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The Use of Similitude in
Analyzing Aircraft Windshield
Anti- Icing Perfor mance
R. Ross, Ross Aviation
Associates, Sedgwick, Kan.
AlAA AIRCRAFT SYSTEMS AND
TECHNOLOGY MEETING
August 20-22,1979/ New York, New York
For P8frnbtiOn lo copy or republish. conlac1 Ih8 Arnsrlcan Instilute of Aeronautics and Aslronaullcs.1290 Avenue of lhe Americas. New York. N.Y. 10019
M 79-1%4/3
T H E U S E O F SIMILITUDE I N ANALYZING AIRCRAFT
WINDSHi E L 0 ANTI-ICING PERFCRMANCE
R . Ross*
Ross Aviation A s s o c i a t e s
Sedgwick, Kansas
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Abstract
Development of the P r e d i c t i o n Model
The p a p e r d i s q u s s e s a technique used in
analyzing the p e r f o r m a n c e of a hot airflow
anti-icing s y s t e m f o r a n a i r c r a f t windshield.
T e m p e r a t u r e s at d i s c r e e t locations on the
windshield of a j e t a i r c r a f t w e r e g a t h e r e d
e x p e r i m e n t a l l y while varying a i r c r a f t flight
condition$ and hot anti-icing airflow. T h e
p r i n c i p l e s of s i m i l i t u d e are used to r e d u c e
the eight v a r i a b l e s in the p r c b l e m to t h r e e
d i m e n s i o n l e s s groups. It i s shown that t h e s e
t h r e e g r w p s can b e used t o p r e d i c t the s u r f a c e
t e m p e r a t u r e distribution on t h e windshield f o r
a l l flight and anti-icing airflow conditions.
T h e f i r s t s t e p i n seeking s i m i l i t u d e i s to
l i s t t h e dependent and independent quantities in
t h e problem. T h k s t e p i s by f a r the m o s t
i m p o r t a n t because the validity of t h e r e s u l t s
depends on the c o r r e c t n e s s of the quantities
c h o s e n . A l i s t of the a p p r o p r i a t e quantities
in t h i s problem i s shown in T a b l e 1 .
Table 1
1). B l e e d a i r m a s s flow
2)
3)
Nomenclature
f
PA
PB
J
TA
TB
TW
V
W6
X
4)
5)
Function in equation (1)
Ambient p r e s s u r e , Ib/ft
Ambient t e m p e r a t u r e ,
6)
2
Bleed a i r f l o w p r e s s u r e , Ib/ft
7)
Bleed a i r t e m p e r a t u r e
Bleed a i r p r e s s u r e
Ambient t e m p e r a t u r e
Ambient p r e s s u r e
Aircraft airspeed
Position on t h e windshield
2
At t h i s s t e p it i s d e s i r a b l e to distinguish
t h e dependent v a r i a b l e f r o m t h e independent
v a r i a b l e s o r quantities and t o e x p r e s s t h e
dependent v a r i a b l e , in t h i s case t h e windshield
s u r f a c e t e m p e r a t u r e Tw. a s a function of.the
independent v a r i a b l e s , i. e.
O R
Bleed airflow t e m p e r a t u r e , OR
Windshield s u r f a c e t e m p e r a t u r e , OR
A i r c r a f t s p e e d , ft/sec
Bleed a i r f l o w r a t e , Ib/sec
Distance along windshield, ft
T h e second s t e p i s the application of
dimensional a n a l y s i s which will provide a
reduction in t h e number of independent quantit i e s by combining t h e m into a smaller n u m b e r
of d i m e n s i o n l e s s g r o u p s . T h e s e a r e f r e q u e n t l y
t h e f a m i l i a r d i m e n s i o n l e s s n u m b e r s s u c h as
Reynolds n u m b e r , Mach n u m b e r , etc. Applic a t i o n of t h e r a m i l i a r Buckingham T t h e o r e m
will s h o w the n u m b e r of d i m e n s i o n l e s s p r o d u c t s
t h a t e x i s t in the p r o b l e m , i . e . the n u m b e r of
d i m e n s i o n l e s s p r o d u c t s i s equal to t h e n u m b e r
of original q u a n t i t i e s in t h e l i s t r e d u c e d by the
r a n k of t h e dimensional m a t r i i f o r m e d f o r t h e
fundamental u n i t s ( m a s s , length, t i m e , t e m p e r a l u r e ) of t h e eight p a r a m e t e r s in Equation
(1). The r a n k of t h i s m a t r i x is Tow so that
there should b e four d i m e n s i o n l e s s p r o d u c t s .
