde'r of 1/5 to 3.0 grams per cubic meter), and
temperatures- near, but below, freezing. Again, due chiefly to
"the warmer temperatures involved, the water droplets impacting
the surface tend not to freeze on impact but rather to strike
the airfoil or existing ice formation and run back somewhat in
a chbrdwise direction before freezing.
Both types of ice cause significant performance
"degradation of*the airfoil. When compared to the aerodynamics
of an airfoil in the clean, or non-iced,; configuration, the
iced airfoil will virtually always exhibit a decrease in lift,
an increase in drag, and a change in pitching moment which
'will yield a detrimental effect on aircraft stability.
Examination of the available icing data base indicates that
the degree of performance degradation, specifically with
respect to drag increment., la generally more severe for the
glaze ice condition. Thia may be attributed to the more
draatic alteration of the leading edge of the airfoil aa a
reault of glaze ice formation, aa compared to the typically
smoother and leaa obtruaive rime ice formation. Increases in
drag coefficient in exceaa of 1OOX or more are not unusual for
either type of accretion.
Both rime and glaze ice act to negatively influence
airfoil performance by physically altering the shape of the
airfoil, thereby changing the flowfield around the airfoil.
In computing this flowfield for the propeller caae, the
rotational and induced components of velocity, as well as the
forward component, must be taken into account aa exhibited in
Figure 2. The reshaping of the airfoil surface by the ice
accretion and the rough peaka and surfaces commonly preaent in
ice accretions, especially in the glaze ice caae, aerve to
induce premature tranaition and often separation of the flow
around the airfoil, thua spoiling ita deaigned aerodynamic
characteristics. The associated ice roughness also acts as an
energy loss device. For the propeller configuration dealt
with in this thesis, these effects may occur along the entire
span of the propeller and have the same effect on propeller
aerodynamics as they are found to have with reapect to fixed
wing aircraft. Ice accretion on a propeller may then
tranalate for example into an increaae in power required to
maintain a given flight condition when ice is allowed to form
on the propeller bladea. As a pilot, passenger, or other
concerned party it would therefore be desirable before
undergoing an icing encounter to have aome idea of just how
much power would be required to maintain a flight condition
with ice accreting on the propeller and other aircraft
components, so that some decision could be confidently made
regarding the safety of undergoing or avoiding such an
encounter. In addition, information provided by this code may
be used in establishing propeller ice protection system
specifications, as well as potentially in future icing
certification efforts.
CHAPTER 2
SUMMARY OF PREVIOUS WORK
Much work haa already been done in att.empt.ing to better
.understand ice accretion and ita effect on aircraft
performance. However, due to the very complicated phyaica
which govern the ice accretion process, many questions remain
unanswered in this area and it ia atill difficult with preaent
technology to accurately predict the degree of performance
degradation which will reault from an arbitrary icing
encounter. Several recent developments have made the
prediction of performance degradation, especially in terms of
drag increase, more reliable and have expanded the range of
conditions over which relatively accurate predictions can now
be made. Yet much of the groundwork for these developments
was laid thirty to forty yeara ago. This initial work
involved both experimental and analytical inveatigatlona of
ice accretion, and much of the icing data used in current
correlation development work was actually collected during
this.early period, from roughly the late 1940'a to the late
1950's.
A. Early Work
1. Experimental Effort
Early propeller performance degradation data waa
gathered using both eimulated ice and actual natural icing
encounters. Coraon and Maynard (1) in 1946 uaed aimulated ice
on propeller bladea and measured average efficiency loaaea on
the order of three percent, with maximum loasea of fifteen
percent, noted. In 1948, Preston and Blackman (2) undertook a
flight, test program in which they also noted average decreases
of roughly ten percent in propeller efficiency due to ice
formation, as well as the associated increase in drag. This
study waa of special significance due to the fact that an
attempt was made to examine the effects of ice accretion on
all major components of the aircraft. Possibly the most
complete and informative work relative to ice accretion on
propellers was performed and documented by Neel and Bright (3)
in 195O. In a flight test program in which efficiency loss
was measured during actual natural icing encounters, they
observed losses of roughly ten percent in most cases, with
maximum losses on the order of twenty percent. The
performance degradation data of Neel and Bright is still used
by present researchers to develop or verify analytical
propeller performance degradation codes.
Also of note with respect to experimental investigations
of airfoil icing are a series of test programs undertaken in
the Icing Research Tunnel at the NASA Lewis Research Center
and documented by a variety of NACA personnel in the early and
mid-195O's. Gray and von Glahn (4,5) looked at the effects of
ice on the performance of NACA 65AOO4 and 65-212 airfoils,
and lesser increases were noted for both airfoils with rime
ice accretions. Brun, et. al. (6,7,8) and Brun and V/ogt (9)
produced a series of reports dealing with experimental
measurements of performance degradation of NACA 65AOO4, 65,-
*2O8, and 65.-212 airfoils due to ice formation. These reports
focused on the impingement characteristics of these airfoils,
which in turn relate directly to.drag increment and decreased
performance. Included in their investigations were the
effects of airfoil thickness and angle of attack on dropletV. " . . ' • - . " ' . • ' . • • •impingement values, noting that thickness tends to increase
the volume of water collected and decrease the rearward limit' • :
of droplet impingement, and as expected total impingement
increases with increasing angle of attack.
Gelder, Smyers, and von Glahn (1O) in 1956 investigated"j " . • : • " • . . 'droplet impingement properties on several airfoil sections of
various thickness and concluded in part that the total and
* • • • ' • ' . -
maximum local collection efficiencies were strong functions of
first of all the modified inertia parameter, a parameter which
takes into account factors such as freestream velocity,
droplet density and diameter, airfoil chord, absolute air
viscosity and air density, and also of thickness ratio and
angle of attack.
These early experimental programs not only provided
valuable insight into the process and effects of ice
accretion, but also established a data base from which
analytical ice growth and performance degradation predictions
could be developed or verified.
2. .Analytical Effort
In the report by Neel and Bright (3), the authors
attempted to predict analytically the degree of propeller
performance reduction to be expected as a reault of ice
accretion. Using blade element theory as the basis for their
analysis, and by relating the change in airfoil drag/lift
ratio to efficiency loss, they predicted efficiency losses
which agreed at leaat to the same order of magnitude with the
experimentally obtained values.
Bergrun (11) in 1951 offered a method for determining
droplet impingement characteristics on an airfoil by solving a
set of simultaneous differential equations which described the
particle dynamics of a water droplet moving in an air stream.
This same principle forms the basis for present droplet
trajectory codes also. Along with Lewis in 1952 (12), Bergrun
also investigated using probability analysis the atmospheric
factors responsible for ice formation and identified with a
quite limited data base the three parameters still felt to be
of primary importance in the ice accretion process: cloud
liquid water content, water droplet size, and ambient
temperature.
In 1958, Gray undertook an icing study of the NACA
65AOO4 airfoil (13) and attempted to develop a drag
coefficient correlation which would relate ice nature and
droplet impingement rates to the associated aerodynamic
penalties for this airfoil. Using experimental icing data, he
obtained a dimensional correlation which he found to be
accurate at all but angles of attack greater than four
degrees, presumably due to the flow separation occurring at
the higher angles of attack. Gray then published in 1964 a
a
report. (14) in which he examined available .aerodynamic icing
data for other airfoils and modified his correlation to make
it applicable to these other airfoils as well. He
accomplished this through the introduction of the factor *r*
. which represents the airfoil leading edge radius of curvature
in percent of chord. This modified correlation represented
,the only available icing drag coefficient correlation at that
time, and saw widespread use for several years. Only recently
.has its validity as a general icing correlation been
questioned, and it will most probably remain in use until a
suitable replacement is offered.
The formulation of Gray's drag coefficient correlation
represented the last ma3or development with respect to ice
accretion effects for several years. The advent and use of
the ;jet engine and turbofan on the propulsion scene then
deemphasized the use of the propeller as a propulsive device. • • < • . • - . -
and subsequently drew much attention away from the problem of
ice accretion, which was of lesser importance for the large
commercial transports and military aircraft of that time.
However, with recent increased fuel costs and a renewed
interest in commuter aircraft and all-weather helicopters, new
interest in ice protection systems and a need to better
understand the phenomenon of ice accretion have again come
about.
B. Recent Work
1. Experimental Effort
Researchers involved in the renewed study of ice
accretion recognized the need to expand the quite limited
experimental data base, especially to include tests of ice
accretion on the newer airfoils designed for use on current
general aviation aircraft, propellers, and helicopter rotors.
Shaw, Sotos, and Solano in a 1982 report (15) discussed the
results of one such program in which aerodynamic performance
degradation data was obtained for a NACA 63 -A415 airfoil.
Glaze and rime ice formations were studied in both cruise and
climb configurations and significant performance degradation
was noted for all cases. Also evaluated was the effect of aft
frost growth on airfoil performance, and this phenomenon was
found to significantly increase section drag coefficient.
This project was also of importance because it provided new
data with which to test Gray's drag coefficient correlation.
The authors found that the correlation was as accurate in most
cases for the new data as it was for the old data upon which
the correlation was developed, but it became poorer in
accuracy for higher liquid water content values. This
conclusion again pointed out the need for a better, more
accurate drag coefficient correlation.
Also in 1982 at the Ohio State University, Bragg and
Gregorek (16), along with Zaguli (17), used simulated ice
shapes to investigate various aspects of the ice accretion
problem. In one test a simulated rime ice shape was applied.
10
.with and without surface roughness, to a NACA 65A413 airfoil
and the ensuing performance degradation waa measured. Surface
roughness was determined to be an important factor in
modelling ice shapes, affecting drag coefficient and C,max
In the second test, they also demonstrated the feasibility of
using wood shapes to model ice accretions on a NACA 63.-A415
airfoil in order to ascertain the effects of the ice shape on
the aerodynamic flowfield.
Flemming and Lednicer in 1983 (Id) tested a series of
scale models of helicopter airfoils to investigate the effects
of artificial ice accretion on airfoils at high speeds.
Aerodynamic performance degradation of all the airfoils waa
noted, with the authors citing drag coefficient increases of
up to roughly 300* in some cases. Also accomplished in this•'. s ."" ' ':
teat were better definitions of the boundaries for ice growth
and ice type in terms of static temperature, Mach number, and
liquid water content.
Motivated by a desire to find a relatively simple,
economical means of collecting performance degradation data
relative to rotating systems, Korkan, Cross, and Cornell
(19,2O) and Korkan, Cross, and Miller, (21,22) in 1984
undertook a test program utilizing a model helicopter with a
53.375-inch diameter, 2.5-inch chord NACA 0012 main rotor with
a simulated ice shape attached and measured main rotor
performance degradation. Trends identical to those previously
seen on larger or full-size airfoils and rotors were noted.
11
with increaaea of up to 30OX in torque coefficient found to be
required to maintain a given thrust coefficient after the
addition of the aimulated ice to the rotor blades. The
aenaitivity of the tip region of the rotor to the adverae
effecta of ice formation was alao seen, with an increaae in
torque coefficient required to maintain a given thruat
coefficient of aa much aa 150* measured when the aimulated ice
waa extended from the 85x rotor radial location out to the
10OX- location.
Juat prior to thia model helicopter teat, the iaaue of
Reynolda number effecta on aerodynamic data waa alao addreaaed
by the same authora <2O,22). In a 2-D airfoil teat uaing a
NACA OO12 airfoil section with a aimulated ice formationi
geometrically identical to that uaed in the model helicopter
teat, the authora collected aerodynamic data for the airfoil
in both clean and iced configurations over a Reynolda number
range which included the operating range of the model
helicopter rotor tip. Reynolda numbera effecta appeared
aignificant only at the highest Reynolda number tested,
3.4 x 1O6.
