Document
R €SEARCH M EMORAN DUM
CASCADE INVESTIGATION OF COOLING CHARACTERISTICS O F A CAST -FINNED 4IR-COOLED TURBINE BLADE FOR USE IN A TURBOPROP ENGINE B y F r a n c i s S . Stepka, Hadley T. Richards, and Robert 0. Hickel Lewis Flight Propulsion Laboratory Ohio Cleveland,
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CLASSIFIED DOCUMENT
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Tbts material con- information affecuag the National Defense of the Unlted States within the meaning o f the espionage laws, Tltle 18, U.S.C., S c s . 799 and 794, the trmmlssion or revelatioo of which I n any mmmr to an unauthorized person i s prohibited by law.
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASHINGTON June 12, 1957 m m m m m e m m m m me a m m a m m a e a m a -CPNFkDENTML : m a m a e em am e m m m m m m a m a m m a m e m a m e m a a m m e me am m m m m m m a m m e m m m m m m emem eem . 0 . . 0 . . ......................
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NATIONAL ADVISORY COMMITTEE F O R AERONAUTICS RESEARCH MEMORANDUM CASCADE INVESTIGATION OF COOLING CHARACTERISTICS O F A CAST-FINNED AIR-COOLED TURBINE BLADE F O R USE I N A TURBOPROP ENGINE By Francis S. Stepka, Hadley T. Richards, and Robert 0. Hickel SUMMARY The cooling c h a r a c t e r i s t i c s of a small air-cooled turbine blade f o r use i n a turboprop engine were experimentally investigated i n a s t a t i c cascade f a c i l i t y . Three test blades of 1.4-inch span and 0.7-inch chord were studied at combustion-gas temperatures of about 1 0 6 0 ° , 1 3 6 0 : , and 1 6 6 0 ' R. The blade cooling-air temperatures ranged from about 580 t o 1 0 6 0 ' R. The gas Reynolds number was varied from about 70,000 t o 170,000, a range comparable t o that which might exist i n a turboprop engine.
O n the b a s i s of a nondimensional method of c o r r e l a t i n g blade m e t a l temperatures with combustion-gas and cooling-air conditions presented herein, average blade m e t a l temperatures a t p a r t i c u l a r span locations, l o c a l metal temperatures, and t h e average m e t a l temperatures of t h e en- t i r e blade c o r r e l a t e within about 7 percent of a mean l i n e drawn through t h e t e s t data. The correlated data are applied t o a t y p i c a l turboprop engine i n an attempt t o obtain an insight i n t o t h e probable cooling c h a r a c t e r i s t i c s of t h e blade configuration under engine operating condi- t i o n s a t a t u r b i n e - i n l e t gas temperature o f 2460° R. The analysis indi- c a t e s that cooling-air requirements are about t h e same f o r both sea- l e v e l s t a t i c conditions and f o r f l i g h t at 300 knots a t a 30,000-foot a l t i t u d e .
A t 30,000 feet t h e r a t i o of cooling-air t o combustion-gas flow necessary t o maintain an average blade temperature of 19850 R i s about This value r e s u l t s i n a blade s t r e s s - r a t i o f a c t o r ( r a t i o of 0.015.
allowable stress-rupture strength f o r blade m a t e r i a l t o calculated average c e n t r i f u g a l stress a t c r i t i c a l span location) of about 3, based on 1000-hour l i f e . Past experience with much l a r g e r air-cooled blades, such as those used i n t u r b o j e t engines, shows that s t r e s s - r a t i o f a c t o r s on t h e order of 1 . 2 t o 1.5 are required t o obtain the desired blade l i f e . Therefore, the finned-blade investigated appears t o have a con- servative ( l a r g e ) value of s t r e s s - r a t i o f a c t o r and a reasonable poten- t i a l i t y f o r s a t i s f a c t o r y high-temperature engine operation a t l o w coolant f l o w .
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INTRODUCTION The benefits t h a t can be obtained by increasing t h e turbine-inlet temperature of turboprop engines and the thermodynamic e f f e c t s of cool- ing the turbines on engine performance have been established and are l reported i n references 1 t o 4. Because of t h e smallness of t h e turbine
i
blades (generally blade chords l e s s than 1 i n . and blade spans of t h e order of 1 t o 2 i n . ) i n present-day turboprop engines, cooling and fab- r i c a t i o n problems a r e l i k e l y t o be more acute than those of larger-sized turbine blades such as are used i n t u r b o j e t engines.
An analysis of the e f f e c t of turbine blade chord s i z e on t h e cool- i n g c h a r a c t e r i s t i c s of air-cooled blades having corrugated i n s e r t s (ref.
5) indicated that, when the blade chord i s l e s s than 1 inch, t h e coolant- flow requirements increase rapidly, being as much as 2- times as g r e a t f o r a 1/2-inch as f o r a 1-inch-chord blade. Also, the coolant pressure losses i n small passages may become large and the blade may be unable t o pass the required airflow a t the pressure l e v e l s available i n engine op- eration (ref. 5). I n addition, f a b r i c a t i o n of small air-cooled blades presents problems because of t h e physical dimensions involved. Although several methods of f a b r i c a t i n g air-cooled turbine blades f o r t u r b o j e t engines have been evolved ( r e f s . 6 t o 9), it i s possible that these methods cannot be scaled and suitably applied t o turboprop turbine blades.
Because of the problems associated with the cooling of turbine blades i n turboprop engines, the NACA L e w i s laboratory has i n i t i a t e d a program f o r investigating cooled turboprop turbine blades. One of the purposes of t h i s report i s t o present the i n i t i a l cooling r e s u l t s ob- tained on the first air-cooled turboprop turbine blade t o be designed, fabricated, and t e s t e d at the Lewis laboratory. Another objective i s t o present a method f o r correlation of the data t o permit i t s use a t other than t e s t conditions.
The blade configuration investigated has a span and chord of 1.4 and 0.7 inch, respectively. The blade was fabricated from two main compo- One an i n t e g r a l l y c a s t base, the a i r f o i l suction surface, and nents: the cooling f i n s ; and the other a formed sheet-metal pressure surface.
The cooling c h a r a c t e r i s t i c s of this blade configuration were determined i n a s t a t i c cascade t e s t f a c i l i t y that accommodated nine blades. Three cooled blades were instrumented with thermocouples and investigated a t combustion-gas temperatures of about 1060°, 1360°, and 1660' R.