B y a n a l y s i s and inspection they c a n be w r i t t e n
Introduction
4
P a r a m e t e r s affecting windshield
s w f a c e tempw,ature
S i m i l i t u d e c a n be defined a s a p r o p e r t y
t h a t p e r m i t s t h e reduction of the number of
p a r a m e t e r s or v a r i a b l e s upon which a p b j s i c a l
phenomenom depends. S u c h a reduction h a s
obvious d e s i r a b l e consequences, e s p e c i a l l y
f o r the e x p e r i m e n t a l i s t . I t m e a n s that a s i n g l e
test m a y r e s u l t in obtaining all of the information n o r m a l l y r e q u i r i n g a whole s e r i e s of tests.
A p r i m e e x a m p l e i s t h e hypersonic s i m i l a r i t y
r u l e . Taking m e a s u r e m e n t s on a s l e n d e r body
a t high Mach n u m b e r and t h e use OF t h e hypers o n i c s i m i l a r i t y r u l e r e s u l t s in data f o r a
whole f a m i l y of r e l a t e d thinner or Fatter bodies
at c o r r e s p o n d i n g l y d i f f e r e n t Mach n u m b e r s .
Thus s i m i l i t u d e c a n a i d in planning a n experiment as well as assist i n analyzing the r e s u l t i n g
d a t a . T h e goal i s to r e d u c e t h e n u m b e r of
independent q u a n t i t i e s in an e x p e r i m e n t b e c a u s e
t h a t p r o v i d e s a n i m p o r t a n t simplification and
reduces the n u m b e r of m e a s u r e m e n t s r e q u i r e d
to define the solution.
as:
The f o r m of the unknown function i s not r e v e a l ed by dimensional a n a l y s i s but i t c a n be d e r i v e d
from a n a l y s i s of o b s e r v a t i o n s .
'Director
A s s o c i a t e Fellow A l M
1
i
?
w’
Condition
Range
Altitude, 1000 ft
Ambient t e m p e r a t u r e , O
Airspeed, KCAS
Bleed flow, Ib/min
Bleed t e m p e r a t u r e , O F
1.8
- 45
-90 - 61
1 5 8 - 225
F
4-9
330
250
-
Data Analysis
TvJTA
i
The t e s t data w e r e reduced to the t h r e e
dimensionless groups a.s indicated by Equation
(3) and plotted on semi-log g r a p h p a p e r .
Inspection of t h e data indicated t h a t t h e r e w e r e
sets of data points corresponding t o n e a r l y
constant values of Te/TA. T h e s e w e r e used
as s t a r t i n g points f o r s t r a i g h t l i n e c u r v e fitting.
Test P r o c e d u r e
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Flight test conditions
Table 2
T h e t h i r d s t e p in the a n a l y s i s i s t o bring
in any supplementary information that might
lead to a f u r t h e r reduction in the number of
independent quantitieg. After the application
of t h i s s t e p we are r e a d y t o t r y t h e r e s u l t s
on me problem a t hand. T h e p r e s s u r e r a t i o ,
Pe/PA, can be eliminated as a p a r a m e t e r by
recalling t h a t in incompressible flow, t h e
absolute l e v e l of p r e s s u r e i s irrelevent,
because p r e s s u r e plays only a e n a m i c and not
a t h e r m o d w a m i c r o l e - only i t s gradient i s
significant. T h u s
2
= f (wBV/X PA. T e n A )
(3)
T h e tests w e r e conducted on a Gates
L e a r j e t M35. T h e M35 i s equipped with G a r r e t t
AiResearch TFE 731 turbofan engines. The hot
anti-icing a i r . i s obtained &:bleed Prom t h e
engines and i s supplied to t h e windshield on t h e
a i r c r a f t through a duct exiting at t h e c e n t e r of
t h e lower s i d e of the windshield as shown in
F i g u r e 1 . Three thermocouples w e r e attached
In o r d e r t o d e t e r m i n e a uniform f a m i l y
o f c u r v e s fitting the data and conforming to
Equation (3). i t w a s helpful t o p r e p a r e
additional working c u r v e s . A plot of
Tw/TA vs TB/Tn f o r d i s c r e e t values of
WBV/X’PA w a s p r e p a r e d to find t h e variation
f o r lower bleed t e m p e r a t u r e s and t o give
b e t t e r definition t o the s h a p e of the c u r v e s .