2. Analytical Effort
Much has been learned in recent years aa a result of
theae experimental programs, and a major contribution of theae
teata haa been in the expanaion of the icing data baae to
provide more current data with which to develop and evaluate
analytical methods for prediction of icing-related performance
degradation. Aa in the experimental area, many analytical
12
advances have also been recently made. These advances have
taken the forms of both better methods of predicting droplet
impingement characteristics as well as better aerodynamic
performance degradation correlations.
Bragg et. al. recently developed a computer program to
calculate water droplet trajectories and thereby determine
airfoil impingement efficiencies and theoretical ice shapes
.(23). Development of this code represented a major step
toward the goal of analytical prediction of airfoil
performance degradation due to ice accretion and the code la
now often used for this purpose. The code itself will be
discussed in more detail in a later chapter as it is one of
.. the major components of the code development which is the
subject.of this report. Along with this droplet trajectory
code, Bragg and Gregorek have also formulated a drag
coefficient correlation for the rime ice condition (16). In
this correlation, the change in drag due to ice is given as a
function of several variables related to flight and
atmospheric conditions, airfoil geometry, and duration of ice
.accretion. This correlation has seen widespread use since its
development and has only recently been studied in any detail
to better define its range of applicability. An unpublished
Investigation performed by this author shows the correlation
to in several cases significantly overpredlct drag increment
, for icing data which appears to be rime-oriented.
. Cansdale and Gent in a 1983 report (24) detailed the
development of another two-dimensional airfoil icing code.
13
Unlike the Bragg code, the effects of compressibility, kinetic
heating, and water runback are taken into account in this
code, thue making it applicable to both rime and glaze ice
conditions. Designed to be applied to helicopter
configurations, the code employs a heat balance analysis to
calculate the kinetic heating and runback effects. The
authors have reported good agreement between predicted and
experimentally obtained ice shapes, temperature distributions,
and icing threshold conditions.
Flemmlng and Lednicer (25) have used experimental icing
data to formulate new rime and glaze ice drag coefficient
correlations. In addition, this data was also used to
formulate separate lift and moment coefficient correlations.
These correlations, recently published in final form (25),
have shown some promise in preliminary evaluations and are
discussed in more detail in a later section.
Using Bragg's droplet trajectory code, Korkan, Dadone,
and Shaw (26) have developed a method for predicting
performance degradation of rotating systems under the
influence of ice accretions. Limited currently to the rime
ice condition, the effects of ice formation on helicopter
rotor or propeller thrust coefficient, torque coefficient, and
efficiency may be calculated. Originally restricted to the
helicopter hover mode, extension of the method to include
forward flight calculations has been performed and documented
in a recent AIAA paper by Korkan, Dadone, and Shaw (27). The
method essentially involves first obtaining non-iced values of
angle of attack and Mach number as a function of radial
location, then determining impingement efficiency and
accumulation parameter for a given set of icing conditions for
, each radial location, and finally determining the resulting
drag increment at each radial location. An existing propeller
or helicopter performance code with the iced drag increment
input .then will produce values of iced performance which may
be compared with,known or calculated clean values to ascertain
.the. degree of performance degradation which results from the
.given icing encounter. Good agreement between theory and
experiment has been obtained for both the propeller and
.helicopter rotor configurations.
Korkan et. al. have also developed a method of averaging
, JC27) to compute rotor or propeller disk performance in which
angle of attack and Mach number are first averaged around the
, disk. From these averaged values, collection efficiency,
accumulation parameter, and finally drag increment are
calculated for given icing conditions. This procedure has
been shown to be virtually as accurate as the previously
described method but provides a significant reduction in the
number of necessary calculations and hence computer run time.
Miller, Korkan, and Shaw in 1983 (28) attempted to
develop a drag coefficient correlation for the glaze ice
condition using statistical analysis of icing data as a basis
of the correlation development. Although a resulting
correlation was presented, it represented only the state of
the study at the time and showed a need for much further
15
modification and analysis. Feasibility of using such an
analysis as the basis for correlation development was
demonstrated, but the results of such an analysis must be
interpreted correctly and in tandem with physical observations
of. the associated phenomenon to make the method truly
beneficial.
Bragg (29) has also recently documented a study in which
he predicted airfoil performance with both simulated rime and
glaze ice shapes. Various codes were examined for possible
use in calculating pressure distributions on an airfoil with
glaze ice attached. The potential flow code of Bristow was
determined to be suitable for this purpose and provided good
agreement between predicted and experimental pressure
distributions. Bragg also investigated the effects of surface
roughness in the laminar boundary layer on drag increment and
offered promising results for predicting drag increase by this
method.
16
:, CHAPTER 3
CODES EMPLOYED
A. Theodoraen Transformation
The firat step In the performance degradation
determination proceaa ia computation of the flowfield about
the airfoil aectlon being investigated. The method used in
this code ia a Theodoraen technique of conformal mapping which
translates the airfoil coordinates to a circle plane and from
that plane determines the velocity distribution about the
.airfoil. The calculations involved in this method make the
assumption of potential flow, in which no viacoua effects are
considered. This haa been found to be an acceptable
assumption, allowing the method to yield accurate results, due
to the fact that viscous effects existing in the boundary
layer near the leading edge of the airfoil have little effect
on droplet trajectory for all but the smallest of droplet
sizes. The magnitude of the Inertia force associated with the
larger dropleta greatly predominatea over any viscous
deflection or interaction phenomena in this region.
This particular flowfield calculation technique ia- . . . . . . . . . . • _
limited to incompressible flow, which ia acceptible aince
compressibility effects on droplet trajectory have been found
to be negligible up to the airfoil section critical Mach
number for all but the smallest of drop sizes. In recent
joint studies between NASA and the Royal Aircraft
Establishment (RAE) (3O), back-to-back comparisons were made
between the impingement efficiency values generated using the
17
incompressible Theodorsen method at NASA and those calculatedi •
using the compressible flowfield code of Garabedian and Korn
for supercritical airfoil sections at the RAE. Good agreement
was observed between the two methods, thereby deemphasizing
any compressibility effects and validating the use of the
Theodorsen transformation in computing the flowfield about
airfoil sections exposed to icing.
Theodorsen'a method makes use of the Karman-Trefftz
transformation to relate the airfoil geometry to a near circle
plane. This particular transformation is used because it has
been found to yield a better near circle for airfoils with
finite trailing edge angles by avoiding any cusp atthe
trailing edge. It is given by the formula
H = nb <z -»-b> * (z -b>
where z is a vector which may define some profile such as an
airfoil section, and z is a vector from the origin, O, to
some arbitrary point on the circle. Here, b represents a
vector directed along.the positive x-axls with length OB',
where B' is a point at which the circle and x-axls intersect.
The value of n is typically just less than two, and it may be
observed that for n=2, the Karman-Trefftz transformation
simplifies to the more familiar Joukowski profile, given by
z = z + b
21 <2>
Finally, an iterative procedure calculates the Fourier
coefficients in the Theodorsen mapping to the exact circle.
18
Using a Newton root-finding scheme, the point in the circle
plane corresponding to a particular point on the airfoil may
be determined and from this the flow velocity at that point
may be obtained given the section angle of attack.
B. Droplet Trajectory Code'"'.••':'•.'.'.'.' ' '
The droplet trajectory code employed in this analysis
was developed by Bragg (31) in 1980. Using basic theory and
equations developed several years earlier as its foundation,
the code extends the earlier work to include the results of
more recent studies as well as much improved computer
technology. Essentially, the code is used to compute single
droplet trajectories and points of impingement on a given
airfoil, and from these calculations it is able to determine
both-'total and maximum local collection efficiencies as well
as a predicted ice shape if desired.
;.; Again, the initial step in the trajectory calculation
process requires a computation of the potential flowfield
about the airfoil under investigation. This flowfield
information, calculated using the Theodorsen transformation
method described in the previous section, is passed to the
trajectory calculation portion of the code in the form of the
aforementioned Fourier coefficients, which yield the flow
velocity at any given point in the airfoil flowfield for a
specific angle of attack. With this flowfield information
available, droplet trajectories may then be computed.
The trajectory calculation requires solving a
differential equation which results from the application of
19
Newton's Second Law to a water. droplet moving in an air
stream. This equation is given aa : . .
KD = CDR <u-i)> i- 1 q
24 Fr8 g <3>where K and Fr are nondimensional parameters known
respectively aa the inertia parameter and Froude number. They
are given by
18cw (4)
andFr= U
. g (5)From Equation 3 a set of four simultaneous first order
ordinary differential equations result, which when solved
yield the droplet trajectory. •
Once the droplet trajectories are known, impingement
efficiencies may then be calculated. Airfoil local
impingement efficiency, &, physically represents a ratio of
airfoil surface droplet mass flux to freestream mass flux, and
is
* « ?LLda <6>
Here, y. is the initial particle y-coordinate and S is
the airfoil surface arc length from the leading edge to the
point of impact. Figure 3 illustrates graphically the
calculation of &, and Figure 4 shows a typical &-S curve. If
yo is plotted versus S, it may be seen that & is simply the
slope of the yo -S curve at a given point. Total, or overall,
20
collection efficiency of an airfoil ia also an important icing
parameter and is defined by
?':•.. t. "•• --7..E = - 0(.7)
where ,YQ is -the distance between the initial y-coordinate of
the upper and lower droplet tangent trajectories and h
represents the maximum airfoil projected height. Total
"- V.i. • ' . - • • • • ; . ! ' •' • ' • . . -. '..'collection efficiency is then a ratio of the amount of water
'mass'.collected by the airfoil to the amount in the freeatream
sector which is swept out by the airfoil. Figure 5 exhibits
typical variation of collection efficiencies with radial
(location, .and Figure & is an example of the radial variation
of local angle of attack and Hach number.
Other capabilities exist within the droplet trajectory
code, perhaps most significantly the ability to develop a
theoretical rime ice shape using a time-stepping routine, but
this function is not necessary in the present study and will
not be employed or further discussed here. Although it is
true that the formation of an ice shape on an airfoil will
indeed alter the flowfield about the airfoil, and hence the P
curve for that airfoil, this phenomenon is not considered in
.this analysis because the values of & and E used in later
calculations are taken for the clean airfoil. The importance
of the collection efficiencies will be manifested in the
following section dealing with aerodynamic coefficient
correlations.
21
C. Aerodynamic Coefficient Correlations
Prior to the initiation of the present study, an effort
was made to identify all of the dimensionless parameters
relevant to an icing encounter using Buckingham's Pi Theorem,
with the goal of identifying and/or justifying the use of
certain variables in empirical correlations. The Pi theom of
Buckingham, presented first in 1914, provides a means of
creating a dimensionless variable set from an Initial group of
dimensional variables. The theorem states that any function
of N variables, of the form
f(Pi 'Pa'P3'"-PN) = °
may also be given in terms of (N-K) dimensionless Pi products,
such that
£<Pi1.Pia....PiI|_K) = O
Here K represents the number of dimensionally independent
quantities necessary to fully express the dimensions of the N
variables, and each Pi term is a dimensionless combination of
an arbitrarily chosen set of K dimensionally independent
variables. The Pi theorem will be used here to
nondimensionalize parameters relevant to an airfoil icing
encounter.
The procedure is initiated by first listing all of the
suspected relevant dimensional parameters. In an icing
encounter, these are taken to be as given in Table 1.
Table 1. Dimensional parameters considered in the ice
accretion process.