The gas Reynolds number ranged from about 70,000 t o 170,000. The blade cooling- air temperatures ranged from 580' t o 1060° R, and t h e cooling-air Reynolds number from about 2400 t o 21,600.
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I SYMBOLS A blade cooling-airflow passage area, sq f t I b effective f i n length, f t I
i C l , c2.. .czo constants
1 1 - \ / n - \ specific neat a t constant pressure, Btu/(ib](-n) C P ~ dh h y h a u i i c ~ a m e t e r (4 x f l o w areaj/(wetted perimeter), f t F constant, function of blade t r a n s i t i o n r a t i o and Euler number fl,f 2...f6 functions I i 3 acceleration due t o gravity, f t/sec heat-transfer coefficient, Btu/(sec) (sq f t ) ( O R ) h i effective inside heat-transfer coefficient, Btu/( sec)
hf
(sq f t ) ( O R ) k thermal conductivity, Btu/(sec) (OR) ( f t ) length of blade or passage, f t L blade w a l l perimeter, f t m exponent, function of blade t r a n s i t i o n r a t i o and Euler number N number of f i n s N u Nusselt number, hdh/k n number of sections of equivalent f i n s P r Prandtl number, gcpp/k Re Reynolds number, pVdh/pg S t Stanton number, Nu/PrRe S f i n spacing, f t ....................... ..........
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temperature, R T velocity, ft/sec
v
W weight-flow rate, lb/sec X distance from blade platform to blade element, ft zL ZT zL
(Reg b)Oo7 ( ? ! b ) 1.25
z T (Rea,i)o*8 Ta,i
x
viscosity, (lb) (sec)/sq ft CI density, lb/cu ft P fin thickness, ft
temperature-difference ratio, (Tg,e - n)/(Tg,e - Ta,i)
cp Subscripts : a cooling air or cooling-air side b blade e effective g combustion gas or combustion-gas side .......... .......................
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Q f u l l y established flow, cooling air APPARATUS Blades The s i z e of the turboprop turbine blades selected f o r investigation (span of about 1.4 i n . and chord of about 0.7 i n . ) i s representative of t h a t of turbine blades used i n the f i r s t - s t a g e turbines of preseht-day turboprop engines with a shaft-power output of about 3000 horsepower.
Smaller turboprop engines (on the order of 1000 hp) would probably have blades of t h i s size i n the second-stage turbine. The a i r f o i l shape of the cooled blade i s t h e same as that employed i n a current uncooled com- mercial turboprop engine.
A i r i s selected as the coolant because considerably more experience has been obtained a t the Lewis laboratory with air-cooled turbojet- engine blades than with liquid-cooled blades.
It i s f e l t t h a t much of t h i s background i n air-cooling (refs.
1 and 2, e . g . ) is a l s o applicable t o the design, fabrication, and operation of air-cooled turboprop blades.
The blade configuration selected f o r investigation was f a b r i c a t e d one includes an i n t e g r a l l y i n two main p a r t s as shown i n f i g u r e l ( a ) : cast base, t h e a i r f o i l suction surface, and the cooling f i n s ; and the other a formed sheet-metal pressure surface. The c a s t part of t h e blade i s made of HS-31, and the formed sheet m e t a l of Its-25. The formed sheet-metal s h e l l was furnace-brazed i n the recesses a t the leading- and trailing-edge regions of the blades t o several of t h e c a s t cooling f i n s (fYg- 2) and t o the base i n the root region of the blade with a cammer- c i a 1 brazing compound. The base w a s then ground t o the shape necessary t o accommodate the blade i n t h e cascade t e s t section.
The completed L l "Lade is o h n m DLrvh*rl in . f i g u r e l ( b ) .
Several cross-sectional views of the blade a i r f o i l are shown i n figure 2 . Ten 0.020-inch-thick cooling f i n s spaced 0.020 inch a p a r t were c a s t i n t e g r a l l y with t h e suction surface. The t h i r d , s i x t h , and ninth f i n s from the leading edge are 0.010 inch longer than the others and are designated primary f i n s ; t h e shorter f i n s a r e hereinafter called secondary f i n s . The purpose of t h e primary f i n s i s t o provide i n t e r - mediate support members t o which the 0.010-inch-thick sheet-metal pressure-surface s h e l l i s brazed. I n the root region (about 0.10 i n .
above base platform, f i g . Z ( c ) > , t h e m a x i m u m thickness of the c a s t w a l l between the base of t h e f i n s and the outer surface of t h e blade i s i n t h e midchord region and i s about 0.070 inch. The thickness of the suction-surface w a l l decreases l i n e a r l y from the value of 0.070 inch a t t h e root section t o 0.015 inch a t the midspan position ( f i g . Z(b)).
A l s o a t the midspan position the suction-surface wall thickness i s essen- t i a l l y constant i n a chordwise direction, decreasing s l i g h t l y i n thick- w a l l i s not tapered ness only near the leading and t r a i l i n g edges. The from the midspan t o the t i p ( f i g s . Z(a) and ( b ) ) .
A l l the f i n s terminate about 1 inch from t h e blade platform, except t h e sixth f i n from the leading edge, which i s a primary f i n (see f i g .
This remaining primary f i n extends t o the t i p of the blade and l ( a ) ) .
a c t s as the only support member (other than the leading and t r a i l i n g edges) f o r the sheet-metal s h e l l i n the t i p region of the blade (see f i g . 2 ( a ) ) . Most of the f i n s are terminated a t t h e 1-inch-span position so that the coolant-flow area a t the t i p w i l l not be reduced excessively.
With t h i s arrangement the free-flow areas of the coolant passages a t the root, midspan, and t i p a r e 0.017, 0.016, and 0 . 0 0 9 square inch, respec- t i v e l y . Eliminating most of the f i n s i n t h e t i p region of the blade re- duces the cooling effectiveness i n t h i s region. I n a c t u a l engine opera- t i o n , however, t h i s region of the blade w i l l not be highly stressed; therefore the lower cooling effectiveness can probably be tolerated.
This cooled-blade configuration i s a v a r i a t i o n of the air-cooled strut-supported blade f o r turbojet engines discussed i n references 7 and 9. The purpose of the secondary f i n s i s t o augment the surface area of the coolant passages. I n t h i s blade configuration t h e secondary f i n s improve removal of heat from the c a s t portion of the blade, which i s the main support member. The clearance between t h e sheet-metal s h e l l on the pressure surface and t h e secondary f i n s keeps the heat flow from the sheet-metal s h e l l t o t h e c a s t portion of t h e blade a t a minimum. This may result i n a r e l a t i v e l y hot pressure surface; but t h i s should be per- missible, since t h e sheet-metal s h e l l i s not the primary load-carrying member of t h e blade.
