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Heat transfer characteristics of a return-flow steam-cooled gas turbine blade
Heat Transfer Characteristics of a Return-Flow Steam-Cooled Gas Turbine Blade M. Obata J. Yamaga Heat and Fluid Department, Research Institute, lshikawajima-Harima Heavy Industries Co., Ltd., Tokyo, Japan
H. Taniguchi Mechanical Engineering Department, Faculty of Engineering, Hokkaido University, Sapporo, Japan
liThe cooling characteristics of a return-flow type of steam-cooled gas turbine blade are investigated theoretically and experimentally. The modeled blade is intended for use in a closed-circuit gaseous coolant system. An arialyrical method for calculating the cooling performance of the blade, based on one-dimensional fluid flow and one-dimensional heat transfer, is proposed. Temperatures of the blade metal, incoming coolant, and outgoing coolant at various spanwise positions of the blade are given by nondimensional expressions and for various blade configurations and operating conditions. To verify the analysis, cascade tests are undertaken to obtain the heat transfer characteristics of a return-flow type of steam-cooled blade of similar design, using steam and air as a coolant. Metal temperature data are obtained for various gas-side Reynolds numbers, coolant/gas flow ratios, gas inlet temperatures, and coolant inlet temperatures. The validity of the analysis is examined in terms of the mean blade metal temperature at midspan and the coolant temperature at the outlet of the outgoing passage by applying a formula that has been confirmed experimentally for gas-side heat transfer coefficients. It is shown that the cooling performance can be predicted with good accuracy. Finally, the cooling characteristics of steam are clarified in comparison with air, using the experimental values normalized to the same set of gas turbine cycle operating conditions.
Keywords:forced convection, turbines, blade cooling INTRODUCTION Modern gas turbines are characterized by their extremely high power concentration and high thermal efficiency. It is well known that one of the main contributing factors of this achievement is the high gas turbine inlet temperature used to attain a high thermal efficiency of the thermodynamic cycle. In modern aerospace engines, especially, high gas turbine inlet temperatures have been attained by employing advanced blade materials and air-cooled blades. For the electric power generation, on the other hand, many projects are under way to develop more powerful power units of higher thermal efficiencies for the duty of base load supply. One of these projects is aimed at the development of a combined cycle power plant, comprising steam-cooled high-temperature gas turbines and steam turbines. These power plants will be able to achieve more than 50% thermal efficiency, whereas that of current steam cycle power plant is about 40%, which is almost their practical limit [1]. One important step toward the realization of such a highefficiency combined cycle power plant is to develop new closed-circuit steam-cooled blades having a high performance suitable for the cycles envisaged and to achieve a higher turbine inlet temperature in the gas turbine cycle. As steamcooled gas turbines call for design fundamentals much different from those available for air-cooling, such design funda-
mentals as cooling method, cooling characteristics, and cooling system have to be established anew. Even though the characteristics of steam-cooling have been clarified in theoretical comparisons with air- and water-cooling [2], the methodology of predicting cooling performance required for the basic design of a steam-cooled blade has not been as well developed as that for air-cooled blades [3]. Besides, at present, very few experimental data are available. In this paper, we describe the fLrst step we have achieved in establishing a design methodology of high-temperature steamcooled gas turbine blades. The primary objective is to present an analytical method for calculating the cooling performance of a closed return-flow gas turbine blade that is internally steam-cooled in a relatively simple manner, and to show experimental results of steam- and air-cooling cascade tests carried out to obtain the heat transfer characteristics of a similarly designed model blade. Then, after having confmned the validity of the analysis, the basic heat transfer characteristics of steam-cooling in comparison with air-cooling are clarified for a reasonably selected gas turbine cycle operating condition [1 ]. The analytical method and experimental results described in this paper are applicable to closed return-flow gas turbine blades that have a number of incoming and outgoing cooling passages of uniform cross section laid spanwise from root to tip. This type of blade, when utilized in a closed-circuit coolant system, would be able not only to use gaseous coolant
Address correspondence to Dr. M. Obata, Heat and Fluid Department, Research Institute, Ishikawajima-Harima Heavy Industries Co., Ltd., 1-15, Toyosu 3-Chome, Koto-Ku, Tokyo 135, Japan.
Experimental Thermaland Fluid Science 1989; 2:323-332 © 1989 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/89/$3.50
323
324 M. Obata et al.
Tm
\\\\\\\\\\\\\~k
Main
\ \ \ \ \ \ \ '-,,'~ ,,, -., \
Tip
gas
T
flow
m+ -d~T-m- 6t
6g
Tg
-
Wg
To, b -
L '
l
1,I
(Out-going)
_
~
'
,
T~.0ut
T.,
"Tc, f (In-coming)
['
Root
I ~
, Coolant
"L,,.
flow
w~
Figure 1. Analytical model for cooling blade. such as air or steam, which has relatively favorable heat transfer characteristics, but also to improve the thermodynamic cycle performance. ANALYSIS Cooling Performance Analysis Figure 1 presents the analytical model for calculating the performance of gas turbine cooling blades. It is a closed returnflow type of cooling blade with a number of incoming and outgoing cooling passages of constant cross section extending from root to tip. The steam as a coolant is introduced at the root, cools the blade internally by forced convection, and is recovered at the root as superheated steam. Therefore, it is assumed that each of the incoming and outgoing passages can be equivalently replaced with a hole of the same hydraulic diameter. The analysis is based on one-dimensional turbulent fluid flow and one-dimensional heat transfer. Now consider a stationary blade that is cooled with superheated steam near saturation. For a blade element 81 at a spanwise distance 1 from the root, the following basic equations are obtained from thermal equilibrium in the blade cross section and from the enthalpy increase of cooling steam between the incoming and outgoing passages, ignoring the radiation heat transfer from the main gas flow to the blade surface. d2 Tra )~rnArn~ + otzSg(Tg - Tin)+ Ogc,fSc,f(Tc,f- Tin) + Otc,bSc,b( Tc, b-- Tin)=0
(1)
dT~,: wcCpc,.:~ + etc,fSc,f(Tc,f- Tin)= 0
(2)
w~Cp¢,o -dTc - ' ~ -b+ Olc,bSc,b( 17,m -- To, b) =
(3)
0
where the boundary conditions for the cooling steam are I=0:
Tc./= To, in,
I=L:
Tc.b = Tc,/
(4)
Here, we assume that the spanwise heat conduction along the blade is negligibly small compared to heat conduction due to forced convection. This is justified in the present work, for the blades envisaged are of an ordinary aspect ratio and are made of ordinary heat-resistant materials [3]. Thus, the first term of Eq. (1) can be ignored. It is assumed further that the distribution of the main gas flow inlet temperature is uniform. Then, we transform Eqs. (1)-(4) by defining necessary functions as in Eqs. (5)-(7): Tm(l
x=O:
+Xf+Xb)-XfTc,
f - X b T c , b=O
(Za)
dyeKf -~Xd"["Xf( T c,f - T~,) = 0
(2a)
Kb ~+XefT:.-
(3a)
T 'c,f-- T= c' , in ~
x=l:
Tc,e)= 0 T 'c,b = T ' c,f
(4a)
where
r;.=r~-T~,
TL:= r g - To,:, T;,i. = Tg- Tc,~.