22
Symbol . Denotes Units
vc ;,-, T temperature at which ice t
:.. f •-• • . ia formed
T reference temperature t
T icing time T
w liquid water content ML
d droplet diameter L '
V freestream velocity LT
•./•:: .:••..'.:<<••:•: •••» . f-. . . -.: •' ice density ' • ' ML~Sice
P air density ML-~5' • 31 IT • '
;-.,'ft u. absolute air viscosity ML"1?"1
' ; . c airfoil chord L
-s' o . <t=temperature, T*=time, M = mass, L=length)
Here, ten dimensional variables (N) and four fundamental
dimensions OK) are given. Therefore, N-K = 10-4 = 6 Pi
products will result. It should be noted that although other
parameters such as total and local collection efficiencies are
also thought to be important parameters in an icing encounter,
they are not included in the above variable set because they
are already dimensionless and would not be affected by the Pi
theorem which deals only with dimensional quantities. They
can, however, be added to the final list of nondimensional
variables which will result from the use of the Pi theorem.
Certain other physical characteristics of the airfoil
which may affect ice accretion and resulting aerodynamic
23
performance losaea, namely leading edge radius of curvature,
airfoil thickness, and camber, are not included in the above
variable set even though they are dimensional quantities.
This is because the only seemingly meaningful way to
nondimenaionalize these terms is with respect to airfoil
chord, so that for the purposes of this analysis it will be
assumed that these parameters are all initially
nondimensionalized by chord and hence are hot Included in the
variable set. Instead they may be added to the list of
nondimensional variables at the conclusion of the application
of the theorem if desired.
It may be noted that the chord term makes its influence
felt in the nbndimensionalization of these airfoil geometry
terms, and has also been included in the dimensional variable
set* to allow -for the possible development of dimensionless
terms which will be consistent with or similar to
dimensionless quantities already in existence. For example:
V wTAC = O (Accumulation Parameter)
. PiceC .
KQ = f<K,Ru> (Modified Inertia Parameter)
where
18cW
R = Vairduu.
The next step in the procedure is to formulate a K set
of four (equal to the number of fundamental dimensions)
24
dimensionally independent, variables, from which .the Pi
products .will be developed. To form the set, any four
variables may be chosen from the dimensional variable list,
with the restriction that they may not themselves combine to
form a dimensionless combination. A K set consisting of
K = <T, T, w, Vo >
is initially chosen. With this K set, the six resulting Pi
products are;
Pii = f (T, T, w, Vo , To >
f ' •..-•'.•-• Pifi = .£ (T, T, w, Vo, d> • • . -
Pi. = f (T, T, w, Vo , P. ) '3 ice
PiH = f<T, T, w, Vo,
,PiB = f (T, T, w, Vo , W)
Pi4 = f (T, T, w, Vo , c)
To create nondimensional terms from these sets, the
following procedure, as illustrated by an example using Pi ,
is employed. The Pi product is first written as a product of
all of its terms, each raised to some power.
Pij = (T) <T)a <w)b <Vo)C (To)d
It is then rewritten in terms of the fundamental dimensions
involved:
Pi = (t) <T)a <ML~3)b<LT~1)C(t)d
25
For this product to be nondimensionalized, all of these '
dimensions must go to zero, i.e., the exponents on each '
dimension must sum to zero.
t: 1+d =0
T: a-c = 0
M: b = o
L: -3b+c = O
This set of equations is then solved for a, b, c, and d.
d = - l b = O c = 0 a = O
The Pi product is then rewritten with these values included.
Pit = (T) (To)'1 = ( T ) .
To
which is the first dimensionless quantity.
Likewise, the other Pi products are found to bev T
Pia
w
. P .ice
Pair
Pis = wVo8
M.
Pi&
The resulting set of dimensionless variables as
determined by the Pi theorem is then
f<t/To, VoT/d, w/P. , wVo8/U, VoT/c) = O,ice
26
or in the case of predicting drag coefficient change due to
these variables,
f (T/To , .... .... . . . . , Vo T/c) = ACT,d
At this point, any other dimensionless variables such as
collection efficiencies or airfoil geometry terms may be
included in the equation of desired. The user may then apply
some correlation development technique to determine the exact
relationship between these dimensionless variables and the
associated dependent variable(s).
It may be demonstrated that the resultant set of
dimensionless variables is dependent on both the set of
dimensional variables which is used and on the K set which ia
Initially chosen. Since there are a finite number of ••
dimensional variables and a finite number of K sets which can
' . ' . - ! • • - .
'be chosen, there will be a finite number of dimensionless
variables which will result for a given problem. However, not
all of these variables will necessarily be produced by one K
set. For the icing encounter problem discussed here, this can
be illustrated by choosing a second K set:
K a ( T, w, c, Vo )
This particular K set is especially noteworthy for the icing
encounter problem since it contains parameters which are
thought to be of primary importance in the ice accretion
process: temperature, liquid water content, freestream
velocity, and airfoil chord length. The Pi products for this
set are:
27
Pit = f<T, w, c, Vo , To)
Pia = f<T, w, c, Vo , T)
Pi3 = f <T, w, c, Vo, d)
- PiH = *<T, w, c, Vo.,. Pice>
PIS = f<T; w, c, vo, Pair>
Pi4 = f(T, w, c, Vo, ix > "
Following the procedure previously outlined for
nondimensionlizing these products, the resultant set of
dimensionless variables is:
f<T/To, VoT/c, c/d, w/P. , w/P . , wcVo/W) = 0,. , . ice air
which differs somewhat from the set produced by the other K
set used. So for any given problem it is necessary to
consider all of the possible K sets to obtain a complete list
of dimensionless variables which may be produced. Knowledge
of the physics of the problem under consideration should then
provide a starting point in the analysis of these variables as
they relate to the given dependent variable(a).
In the icing encounter problem, it was desired to use
the Pi theorem to provide some justification for the use of
the terms AC and Ko, previously defined, in the development of
a glaze ice drag coefficient correlation. Although the Pi
theorem does not produce these terms directly, it does provide
the following dimensionless terms:
28
< 1) Vo T/.c
<2) w/Pice
(3) PiceV0d
<4) d/c
M.. -i . . . . . • .• . '
; •/.:- -i- it may be noted that AC is simply the product of terms
(!') 'and '(2). Ko is a function of K, the product of terms (3)
and (4) , and R , which is identical to term (5) , e.g. ,
-AC = OT w
4ice
-.-.-.. .--. -; :--p.i . V d P V dK = ice O d_ = ice 0
H1 c M>c
(3) (4)
R = PairVAdu o•';'•'• ' ' : P.
(5)
; : Should the reader wish to verify that these terms are indeed
obtainable from the original set of dimensional variables,
they can be found as follows:
. (1) - from K set (T, T, w, Vo)
(2) - from K set (T, T, w, Vo)
(3) - from K set (T, d, Vo, P. >ice
(4) - from K set (T, w, c, Vo>
(5) - from K set (T, d, Vo, P >d 1 IT
29
It can be seen that the Pi theorem does indeed provide
some justification for the use of the variables AC and Ko in
developing a correlation, and any correlation which does
result will be in terms of dimensionless variables obtainable
by Buckingham's Pi theorem.
At present, the only means available for analytically
determining performance degradation of an airfoil in terms of
its .aerodynamic coefficients is through the use of empirical
correlations. As previously indicated, several individuals
have attempted development of one or more of these
correlations and generally have met with only limited success
in terms of accuracy and range of application. Incorporated
into the present study are the two correlations currently most
widely used to predict drag increment, as well as a aeries of
new correlations. These empirical correlations represent only
an interim solution to the problem of assessing aerodynamic
performance losses due to ice formation. A potentially more
precise solution technique currently under development
involves a Navier-Stokes solution for the flowfield around an
iced airfoil (32).
1. Gray Correlation
The first correlation, formulated by Gray (14) roughly
twenty years ago is of the form
AC=[8.7 x 10~S Tu WB <32-To)°"J] (1+6 {l + 2.52r°-i sin1* 12*)D c~ max
30
sin2 C543 w < E )i /J - 81 * 65.3 ( 1 - 1 )3
... 32-To 1.35*1 1?35*
^0.17 sin* Ilex) > (8);: , r • ' '
where here AC . represents the actual numerical value of drag
coefficient increment; i.e., AC, = C.(iced>- C,(clean). As" • • ' • • a a a ..
can be seen, this correlation involves combinations of various
dimensional parameters, and the dimensionlesa total and local
-collection efficiencies calculated in the droplet trajectory
code'previously discussed also appear. This correlation also
has the capability of computing drag coefficient increment at
'angles of attack other than that at which the ice was formed,
through the use of the ex and ex terms. Here et. represents the
angle of attack at which the experimental data was taken, or
the angle at which the effects of the ice accretion are to be
evaluated, and o< represents the angle of attack at which the
ice was formed.
The dimensional variables have not in all cases been
grouped so as to form dimensionless quantities, and this has
evoked some criticism by various persons since the
correlation's development. This criticism is based on the
idea that any correlation which involves dimensional
' • • • > • •quantities will be to some extent a function of the data set
from which it was formulated. Thus, if the correlation was
applied to some other set of data in which the range of one or
more of the relevant parameters differed from that of the
original data aet, the variable affected may have an undue
31
effect on the prediction which waa not accounted for in the
original, limited data set. Indeed, aa ia aeen in Figure 7,
Gray'a correlation haa been found to predict quite poorly for
much of the recently generated NASA glaze ice data, which ia
typefied by significantly higher liquid water content valuea
than are found in the data aet uaed by Gray in developing hla
correlation. Nevertheless, since no other glaze ice drag
coefficient existed until quite;recently, Gray'a correlation
still sees widespread uae and haa been included in this
program aa an option available to the uaer.
Because Gray's correlation accounts for only changes in
drag coefficient, modification of C haa been added to take
into account the decambering effect of ice accretion.
maxresulting in a ahift in the C -at curve and a decreaae in C
i
due to flow separation on the airfoil upper surface. Trial
valuea teated by the author have indicated that reducing C to
95X of its clean configuration value yields an acceptable
approximation for iced C . This factor is incorporated into
the present study for both Gray's and Bragg's correlations.
2. Bragg Correlation
A correlation has been developed by Bragg (16) for the
rime ice condition. It has the form
AC_, = O.01 (15.8 ln(k/c) «• 28000 A E * I) (9)d . • c
where Ac is accumulation parameter, given by
Ac = uwf4 c (1O)ice
32
,,, and I repreaenta a drag constant which variea according to
airfoil type ae shown in Table 2.
Table 2. Conatanta in Bragg Drag Coefficient
Correlation
Airfoil Type Drag Constant. I
NACA 4 and 5 digit 184
NACA 63 aeriea 218
NACA 64 aeriea 232
NACA 65 aeriea 252
NACA 66 aeriea 290• - • • ' *•'•',-'., ' " " ' ' • ' ; ...
In thia correlation, AC . repreaenta a fractional changed
in, rather than an actual numerical value of, drag••# - T- . •.. - v , . , . .
coefficient. Here AC, may be uaed to find the iced airfoil
drag coefficient uaing
Cd = (lfACd>Cd (11)iced clean
'•' - 3. . .5 Previoua studies of thia correlation applied to NACA and
NASA 2-D icing data have indicated a atrong tendency for the
correlation to overpredict drag increment. Because the
predictiona are commonly off by a relatively conatant
percentage with reapect to the Neel and Bright propeller
performance data, a factor waa Introduced which reducea the
degree of drag coefficient increase calculated by the Bragg
correlation. Replacement of the initial conatant in the
equation, O.01, by O.OOO8 produced much more acceptable
predictiona and waa therefore incorporated into the preaent
analyaia.
33
Bragg has also recently proposed a new, modified form of
his correlation (33) which has also been included in the
present study. This new form of the correlation given below,
appears to work well for the cases examined to date, but it
has not yet been applied to the 2-D NACA and NASA icing data
with which the other correlations were tested.