Test F a c i l i t y air passed successively through In the t e s t f a c i l i t y , combustion a measuring o r i f i c e , a combustion chamber, a plenum chamber, the t e s t .......... .......................
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NACA RM E57DkL. : : .... tltfiSFIPEmTiiY& : ..........
I 7 section, and i n t o the exhaust system. A standard jet-engine combustion chamber was used i n order t o obtain temperatures of the combustion a i r from 1060° t o 1660° R. The i n l e t t o the test section was equipped with a gradually converging duct t o provide a uniform velocity p r o f i l e a t t h e I cascade entrance. The blade cooling air passed through a f i l t e r , a pressure regulator, and a rotameter t o the t e s t blades.
~ The t e s t section ( f i g . 3) consisted of a cascade of nine blades, of which only the middle three blades were instrumented and cooled. The nine blades were inserted i n a holder that provided f o r removal of t h e e n t i r e u n i t from the test section f o r thermocouple r e p a i r if necessary.
The holder had flow passages f o r t h e cooling air and openings through which t h e thermocouple leads from the blades were passed. A l l the j o i n t s between the blades, the holder, and the t e s t section were sealed with ceramic cement t o eliminate or reduce cooling-air leakage i n t o the t e s t section. ~ A top view of the gas passage shows the blades and holder i n place ( f i g . 4 ) . The cascade w a s s o oriented i n the passage as t o pro- vide a zero angle of incidence of the gas r e l a t i v e t o t h e blade midspan section. The deviation from a zero angle of incidence at other than the midspan position of the blades (approx. k t 1 0 ) was assumed t o have a
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negligible e f f e c t on the heat-transfer data (ref. 10).
The t o p w a l l of the gas passage ( f i g . 3) was an adjustable machined p l a t e . The p l a t e was made adjustable i n order t o permit t e s t i n g blades of various lengths and a l s o t o allow variations i n t i p clearance. The t i p clearance f o r the blades i n the present investigation was 0.030 inch, which corresponds t o the clearance of the conventional uncooled blades i n a n engine.
The air plenum chamber (inside diam., 4.7 i n . ) was large enough t o permit i n s e r t i o n or removal of the blades and blade holder from the t e s t section. In order t o reduce t h e heat conduction i n t o t h e cooling-air plenum chamber, a layer of insulating material was cemented t o the under side of the gas-passage bottom w a l l within t h e air chamber. A t the en- trance the cement was f a i r e d i n t o provide a smooth entrance f o r the cooling air ( f i g . 3 ) .
Instrumentation
Blades. - Eighteen thermocouples, six i n each blade, were i n s t a l l e d
i n the t e s t blades a t the locations shown i n figure 2. These locations correspond approximately t o the root, midspan, and t i p . The blades
were instrumented by cementing thermocouples made of 36-gage (0.005-in. -
diam.) Chromel-Alumel w i r e i n shallow (approx. 0.008 i n . deep) grooves i n t h e surface of t h e blade. Reference 11 describes i n more d e t a i l the method of i n s t a l l i n g these s m a l l leads i n thin-walled blades. The out- puts of t h e thermocouples were read from a c a l i b r a t e d potentiometer.
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Cascade. - The instrumentation of the cascade, shown schematically
in figure 3, was such as to provide information for the reduction of the data to dimensionless parameters so that the data can be used at condi- tions other than those of this investigation.
Before the actual heat-transfer investigation, the gas-flow direction and the total-pressure distribution in a plane about 1 / 4 inch ahead of the three test blades were obtained with a probe that measured flow angle and total pressure. Because of space limitation, only one probe was used; it was moved to various transverse positions by use of suitably spaced holes in the top wall of the gas passage. After the survey of the gas passage, this probe was removed from the cascade and not used further. Instead, three fixed total-pressure probes were inserted at the mid-height of the gas passage. Also located at the mid-height (7.6 in. ahead of the blades) was a total-temperature rake having five open- end Chromel-Alumel probes equally spaced across the passage. Seven static-pressure wall taps were located across the gas passage in the bottom wall, 1 inch ahead of the cascade. Four static-pressure taps were also located at the exit of the cascade of blades in the adjustable w a l l of the gas passage.
The instrumentation in the cooling-air plenum chamber (fig. 3) con- sisted of four static taps equally spaced around the chamber wall and two open-end thermocouple probes approximately 0 . 5 inch from the en- trance to the cooled blades. The cooling airflow and the cooling-air leakage flow (obtained by a calibration described in the next section) were measured by rotameters.
EXPERIMENTAL PROCEDURF: Gas-Flow Conditions in Cascade Before determining the heat-transfer characteristics of the cooled blades, it was necessary to calibrate the cascade and to.determine the flow characteristics of the hot gases. This calibration indicated that a single total-pressure probe ahead of each of the test blades would produce total-pressure readings proportional to the average total pres- sure ahead of the blades.
Blade Cooling Characteristics The cooling characteristics of the blades were obtained by measur- ing the temperatures of the blades over a range of cooling airflows, gas flows, gas densities, and gas temperatures. The procedure for testing the blades was to set the gas conditions and then measure the blade tem- peratures, starting with no cooling airflow to the blades and then .......... .......................
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NACA RM E57D1.9. * e * :~**C?ONPIDIP??~ ..........
increasing the cooling airflow i n steps u n t i l the flow i n t h e coolant passages was approximately choked. The gas-flow conditions were then changed and the procedure was repeated. The gas flows per u n i t flow area ahead of the three t e s t blades ranged from 24 t o 53 pounds per sec- ond per square foot. This range of flows corrected t o s t a t i c sea-level conditions varied from 34 t o 36 pounds per second per square f o o t . The r a t i o of cooling-air t o combustion-gas f l o w ranged from 0 t o about 0.03.
The tests were conducted a t three gas-temperature levels: 1 0 6 0 ° , 1360°, i c c n O E.
allu LUUV Leakage calibrations were made a t the start and f i n i s h of a s e r i e s of t e s t runs a t each gas-temperature l e v e l by capping and sealing t h e t e s t blades with gasket material so that no cooling air could t i p s of the flow from t h e blade t i p . The leakage from t h e base j o i n t s was then de- termined f o r the required range of cooling-air pressure differences be- tween t h e blade cooling-air i n l e t and the s t a t i c pressure i n t h e combustion-gas passage ahead of the blades (see f i g . 3).