x:= e~,:&,:/%sv
Xo = ac, o Sc, j % S~
K/= wcCpc,f/%SgL,
Kb = wcCpc, b / • S g L x =t/L
(5) (6)
(7)
Assuming X and K for cooling passages to be constant, such that X = X and K = /~, on the basis of an observation that they do not change much as x changes, and solving the simultaneous ordinary differential equations for T~,, T ' : , and
A Return-Flow Steam-Cooled Gas Turbine Blade 325 Tc',b, we obtain as the general solution
(9)
assumed that the following formula describes adequately the heat transfer from the main gas flow to the blade surface, occurring at a suitably given gas turbine operating temperature:
(10)
Nu,= 3, Re~ Pr~
T~, = hm(Gkt + l)etl x + h2(Gk2 + l)e t2x
(g)
T~d= h~e klx + h2ek2x T c,o=h~(BGkl + E)ek~X + h2(BGk2 + E ) e ~2~
where h~ and h2 are integration constants and k~ and k2 are the roots of the characteristic equation of the differential equation for Tc.f. That is, k~ = [ - a2 + (a~ - 4a~ a3) I / 2 ] / 2 a l
(11)
Ice= [ -- a~-- (a2~- 4ai a~) In]/2at
Hence, the coefficients a~, a2, and a~ are given by a2=E-(B-
a~=BG,
I)G/R,
&
a3=(1-E)/R
E= l-l-rEb ,
~l(f
&
where the constants % m, and n are to be determined experimentally or theoretically. It is also assumed that the turbulent heat transfer formula for the inside of a hole of constant cross section [3] is applicable to the present cooling passages for the range of operating temperatures concerned. Namely, Nuc=O'O34(L/Dc)-°'l(Tc/Tm)°'55 Re°'S Pr°'4c
(12)
where
B =l+''~f+'f~b ,
(19)
R_K__b
(13)
It is assumed further that for the operating range concerned the fluid property ratios between cooling steam and main gas flow may be presented approximately as a function of temperature ratio. Namely, CPc-icp(Tc~J*P
~--~--i (Tc~'~'
\ r,/
The constants hi and h2 in Eqs. (9) and (10) are obtained from the boundary conditions (4a) as N2T;.m N2- N I '
he
=
NI Tc,in Ni-N2 -
-
(14)
(20)
(21) Now, according to the definition, the relation of Reynolds number and Prandtl number between the cooling steam and main gas flow in the operating temperature range is given by
where Nl = (BGkl + E - 1)ekl,
N 2 = ( B G k 2 + E - l)e k2 (15)
(cos B2) ~c R%
c
(22)
Relative Temperatures The blade metal relative temperature, or the blade cooling efficiency ~lm,may be given by substituting Eq. (14) into Eq. (8) as (T,- Tin) = T~ ~" = (Tg - Tc, in) T c,'In , =N2 ~Gkl + 1 e~lX+N, ~Gk 2 + 1 e k-x z
(16)
whereas the steam relative temperature of the incoming cooling passage ~,o' is calculated from Eq. (9) as
r s_ r:s rLn N2 - N 2 _ N | e klx + NI--N_--IN2e k2x
Prc=~pg \ ~ - 8 8 ] \ ~ / Pr,
(23)
Then it can be shown that the calculation formula of Xf for the incoming passage is derived from Eqs. (19)-(23) by taking an average Nu~ for L / D c = 25 and L / D , = 100. That is, J~f=0.O174{ [ L ( ~ ) c o s , 2 ] ° ' s ( ~ ) X Zf~0.s R 0 . S - m
-°''
( T c d ' ~ J ( T c d ' ~ °'5s
\ r, /
e,
(u)
where i, j, and Z:, the cooling passage shape factor [3], are given by (1"/) i=i°'p4i°'6/i °'4,
j=O.4jcp+O.tjx-O.4j~,
(25)
and that of the outgoing cooling passage ~c,b from Eq. (10) as ZI
Tg -- Tc.b-- T'c,b
= r,- :r,in-r:,,n _ ,,r BGkt + E
-1.2 ~
B G k 2 + E ek2X eklX+Ni N I - N 2
(&Jc)L2
= A
(18)
Thus, ~m, ~,d, and ~/,,b can be calculated once X" a n d / ( are determined for the incoming and outgoing cooling passages.
+/d
(26)
With regard to/(f for the incoming passage, the calculation formula is obtained by rearranging Eqs. (19) and (20) and converting wc into the gas-side variables:
.,xfA~" _ lcp~
~ (COS •2)
Rel-m prlg-n k Tg /
Calculation of X and 1~ Functions
The .,~'/,R:, Xb, and/~b for incoming and outgoing cooling passages are calculated as defined in Eq. (6). Here, it is
The formulas for -'X'b,/~'b,and Zb for the outgoing passage are obtained simply by changing the subscriptsin Eqs. (24), (27), and (26), respectively,from f to b.
326 M. Obata et al.
Calculation Procedure Figure 2 presents the flow chart of calculation. First, multiples and exponents of Eq. (21) are given for the operating range of the cooling blade, and the empirical constants 7, m, and n of Eq. (19) are specified. Second, by calculating Zfand Z~ in Eq. (26) and selecting ~b appropriately, X ' s and /('s for the incoming and outgoing passages are obtained as a function of Tc/Tg and TJTm from Eqs. (24) and (27). Then, taking an appropriate value as the first approximation for Tm and Tc, respectively, calculation of 7/,~ and 7/c is reiterated by Eqs. (16)-(18) until Tm and Tc have converged.
APPARATUS A N D METHOD OF EXPERIMENT Test Blade The cascade arrangement and profile of the test blade are shown in Fig. 3. It is a two-dimensional blade with a chord length c = 79.46 mm and a span length L = 180.0 mm. The arrangement of cooling passages of the test blade is shown in Fig. 4 in cross section. There are 10 incoming passages (one 6.0 mm diameter hole in the leading edge; nine holes 2.0-5.0 mm in diameter to cover the middle to tailing-edge parts) and three outgoing passages (all 6.0 mm in diameter, provided in the part where the blade is sufficiently thick). Thirteen thermocouplcs are embedded just inside the blade surface along the midspan periphery. Figure 3. Cascade arrangement and profile of test blade.