L i n e a r r e g r e s s i o n analysis WGS applied to the
points in t h i s c u r v e as they w e r e d e t e r m i n e d
f r o m t h e p r e l i m i n a r y l i n e s drawn through t h e
data in t h e initial W V/X2PA “ e r s u s TB/’T~
plot. T h e end r e s u a i s a family of c u r v e s as
shown i n F i g u r e s 3 and 4 .
t
w Bv/x 2PA
M
+6k
Fig. 1 Windshield anti-icing s y s t e m
.1
l1 m
.0 1
4
.0
to t h e windshield at t h e locations shown in
F i g u r e 2. Test d a t a w e r e r e c o r d e d f o r a
1.4
1.8
2.2 .01
T ~ ’ T ~
Fig. 3 Auxillia-y c o r r e l a t i o n c u r v e s
Further inspection of the l i n e s o f F i g u r e s 3
and 4 r e v e a l e d the n u m e r i c a l equation t h a t
r e p r e s e n t s t h e l i n e s of F i g d r e 4. T h i s is given
by
F i g . 2 Location of thermocouples
TflA
v a r i e t y of flight conditions as shown in T a b l e 2.
= 1 +L2508 +
.0952logl0(wBV/x 2 PA]
VBnA
-1)
2
(4)
I
L'
that p r o p e r ' information about the a i r c r a f t
conditions, weather conditions and hat bleed
a i r conditions i s known. The following i o n c l u s i o n s are reached:
TsflTn
1 . 2 1.4 1.6 1.8 2 . 0 2.2'
1)
A dimensional a n a l y s i s technique c a n successFul:y e x p r e s s
windshield t e m p e r a t y e s in the
Form of a mathematical function
Whose mathematical equation i s
unknown.
2)
Experimental data f r o m a i r c r a R
flight tests a r e r e q u t r e d to
d e t e r m i n e the f o r m of the c o r r e lation leading to the prediction
technique.
3)
With t h e a p p r o p r i a t e a i r c r a f t
and a t m o s p h e r i c information
available, windshield s u r f a c e
t e m p e r a t u r e s c a n be predicted
with acceptable a c c u r a c y .
4)
Given sufficient e x p e r i m e n t a l data,
t h e exact mathematical equation
r e p r e s e n t i n g the p r o b l e m under
investigation can b e derived.
Q
a
N
X
\
>ul
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3
T dT A
F i g . 4 Data c o r r e l a t i o n
Discussion of R e s u l t s
~.
T h e test of validity of s u c h a technique as
d e r i v e d i s to c a l c u l a t e t h e value of the winds h i e l d s u r f a c e t e m p e r a t u r e based on known
test conditions and c o m p a r e t h a t Value with the
corresponding m e a s u r e d value f r o m the test.
T h i s w a s done f o r all of t h e available test d a t a .
T h e r e s u l t s are shown as m e a s u r e d v s calculated T W F Ain F i g u r e 5. Error bands of
d'
Acknowledgement
T h e author e x p r e s s e s appreciation to
The G a t e s L e a r j e t Corporation for t h e i r
cooperation in r e l e a s i n g t h e data f o r publication.
I
References
1.
Bridgeman, P. W . , "Dimensional
Analysis", Yale U n i v e r s i t y Press, 1 9 3 1
( P a p e r b a c k , 1963).
Birkhoff, G . , "Hydrodynamics - A
S t u d y in Logic, Fact, and Similitude",
P r i n c e t o n University Press, 1950 (Dover
Press, 1955).
2.
Sedov, L. I . , " S i m i l a r i t y and Dimen3.
s i o n a l Methods in Mechanics", Academic
P r e s s (Translation f r o m t h e 4th Russion
Edition), 1959.
F i g . 5 Computational a c c u r a c y
2
2 and 2 5 p e r c e n t a r e shown and t h e a c c u r a c y
i s s a t i s f a c t o r y . O n the b a s i s of 4 5 test points
t h e a v e r a g e difference between m e a s u r e d and
predicted Tw/TA is 0.016.
v
Cmclusions
T h e formulation of a prediction technique
hcas been accomplished with t h e u s e of s i m i l i tude. T h e method allows t h e prediction of
windshield s u r f a c e t e m p e r a t u r e , a s s u m i n g
3