The leakage a t the start of a s e r i e s of test runs was a m a x i m u m of 8.1 percent of t h e cooling a i r supplied and increased t o a m a x i m u m of 9.6 percent a t t h e conclusion of the s e r i e s of t e s t runs. A curve of t h e mean leakage (leakage a t start of series of t e s t s ylus leakage tit con- clusion of tests divided by 2 ) w a s plotted against the static-pressure differences and used f o r determining the actual coolant flow through t h e test blades f o r each s e r i e s of tests a t a given combustion-gas tempera- ture.
CALCULATION PROCEDURE Correlation of Cooled- Blade Temperatures The data of t h e investigation a r e not presented on an absolute basis, but r a t h e r are correlated with dimensionless parameters t o per- m i t more general use. The a c t u a l blade temperatures are not presented, because the low blade metal temperatures a t which the t e s t s were made (because of the temperature limitations of existing t e s t equipment) a r e not representative of those that e x i s t i n p r a c t i c a l engine operation.
The blade temperature i s correlated by using an approximate equation t o determine t h e spanwise temperature distribution of a blade s h e l l (ref.
1 2 ) . Neglecting the terms r e l a t i n g t o the r o t a t i o n of the blades, the equation i n the notation of the present report i s
- - - -
where X = hgigbfia.
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10 mCQ&DE3TIYIL?~*: **'NACA RM E57D19 ~
- -
The gas-to-blade heat-transfer c o e f f i c i e n t hg i s obtained from t h e correlation equation of reference 13: I a = F ( Z ) m = (Prg,b) 1/3 g,b where F = 0.092 and m = 0.70. The values of F and m, which were obtained from reference 14, are t h e average values of t e n r o t o r blade For a given blade p r o f i l e s including both impulse and reaction blades.
I geometry, equation ( 2 ) can be reduced t o
-
"he blade-to-air heat-transfer c o e f f i c i e n t Ea i s obtained from I
I n correlation equations f o r flow through rectangular tubes ( r e f . 15).
t h e notation of t h i s report, t h e equations f o r turbulent and laminar flow are, respectively,
- -0.4
= - - -0.2 6
- -
(4) S t a ( s a ) Z ' S = 0.02(Rea) -
Ta and For a blade i n which t h e i n t e r n a l coolant configuration can be replaced by equivalent f i n s ( r e f . 16), the equation f o r the e f f e c t i v e blade-to-ai?
heat-transfer c o e f f i c i e n t may be w r i t t e n as follows: This equation, f o r t y p i c a l i n t e r n a l blade configurations (ref. 161, i n - cluding that f o r the t e s t blade herein, can be reduced t o .......
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......
NACA RM E57D19 :: *: : &&;m&.* : :.. 0 . 0 . 11
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Then, f o r a specified blade (fixed geometry), equations (4) t o (7) c m - bine t o give the following equations for turbulent and laminar flow, respectively: and By writing the f l u i d properties of the canbustion gas based on blade temperatures from 8000 t o 22000 R and of the cooling air based on bulk temperatures from 600' t o 1200° R as and and s u b s t i t u t i n g i n equations (3), (a), and (9), the following expres- sions can be obtained: By s u b s t i t u t i n g equations (lo), (ll), and (12) i n t o equation (1)
and assuming that CP,a sC15(?a) - Ooo6 and pa C ~ S ( ? & ) O * ~ f o r the
range of cooling-air temperatures from 600' t o 1200° R, t h e following r e l a t i o n s a r e obtained for turbulent and laminar flow, respectively: ....... : . . c O ~ J p ~ - @ ~ . ' . .... ..........
. 0 . 0 .
...... 0 . 0 .
. 0 .
. . . . . . . . . . . . . . . .
........
. 0 .
. 0 .
. 0 . . 0 . . ......................... 0 . 0 .
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0 . . ........
1 2 where and (13) and (14) a t Since t h e second term i n t h e exponential of equations any given value of Z does not vary appreciably, t h e terms are assumed constant; therefore, f o r any span position, By assuming that t h e air temperature and Reynolds number terms i n t h e parameters ZT and ZL vary as a function of distance along t h e span, t h e equations a r e converted t o t h e form used t o c o r r e l a t e t h e heat-transfer data presented i n t h i s report: where and r 1 Parameters f o r Correlating Blade Temperatures ~
-
I Effective gas temperature. - The effective gas temperature Tg,e
( o r the temperature t h a t an uncooled blade i n the gas stream would at- t a i n ) at the blade root, midspan, and t i p i s the arithmetic average of I I t h e temperature readings indicated by the s i x thermocouples a t each of these locations (fig. 2) with no cooling air flowing.
r: 001 -
-b 1 ad e + PTnrn.n.n yL”c.I Q ~ w “ + . .- = ~ . - -
The teqjei=a$-m=e UT tilt: cooied--oiade
-
metal Tb a t the root, midspan, and t i p i s obtained with the same thermo- %-e couples and i n the game manner as the effective gas t . e q e r a t w e .
i s the arithmetic average of the eighteen thermo- blade temperature l!t, couples on the blades.
Cooling-air i n l e t temperature. - The cooling-air temperature a t the
i n l e t t o t h e blades Ta,i i s the arithmetic average of two thermocouples located a t t h e blade entrance ( f i g . 3 ) .
Cooling-air i n l e t Reynolds number. - The cooling-air i n l e t Reynolds
number Rea,i i s obtained from the equation The v i s c o s i t y term i s evaluated a t t h e measured air i n l e t temperature T a , i
-
Gas Reynolds number. - The gas Reynolds number i s the
Reg,b arithmetic average of the Reynolds numbers a t the i n l e t and e x i t of the cascade.
-
I n l e t gas Reynolds number: The i n l e t gas Reynolds number Reg,b,i i s calculated from the equation
-
= = -
- ‘ g , i b , i dh, (3
Reg,b,i - -
Pg,b,ig =: The average gas i n l e t velocity i s determined by the use of a Vg,i proportionality constant that r e l a t e s the velocity a t the midspan of the blades t o the average of the spanwise velocity d i s t r i b u t i o n . The mid- span velocity measurements a r e obtained by use of the r a t i o of s t a t i c t o total gas pressure and t h e t o t a l gas temperature a t the i n l e t . The gas -kntnl t.Pqera+;lXe is the arith-qetic =...erage zf t h e five t?,eruoco.qle readings across t h e gas passage ( f i g . 3 ) . The t o t a l pressure i s the . . . . . . . .........................