Tip [Specify c, t, L,
~#,
Re,, Pr,, Tg and Tc,i, [
t
l Specify ~, j~p, ia, h, i . , j . , r, m and n l
ll'
A'
A
|
I
[Specify S¢,r, A©.f, De,f, So,b, A¢,b and De,b [
f [ Calculate
[
I
~
et n _Tn+I
I
7-_-:n+, c,f --Xe,f n _mn+l c,b --~c,b
Zr and Zb
t Specify ~ and x Assume
] [
nth, T n , Tent and
Calculate
~f, Xb, Kf
Tn, b
and ~b
t
jCalculate#m,
Root (a) Direction of coolant flow ~6
I
¢5
[ i
O¢,f and #c,b
] !
I ran-l-1 mn+l [ I Calculate Tn+I m '~c,f and Xc, b I I
No
1
'"-°-
P
(b) A-A' cross-sectional view & Cooling hole arrangement uple
n+l
n
(c) Cross-sectional view of midspan Figure 2. Flow chart of calculation.
Figure 4. Arrangement of cooling holes and positions of thermocouples.
A Return-Flow Steam-Cooled Gas Turbine Blade 327
e
ation
wall mocouple sure tap ~ming cooling age
going cooling age wning chamber
Coolant inlet Figure 5. Configuration of test blade. The configuration of the test blade is schematically illustrated in Fig. 5. In consideration of machinability and to ensure in experiment a Biot number (Bi) of the order of 0.1 as in actual operation, a 13 Cr stainless steel was used. The thermocouples for measuring the metal temperatures were grounded sheath-type chromel-alumel 0.5 nun in diameter (the one at the trailing edge was 0.34 nun) with an accuracy of 0.2 K and were brazed on and buried in respective grooves cut in from root to midspan. The thermocouple and pressure hole for measuring the temperature and static pressure of the coolant flow were set at the inlet and outlet ducts, one point each. The
thermocouples were of the same type as for metal temperature measurement; the pressure hole was 0.5 mm in diameter. The blade tip and platform were insulated against the side wall and main gas flow to avoid heat loss. Test Apparatus and Experimental Method The test apparatus system is schematically shown in Fig. 6 together with positions of temperature and pressure measurements. The main air flow is taken from a 0.6 MPa air source and led to the measuring section of the cascade test wind tunnel
Temperature measurements " ( ~ - ( ~ ) Pressure measurements" ( ~ ) - ( ~
L~e~l~_((~) Test section ~ l ~ ) I Steam " t flow meter
Air
source
S/W separator "
] Trap I'~ r ~ l
Air orifice
Figure 6. Schematic diagram for experimental arrangement.
328
M. Obata et al. Table 2. Maximum Possible Uncertainties
Parameter
iide wall
ade ide
Total pressure tube
Figure 7. Arrangement in measuring section of cascade test wind tunnel. through an orifice, a ke,,~sene-fired combustor, and a settling chamber. The measuring section, which is depicted in Fig. 7, consists of a five-blade cascade, the middle of which is the test blade. The cooling steam is supplied from a miniboiler (1.0 ton/h), heated by an electric heater (5 kW), and fed to the test blade through a flowmeter. The cooling air, on the other hand, is taken directly from a shop air line through a branch drier and fed to the test blade through an orifice. Besides the steam-cooling experiments, steam-heating and air-cooling experiments were conducted to establish comparison bases. At first, the main gas flow was introduced, and when a steady state was reached the coolant was fed in. Its mass flow rate was increased little by little to the desired value and then held for a while to stabilize, and then temperatures and pressures were measured. The temperatures for the main gas flow were measured by eight sheath-type chromel-alumel
Temperature T Mass flow ratio w Relative temperature ~ Cooling flow ratio ~ Gas-side Reynolds number Reg Gas-side mean Nusselt number/qUg
Bias (%)
Precision (%)
Uncertainty (%)
_+0.3 + 1.2 + 1.4 + 1.7
_+0.8 __.0.8 + 3.6 + 1.1
+ 1.6 + 2.0 + 7.3 + 2.8
+ 1.2
__.1.1
___2.5
+_2.5
+ 6.3
_+ 12.8
thermocouples of 1.0 mm diameter with an accuracy of 0.2 K and recorded with an automatic recorder, while the pressures were measured either with precision Bourdon tubes for steam or with mercury manometers for air. By providing a suitable mixing section in the inlet duct a good velocity profile was obtained, so that the inlet gas velocity could be calculated from a central Pitot tube without incurring large inaccuracy due to the boundary layer effect, while the main gas flow temperature was calculated as an instantaneous mean of the eight thermocouple measurements. The method of coolant flow measurement was to time the flow of a given quantity. Table 1 shows the experimental conditions. The ranges for steam heating and steam cooling were: main gas temperature, Ts = 353-813 K; steam inlet temperature, Tc,in = 383--423 K; and gas-side Reynolds number, Reg = 0.74 x 10~-4.67 x 105. The steam inlet temperature was controlled so that the heating or cooling steam would remain superheated and nearly saturated, or would not become wet, at the test blade outlet or inlet. On the other hand, the ranges for air cooling were: T~ = 473-573 K; air inlet temperature constant at Tc.i, = 293 K; and Reg = 0.72 × 105-3.59 × 105. In each case, the flow ratio ~ was varied in a range of 1-8%. The uncertainty analysis of the experiments was made by the method of Ref. 4. The estimated maximum possible uncertainties at 20:1 odds in the present measurements are shown for the main parameters in Table 2. These measurements were also found to be reproducible within the same accuracy. The main error factors in calculating the uncertainty of relative tempera-
Table 1. Test Conditions Gas-Side Reynolds Number Test Regime
Run Number
Rex ( x 105)
Steam heating
SH-I SH-2 SH-3 SC-1 SC-2 SC-3 SC-4 AC-1 AC-2 AC-3 AC-4
1.42 2.27 4.67 0.74 1.40 1.94 4.58 0.72 1.28 1.95 3.59
Steam cooling
Air cooling
Coolant/gas flow ratio q~ = 1-8%.