AC. = O.O1 (15.81n(k/c) + 1171 AcE •* I) (12)d
3. Flemming Correlations
The third correlation, or more precisely set of
correlations, are those developed by Flemming (25). Whereas
Gray and Bragg dealt strictly with drag coefficient
correlations, Flemming has also formulated correlations for
lift and moment coefficients for both glaze and rime
encounters. These correlations are of the forms:
For a glaze ice encounter,
AC_, = KD..C.OO686 Ko ( t/c) * "S (<*+6) - .O313(r/c)2 «-KD( .OO6)M2 "H ]d »
[WTC,(_C >°'2/(_c )* *2] C1-8AC / (Vhelo)] (13)£j
.1524 .1524 278
For a rime ice encounter,
AC., = C.1581n<k/c)*175< V )«T E + 1.7Q] (<*•••&)d . — cP4 c 10ice
[1-8AC '(Vhelo)3C . (14)278 clean
and for both glaze and rime encounters,
AC. = <-.6i335Ko (t /c) [<x+2 + KL, < .OO555) ( < x - 6 ) 8 ] K L ] CWTi 1 C
(_c__)° • 2 / (_c__) 1 '2] (15).1524 .1524
34
and . , .
ACm = [<.00179-.OO45M> (.O0544>Ko*/<t/c>2 '7 +
.OO383M<l-63.29r/c>3 (16)
EU)T < cc.1524 .1524
'where Ko la the modified inertia parameter, given by
Ko = KC1+.0967 R •&I97> (17)
and KL, KL4 •', and KD, and KD4 are functions of temperature and
angle of attack and are defined within the subroutine.
These correlations were developed using data obtained in
a series of tests conducted in the Canadian National Research
Council's High Speed Icing Wind Tunnel in late 1982. The ten
airfoil scale models tested, with typical chords of roughly
six inches, were designed primarily for use in helicopter
applications and cover a wide range of helicopter airfoil
shapes. For correlation development purposes this range
should enable the resulting correlations to adequately account
for airfoil geometry as a factor in aerodynamic coefficient
increments due to icing.
The correlations are, however, dimensional in nature and
again were developed using model data for high speed
applications. The full effects of these two items on the
range of applicability of the correlations remains to be seen.
The correlations have been found in a recent study to
underpredict AC . in many cases however. In spite of this,
35
Flemming'a correlations still hold promise and do in fact work
well in many cases.
4. Miller Correlation
A fourth general drag coefficient correlation
development has been attempted by Miller, et. al. Described
in detail in Reference 28, this effort used as the basis for
the correlation formulation the method of statistical analysis
as applied to a set of experimentally obtained icing data.
Although a correlation was presented in Reference 28, it
represented only a status report and not a final result.
Further study and modification of this correlation is
, necessar,y before it may be deemed useable, and no
modifications made to date have proven satisfactory. The
method of statistical analysis is a powerful tool in
correlation in development and should yield greater success at
some future date, but because the present form of the
correlation is not acceptable in terms of accuracy of
prediction it will not be incorporated into the code.• - , ' " ' • / - - . . . •
So there are presently available three correlations or
sets of correlations which are integrated into the code. They
provided values of drag, lift, and/or moment coefficient
increment for both glaze and rime ice encounters. These
increments may then be passed to a propeller performance code,
described in the following section, to evaluate the ensuing
propeller rotor performance degradation.
36
; D. Propeller Performance Code• - r ' • • . . 7 : - " 1. . :-
The, propeller performance code which is integrated into
the performance degradation program ia based upon a linearized
inflow propeller strip analysis, developed by Cooper (34) in
1957,. Strip analysis involves the calculation of aerodynamic
forces at selected spanwise blade locations for a, given
operating condition and propeller geometry. From these
differential forces, given in terms of thrust and torque
coefficients by
dCT = k £ M 8 (C. COS4--C .sin*-) (18), - D x A d '
where k= 9OOa8 b (19)
N » D »
and
dx 2 dx C. cos*- C .sin** dthrust and torque coefficients may be obtained by integrating
these terms along the blade. Propeller efficiency and power
absorbed may then be calculated by
p \f pD = j :u_ = <__) IT _ <2 i )C nD 21TC
p Q
and
BMP = Cp Pt)?D' (22)550
Cooper's propeller performance analysis is unique due to
the fact that it assumes, or actually approximates, a linear
induced flow distribution on the propeller blade. Typically
37
an iterative process is required to obtain the induced angle
of attack and" lift coefficient at a specific radial location
since they are interrelated. However, Goldstein (35) has
solved for the radial distribution of circulation for a
lightly loaded propeller having a finite number of blades and
has established the relationship between ff C, and ot . Cooper
has then approximated the 9 C. - e* curves by straight lines
and has plotted the slopes of these lines versus advance ratio
for various spanwise locations. From these plots, and using
available aerodynamic data, it is then possible to determine
values for an induced angle of attack. When experimental and
analytical results obtained using this method were compared,
agreement to within three percent was seen for over ninety
percent of the cases investigated.
38
CHAPTER 4 ,
PERFORMANCE DEGRADATION CODE ASSEMBLY
• •.,- In order to integrate each of the codes involved. into a
single performance degradation code, heretofore known as
ICEPERF, several .phases of modifications were required. These
modifications were relatively minor in that they did not
change the basic functions, operation, or logic of any of the
codes but rather served to make the transition from one
section to the next more simple and automatic. This
automation then eliminated the necessity of any user
.intervention in the run stream.
The user-friendly nature of the code was a primary
objective of this effort, and although several files are
necessary to run the code very few changes are required from
one run to another, for the same airfoil. The various
components of the code were selected on the basis of
availability and accuracy of results. Each component was run
and tested separately and extensively to demonstrate its
capability to consistently function properly, and all
displayed good performance in these runs. Also of importance
in the component selection and modification was a desire to
maintain a high degree of modularity in the code, such that a
different flowfield computation, new correlation, different
propeller analysis, etc. could be inserted with a minimum of
changes to the code. This also permits the code, now applied
to propellers, to be relatively easily extended to a
39
helicopter configuration. A flowchart denoting the current
major elements of the program is provided in Appendix 1.
The firat phase in the code integration process involved
combining the flowfield and droplet trajectory codes
previously described. Because the droplet trajectory code was
designed to operate using much of the output from the
Theodorsen transformation code, this step was relatively
straightforward. The modified code has been set up to handle
a maximum of four input propeller radial locations, and
current runs of the code have been made with four input
stations, at the 3O, 5O, 7O, and 9O percent radial locations.
An investigation of the benefits of using more input stations,
offset by the additional cost due to the extra run time
required, has not yet been performed.
Next, a set of subroutines was created to predict drag
increment due to ice accretion, given the appropriate
impingement efficiency values output from the trajectory code.
The AC. correlations of Gray, Bragg, and Flemming are included
in the subroutines, with Flemming'a correlation also being
capable of determining lift and moment coefficient increments.
The user may select any of these correlations in each run of
the program, and the choice of correlation should be dependent
on the type of ice formation expected for a given input
condition.
The correlations of Gray and Bragg use values of total
and maximum local collection efficiencies in computing drag
coefficient increment. One value for each of these parameters
40
is generated for each radial location input, so that a maximum
of four sets of collection efficiencies are available as
output from the trajectory calculation section. However, it
is best when using the propeller performance code to include
considerably more input radial locations in the calculations
(eleven stations are used in the analysis of a propeller
utilizing double-cambered Clark-Y airfoil sections which
follows in Chapter 5). In order to obtain values for drag
coefficient increment at each of these locations, the
collection efficiencies at these stations must be known.
Rather than running the Theodorsen transformation and droplet
... trajectory codes eleven times to obtain collection efficiency
values at each of these stations however, a curve fit routine
is employed which takes the values computed at each of the
four input radial locations and fits a curve through them.
Flemming's correlations compute values of collection
efficiencies empirically, so that it is not necessary to run
the Theodorsen and droplet trajectory sections of the code if
Flemming's correlations are to be employed.
In this code, a cubic spline fit routine is used to fit
separate curves for total maximum local collection
efficiencies between the 30H and 90* radial locations, or
between the two most extreme sections input by the user. This
method has been found to yield good results due to the fact
that the .collection efficiencies are both smooth, continuous
.functions or propeller radial location. Due to the nature of
the spline fit routine, it is applicable .only between the
41
innermost and outermost radial locations input. Outboard of
the outermost input station, and inboard of the innermost
station, some other technique is required to compute values
for the collection efficiencies as a function of radial
location. In this analysis a linear fit, computing the slopes
at the endpoints of the spline fit and extending straight
lines inboard and outboard of these endpoints, is used to
approximate the curves where the spline fit is not. applicable.
With this method, values for both total and maximum local
collection efficiencies are available for any radial location.
Cooper's propeller performance code has been utilized to
calculate values of propeller thrust, torque, and efficiency
for a given condition. The previously mentioned drag
increment subroutines have been incorporated into the
propeller performance code to modify the drag coefficient and
values used by the code in computing iced propeller thrust and
torque. In Equations 18 and 2O, the C. and C. terms areA d
modified by the factors (1 + AC,) and (1 + AC .) respectively, such
that
C = C (clean)- <1 +AC ) (23)* ft A
and
C =CJ<clean) *(1 +AC.) (24)d d d
so that iced propeller thrust and torque coefficients as well
as propeller efficiency may then be computed. The code first
calculates clean, or non-iced, values for these quantities,
and then calculates using the user-selected aerodynamic
42
coefficient correlation the iced valuea for theae aame
parameters. Varioua input parameters have been altered or
omitted from the original code to make it more conducive to
the purposes pf the present program, but the esssence and
mechanics of the code remain unchanged. ..
The entire code then operates by first.computing clean
propeller performance values for one advance ratio. Next, the
Theodorsen transformation is performed, or previously
calculated results^ are read for the first input radial
location. The droplet trajectory section then computes
impingement efficiency values for the radial location using
the flowfield from the Theodorsen transformation and a section
angle of attack computed in the propeller performance section.
Impingement efficiencies are then calculated for the remaining
input radial stations following the same procedure. The code
spline fits the impingement efficiency curves and computes
using these values and the selected aerodynamic coefficient
increment correlation the iced propeller performance data.
This entire procedure is then repeated for each additional
advance ratio input.
43
CHAPTER 5
RESULTS
In the Neel and Bright teat, a C-46 twin-engine aircraft
was used to obtain propeller efficiency losses as a result of
ice formation. Ice was allowed to form on the propeller of
the right engine while the left engine propeller was kept
clean. Following this procedure, data was recorded for twelve
natural icing encounters and typical efficiency losses of four
to ten percent were noted. The propellers on the C-46
utilized double-cambered Clark-Y airfoil sections, for which
airfoil coordinates used in ICEPERF were obtained from Borst
(36) .
The Neel and Bright experimental data provided a data
base with which to evaluate the ICEPERF iced propeller
performance code. For ten of the twelve encounters documented
in the test program report (Table 3), calculations were
performed for the propeller in both clean and iced
configurations. Results and comparison of analytical and
experimental performance values are here presented for each of
the three correlations employed, specifically those of Bragg,
Gray, and Flemming. It should be noted that in all
performance calculations presented in this report,
consideration was given to the radial extent of icing such
that no ice was allowed to accrete analytically outboard of
the experimentally observed radial icing extent. These
results therefore differ from previous calculations shown by
44
this author (37) in which.no restriction was placed
analytically on the radial extent of icing.
The results presented in this paper may also be compared
directly with calculations performed by Korkan, et. al (27).