......................... . . . . . . .
. . . . . . .......
...... . ... . : : G C A RM E57D19
. . . . **: : .COiF&<.& : ....................... ..........
arithmetic average of the three f i x e d probes ahead of the t e s t blades.
The s t a t i c pressure i s the arithmetic average of the three s t a t i c taps located i n the f l o o r of t h e gas passage ahead of the t e s t blades. It i s assumed that no static-pressure gradient existed along the height of the gas passage so that the s t a t i c preszure a t the wall i s the average of the passage. The average velocity V g , i i s then calculated from where the constant of proportionality C20 i s 0.96.
The density term of equation (20) is sglved by use of the average s t a t i c pressure and t h e blade temperature Tb. The v i s c o s i t y pg,b,i i s evaluated a t the same blade temperature.
Outlet gas Reynolds number: The o u t l e t gas Reynolds number
- -
i s obtained with the same terms as equation (201, except that Reg,b,o t h e values of the terms are obtained a t the e x i t of the blades.
With the assumption that t h e heat and f r i c t i o n - losses across the
vg,o i s calculated
blade a r e negligible, the average e x i t velocity with the use of the i n l e t values of the t o t a l gas temperature and pres- sure and the e x i t value of gas s t a t i c pressure. The s t a t i c gas pressure used is the arithmetic average of f o u r s t a t i c taps located i n the top of t h e gas passage and a t the cascade e x i t i n the center of gas passages between the t e s t blades.
The density of t h e gas at the o u t l e t ?g,b,o i s calculated from
-
t h e average e x i t s t a t i c pressure and the blade temperature Tb.
RESULTS AND DISCUSSION Gas-Flow Conditions i n Cascade Test Section A s discussed previously i n the EXPERIMENTAL P R O U R E , the combustion-gas flow conditions i n the t e s t section of the cascade were determined before t e s t data were taken. The r e s u l t s of pressure and temperature surveys i n the gas-flow passage upstream of the t e s t blades indicate that t h e velocity ahead of the three t e s t blades was essen- t i a l l y constant i n both v e r t i c a l and horizontal directions f o r the en- t i r e r a g e of combustion-gas flows. The maximum boundary-layer thick- ness a t the top and bottom of t h e cascade was l e s s than 0.1 and 0.2 inch, respectively. The maximum angular deviation of the flow from a plane p a r a l l e l t o the cascade walls was & 3 ' . These varying flow condi- tions do not s i g n i f i c a n t l y influence t h e cooling c h a r a c t e r i s t i c s of the .......... . . .... . . . e o ~ ~ r ~ . : .......
. . . . .
. . . .
. . . . . . . . . . . . . . . . ......
.
. . . . . . . . . . ........
......................... . . . . . . .
I blades ( r e f . 10). The survey data a l s o show that t h e proportionality constant used i n equation (21) and discussed i n the CALCULATION Czo PROCEDURE i s 0.96 (33 percent). This value of C20 r e l a t e s t h e value I of velocity a t the midspan of the blades t o the average velocity i m e d i - a t e l y upstream of the blades.
In t h e CAI.CULATION PRocElxlRE two correlation equations (eqs. ( 1 7 ) and (18) ) were derived f o r application when the cooling-air Reynolds number a t the i n l e t t o t h e cooled turbine blades i s e i t h e r i n turbulent o r laminar flow. For the range of coolant flows investigated herein, the coolant-flow Reynolds number at t h e blade i n l e t ranged from about 2400 t o about 21,600. Since these values of Reynolds number indicate that t h e flow i s e i t h e r i n the transition o r turbulent flow range, the correlation of the data i s attempted by use of the correlation param- e t e r f o r turbulent flow; that is,
Blade temperature a t a p a r t i c u l a r span location. - The experimental
heat-transfer data (a tabulation of typical conditions i s shown i n t a b l e I) were correlated by p l o t t i n g the temperature parameter against the parameter f o r t h e blade root, midspan, and t i p locations as shown zT 5. The data c o r r e l a t e well about mean l i n e s through the data.
i n figure The value of the temperature parameter (P a t the root, midspan, and t i p correlates within about 5, 6, and 1 2 percent, respectively. This devia- t i o n of t h e (p data from the mean l i n e corresponds t o a maximum devia- t i o n i n blade temperatures of about 1S0 R.
Average blade temperature. - Since the data f o r a p a r t i c u l a r span
location correlated well, the average - blade temperature data should
a l s o correlate, because the spanwise CP d i s t r i b u t i o n s a r e approximately l i n e a r . The correlation of the average blade temperatures i s therefore
-
attempted - by p l o t t i n g the parameter 'P, defined as
% ) / F g , e - T a , i ) , - against the parameter ZT ( f i g . 6 ) . The use
(Fg, e -
of the average parameters CP and ZT correlates a l l the data about a mean l i n e within approximately 7 percent.
Local b d d e temperature. - The parameter ZT includes terms t h a t
a r e generally r e l a t e d t o blade metal temperature. Therefore, correla- t i o n of the l o c a l blade temperature w a s attempted by p l o t t i n g a t constant values of ZT the parameter 'F, defined as (Tg,e - Tb)/(Tg e - Ta,i), > against peripheral locations around the blade. The p l o t s were made a t approximate value of the parameter ZT f o r which a t least three data points were available. A t y p i c a l v a r i a t i o n of the l o c a l correlated blade temperatures i s shown i n f i g u r e 7 f o r a value of zT equal t o approximately 6.9; the reason f o r s e l e c t i n g t h i s p a r t i c u l a r value f o r presentation of the l o c a l correlation data i s discussed i n the next section. The values of the terms i n the c o r r e l a t i n g parameter f o r each of t e s t conditions considered a r e tabulated i n the figure. The maximum deviation of the data from the curve i n f i g u r e 7 i s a b o u t & 7 percent.
This represents a deviation i n blade m e t a l temperature of about A S o R a t t h e blade t i p and about A-5' R a t t h e blade base. Because of f a i l u r e of several of the thermocouples on the pressure surface i n the root re- gion of the blade, the variation of CP a t the root i s estimated t o be similar t o t h a t observed a t the midspan and t i p of the blade.