Gas Inlet Temperature Tg
Coolant Inlet Temperature Tc,in
Temperature Ratio Tg / Tc, in
(K)
(K)
( )
353 353 353 813 573 623 503 573 473 623 473
423 423 423 383 383 383 383 293 293 293 293
0.8 0.8 0.8 2.1 1.5 1.6 1.3 2.0 1.6 2.1 1.6
A Return-Flow Steam-Cooled Gas Turbine Blade 329
1.0
] Concaveside
S
0.8
II E
o.,
Symbol Reexl05 ~% Steam heat=ng
0.2
--0-~-
test data
1
0 1.0
0.5
1.48 2.30 4.79
5.02 2.76 1.42
0.5
0
1.0
Figure $. Blade metal temperature distribution along mid-
s/e
span section surface. with respect to the mean relative temperature was greater for lower flow ratios, but it remained less than 15% for # of more than 1.5%.
ture 7/, cooling flow ratio ~, gas-side Reynolds number R%, and gas-side mean Nusselt number lqus come from the uncertainties associated with the thermocouples, the air orifices, and the steam flowmeter used. For the uncertainty associated with temperature and mass flow rate measurements, on the other hand, the readings of fractional data in a steadystate test condition are dominant.
Gas-Side Mean Heat Transfer Coefficient The mean heat transfer coefficient oTg for the gas-side blade surface was obtained from the thermal equilibrium between the heat transferred from the main gas flow to the blade surface and the enthalpy increase in the coolant. That is,
RESULTS A N D D I S C U S S I O N
Metal Temperature Distribution on Blade Surface
&e= we(he,o=- hc,i~)/SgL*(T e- "i'm)
An example of blade surface metal temperature distribution at the midspan section for steam-heating experhnents is illustrated in Fig. 8, in terms of the metal relative temperature 7,, versus nondimensional distance s/c for various O's and Res's. It will be seen that the blade is cooled comparatively uniformly as a whole, though some drop in 7/,, is noted at the trailing edge. Similar results were obtained both for steam cooling and for air cooling, indicating that the metal temperature distribution was not much influenced by ~ or by Reg. The deviation
(28)
where hc is the enthalpy at the temperature of the coolant and 7'm is the arithmetic mean value of the temperatures taken along the blade midspan section periphery. The experimental results are summarized in Fig. 9 as a function of R% and lqu8 ( = asc/Xs), where the half-filled circles mark the calculation results by Wilson and Pope's method [5], using the theoretical velocity distribution. From this, the empirical constants of Eq. (19), % m, and n for lqug, were determined to calculate the mean heat transfer coeffi-
15
xlO 2 tO
Io0 IZ
Nus = 0.0903 Re °'72 Prs 1/3 7
Presentdata Steam-heating Steam-cooling
-
]~F "
~7 Air-cooling O Calculated
2 0.5
'0.7
i
2
[
I
3
4
=
5
6
Res x 105
I
8
Figure 9. Relation between gas-side mean Nusselt number l~ug and Reg.
330
M. Obata et al.
1.0
cients of the present test blade for Reg = 0.7 × 105-5.0 × 10 ~ as lqUg= 0.0903 Re °'72gPr~/3
~b% In-coming
(29)
Comparison o f Calculations and Experiments on Relative Temperatures
:
:I
....
II
The accuracy of the present analysis has been examined in terms of the mean blade metal temperature at midspan and the coolant temperature at the outlet of the outgoing passage by applying the experimentally confirmed Eq. (29). An example is shown in Fig. 10 for three cases of ~ in terms of the root-totip distribution of relative temperatures ~/m (solid lines) and ~/~ (broken lines) to represent the nondimensional temperature Tm and T~, along with experimental values obtained from the mean metal temperature at a blade midspan section (for ~/m) and those obtained from the steam outlet temperature (for ~/c). It will be noted that calculations agree with experiments to within 5 %, and this agreement has also been confirmed for other test conditions. Calculated values and experimental values of ~/m are compared as a function of ~b in Fig. 11, although only for steam-cooling test conditions. Thus, it has been concluded that, even for superheated steam near saturation, which suffers a comparatively large change in fluid properties as temperature changes, cooling performance can well be calculated by means of values estimated on the temperature basis as in Eq. (21). Also, it is to be appreciated that other essential assumptions included in the present analytical method are not too critical in a quantitative sense.
:..(----
Out-going passage
~ [~
- -
Tim
Estimated icp= 1.70 , jcP = - 0 . 250 curve ip =0.719 , jp =1.10 - - - - - - i ~ =0.709, jA =1.16
, ~ 0.5
0.4
~ Present data /7c r/rn ~ %
0.3
O
• • •
[3
0.2
5.29 2.72 1.25
I 0.2
0
T~ = 623 K To.in=383 K Re8 =1.94Xl0 s
0.4
0.6
0.8
.0
~/L
~p
Figure 10. Comparison of calculations and experimental results for ~m and ~c.
Since steam cooling and air cooling differ in the experimental conditions, comparison was made on the values normalized to an operating condition selected as a reasonable gas turbine cycle [1], that is, Tg = 1473 K, Tc,in 473 K, R% = 3.37 x 105, and Prg = 0.705, by means of the following formula:
right-hand side is obtained as a constant value in the present analytical method and that ~.... g is obtained for empirically determined r/m,~. Figure 12 compares calculated and experimental values for steam cooling and air cooling for blade relative temperature ~m as a function of mass flow ratio ~. For both cases of cooling, agreement between calculation and experiment is fairly good. It will be noted, furthermore, that the way ~/m increases as 4) increases testifies to the superiority of steam cooling. To achieve 7/,, = 0.5, for example, as much as ~b = 5.6% of air is
:
~m,eng=f en~(Tc/ Ts, Tc/ Tm, Reg, Prg) ~I. . . . A~s(T~/T#, T~/Tm, Ree,Prg)
.~1.25
Steam-cooling
Root Comparison o f Cooling Characteristics between Steam and Air
--
(30)
where ~/m,e,g and l~m.cas denote the blade metal relative temperature in the operating condition and in the experiments, respectively. It will be noted that the function ratio on the
1.0 0.8 I** 0.6
I II
E
0.4 0.2
--Steam-cooling test
~ /
o A
Estimated
0 Figure 11. Comparison of calculations and experimental values of ~m as a function of ~b.
Present data
I
I
2
3
0.74 ! .40 1.94 [3, 4.58, 4
5
813 573 623 503A 6
383 383 383 383, 7
A Return-Flow Steam-Cooled Gas Turbine Blade 331 1.0
,
compared with those of an air-cooled blade and that the present method is capable of designing such blades to attain high efficiency cooling. Although the present method involves many assumptions, they are not critical in a quantitative sense. In particular, the method should enable designers to predict the influence of geometric and aerodynamic variables that affect the cooling performance of closed return-flow steam-cooled blades with a useful degree of accuracy and without a great deal of effort, and might be equally applicable to other gaseous coolants and to more complex cooling arrangements.
j Present data
Estimated
O Steam-heating
0.8--
Z~ Steam-cooling
E
~7 Air-cooling O.