Their work involved generation of propeller performance
predictions for the Neel and Bright data as well, using the
Theordorsen transformation flowfield code, Bragg droplet
trajectory code, and Cooper propeller performance codes
separately. In this initial study by Korkan, et. al.,
pressure altitude was input and the standard atmospheric
pressure, temperature, and density were then used in the
calculations rather than the experimentally obtained values
for these parameters. The use of actual flight conditions, as
employed in all calculations presented in this report, was
found to alter the computed thrust and power coefficients by
roughly one percent. Potential differences in blade angle
specification from study to study may also have a significant
impact on the predictions. Finally, the initial constant in
the original Bragg correlation was decreased in both studies%
in an attempt to produce reasonable performance values. This
then introduces additional variation between the corresponding
iced calculations.
Clean performance predictions were found to agree well
with the experimental data for all of the encounters
investigated. (Tables 4-6 summarize the analytical and
experimental data for Encounters 2, 7, and 12 respectively.)
In all cases, calculated thrust and power coefficients were
45
found to agree with the corresponding experimental values
within an average of 12.5 percent. C_ and C for a given
encounter and advance ratio tended to be underpredicted by
roughly the same percentage, so that resulting propeller
efficiencies compared with experimental measurements to within
six percent. Since propeller efficiency is essentially a
ratio of thrust coefficient to power coefficient however,
errors of similar magnitude in C_ and C should then cancel so
that the resulting efficiency values would be much less
sensitive to error in performance calculations and would not
be as good an indicator of analytical prediction accuracy.
Therefore statements herein relate primarily to thrust and
power coefficient calculations rather than propeller
efficiency.
The results shown in thia report all involved use of the
actual blade angles as measured and reported in the
experimental test program. It was found however that by
increasing the reported blade angle setting by 0.7 degrees,
much better agreement between theory and experiment could be
obtained for all encounters. Figures 8-10 are illustrations
of the effect of blade angle variation on clean thrust and
power coefficients for Encounter 2. This anomaly could be an
indication of a deficiency in the performance calculations,
but because a constant increase in blade setting produces much
better correlation with experiment for several encounters over
a range of flight conditions, it more likely signifies the
existence of a bias error in the experimental measurement of
46
blade angle. Theae calculations serve also to indicate the
sensitivity of propeller performance predictions to propeller
geometry.
The code was found to often overpredict the clean
propeller efficiency at the higher advance ratios.. Typically,
performance predictions agreed with experiment to within a.few
percent at the lowest advance ratios and gradually worsened to
the point where they were often off by roughly twenty percent
at the highest advance ratios investigated. It is postulated
that this may be due to an inability of the code to adequately
account for compressibility effects, which become more
significant as advance ratio increases (via increased forward
velocity for a fixed rpm>. This effect should be studied
further in subsequent efforts.
When the restriction on radial icing extent was imposed
in the present study's calculations, better agreement with the
experimental data was obtained than was previously presented.
Currently there is no mechanism in the code for determining
the actual radial icing extent. Rather, the user must specify
the desired or assumed radial location inboard of which iced
calculations are to be performed. In this study, approximate
radial icing extent for each encounter was reported by Neel
and Bright and these values were then input for the iced
performance calculations. The following discussion details
results obtained by each correlation for the several
encounters investigated.
47
A. BRAGG
Two forms of Bragg'a basic rime ice correlation are
available in ICEPERF, aa discussed in a previous section. The
first of these is a modified form of Bragg's original
equation, in which the leading constant was changed from O.O1
to O.OOO8 in an effort to produce more realistic drag
coefficient increments. This change was made after initial
runs of the code indicated that the original equation was
producing quite unreasonably large performance changes due to
ice formation, as a result of inordinately large predicted
AC values. The O.OOO8 constant was arrived at by best-
fitting the correlation's performance predictions to Encounter
2 data and was then found to perform acceptably for the other
encounters as well. Future use of the correlation may suggest
additional modifications of this constant.
This modified form of Bragg's original correlation was
then applied to all of the available Neel and Bright data
regardless of assumed rime or glaze ice type, as was Bragg's
new form of the correlation. Reasonably good agreement
between experiment and theory was obtained using both
correlations for all encounters. In all cases the original
but modified Bragg correlation produced more accurate results
than did the newer correlation, but the differences were
generally small. The fact that the newer, unmodified
correlation gave results almost as accurate as those of the
older form which was specifically modified to better fit the
propeller data indicates that the changes made by Bragg in
48
forming the new correlation improved the quality of the
correlation significantly. Both correlations handled the lesa
severe icing encounters (icing extents below 60* > well (i.e..
Encounter 7, Figures 14-16), much better than did the Gray or
Flamming correlations. In the most severe case however
(Encounter 12, Figures 17-19) both correlations seriously
overpredict the degree of degradation, especially in terms of
C , and produce C -J curves which inflect upward at the lowerP P
advance ratios rather than downward as would be expected.
It should also be noted that Bragg'a equations are for
AC. only. Lift coefficient will also generally decrease as ad •• . '
result of ice formation at the leading edge as the flow there
is spoiled to some extent, but this is not accounted for in
the Bragg equations. A factor was therefore introduced to
provide a simple representation of this phenomenon by
assigning the iced section lift coefficient a value equal to
95* of its clean value. Although this seems to be a
reasonable typical value for AC., it would be desirable to
incorporate a more discriminating form of determining AC. in
future calculations.
B. GRAY
As was the case with the Bragg correlations, the Gray
correlation also provides its most accurate performance
predictions when radial icing extent is small. It is
difficult to make any Inference regarding the quality of the
correlation under such conditions due to the fact that the
49
propeller Is loaded moat heavily at the tip and its
performance will be moat sensitive to geometry changes (i.e.,
ice accretions) in the tip region. Farther Inboard, even
"quite severe ice growths will have much less effect on the
overall performance and consequently any correlation,
regardless of how great its predicted AC. values may be, will
appear to work well in low radial icing extent cases. Thus
the true measure of the quality of these correlations comes in
the more severe icing encounters such as Encounters 2 and 12.
In these two encounters, as can be seen in Figures 11-13 and
17-19, the Gray correlation fails to accurately predict the
iced performance, yielding values which overpredict the degree
of degradation. Indeed, upon examining the actual AC . values
predicted by Gray for Encounter 12 it was found that this
correlation was predicting drag coefficient increases of
typically 3OOH at lower advance ratios to as much as 6OOOX at
the outer stations at high advance ratios. The Gray
correlation, like that of Bragg, also predicts only drag
coefficient increment, so the same five percent reduction in
C. for the iced configuration was again employed when Gray's
correlation was used. The Gray correlation itself was
unmodified for use in this study, and it is likely that
introducing some constant into Gray's equation to affect a
constant percentage decrease in its calculated AC , values, as
was done with the original Bragg equation, would greatly
5O
improve its ability to calculate iced drag coefficient
increment and hence iced propeller performance.
C. FLEMMING
The Flemming correlations were applied twice to each
encounter, once with icing restricted by the user-input value
and then allowing the Flemming correlations to predict the
radial icing extent. The second runs were performed to check
the no-icing capability of the correlations and to ascertain
.whether this capability would properly reflect existence of
ice. under the influence of 3-D, rotating forces (kinetic
heating and shedding). Instead of properly predicting radial
icing extent however, this feature dictated no icing in the
first 30* of propeller radius for any encounter, and then
overpredicted the radial icing extent outboard of the 30x
station for eight of the ten encounters (Table 7).
In the case of the user-input icing extent, the no-icing
problem manifests itself in an underpredictlon of the
propeller performance degradation for all encounters. As the
figures illustrate, many of the Flemming-predicted iced thrust
and power coefficient values are identical or virtually
identical to the clean values, indicating analytically little
if any degradation. While these results may appear reasonable
at first glance in cases where the actual degradation ia
minimal, they actually serve only to mask the underlying
problem and reason for the negligible degradation prediction.
It should also be noted that in Figures 11 through 19, in
cases where the clean theoretical curve is not easily visible,
51
it has been hidden by the Flemming correlation curves which
are often virtually coincident with the clean data curve.
When no restriction is imposed upon radial icing extent,
Flemming's correlations still tend to underpredict the degree
of iced performance degradation in several cases. This occurs
even though Flemming's correlations predict more extensive
icing radially than was seen experimentally, which would
indicate that the percentage decreases in thrust and power
coefficients predicted by Flemming are actually smaller than
the experimental values. For the encounters in which the non-
restricted Flemming correlations do predict C_ and C well,
the predicted radial icing extent is always greater than the
measured extent, sometimes by as much as 60%.
It would therefore appear that the Flemming correlations
have two significant deficiencies. The first of these is the
no-icing calculation which has failed in this study to
properly indicate either ice existence or icing extent. In
fairness to the correlations it should be pointed out though
that various forces not stressed in the 2-D correlation
development (i.e., centrifugal forces leading to ice shedding)
may have a significant effect on the radial icing extent, and
in only one out of ten encounters did the Flemming
correlations actually underpredict the extent of ice. The
second apparent shortcoming of the correlations is the
underprediction of section drag and possibly lift coefficient
increments. This same trend toward underprediction of section
C has also been seen in application of the Flemming
52
correlationa to available NACA and NASA 2-D icing data in a
separate study (38).
53
SUMMARY AND CONCLUSIONS
Application of the ICEPERF code to the Neel and Bright
experimental data baae has provided much insight into the
code's performance prediction capability for both clean and
iced configurations. The code has been shown to run properly
and to produce realistic thrust and power coefficient values,
especially when radial icing extent is known and input. As a
result of this study several areas of future development and
potential improvement, discussed in the following paragraphs,
have been identified.
Currently restrictions and simplifications exist within
the code which, if removed or modified, should yield better
performance evaluations. Development of a AC correlation to
be used in conjunction with the Bragg or Gray correlations
would provide a more precise and complete representation of
the effects of ice formation on section aerodynamics.
Secondly, incorporation of some computational mechanism of
predicting the transition from rime to glaze.ice, or vice
versa, on the blades would enable the code to use the proper
correlation at each radial computational station, rather than
assuming all rime or all glaze ice in any given encounter.
Because of the generally moderate radial icing extent and only
slight degree of ensuing degradation, this change will
probably have only a very minor effect on the predicted
propeller performance. This is in contrast to the helicopter
rotor icing situation in which radial icing extent and the
54
related performance degradation are typically more severe for
a given icing condition.
Another potential area of improvement liea in the
accuracy of the experimental data used for comparison with
analysis. One such area with respect to the Neel and Bright
data is the actual radial icing extent for each encounter. As
specified in the report, the true extent is somewhat unclear
and may possibly vary by as much as 2Ot. Values of radial
icing extent presented in this report represent a best
estimate of the extent as interpreted from the Information in
Neel and Bright's report.
The present study has also provided insight into the
type and accuracy of experimental data which would be
desirable in future test programs. Additional propeller icing
data of any type would be useful in further validating and
analyzing the code at the present time. Future tests though
should include, in addition to flight and atmospheric
parameters and icing time, specification of icing extent as
accurately as possible. Also desirable would be some
photographic or other indication of the ice type so that the
proper correlation could be applied at each radial location.
Finally, sensitivity of propeller performance to blade angle
setting also has indicated the need for quite accurate blade
angle measurements. Certainly it is desirable to have a high
degree of accuracy in the thrust and power measurements as
well.
55
With respect to the empirical lift and drag correlations
used in this code, results obtained in this study concurred
with previous work done involving these correlations in
indicating deficiencies which exist in each correlation.
Overall, 'the Bragg correlation(s) produced the moat reasonable
iced propeller performance predictions but overprediction of
drag coefficient increment by Bragg'a correlation(s) remains a
problem, as illustrated in the more,severe icing encounters.