Local correlation curves similar t o those shown i n f i g u r e 7 were obtained f o r the e n t i r e range of values of ZT, but they a r e not pre- sented herein. I n most instances the maximum v a r i a t i o n of individual data points from a curve representing an approximate average of all the data w a s of the same order as that shown on f i g u r e 7; that is, &7 percent.
Application of Correlated Data t o Typical Ehgine
Correlated average blade metal temperatures. - Since the heat-
transfer c h a r a c t e r i s t i c s of the blades c o r r e l a t e s a t i s f a c t o r i l y , the data were used t o determine the cooled-blade temperatures a t conditions other than those of the cascade t e s t s . The conditions selected for an example a r e those of a t y p i c a l turboprop engine operating (1) a t zero f l i g h t speed a t sea l e v e l and ( 2 ) a t a speed of 300 knots a t an a l t i - tude of 30,000 f e e t . A turbine-inlet gas temperature of 2460' R i s assumed f o r both engine operating conditions. Table I1 lists some of the other engine conditions that a r e required i n making the calcula- tions. The gas-flow conditions r e l a t i v e t o t h e first-stage-turbine rotor blades a r e determined from the assumed engine conditions. The cooling-air temperature at the blade entrance i s obtained by assuming t h a t t h e a i r i s bled from the last stage of the compressor and t h a t a 1 0 0 ' R r i s e i n the air temperature r e s u l t s as the air i s ducted from the compressor t o the entrance of t h e turbine r o t o r blades. With the gas and cooling-air conditions r e l a t i v e t o the blade known, t h e corre- l a t i n g parameter i s calculated f o r a range of r a t i o s of blade ZT cooling-air t o combustion-gas flow wa/wg and average blade tempera-
-
tures 6. (Hereinafter the cooling-airf low t o combustion-gas-flow
r a t i o i s referred t o as the coolant-flow r a t i o . ) .........................
* . 0 .
0 . . 0 . . 0 . .
..........
....... . 0 .
0 .
0 .
..........
: 1 7 b@'&&lTG .:. : NACA RM E5&9: ............ : 0 : : A p l o t of t h e correlating parameter against coolant-flow r a t i o i s then made f o r the two engine conditions considered, as shown on the r i g h t side of f i g u r e 8. O n the l e f t side of f i g u r e 8 i s p l o t t e d the l i n e representing the correlated data of figure 6. I n applying the same
r e l a t i o n of and ZT from the cascade - data t o an engine as i n f i g u r e
8, t h e e f f e c t s of rotation on the (p and ZT r e l a t i o n are neglected.
Calculations indicate that consideration of r o t a t i o n would cause changes i n the curve shown i n figure 8 that would be within t h e spread of the data points of figure 6 from which the curve was o r i g i n a l l y drawn.
Eiie r e q i i r e d coolant-flow ratio f o r a desired average blade temper- A specific example i s indi- a t u r e can be determined by use of figure 8.
cated i n t h e f i g u r e by the dashed l i n e s . A desired average blade tem- R is selected f o r a f l i g h t condition of 30,000 f e e t perature of 1985'
and 300 knots. The r e s u l t i n g value of 7 i s 0.278, and the associated
value of Z T is 6.9. For an ordinate value of 6.9 and the selected en- gine operating conditions, the coolant-flow r a t i o is 0 . 0 1 5 .
The required coolant-flow r a t i o f o r other average blade metal tem- peratures and engine operating conditions can be determined by the method j u s t described. Curves such as those shown i n figure 9 a r e obtained by using f i g u r e 8 and assuming a s e r i e s of different average blade metal temperatures f o r the two engine conditions considered herein. Figure 9 shows that, f o r the range of average blade metal temperatures con- sidered, the coolant-flow requirements are about the same f o r sea-level s t a t i c and a l t i t u d e f l i g h t operation. For average blade temperatures above about 1825' R, the a l t i t u d e f l i g h t condition requires s l i g h t l y more cooling air than the sea-level s t a t i c operation. For blade metal temperatures below 1825' R, the r e l a t i o n between the coolant require- ments of t h e sea-level and a l t i t u d e conditions reverses. Figure 9 shows that, if average blade metal temperatures below about 1800' R were neces- sary, the coolant-flow requirements would increase rapidly r e l a t i v e t o the amount of metal temperature reduction achieved. This would lead t o excessive engine performance losses due t o cooling requirements (refs.
1 and 3). It should be noted t h a t the cooling-requirement trends shown i n figure 9 a r e not necessarily t y p i c a l of a l l cooled-blade configura- t i o n s nor of a l l cooled turboprop engines; the r e l a t i o n s between the curves can change with blade cooling c h a r a c t e r i s t i c s and engine per- formance characteristics.
Correlated l o c a l blade metal temperatures. - Since the l o c a l values
of the temperature-difference r a t i o CP around the periphery and along the span of the blade a r e a l s o correlated by the parameter ZT, the blade temperature d i s t r i b u t i o n at other than t e s t conditions can be de- + , . - : - , . a nrhm nrr*ai+i,.n- ..--a - - - . - < - . . - l . . --- +L^ --*---- a.1-a- &----- IIGIIILLIICU. LUG LWUU IIAVIIU uocu PA c v r w u a ~ ~ I VI uic a v c i a e j c u I a u c t,cupc~- a t u r e correlations a r e employed t o i l l u s t r a t e t h e use of the correlated local temperature data. For the required value of coolant-flow ratio of 0.015 and the assumed flight conditions used in the example of figure 8, the value of ZT is 6 . 9 . The local values of cp are plotted for this value of ZT in figure 7 . With the peripheral distribution of cp in figure 7 and the values of Tg,e and Ta,i for the assumed flight con- ditions, the local blade metal temperature distributions shown in figure 10 are obtained. A constant spanwise distribution of Tg,e is assumed for this example. The resulting blade temperature distribution for the small blade investigated herein is approximately the same as that for larger turbojet-engine blades, such as those discussed in references 17 and 18, the temperature difference between the leading edge and the mid- chord region being about 2 5 0 ' R.
A method of evaluating the cooling effectiveness of turbojet blades (ref. 16) makes use of a factor called the stress-ratio factor, which is defined as the ratio of the allowable stress-rupture strength for the blade material and for a desired blade life to the calculated average centrifugal stress at the critical span region of the blade. The criti- cal region is defined as the spanwise location in the blade airfoil at which a curve of the allowable spanwise blade temperature distribution is tangent to a curve of the measured or calculated spanwise blade tem- perature distribution. The critical location for the small turbine rotor blade for the assumed altitude flight conditions and a coolant-flow ratio of 0.015 is approximately at the midspan of the blade. The calcu- 6750 psi. The average blade lated centrifugal stress at this location is metal temperature at this location is 2010° R. Assuming that a blade life of 1000 hours is desired and that the blade is made of a high- temperature alloy such as HS-31, the calculated stress-ratio factor for the blade is found to be about 3. This value of the stress-ratio factor appears adequate compared with results of experimental investigations of the durability of air-cooled turbojet-engine blades made of high- temperature alloy.