6
Stelam
O. 4
~x,
CONCLUSIONS
Tg = 1473K To. in=473 K
0.2
0
I
0
,
2
~
From the results of this investigation, the following conclusions have been drawn:
I
4
,
6
8
¢% Figure 12. Comparison of cooling characteristics of steam and with those of air.
needed, whereas ck = 2.3% is ample enough for steam, a saving of about 60% in the mass flow ratio for a given cooling blade and operating condition. This is shown in Fig. 13 in terms of the ratio of blade relative temperature of steam cooling to that of air cooling, "Om.s/'Om,o,as a function of the mass flow ratio 0. It will be observed that the superiority of steam cooling over air cooling is more apparent for smaller mass flow ratios, and that at q~ = 2% or thereabouts, the blade relative temperature, or the cooling efficiency, of steam cooling can be as much as 1.5 times that of air cooling.
1. A one-dimensional analytical method that calculates the spanwise metal temperatures and the coolant temperatures for a closed return-flow type of gas turbine blade cooled by a gaseous coolant has been developed. 2. The metal temperature in the blade midspan section and the coolant temperature at the cooling passage outlet have been predicted for the experimental conditions with reasonable accuracy, thus confirming the reliability of the present analytical method. The range of validity is Re~ = 0.74 x 105-5.0 x 105, Tg/Tc.in = 0.8-2.1, and 0 = 1-8%. 3. In comparing the cooling characteristics of steam and air for the same blade configuration and operating condition, it has been ascertained that steam is superior to air and that when a coolant/gas flow ratio is about 2%, steam is - 1.5 times more effective than air. We wish to acknowledge the support extended to us by IshikawajimaHarima Heavy Industries Co., Ltd. NOMENCLATURE A
PRACTICAL SIGNIFICANCE The analytical method and experimental data of the present work are restricted to stationary return-flow blades that are internally cooled by forcing steam through a number of incoming and outgoing passages of constant cross section laid spanwise from root to tip. Nevertheless, it has been shown that such a steam-cooled blade has attractive cooling characteristics
1.8
Tg = 1473 K
\
Tc,in =473 K
Res = 3 . 3 7 x 10s t~
-.~~0.~5
1.4
~.0
I
0
I
2
I
I
4
I
6
8
¢% Figure 13. Relation between ratio of ~m of steam cooling to that of air cooling and ~.
cross-sectional area, m 2 Bi Biot number ( = ~gC/hm), dimensionless C chord length, m Cp specific heat at constant pressure, J/(kg K) D hydraulic diameter, m h enthalpy, J i~p, i~, ix multiple in Eq. (21), dimensionless ic., j~, jx exponent in Eq. (21), dimensionless K defined by Eq. (6), dimensionless 1 distance from blade root, m L, L* blade span length and effective length, m m, n exponent in Eq. (19), dimensionless Nu Nusselt number ( = oLD/h or o~c/X), dimensionless Pr Prandfl number ( = Cp#/h), dimensionless Re Reynolds number ( = puD/# or puc/p.), dimensionless S distance along blade surface, m S peripheral length, m t blade pitch, m T temperature, K U velocity, m/s W mass flow rate, kg/s
332
M. Obata et al. x X Z
nondimensionai span length ( = I/L), dimensionless defined by Eq. (6), dimensionless defined by Eq. (26), dimensionless
# p 7
Greek Symbols heat transfer coefficient, W/(m 2 K) gas outlet angle, rad cooling flow ratio ( = wc/wg), dimensionless thermal conductivity, W/(m K) relative temperature, dimensionless viscosity, Pa s density, kg/m 3 multiple in Eq. (19), dimensionless
a b c f g
air cooling outgoing passage coolant flow or cooling-side incoming passage main gas flow or gas-side
c~ /~2 ~b X
Subscripts
in m out s
cooling passage inlet blade metal cooling passage outlet steam cooling REFERENCES
1. Obata, M., and Taniguchi, H., Steam Cooling of Gas Turbine Blades, J. JSME, 87-788, 690-695, 1984. 2. Louis, J. F., Hiraoka, K., and EI-Masari, M. A., A Comparative Study of the Influence of Different Means of Turbine Cooling Performance, ASME Paper No. 83-GT-180, 1983. 3. Ainley, D. G., Internal Air Cooling for Turbine Blades--A General Design Survey, ARC R&M No. 3013, 1957. 4. Moffat, R. J., Describing the Uncertainties in Experimental Results, Exper. Thermal Fluid Sci., 1, 3-17, 1988. 5. Wilson, D. G., and Pope, J. A., Convective Heat Transfer to Gas Turbine Blade Surface, PIME, 168, 861-874, 1954.
Received April 15, 1988; revised January 17, 1989
H. Taniguchi Mechanical Engineering Department, Faculty of Engineering, Hokkaido University, Sapporo, Japan
liThe cooling characteristics of a return-flow type of steam-cooled gas turbine blade are investigated theoretically and experimentally. The modeled blade is intended for use in a closed-circuit gaseous coolant system. An arialyrical method for calculating the cooling performance of the blade, based on one-dimensional fluid flow and one-dimensional heat transfer, is proposed. Temperatures of the blade metal, incoming coolant, and outgoing coolant at various spanwise positions of the blade are given by nondimensional expressions and for various blade configurations and operating conditions. To verify the analysis, cascade tests are undertaken to obtain the heat transfer characteristics of a return-flow type of steam-cooled blade of similar design, using steam and air as a coolant. Metal temperature data are obtained for various gas-side Reynolds numbers, coolant/gas flow ratios, gas inlet temperatures, and coolant inlet temperatures. The validity of the analysis is examined in terms of the mean blade metal temperature at midspan and the coolant temperature at the outlet of the outgoing passage by applying a formula that has been confirmed experimentally for gas-side heat transfer coefficients. It is shown that the cooling performance can be predicted with good accuracy. Finally, the cooling characteristics of steam are clarified in comparison with air, using the experimental values normalized to the same set of gas turbine cycle operating conditions.