Overprediction also remains a problem with Gray's correlation,
whereas Flemming's correlations typically underpredict the
aerodynamic coefficient increments. It is evident then that
much more 2-D validation of all these correlations is
necessary before iced propeller performance can be predicted
consistently using this method and before results of this
analysis can be fully evaluated. It should be realized that
any ultimate analytical treatment of ice accretion on rotating
systems will potentially involve much less empiricism than is
currently required and that the use of these correlations
represents an interim approach to the problem, which will
continue to be used until more aophiaticated analytical
procedures such as Navier-Stokes or interactive boundary layer
analyses of iced airfoil flowfielda become available.
56
REFERENCES
1. Corson, B. W. and Maynard, J. D., "The Effect of
Simulated Ice on Propeller Performance," NACA TN 1O84,
1946.
2. Preston, C. M. and Blackman, C. D., "Effects of Ice
Formation on Airplane Performance in Level Cruising
Flight," NACA TN 1598, May 1948.
3. Neel, Jr., C. B. and Bright, G. L., "The Effect of Ice
Formations on Propeller Performance," NACA TN 2212,
October 1950.
4. Gray, V. H. and von Glahn, U. H., "Effect of Ice and
Frost Formations on Drag of NACA 65t-212 Airfoil for
Various Modes of Thermal Ice Protection," NACA TN 2962,
June 1953.
5. Gray, V. H. and von Glahn, U. H., "Aerodynamic Effects
Caused by Icing of an Unswept NACA 65AO04 Airfoil," NACA
TN 4155, Feb. 1958.
6. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,
"Impingement of Water Droplets on NACA 65i-208 and 65i -
212 Airfoils at 4 Degrees Angle of Attack," NACA TN 2952,
May 1953.
7. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,
"Impingement of Water Droplets on NACA 65A004 Airfoil and
Effect of Change in Airfoil Thickness from 12 to 4
Percent at 4 Degrees Angle of Attack," NACA TN 3047,
November 1953.
57
8. Brun, R. J., Gallagher, H. M., and Vogt, D. E.,
"Impingement of Water Droplets on NACA 65AOO4 Airfoil at
8 Degrees Angle of Attack," NACA TN 3155, July 1954.
9. Brun, R. J. and Vogt, D. E., "Impingement of Water
Droplets on NACA 65AOO4 Airfoil at O Degrees Angle of
Attack" NACA TN 3586, November 1955.
10. Gelder, T. F., Smyera, Jr., W. H., and von Glahn, U. H.,
"Experimental Droplet Impingement on Several Two-
Dlmensional Airfoils with Thickness Ratios of 6 to 16
Percent," NACA TN 3859, December 1956.
11. Bergrun, N. R., "An Empirical Method Permitting Rapid
Determination of the Area, Rate, and Distribution of
Water-Drop Impingement on an Airfoil of Arbitrary Section
at Subsonic Speeds," NACA TN 2476, September 1951.
12. Lewis, W. and Bergrun, N. R., "A Probability Analysis of
the Meteorological Factors Conducive to Aircraft Icing in
the United States," NACA TN 2738, July 1952.
13. Gray, V. H., "Correlations Among Ice Measurements,
'Impingement Rates, Icing Conditions, and Drag
Coefficients for Unswept NACA 65AOO4 Airfoil," NACA TN
4151, February 1958.
14. Gray, V. H., "Prediction of Aerodynamic Penalties Caused
by Ice Formations on Various Airfoils," NASA TN-D 2166,
February 1964.
15. Shaw, R. J., Sotos, R. G., and Solano, F. R., "An
Experimental Study of Airfoil Icing Characteristics, AIAA
82-O282, January 1982.
58
16. Bragg, M. B. and Gregorek, G. M., "Aerodynamic
Characteristics of Airfoils with Ice Accretions," AIAA
82-0282, January 1982.
17. Bragg, M. B., Zaguli, R. J., and Gregorek, G. M., "Wind
Tunnel Evaluation of Airfoil Performance Using Simulated>•
Ice Shapes," NASA CR 16796O, November 1982.
18. Flemming, R. J. and Lednicer, D. A., "High Speed Ice
Accretion on Rotorcraft Airfoils," AHS A-83-39-O4-OOOO,
May 1983.
19. Korkan, K. D., Cross, Jr., E. J., and Cornell, C. C.,
"Experimental Study of Performance Degradation of a Model
Helicopter Main Rotor with Simulated Ice Shapes," AIAA
84-0184, January 1984.
20. Korkan, K. D., Cross, Jr., E. J., and Cornell, C. C.,
"Experimental Aerodynamic Characteristics of a NACA O012
Airfoil with Simulated Ice," to be published in AIAA J.
of Aircraft.
21. Korkan, K. D., Cross, Jr., E. J., and Miller, T. L.,
"Performance Degradation of a Model Helicopter Main Rotor
in Hover and Forward Flight with Generic Ice Shape," AIAA
84-0609, March 1984.
22. Korkan, K. D., Cross, Jr., E. J., and Miller, T. L. ,
"Performance Degradation of a Model Helicopter Rotor with
a Generic Ice Shape," AIAA J. of Aircraft, Vol. 21, No.
1O, October 1984, pp. 823-83O.
59
23. Bragg, M. B., Gregorek, G. M.', and Shaw, R. J., "An
Analytical Approach to Airfoil Icing," AIAA 81-0403,
January 1981.
'24. Cansdale, J. T. and Gent, R. W., "Ice Accretion on
Aerofoils in Two-Dlmensional Compressible Flow - A
Theoretical Model," RAE TR 82128, January 1983.
25. Flemming, R. J., and Lednicer, D. A., "High Speed Ice
Accretion on Rotorcraft Airfoils," NASA CR 391O, August
1985.
26. Korkan, K. D., Dadone, L., and Shaw, R. J., "Performance
Degradation of Propeller Systems Due to Rime Ice
Accretion," AIAA J. Of Aircraft, Vol. 21, No. 1, January
1984, pp. 44-49.
27. Korkan, K. D'. , Dadone, L., and Shaw, R. J., "Performance
Degradation of Helicopter Rotor Systems in Forward Flight
Due to Rime Ice Accretion," AIAA 83-O028, January 1983.
28. Miller, T. L., Korkan, K. D., and Shaw, R. J.,
"Statistical Study of a Glaze Ice Drag Coefficient
Correlation," SAE 83O753, April 1983.
29. Bragg, M. B., "Predicting Airfoil Performance with Rime
and Glaze Ice Accretions," AIAA 84-O106, January 1984.
30. Shaw, "R. J., Private Communication, NASA Lewis Research
Center, Cleveland, Ohio, August 1984.
31. Bragg, M. B., "Rime Ice Accretion and Its Effect on
Airfoil Performance," NASA CR'l65599, March 1982.
32. Potapczuk, M. G. and Gerhart, P. M., "Progress in
Development of a Navier-Stokes Solver for Evaluation of
Iced Airfoil Performance, AIAA 85-0410, January 1985.
60
33. Bragg, M. B., Private Communication, The Ohio State
University, Columbus, Ohio, December 1985.
34. Cooper, J. P., "The ^Linearized Inflow' Propeller Strip
Analysis," WADC TR 56-615, March 1957.
35. Goldstein, S., "On the Vortex Theory o£ Screw
Propellers," Proceedings of the Royal Aeronautical
Society (London), Ser. A, Vol. 123, No. 792, April 6,
1929.
36. Borat, H. V., Private Communication, Henry V. Borat and
Associates, Wayne, Pennsylvania, June 1984.
37. Miller, T. L., "Analytical Determination of Propeller
Performance Degradation Due to Ice Accretion," AIAA 85-
0339, January 1985.
38. Sanchez-Cantalejo, P. G., Private Communication, NASA
Lewis Research Center, Cleveland, Ohio, September 1985.
61
rime
glaze
FIGURE 1. The two basic ice types
thrust
f r ees t ream
rotational
FIGURE 2. Velocity components of propeller section
62
8 -I00sI
tfl
I<J«J.gs
63
1 oO
O c 8
UJ
LUCD
0.-6
oCD
0.2
O o O
E N C O U N T E R 2
y l o O - '0.7 - O o f - O o l 0 . 1 O o f O o 7
SURFACE ARC LENGTH
FIGURE 4. Variation of local impingement efficiency withairfoil surface arc length; r/R = 0.9, J = 1.18
1 oO
64
Oo9
Oo6
Oo3
oD
A C C U M U L A T I O N P A R A M E T E RTOTAL C O L L E C T I O N E F F I C I E N C YMAX. LOCAL C O L L E C T I O N E F F I C I E N C Y
E N C O U N T E R 2
oO 0 o 2 0 o 4 Oo6 Oo8
R A D I A L L O C A T I O N
FIGURE 5. Radial variation of accumulation parameter, maximumlocal collection efficiency, and total collectionefficiency for Encounter 2, J = 1.18
1 oO
65
1 0
CDLUQ
CJ<t
8
CD ,
_J<£
O -
oD
ANGLE OF A T T A C KMACH ND:c; E N C O U N T E R 2
I 0 o 2 Oof Oo6 0 o 8
R A D I A L L O C A T I O N
FIGURE 6. Radial variation of local angle of attack and Mach• no. for Encounter 2, J = 1.18
c\jo
O- O
CO
O "o
COo
o
66
.0*
.05
.M
Oa
40«/s*c5140405151
it
SPREAD IN NACA DATA
L5gm/ra3
1.52.91.51.5134
FIGURE 7. Comparison of experimental results with Gray'spredicted AC, values
67
25
20
LU -»—i ;.O ic^ o 1 5
u_ ?•u_LUOO
o 1 0
05
OCbo8
oa CLEAN* EXPT.
ICED* EXPT,C L E A N s BLDSET=13«75C L E A N s BLDSET=13o05
DEGcDEG.
E N C O U N T E R 2
Oo9 -1 o 1 1 o2 1 o3A D V A N C E R A T I O
FIGURE 8. Effect of propeller blade setting on predictedthrust coefficient, Encounter 2
1 o5
68
30
LU
UJoCJ
UJ3OCL
1 8
12
06
oo CLEANs EXPT,
ICED* EXPT.CLEAN. BLDSET=13o75CLEANs BLDSET=13o05
DEG.DEG.
E N C O U N T E R 2
° % o 8 O o 9 1 o O 1 o 1 1 . 2 1 . 3 1 c
A D V A N C E R A T I O
FIGURE 9. Effect of propeller blade setting on predictedpower coefficient, Encounter 2
1.5
69
1 .3
1 o 1
Oo9
LU
Oo7
Q.CD
Oo5
Oo L E A N p EXPT.
CED» E X P T cCLEAN* BLDSET=13.75CLEAN* BLDSET=13c05
DE6.D E G c
E N C O U N T E R 2
° ° % o 8 O o 9 0 1 o 1 1 o 2 1 o 3
A D V A N C E R A T I O
1 0 1 O 5
FIGURE 10. Effect of propeller blade setting on predictedpropeller efficiency, Encounter 2
70
30
LU
u_LJ_LUCDO
CO
18
12
06
oa C L E A N 9 EXPTc
ICEDs E X P T cC L E A N » THEORYBRAGGNEW B R A G GGRAYF L E M M I N G sF L E M M I N G p
E N C O U N T E R .2
U N R E S T R I C T E DR E S T R I C T E D
o
Oo9 0 1 o 1 1 o 2 1 o 3
A D V A N C E R A T I O
1.5
FIGURE 11. Variation of thrust coefficient with advance ratio,clean and iced (iced to r/R = 0.7), Encounter 2
71
o o 3
oo
LU3OO_
OQ
s"C L E A N * EXPT,ICED* E X P T oC L E A N * THEORYBRAGGNEW BRAGGGRAYF L E M M I N G sF L E M M I N G s
E N C O U N T E R 2
U N R E S T R I C T E DR E S T R I C T E D
%.8 • 0.9 1 oO 1 o 1 1.2 1.3'
A D V A N C E R A T I O
1.1- 1.5
FIGURE 12. Variation of power coefficient with advance ratio,clean and iced (iced to r/R = 0.7), Encounter 2
72
1 oO
O o 9
>-ozLJU
° 0 o 8
0 - 7UJQ.D
O c 6
oD
CLEAN. EXPToICED. E X P T cCLEAN. THEORYBRAGGNEW BRAGGGRAYF L E M M I N G sF L E M M I N G .