References 9 and 19 indicate that values of stress-ratio factor be- The blades in these references tween about 1.2 to 1 . 5 may be adequate.
were either investigated uncooled or with small quantities of cooling air, with the result that the peripheral temperature gradients and the resulting thermal stresses were small. The stress-ratio factors ob- tained are nevertheless indicative of the margin of safety required for cooled-blade configurations under engine test conditions. Since the stress-ratio factors presented in these references were based on average blade temperatures at a particular span location, local values of the stress-ratio factors at the hot leading and trailing edges would be less, assuming that the centrifugal-stress distribution across the blade chord is constant. For the small blade of this report, even with the high metal temperature at the leading edge, the stress-ratio factor based on t h e temperature of the leading edge at the c r i t i c a l midchord location i s about 1.63. This value is a more conservative l o c a l value I than those of the turbojet blades of references 9 and 19. Based on the r e l a t i v e l y conservative s t r e s s - r a t i o factors, a reasonably s a t i s f a c t o r y I blade l i f e may be predicted f o r the air-cooled turbine blade configura- t i o n investigated herein.
S W I Y O F RESULTS I The r e s u l t s of a s t a t i c cascade investigation t o determine t h e cooling effectiveness of a s m a i i air-cooled tiir"vliie %lade ir,ter,ded for use i n a turboprop engine a r e as follows: 1. A nondimensional method of correlating the experimental heat- t r a n s f e r data of t h e blades was developed that correlated the blade tem- peratures with the gas and cooling-air conditions of the t e s t s .
The correlated data were within about 7 percent of a mean l i n e drawn through
t h e data. The correlation method i s applicable t o average blade temper- I
atures a t p a r t i c u l a r span locations, local metal temperatures, and the average m e t a l temperatures of the e n t i r e blade.
2. Application of the correlated data t o a t y p i c a l turboprop engine operating a t a turbine-inlet tezpemt'zre ~ f ' 2460' E e i t h e r a t sez-level s t a t i c conditions or a t 30,000 f e e t a l t i t u d e and 300 knots revealed that appreciable cooling of the blades can be expected with small coolant- flow r a t i o s . The average blade temperature at the a l t i t u d e f l i g h t condi- t i o n f o r a coolant-flow r a t i o of 0.015 was 1 9 8 5 ' R.
3. A t the a l t i t u d e f l i g h t conditions the blade peripheral tempera- t u r e d i s t r i b u t i o n f o r the smaii blade was aFproxhately the sane as t h a t obtained experimentally i n the past f o r much l a r g e r turbojet-engine blades. The temperature difference between the leading edge and the midchord region of the blade was about 250' R.
4. The calculated s t r e s s - r a t i o factor f o r a 2460' R turbine-inlet I This value temperature and a coolant-flow r a t i o of 0.015 w a s about 3.
of s t r e s s - r a t i o f a c t o r appears adequate when conpared with required I values of about 1.2 t o 1.5 determined from t e s t s of l a r g e r air-cooled turbine blades intended f o r use i n turbojet engines.
Lewis F l i g h t Propulsion Laboratory National Advisory Committee for Aeronautics Cleveland, Ohio, April 22, 1957 REFERFLNCES 1. Esgar, Jack B . , and Ziemer, Robert R . : Review of Status, Methods, and Potentials of Gas-Turbine Air-Cooling. NACA RM E54123, 1955.
2 . Esgar, J . B . , Livingood, J. N. G . , and Hickel, R. 0 . : Research on Application of Cooling to Gas Turbines. Paper No. 56-SA-54, ASME, 1956.
3 . Esgar, Jack B . , and Ziemer, Robert R . : Effect of Turbine Cooling with NACA RM Compressor Air Bleed on Gas-Turbine Engine Performance.
E54L20, 1955.
4 . Esgar, Jack B . , and Slone, Henry 0 . : Gas-Turbine-Engine Performance When Heat from Liquid-Cooled Turbines Is Rejected Ahead of, Within, or Behind Main Compressor. NACA RM E56B09, 1956.
5 . Esgar, Jack B . , Schum, Eugene F . , and Curren, Arthur N . : Effect of Chord Size on Weight and Cooling Characteristics of Air-Cooled Turbine Blades. NACA TN 3923, 1957.
6. Long, Roger A., and Esgar, Jack B . : Experimental Investigation of
Air-Cooled Turbine Blades in Turbojet Engines. VI1 - Rotor-Blade
Fabrication Procedures. NACA RM E5U23, 1951.
7 . Schum, Eugene F . , and Stepka, Francis S . : Analytical and Experi- mental Investigation of a Forced-Convection Air-Cooled Internal RM E53L22aJ 1954.
Strut-Supported Turbine Blade. NACA 8. Freche, John C . , and Oldrieve, Robert E . : Fabrication Techniques and Heat-Transfer Results for Cast-Cored Air-Cooled Turbine Blades.
NACA RM E56C06, 1956.
9. Schum, Eugene F . , Stepka, Francis S . , and Oldrieve, Robert E . : Fabrication and Endurance of Air-Cooled Strut-Supported Turbine NACA RM E56A12, 1956.
Blades with Struts Cast of X-40 Alloy.
10. Ainley, D. G . , Waldren, N. E . , and Hughes, K . : Investigations on
an Experimental Air-Cooled Turbine. I1 - Cooling Characteristics
of Blades Having a Multiplicity of Small Diameter Coolant Passages.
Rep. No. R.154, British NGTE, Mar. 1954.
1 1 . Stepka, Francis S., and Hickel, Robert 0 . : Methods for Measuring Temperatures of Thin-Walled Gas-Turbine Blades. NACA RM E56G17, 1956.
12. Livingood, John N . B . , and Brown, W . Byron: Analysis of Spanwise Three Types of Air-Cooled Turbine Temperature Distribution in Blades. NACA Rep. 994, 1950. (Supersedes NACA RM's E7Blle and E7G30.)
13.,Brown, W . Byron, and Donoughe, Patrick L . : Extension of Boundary- Layer Heat-Transfer Theory to Cooled Turbine Blades.