Keywords:forced convection, turbines, blade cooling INTRODUCTION Modern gas turbines are characterized by their extremely high power concentration and high thermal efficiency. It is well known that one of the main contributing factors of this achievement is the high gas turbine inlet temperature used to attain a high thermal efficiency of the thermodynamic cycle. In modern aerospace engines, especially, high gas turbine inlet temperatures have been attained by employing advanced blade materials and air-cooled blades. For the electric power generation, on the other hand, many projects are under way to develop more powerful power units of higher thermal efficiencies for the duty of base load supply. One of these projects is aimed at the development of a combined cycle power plant, comprising steam-cooled high-temperature gas turbines and steam turbines. These power plants will be able to achieve more than 50% thermal efficiency, whereas that of current steam cycle power plant is about 40%, which is almost their practical limit [1]. One important step toward the realization of such a highefficiency combined cycle power plant is to develop new closed-circuit steam-cooled blades having a high performance suitable for the cycles envisaged and to achieve a higher turbine inlet temperature in the gas turbine cycle. As steamcooled gas turbines call for design fundamentals much different from those available for air-cooling, such design funda-
mentals as cooling method, cooling characteristics, and cooling system have to be established anew. Even though the characteristics of steam-cooling have been clarified in theoretical comparisons with air- and water-cooling [2], the methodology of predicting cooling performance required for the basic design of a steam-cooled blade has not been as well developed as that for air-cooled blades [3]. Besides, at present, very few experimental data are available. In this paper, we describe the fLrst step we have achieved in establishing a design methodology of high-temperature steamcooled gas turbine blades. The primary objective is to present an analytical method for calculating the cooling performance of a closed return-flow gas turbine blade that is internally steam-cooled in a relatively simple manner, and to show experimental results of steam- and air-cooling cascade tests carried out to obtain the heat transfer characteristics of a similarly designed model blade. Then, after having confmned the validity of the analysis, the basic heat transfer characteristics of steam-cooling in comparison with air-cooling are clarified for a reasonably selected gas turbine cycle operating condition [1 ]. The analytical method and experimental results described in this paper are applicable to closed return-flow gas turbine blades that have a number of incoming and outgoing cooling passages of uniform cross section laid spanwise from root to tip. This type of blade, when utilized in a closed-circuit coolant system, would be able not only to use gaseous coolant
Address correspondence to Dr. M. Obata, Heat and Fluid Department, Research Institute, Ishikawajima-Harima Heavy Industries Co., Ltd., 1-15, Toyosu 3-Chome, Koto-Ku, Tokyo 135, Japan.
Experimental Thermaland Fluid Science 1989; 2:323-332 © 1989 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010
0894-1777/89/$3.50
323
324 M. Obata et al.
Tm
\\\\\\\\\\\\\~k
Main
\ \ \ \ \ \ \ '-,,'~ ,,, -., \
Tip
gas
T
flow
m+ -d~T-m- 6t
6g
Tg
-
Wg
To, b -
L '
l
1,I
(Out-going)
_
~
'
,
T~.0ut
T.,
"Tc, f (In-coming)
['
Root
I ~
, Coolant
"L,,.
flow
w~
Figure 1. Analytical model for cooling blade. such as air or steam, which has relatively favorable heat transfer characteristics, but also to improve the thermodynamic cycle performance. ANALYSIS Cooling Performance Analysis Figure 1 presents the analytical model for calculating the performance of gas turbine cooling blades. It is a closed returnflow type of cooling blade with a number of incoming and outgoing cooling passages of constant cross section extending from root to tip. The steam as a coolant is introduced at the root, cools the blade internally by forced convection, and is recovered at the root as superheated steam. Therefore, it is assumed that each of the incoming and outgoing passages can be equivalently replaced with a hole of the same hydraulic diameter. The analysis is based on one-dimensional turbulent fluid flow and one-dimensional heat transfer. Now consider a stationary blade that is cooled with superheated steam near saturation. For a blade element 81 at a spanwise distance 1 from the root, the following basic equations are obtained from thermal equilibrium in the blade cross section and from the enthalpy increase of cooling steam between the incoming and outgoing passages, ignoring the radiation heat transfer from the main gas flow to the blade surface. d2 Tra )~rnArn~ + otzSg(Tg - Tin)+ Ogc,fSc,f(Tc,f- Tin) + Otc,bSc,b( Tc, b-- Tin)=0
(1)
dT~,: wcCpc,.:~ + etc,fSc,f(Tc,f- Tin)= 0
(2)
w~Cp¢,o -dTc - ' ~ -b+ Olc,bSc,b( 17,m -- To, b) =
(3)
0
where the boundary conditions for the cooling steam are I=0:
Tc./= To, in,
I=L:
Tc.b = Tc,/
(4)
Here, we assume that the spanwise heat conduction along the blade is negligibly small compared to heat conduction due to forced convection. This is justified in the present work, for the blades envisaged are of an ordinary aspect ratio and are made of ordinary heat-resistant materials [3]. Thus, the first term of Eq. (1) can be ignored. It is assumed further that the distribution of the main gas flow inlet temperature is uniform. Then, we transform Eqs. (1)-(4) by defining necessary functions as in Eqs. (5)-(7): Tm(l
x=O:
+Xf+Xb)-XfTc,
f - X b T c , b=O
(Za)
dyeKf -~Xd"["Xf( T c,f - T~,) = 0
(2a)
Kb ~+XefT:.-
(3a)
T 'c,f-- T= c' , in ~
x=l:
Tc,e)= 0 T 'c,b = T ' c,f
(4a)
where
r;.=r~-T~,
TL:= r g - To,:, T;,i. = Tg- Tc,~.