E N C O U N T E R 2
U N R E S T R I C T E DR E S T R I C T E D
° ° % o 8 Oo9 loO Id 1 , ,2 1..3 1.1- 1.5
A D V A N C E R A T I O
FIGURE 13. Variation of propeller efficiency with advance ratio,clean and iced (iced to r/R = 0.7), Encounter 2
73
20
16
o
08
S
o
CLEAN*
CL E A N *BRAGGNEW BRAGGGRAYF L E M M I N G pF L E M M I N G s .
EXPTo
THEORY E N C O U N T E R 7
U N R E S T R I C T E DR E S T R I C T E D
O
O
O
o 7 0 o 8 0 o 9 1 o 0 1 o 1 1.2. 1 c 3
A D V A N C E R A T I O
FIGURE 14. Variation of thrust coefficient with advance ratio,clean and iced (iced to r/R = 0.4), Encounter 7
1 of
74
20
GJ o 1 5
10
DCL
05
C L E A N * E X P T
CLEAN*BRAGGNEW BRAGGGRAYF L E M M I N G pF L E M M I N G p
THEORY E N C O U N T E R 7
U N R E S T R I C T E DRESTRICTED
O
O
O o 8 0 » 9 1 . 0 1 . 1 1 . 2
A D V A N C E R A T I O
1 »3 1 of
FIGURE 15. Variation of power coefficient with advance ratio,clean and iced (iced to r/R = 0.4), Encounter 1
75
o2LUi—i
Oi—iu_u_LU
CZLU
Oo9
Oo6LUQ_o
Oo3
0
oD
CLEANs EXPT.1CED 9 E X P T cCLEAN* THEORYBRAGGMEN BRAGG.GRAYF L E M M I N G * U N R E S T R I C T E DF L E M M I N G s R E S T R I C T E D
E N C O U N T E R 7
. IOo8 Oo9 1.0 1 o 1 1,2
A D V A N C E R A T I O1 .H-
FIGURE 16. Variation of propeller efficiency with advance ratio,clean and iced (iced to r/R = 0.4), Encounter 7
76
c30
CDCJ
(/) 12
06
S1CED» EXPT.CLEAN* THEORYBRAGGNEW BRAGGGRAYF L E M M I N G * UNRESTRICTEDF L E M M I N G p RESTRICTED
ENCOUNTER 12
nn_ ' i i i 1 '—U L to7 Oo8 Oo9 1 oO 1 o 1 1 ,2
A D V A N C E R A T I O
1 o3 1 of
FIGURE 17. Variation of thrust coefficient with advance ratio,clean and iced (iced to r/R = 0.9), Encounter 12
77
LU
o 3
o
oQ.
S
ICED9 EXPT.CLEAN* THEORYBRAGGNEW BRAGGGRAYF L E M M I N G * U N R E S T R I C T E DF L E M M I N G p RESTRICTED
E N C O U N T E R 12
Oo8 0«9 1 oO 1 .1
A D V A N C E R A T I Oo3 1 of
FIGURE 18. Variation of power coefficient with advance ratio,clean and iced (iced to r/R = 0.9), Encounter 12
78
1 ,,2
a:LU
Oo6LUQ.D
0,3
0
T ToO
SC L E A N s EXPToICED» EXPT.CLEAN* THEORYBRAGGNEW BRAGGGRAYF L E M M I N G *F L E M M I N G p
E N C O U N T E R 12
U N R E S T R I C T E DR E S T R I C T E D
O
7 Oo8 0»9 1 oO 1 o 1 1.2
A D V A N C E R A T I O
1 of
FIGURE 19. Variation of propeller efficiency with advance ratio,clean and iced (iced to r/R = 0.9), Encounter 12
79
4J41
a0i<o•
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83
Table 7. Experimental and predicted (Flemming correlationa) radialextent for each encounter.
Encounter 2 3A 3B 4A 4B 66 7 8 12r / R E T E T E T E T E T E T E T E T E T E T
.20 V V V V V V V V V V
. 2 5 V V V V V V V V V V
.30 V V V V v V V V V V
. 4 0 V R V G V G V R V R V R V G V V R V R
. 5 0 V R V G V G R R - / R V G V R V R
.60 V G G G G G G G V R
. 7 0 V G G G G G G V R
. S O G G G G G V R
.90 G G G V R
.95 G G G R
.975 G G G R
E - experiment T - theoryV - iced G - glaze
R - rime
8A
APPENDIX 1
PROGRAM FLOWCHART
f START J
1 t
READ USER INPUT
READ PROP
PERFORMANCE INPUT
ARE
ADVANCE
RATIOS
INPUT?HAVE
J VALUESALREADY
BEEN CALCULATE J FROM
INPUT Vg, RPM
READ J VALUES
CALCULATE CLEAN PROPPERFORMANCE FOR GIVEN J
WRITE RESULTS
85
IS
FLEMMING
CORRELATION
TO BE
SED'HAS
THEODORSENALREADY
BEEN RUN FORGIVENr/R?
READ TRANSFORMATION
RESULTS FROM FILE
.DO THEODORSEN
TRANSFORMATION FORGIVEN r/R
STORE RESULTS
IN FILE
READ DROPLET
TRAJECTORY INPUT
FOR GIVEN r/R
00 DROPLET TRAJECTORY
CALCULATIONS FOR r/R
STORE COLLECTION
EFFICIENCY VALUES
IN ARRAYS
86
NO
SPLINE FIT COLLECTION
EFFICIENCIES FOR ALL r/R
ICED PROP PERFORMANCE
CALCULATIONS FOR GIVEN J
NEXT r/R
87
APPENDIX 2
USER'S GUIDE
ICEPERF has been designed auch that user Intervention In
the run stream has been eliminated and the amount of user
input is minimized. Still, with the wide scope of work and
calculations which the code must perform, a substantial degree
of input is required of the user. This information is
provided through several files which are read at various
points in the program and which are separated such that each
contains input data relative to a particular phase of the
program and to a particular radial location. As previously
mentioned, the code handles four input radial locations, and a
complete set of input data is required at each radial
location.
The actual parameters in each file are described in the
Comments section of the code listing which will follow. They
are redescribed here to provide the user with a better idea of
how to specify and use each variable.
Files 1 through 4 contain airfoil coordinates and other
information related to the airfoil geometry at each radial
location. These files are used in computing the flowfield
about the airfoil. File 1 contains information for the most
inboard radial station input, with files 2 through 4
containing input data for progressively more outboard
stations.
Card 1 of files 1 through 4 contains the title for the
Theodorsen transformation input. This title is printed at the
88
beginning of the airfoil section geometry output for the
particular radial location input. It may typically read
similarly to, "CLARK-Y COORDINATES AT 30X STATION".
Card 2 contains five variables: LPT, ITAU, IZ1N, TAU,
and XZ1N, input in the format <3I5,2F1O.O).
LPT represents the number of harmonics which the user
desires in the exponential transformation of the airfoil to
the circle plane. A value of 5O to 60 is typically used for
LPT to attain a satisfactory degree of accuracy.
ITAU is a flag which indicates whether or not the user
wishes to input the trailing edge angle of the airfoil
section. A value of 0 indicates that the trailing edge angle
is not known or will not be input, and any value greater than
0 indicates that the user will input the section trailing edge
angle.
IZ1N is a flag which indicates whether or not the user
will input the nose singularity coordinates. An IZ1N value of
0 means that the nose singularity will not be input, and IZ1N
should be set to any value greater than 0 to input the nose
singularity coordinates.
TAU is the trailing edge angle in degrees, to be input
if ITAU is greater than O.
XZ1N and YZ1N are the x- and y-coordinates of the nose
singularity, to be input if IZ1N is greater than O.
Card 3 contains the variables NU and NL, which are the
number of upper and lower surface coordinates to be input,
respectively. This card has the format 215.
89
'. Cards 4 through the last contain the airfoil section
coordinates, nondimensionalized with respect to chord. Eight
values are listed on each line in format 8F1O.O. Upper
surface x-coordinates are all listed first, followed by upper
surface y-coordinates, lower surface x-coordinates, and
finally lower surface y-coordinates. i
-This then completes the input required to map the
airfoil sections to the circle plane.
File 8 contains input parameters which are used to
compute droplet impingement values for the airfoil. The same
File 8 input data is used for each input radial location.
Card 1 of file 8 contains the title for that particular
radial location, and would typically read similarly to "30*
STATION TRAJECTORY INPUT." This title is printed at the
beginning of the droplet trajectory section at each radial
location.
Card 2 contains the variables IPRINT, MSPL, XFIRST,
XLAST, and EPS.
IPRINT is a print option, with a value of O used for the
shortened version of the trajectory summary output, and a
value of 1 producing the complete printed output. The
shortened version will print only the general input to the
trajectory section, the tangent trajectories, and the
impingement efficiencies. The trajectory tabulation and
summary and surface impingement values are not printed when
IPRINT equals 0.
90
MSPL ia a variable which ia uaed to aelect the method
deaired to calculate the impingement efficiency curve.
Setting MSPL equal to O requeata the program to aelect the
beat of three methoda poaaible for calculating the curve. An
MSPL value of 1 causea the program to uae a simple cubic
apline routine to calculate the curve. An MSPL value of 2
inatructa the program to uae a cubic apline but to piece in a
linear fit where the cubic spline faila. An MSPL value of 3
causes a quadratic apline to be uaed, in which the
coefficienta are aelected to optimize the fit of the curve.
Setting MSPL equal to O haa alwaya produced satiafactory
results in all cases run for thia inveatigation.
XFIRST ia the x-coordinate after which each atep ia
checked for droplet impingement on the airfoil. A value of -
0.05 ia typically uaed for XFIRST.
XLAST ia the x-coordinate at which droplet trajectory
calculationa are terminated. Thia value typically rangea from
0.5 to l.O, and if the uaer lacka a good feel for the
impingement characteriatica to be expected for a given case, a
value of 1.0 should be used for XLAST to ensure that no
trajectoriea are terminated prematurely.
EPS is the maximum error allowed in the step integration
process. A value of l.xlO ia generally used for EPS.
Card 3 contains the variables XO, UDO, YO, VDO, and FR,
in format 5F1O.5.
XO ia the initial droplet x-coordinate. Thia is the x-
value of the point at which the trajectory inveatigation ia
91
begun, and it ia typically given a value of -5.0, representing
a starting point five chord lengths in front of the airfoil.
UDO ia the initial droplet x-velocity with reapect to
freestream, and is commonly set equal to 1.
YO is the initial droplet y-coordlnate. Thia ia the
starting point for the first trajectory calculation only, and
ita value will depend on the section angle of attack. For a
positive angle of attack, it is suggested that to maximize the
chance of initial droplet impingement a slightly negative
•value of YO be used, perhaps approximately -0.05.
VDO is the initial droplet*y-velocity with respect to
freestream, and ia generally equal to O in the undisturbed
flowfield five or more chordlengths in front of the airfoil.