NACA RM E50F02, 1950 .
14. Donoughe, Patrick L . : Outside Heat Transfer of Bodies in Flow - A
Comparison of Theory and Experiment. M.S. Thesis, Case Inst.
Tech., 1951.
15. Kays, W . M., and Clark, 'S. H . : A Summary of Basic Heat Transfer and Flow Friction Design Data for Plain Plate-Fin Heat Exchanger Sur- faces. Tech. Rep. No. 17, Dept. Mech. Eng., Stanford Univ., Aug.
15, 1953. (Contract N6-ONR-251, Task Order 6 (NR-090-104) for Office Naval Res. ) 16. Ziemer, Robert R . , and Slone, Henry 0 . : Analytical Procedures for Rapid Selection of Coolant Passage Configurations for Air-Cooled Turbine Rotor Blades and for Evaluation of Heat-Transfer, Strength, and Pressure-Loss Characteristics. NACA RM E52G18, 1952.
17. Bartoo, Edward R . , and Clure, John L . : Experimental Investigation
of Air-Cooled Turbine Blades in Turbojet Engine. XI1 - Cooling
Effectiveness of a Blade with an Insert and with Fins Made of a Continuous Corrugated Sheet. NACA RM E5ZF24, 1952.
1 8 . Stepka, Francis S . , Bear, H . Robert, and Clure, John L . : Experi- mental Investigation of Air-Cooled Turbine Blades in Turbojet
Engine. XIV - Endurance Evaluation of Shell-Supported Turbine
NACA RM E54F23a, 1954.
Rotor Blades Made of Timken 17-22A(S) Steel.
Cooling Performance and 19. Freche, John C . , and Schum, Eugene F . : Structural Reliability of a Modified Corrugated-Insert Air-Cooled NACA RM Turbine Blade with an Integrally Cast Shell and Base.
E56K09, 1957.
.......... .......................
0 . 0 . . . .... . 0 . 0 .
0 .
.
. . . . . . . . . . . . . . . . ......
........
0 . 0 .
. 0 . . e . .
.......... 0 . 0 : . r n ~ r n T r n . . *
TABU I. - TYPICAL C A S C A D E OPERATING CONDITIONS
- -
4 =
T a , i 9 1 , T b ~ OR , 1 Re,, i X I O - Reg,bX10-5
Tg,e, OR OR Root Midspan Tip 1311 639 875 954 1033 1.68 0.99 1311 700 948 1041 1112 1.07 .88 1311 802 1060 1160 1219 .24 .75
1619 668 999 1126 1242 1.61 - 88
1619 754 1099 1225 1339 .96 .86 1619 953 1296 1441 1522 .39 .66
T A B U 11. - ASSWD ENGINE AND FLIGHT CONDITIONS
[Combustor pressure r a t i o , 0.95; turbine- i n l e t temperature, 24600 R ; turbine efficiency, 0.85; exhaust-nozzle pressure r a t i o , 0.92.1 Altitude, f t ISea l e r l 30,003
Flight speed, knots 1 300
10.88 Compressor pressure r a t i o 9.4 13.4 Compressor airflow, lb/sec 32.5 0.77 0.84 Compressor efficiency ~ 2331 Av. e f f e c t i v e gas temp., OR 2335 Blade cooling-air i n l e t I
i 1083 117 3
temp., OR ••• •• • ••• • ••• ••• •
••• •• • .. ••
• • • • • .
• · • ...
• • •
· •• • • •
· • • •
· ••• •• •
•• t • •• • • • • • • • • . ..
NACA EM E57~1 g: • ••• : e~VF.I.n1!N'l'IA!' .:. • •••• ... ....
..
·
·
Sheet-metal shell Integrally cast ba se, (pressure surface) su c tion surface, and coolin g fins (a) Bla de before a ssembly .
Base machined for installa- tion in cascade blade holder (b) Assembled blade. 44 C- 787 Figure 1. - Blad e components before and afte r a ssembly.
.... ...
• ••• •• • •••• • • •• • ••• • • • • ••• •• • •••• • ••••• • • • • ••• •••••• • •••••• • • •••
· • •• • •• ••• • ••• •
• • ...
••• •••• · VO~!D~IAL ·· • •• • ••• • ......................... . . . . . . .
0 . 0 . 0 . . . . . ........
0 . 0.. 0 0 . 0
. 0 . .. : :NACA ,RM E57D19
a . .......... a . .... . : C4&IB%W ... i .......
(b) Midspan.
Primary fins, ,- Casting
Thermocouples Secondary f i n Formed sheet W ( c ) Root.
......................... .
0 . 0 .
. 0 . . 0 . .
0 .
.......... ....... . 0 .
0 . 0 .
NACA RM E57i19: ............ : ': : : b&&K&.:.: ..........
Gas-fl L Gas inlet total- temperature rake Fixed top wall A d justable inner wall Gas inlet total-press it static-pressure taps Insulating cement Gas inlet static-pressure taps Cooling-air plenum chamber Cooling-air inlet Cooling-air inlet static taps 1 thermocouples / - Figure 3. - Cascade test section with instrumentation.
.......... .......................
0 . 0 . 0 . . e .... . 0 . 0 . .
. . . . . . . . . . . . . . . . ......
.
0 . 0 . 0 . . ........
0. 0 . e ............. ..
...
. ... ...
. ...
. ..
• • • .
. • ••
. • •
• • • • 0 0 • • • 0 •
· •
••• • • • • • • • • • • • • .
• • • RM E57D19 .. . . .. .
26 : NftCA . .. .
~PN}~~~ · ... •
• •• •• • • • ' 0 • C-44788 --- Figure 4 . - Top view of cascade test section • . .. . ...
. .. . ..
•• . ... . ..
• • • • •• • • • • • • •• • • • • • •
· • •
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2 100 Engine conditions - 30,000 f t , 300 knots
f - Sea-level s t a t i c
.01 .02 .03 .04 .OS Coolant-flow r a t i o , wJwg
Figure 9. - Variation of calculated average blade temperature
at turbine-inlet gas temperature of 2460' R with coolant- flow r a t i o .
Figure 10. - Blade temperature d i s t r i b u t i o n at t u r b i n e - i n l e t gas tempera- ture of 2460' R, airspeed of 300 knots, a l t i t u d e of 30,000 f e e t , and coolant-flow ratio of 0.015.
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N A C A - Langley Field, Va.
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