x:= e~,:&,:/%sv
Xo = ac, o Sc, j % S~
K/= wcCpc,f/%SgL,
Kb = wcCpc, b / • S g L x =t/L
(5) (6)
(7)
Assuming X and K for cooling passages to be constant, such that X = X and K = /~, on the basis of an observation that they do not change much as x changes, and solving the simultaneous ordinary differential equations for T~,, T ' : , and
A Return-Flow Steam-Cooled Gas Turbine Blade 325 Tc',b, we obtain as the general solution
(9)
assumed that the following formula describes adequately the heat transfer from the main gas flow to the blade surface, occurring at a suitably given gas turbine operating temperature:
(10)
Nu,= 3, Re~ Pr~
T~, = hm(Gkt + l)etl x + h2(Gk2 + l)e t2x
(g)
T~d= h~e klx + h2ek2x T c,o=h~(BGkl + E)ek~X + h2(BGk2 + E ) e ~2~
where h~ and h2 are integration constants and k~ and k2 are the roots of the characteristic equation of the differential equation for Tc.f. That is, k~ = [ - a2 + (a~ - 4a~ a3) I / 2 ] / 2 a l
(11)
Ice= [ -- a~-- (a2~- 4ai a~) In]/2at
Hence, the coefficients a~, a2, and a~ are given by a2=E-(B-
a~=BG,
I)G/R,
&
a3=(1-E)/R
E= l-l-rEb ,
~l(f
&
where the constants % m, and n are to be determined experimentally or theoretically. It is also assumed that the turbulent heat transfer formula for the inside of a hole of constant cross section [3] is applicable to the present cooling passages for the range of operating temperatures concerned. Namely, Nuc=O'O34(L/Dc)-°'l(Tc/Tm)°'55 Re°'S Pr°'4c
(12)
where
B =l+''~f+'f~b ,
(19)
R_K__b
(13)
It is assumed further that for the operating range concerned the fluid property ratios between cooling steam and main gas flow may be presented approximately as a function of temperature ratio. Namely, CPc-icp(Tc~J*P
~--~--i (Tc~'~'
\ r,/
The constants hi and h2 in Eqs. (9) and (10) are obtained from the boundary conditions (4a) as N2T;.m N2- N I '
he
=
NI Tc,in Ni-N2 -
-
(14)
(20)
(21) Now, according to the definition, the relation of Reynolds number and Prandtl number between the cooling steam and main gas flow in the operating temperature range is given by
where Nl = (BGkl + E - 1)ekl,
N 2 = ( B G k 2 + E - l)e k2 (15)
(cos B2) ~c R%
c
(22)
Relative Temperatures The blade metal relative temperature, or the blade cooling efficiency ~lm,may be given by substituting Eq. (14) into Eq. (8) as (T,- Tin) = T~ ~" = (Tg - Tc, in) T c,'In , =N2 ~Gkl + 1 e~lX+N, ~Gk 2 + 1 e k-x z
(16)
whereas the steam relative temperature of the incoming cooling passage ~,o' is calculated from Eq. (9) as
r s_ r:s rLn N2 - N 2 _ N | e klx + NI--N_--IN2e k2x
Prc=~pg \ ~ - 8 8 ] \ ~ / Pr,
(23)
Then it can be shown that the calculation formula of Xf for the incoming passage is derived from Eqs. (19)-(23) by taking an average Nu~ for L / D c = 25 and L / D , = 100. That is, J~f=0.O174{ [ L ( ~ ) c o s , 2 ] ° ' s ( ~ ) X Zf~0.s R 0 . S - m
-°''
( T c d ' ~ J ( T c d ' ~ °'5s
\ r, /
e,
(u)
where i, j, and Z:, the cooling passage shape factor [3], are given by (1"/) i=i°'p4i°'6/i °'4,
j=O.4jcp+O.tjx-O.4j~,
(25)
and that of the outgoing cooling passage ~c,b from Eq. (10) as ZI
Tg -- Tc.b-- T'c,b
= r,- :r,in-r:,,n _ ,,r BGkt + E
-1.2 ~
B G k 2 + E ek2X eklX+Ni N I - N 2
(&Jc)L2
= A
(18)
Thus, ~m, ~,d, and ~/,,b can be calculated once X" a n d / ( are determined for the incoming and outgoing cooling passages.
+/d
(26)
With regard to/(f for the incoming passage, the calculation formula is obtained by rearranging Eqs. (19) and (20) and converting wc into the gas-side variables:
.,xfA~" _ lcp~
~ (COS •2)
Rel-m prlg-n k Tg /
Calculation of X and 1~ Functions
The .,~'/,R:, Xb, and/~b for incoming and outgoing cooling passages are calculated as defined in Eq. (6). Here, it is
The formulas for -'X'b,/~'b,and Zb for the outgoing passage are obtained simply by changing the subscriptsin Eqs. (24), (27), and (26), respectively,from f to b.
326 M. Obata et al.
Calculation Procedure Figure 2 presents the flow chart of calculation. First, multiples and exponents of Eq. (21) are given for the operating range of the cooling blade, and the empirical constants 7, m, and n of Eq. (19) are specified. Second, by calculating Zfand Z~ in Eq. (26) and selecting ~b appropriately, X ' s and /('s for the incoming and outgoing passages are obtained as a function of Tc/Tg and TJTm from Eqs. (24) and (27). Then, taking an appropriate value as the first approximation for Tm and Tc, respectively, calculation of 7/,~ and 7/c is reiterated by Eqs. (16)-(18) until Tm and Tc have converged.
APPARATUS A N D METHOD OF EXPERIMENT Test Blade The cascade arrangement and profile of the test blade are shown in Fig. 3. It is a two-dimensional blade with a chord length c = 79.46 mm and a span length L = 180.0 mm. The arrangement of cooling passages of the test blade is shown in Fig. 4 in cross section. There are 10 incoming passages (one 6.0 mm diameter hole in the leading edge; nine holes 2.0-5.0 mm in diameter to cover the middle to tailing-edge parts) and three outgoing passages (all 6.0 mm in diameter, provided in the part where the blade is sufficiently thick). Thirteen thermocouplcs are embedded just inside the blade surface along the midspan periphery. Figure 3. Cascade arrangement and profile of test blade.
Tip [Specify c, t, L,
~#,
Re,, Pr,, Tg and Tc,i, [
t
l Specify ~, j~p, ia, h, i . , j . , r, m and n l
ll'
A'
A
|
I
[Specify S¢,r, A©.f, De,f, So,b, A¢,b and De,b [
f [ Calculate
[
I
~
et n _Tn+I
I
7-_-:n+, c,f --Xe,f n _mn+l c,b --~c,b
Zr and Zb
t Specify ~ and x Assume
] [
nth, T n , Tent and
Calculate
~f, Xb, Kf
Tn, b
and ~b
t
jCalculate#m,
Root (a) Direction of coolant flow ~6
I
¢5
[ i
O¢,f and #c,b
] !
I ran-l-1 mn+l [ I Calculate Tn+I m '~c,f and Xc, b I I
No
1
'"-°-
P
(b) A-A' cross-sectional view & Cooling hole arrangement uple
n+l
n
(c) Cross-sectional view of midspan Figure 2. Flow chart of calculation.
Figure 4. Arrangement of cooling holes and positions of thermocouples.
A Return-Flow Steam-Cooled Gas Turbine Blade 327
e
ation
wall mocouple sure tap ~ming cooling age
going cooling age wning chamber
Coolant inlet Figure 5. Configuration of test blade. The configuration of the test blade is schematically illustrated in Fig. 5. In consideration of machinability and to ensure in experiment a Biot number (Bi) of the order of 0.1 as in actual operation, a 13 Cr stainless steel was used. The thermocouples for measuring the metal temperatures were grounded sheath-type chromel-alumel 0.5 nun in diameter (the one at the trailing edge was 0.34 nun) with an accuracy of 0.2 K and were brazed on and buried in respective grooves cut in from root to midspan. The thermocouple and pressure hole for measuring the temperature and static pressure of the coolant flow were set at the inlet and outlet ducts, one point each. The
thermocouples were of the same type as for metal temperature measurement; the pressure hole was 0.5 mm in diameter. The blade tip and platform were insulated against the side wall and main gas flow to avoid heat loss. Test Apparatus and Experimental Method The test apparatus system is schematically shown in Fig. 6 together with positions of temperature and pressure measurements. The main air flow is taken from a 0.6 MPa air source and led to the measuring section of the cascade test wind tunnel
Temperature measurements " ( ~ - ( ~ ) Pressure measurements" ( ~ ) - ( ~
L~e~l~_((~) Test section ~ l ~ ) I Steam " t flow meter
Air
source
S/W separator "
] Trap I'~ r ~ l
Air orifice
Figure 6. Schematic diagram for experimental arrangement.