PR represents Froude number. This parameter may be aet
equal to 0 to ignore the force of gravity on the droplet
trajectories, and this is commonly done.
Card 4 contains four variables, DYO, CON, ERRY, and HGT,
in the format 4F1O.6.
DYO is the increment in YO used by the program to vary
the beginning droplet y-coordinate. Valuea of DYO are
commonly on the order of .001 to .Ol. The code has been set
up to assign a value for DYO if the user inputs a value of 0
for this parameter. The internally assigned value will change
with section angle of attack. If the user inputs a DYO value
however, this value will be used regardless of the section
angle of attack. When internally assigned, DYO ia given a
value of O.OO3 for section angles of attack less than or equal
92
to 4.6 degrees and is set equal to O.OO5 for section angles of
attack greater than 4.6 degrees.
CON is a multiplication constant for the impingement
efficiency curve output. It is generally set equal to 1.
ERRY is the maximum error acceptable in total collection
efficiency. A value of 2 (in percent) has commonly been used.
HGT is a reference height in the y-direction used to
compute total collection efficiency. If this parameter is set
equal to 0 the code will calculate and use for HGT the
projected height of the airfoil section.
This then completes the droplet trajectory section
input.
Files 12 through 15 contain binary flowfield information
which is output by the flowfield computation section of the
code when airfoil coordinates (files 1 through 4) are input.
Since this flowfield information is independent of angle of
attack and velocity, it is necessary to run the code with
airfoil coordinates input only once for a particular geometry.
In subsequent runs using the same geometry, the flowfield
information calculated and stored in the initial run is read
and used by the code, thereby eliminating the need for
recalculation of propeller flowfield information in each run.
The user must only set up the computer job control language
(JCL) appropriately to exercise this option. For example, in
the initial run of a particular geometry, units 12 through 15
must be set up to have the binary flowfield data written to
them. In subsequent runs these files must be established as
93
existing data files from which data is to be read. When
previously computed airfoil flowfield information is used, it
is not necessary to input airfoil coordinates, and the
flowfield calculation section of the code will be bypassed.
File 16 contains input data for the propeller
performance calculations. This file contains data for the
entire propeller, so no duplicate files are required for
different radial locations. Data for a maximum of 15 radial
locations may be input.
Card 1 of this file contains the flight and atmospheric
variables VO, TO, DD, W, TAUM, and ALTUDE in format 6F1O.4.
VO is the freestream velocity in miles per hour.
TO is the freestream temperature in degrees Fahrenheit.
DD represents the volume mean droplet diameter of the
icing cloud in microns.
W is cloud liquid water content in grams per cubic
meter.
TAUM is the icing exposure time in minutes.
Finally, ALTUDE is the pressure altitude in feet at
which the icing encounter occurred.
Card 2 contains the variables NUMBLD, NUMSTA, INCOMP and
NUMADV/ in format 415.
NUMBLD represents the number .of propeller blades.
NUMSTA is the number of radial locations to be input by
the uaer (maximum is 15.)
INCOMP is a compressibility check flag which provides
the uaer with the option of obtaining either a compressible or
94
incompressible solution. If set equal to O, a compressible
solution is obtained and if set equal to 1, an incompressible
solution is computed. Recall however that the flowfield
around the various propeller sections was computed using a
method which assumes imcompressible flow.
NUMADV is the number of advance ratios to be input. Set
equal to 0 if advance ratio is to be calculated using input
RPM and freestream velocity. NUMADV may have a maximum value
of 1O.
Card 3 contains the variables RADHUB, BLSET, RPM,
CPDESI, DESIHP, and DIVIS in format 6F10.5.
RADHUB is the propeller hub radius in feet.
BLDSET represents the propeller blade setting in
degrees. If either CPDESI or DESIHP are assigned values other
than O, the program will derive a BLDSET value based upon
these input parameters.
RPM is the number of propeller revolutions per minute.
If specified, RPM will be held constant. Otherwise RPM will
be calculated based on the input freestream velocity and
advance ratio. Either RPM or advance ratio must be specified
in the input.
CPDESI is the design power coefficient. If set equal to
O, power coefficient will be calculated based upon the input
value of BLDSET.
DESIHP is the design horsepower, and if it is input as
0, a value for DESIHP will be calculated based on the input
BLDSET value.
95
DIVIS la a convergence aid variable for the design mode
in which a BLDSET value must be computed. It is generally
assigned a value between .OO1 and 1. When BLDSET is
specified, the DIVIS variable is not employed.
Card 4 contains the variables CORTIP, RADIUS, STUBLT,
CDINT, and CORHUB in format 5F10.5.
CORTIP is the propeller tip chord in feet.
RADIUS is the propeller radius in feet.
STUBLT is the propeller stub length in feet.
CDINT is a blade shank correction factor which takes
into account interference from the blade shank. If a value
for CDINT is unknown, a value of O.567 should be used.
CORHUB represents the propeller hub chord in feet.
Card 5 is a title card which denotes the variables on
the card to follow exactly as shown in the code input
comments:
R/RAD= BLDANG= CHORD= T/C= ALPHAO= CLD=
VDIS= RC=
Cards 6 through NUMSTA contain values for these
variables, in format 8F1O.6.
XPR is the nondimensional radial location to be input.
BLDANG is the propeller blade angle in degrees of this
section. Generally this is just.the twist distribution built
into the propeller.
CHORD is the propeller section chord in feet.
TC is the section thickness to chord ratio.
96
ALO la the angle of attack for zero lift. In degrees,
referenced to the longest chordline.
CLD is the section design lift coefficient.
VDIS represents the velocity distribution seen by the
section, taking into account nacelle effects. This parameter
equals the local velocity divided by that of freeatream.
Finally RC is the section leading edge radius of
curvature, nondimensional with respect to section chord.
The final card(a), in format F1O.6, with one value per
card, are ADVRAT values.
ADVRAT ia the propeller advance ratio, and as many as 1O
values of ADVRAT may be input by the user, with performance
calculations performed by the code for each advance ratio. If
NUMADV is set equal to 0, such that advance ratio ia to be
calculated by the code given RPM and freestream velocity, no
ADVRAT values should be input.
This completed the propeller performance section input.
File 17 contains input for options available to the
user, including choice of aerodynamic coefficient correlation
to be used as well as print options.
Card 1 is the title card for the run. This title is
printed at the beginning of each section of calculations
within the program and so should be general in nature, such
as, "ENCOUNTER 2 FROM NEEL AND BRIGHT REPORT."
Card 2 contains the variables NCD, RADEXT, IREAD,
IPRCOR, and NSECT in format 15,F10.5,315.
97
NCD ia the aerodynamic coefficient correlation selector.
A value of 1 for NCD calls for the use of Bragg'a rime ice AC ,d
correlation. A value of 2 calls for the use of Gray's glaze
ice AC, correlation. A value of 3 calls for the use ofd
Flamming'a AC, and AC correlations for rime and glaze ice.
RADEXT is the fractional radial extent of icing.
IREAD is a flag which determines whether or not the code
will calculate the flowfield at the input radial locations.
The option is to use previously calculated and stored
flowfield data. For each radial location input, the code will
write the flowfield information to a file if it has not been
computed in a previous run. Set IREAD equal to O to calculate
the flowfield, or set it equal to 1 to use the previously
computed data. The user must also be sure that the
corresponding JCL for each of these files is set up correctly,
i.e., if IREAD equals 0 the JCL must be write-oriented, and if
IREAD equals 1 the JCL for these files must be read-oriented.
IPRCOR is a flag which indicates whether or not the user
wishes to have the airfoil coordinates at each of the four
input radial locations printed. An IPRCOR value of O
instructs the code to not print the coordinates, and an IPRCOR
value of 1 causes the coordinates to be printed.
NSECT is a variable which indicates the number of radial
locations to be input, with a maximum of four possible.
Cards 3 through 7 contains values for the variable RSTA
in format F1O.5.
98
RSTA is the nondimenaional radial location at which
flowfield calculations are to be performed. A maximum of four
radial locations may be input. These radial locations must
for the current version of the code be the aame as any four of
the radial locations input in the propeller performance
section.
It may be shown that the curves of total and maximum
local collection efficiencies are relatively smooth functions
of radial location, ao that four points should provide a
reasonable representation of the variance of these impingement
efficiencies with radial location. However, it is obvious
that the fewer points one uses to fit these curves, the less
accurate they will tend to be. It is recommended therefore
that whenever possible, no less than the maximum of four
stations should be input to maximize the available accuracy in
the impingement efficiency calculations, which then affect the
propeller performance computations for the iced configuration.
This then completes the required input to the code.
99
APPENDIX 3
SAMPLE CASE
The following output was produced for Encounter 2 at an
advance ratio of 1.18. The Iced calculations were performed
uaing Bragg'a older, modified correlation. This same format
la output regardleaa of the user's choice of correlation. Uae
of the Bragg or Gray correlations will generate output similar
In appearance to that shown here. When the Flemming
correlations are used, no flowfield or droplet trajectory
information is printed out.
The code requires approximately 57OK of computer memory.
Typical run times are roughly five minutes (CPU time) on an
IBM 370 and 33 seconds on a CRAY-IS for one advance ratio
using either the Bragg or Gray correlations. Use of the
Flemming correlations significantly reduces run time because
the flowfield and droplet trajectory calculation sections of
the,code are bypassed, resulting in typical run times for the
Flemming runs of 8.4 seconds on the IBM 37O and O.57 seconds
on the CRAY-IS.
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1. Report No.
NASA CR-175092
2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle
Analytical Determination of Propeller PerformanceDegradation Due to Ice Accretion
5. Report Date
April 1986
6. Performing Organization Code
7. Author(s)
Thomas L. Miller8. Performing Organization Report No.
None
10. Work Unit No.
9. Performing Organization Name and Address
Sverdrup Technology, Inc.Lewis Research CenterCleveland, Ohio 44135
11. Contract or Grant No.
NAS 3-24105
12. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, D.C. 20546
13. Type of Report and Period Covered
Contractor Report
14. Sponsoring Agency Code
505-68-11
15. Supplementary Notes
Final report. Project Manager, Robert J. Shaw, Propulsion System Division, NASALewis Research Center, Cleveland, Ohio 44135.
16. Abstract
A computer code has been developed which 1s capable of computing propellerperformance for clean, glaze, or rime Iced propeller configurations, therebyproviding a mechanism for determining the degree of performance degradationwhich results from a given U1ng encounter. The 1nv1sc1d, Incompressible flowfield at each specified propeller radial location 1s first computed using theTheodorsen transformation method of conformal mapping. A droplet trajectorycomputation then calculates droplet Impingement points and airfoil collectionefficiency for each radial location, at which point several user-selectableempirical correlations are available for determining the aerodynamic penaHtleswhich arise due to the 1ce accretion. Propeller performance 1s finally computedusing strip analysis for either the clean or Iced propeller. In the Iced mode,the differential thrust and torque coefficient equations are modified by thedrag and 11ft coefficient Increments due to 1ce to obtain the appropriate Icedvalues. Comparison with available experimental propeller 1c1ng data shows goodagreement 1n several cases. The code's capability to properly predict Icedthrust coefficient, power coefficient, and propeller efficiency 1s shown to bedependent on the choice of empirical correlation employed as well as properspecification of radial Icing extent.
1 7. Key Words (Suggested by Authors))
Propeller 1c1ng; Performance degradation;Analytical prediction
19. Security Classif. (of this report)Unclassified
18. Distribution Statement
UnclassifiedSTAR Category
20. Security Classif. (of this page)Unclassified
- unlimited03
21. No. of pages137
22. Price'A07
*For sale by the National Technical Information Service, Springfield, Virginia 22161
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