328
M. Obata et al. Table 2. Maximum Possible Uncertainties
Parameter
iide wall
ade ide
Total pressure tube
Figure 7. Arrangement in measuring section of cascade test wind tunnel. through an orifice, a ke,,~sene-fired combustor, and a settling chamber. The measuring section, which is depicted in Fig. 7, consists of a five-blade cascade, the middle of which is the test blade. The cooling steam is supplied from a miniboiler (1.0 ton/h), heated by an electric heater (5 kW), and fed to the test blade through a flowmeter. The cooling air, on the other hand, is taken directly from a shop air line through a branch drier and fed to the test blade through an orifice. Besides the steam-cooling experiments, steam-heating and air-cooling experiments were conducted to establish comparison bases. At first, the main gas flow was introduced, and when a steady state was reached the coolant was fed in. Its mass flow rate was increased little by little to the desired value and then held for a while to stabilize, and then temperatures and pressures were measured. The temperatures for the main gas flow were measured by eight sheath-type chromel-alumel
Temperature T Mass flow ratio w Relative temperature ~ Cooling flow ratio ~ Gas-side Reynolds number Reg Gas-side mean Nusselt number/qUg
Bias (%)
Precision (%)
Uncertainty (%)
_+0.3 + 1.2 + 1.4 + 1.7
_+0.8 __.0.8 + 3.6 + 1.1
+ 1.6 + 2.0 + 7.3 + 2.8
+ 1.2
__.1.1
___2.5
+_2.5
+ 6.3
_+ 12.8
thermocouples of 1.0 mm diameter with an accuracy of 0.2 K and recorded with an automatic recorder, while the pressures were measured either with precision Bourdon tubes for steam or with mercury manometers for air. By providing a suitable mixing section in the inlet duct a good velocity profile was obtained, so that the inlet gas velocity could be calculated from a central Pitot tube without incurring large inaccuracy due to the boundary layer effect, while the main gas flow temperature was calculated as an instantaneous mean of the eight thermocouple measurements. The method of coolant flow measurement was to time the flow of a given quantity. Table 1 shows the experimental conditions. The ranges for steam heating and steam cooling were: main gas temperature, Ts = 353-813 K; steam inlet temperature, Tc,in = 383--423 K; and gas-side Reynolds number, Reg = 0.74 x 10~-4.67 x 105. The steam inlet temperature was controlled so that the heating or cooling steam would remain superheated and nearly saturated, or would not become wet, at the test blade outlet or inlet. On the other hand, the ranges for air cooling were: T~ = 473-573 K; air inlet temperature constant at Tc.i, = 293 K; and Reg = 0.72 × 105-3.59 × 105. In each case, the flow ratio ~ was varied in a range of 1-8%. The uncertainty analysis of the experiments was made by the method of Ref. 4. The estimated maximum possible uncertainties at 20:1 odds in the present measurements are shown for the main parameters in Table 2. These measurements were also found to be reproducible within the same accuracy. The main error factors in calculating the uncertainty of relative tempera-
Table 1. Test Conditions Gas-Side Reynolds Number Test Regime
Run Number
Rex ( x 105)
Steam heating
SH-I SH-2 SH-3 SC-1 SC-2 SC-3 SC-4 AC-1 AC-2 AC-3 AC-4
1.42 2.27 4.67 0.74 1.40 1.94 4.58 0.72 1.28 1.95 3.59
Steam cooling
Air cooling
Coolant/gas flow ratio q~ = 1-8%.
Gas Inlet Temperature Tg
Coolant Inlet Temperature Tc,in
Temperature Ratio Tg / Tc, in
(K)
(K)
( )
353 353 353 813 573 623 503 573 473 623 473
423 423 423 383 383 383 383 293 293 293 293
0.8 0.8 0.8 2.1 1.5 1.6 1.3 2.0 1.6 2.1 1.6
A Return-Flow Steam-Cooled Gas Turbine Blade 329
1.0
] Concaveside
S
0.8
II E
o.,
Symbol Reexl05 ~% Steam heat=ng
0.2
--0-~-
test data
1
0 1.0
0.5
1.48 2.30 4.79
5.02 2.76 1.42
0.5
0
1.0
Figure $. Blade metal temperature distribution along mid-
s/e
span section surface. with respect to the mean relative temperature was greater for lower flow ratios, but it remained less than 15% for # of more than 1.5%.
ture 7/, cooling flow ratio ~, gas-side Reynolds number R%, and gas-side mean Nusselt number lqus come from the uncertainties associated with the thermocouples, the air orifices, and the steam flowmeter used. For the uncertainty associated with temperature and mass flow rate measurements, on the other hand, the readings of fractional data in a steadystate test condition are dominant.
Gas-Side Mean Heat Transfer Coefficient The mean heat transfer coefficient oTg for the gas-side blade surface was obtained from the thermal equilibrium between the heat transferred from the main gas flow to the blade surface and the enthalpy increase in the coolant. That is,
RESULTS A N D D I S C U S S I O N
Metal Temperature Distribution on Blade Surface
&e= we(he,o=- hc,i~)/SgL*(T e- "i'm)
An example of blade surface metal temperature distribution at the midspan section for steam-heating experhnents is illustrated in Fig. 8, in terms of the metal relative temperature 7,, versus nondimensional distance s/c for various O's and Res's. It will be seen that the blade is cooled comparatively uniformly as a whole, though some drop in 7/,, is noted at the trailing edge. Similar results were obtained both for steam cooling and for air cooling, indicating that the metal temperature distribution was not much influenced by ~ or by Reg. The deviation
(28)
where hc is the enthalpy at the temperature of the coolant and 7'm is the arithmetic mean value of the temperatures taken along the blade midspan section periphery. The experimental results are summarized in Fig. 9 as a function of R% and lqu8 ( = asc/Xs), where the half-filled circles mark the calculation results by Wilson and Pope's method [5], using the theoretical velocity distribution. From this, the empirical constants of Eq. (19), % m, and n for lqug, were determined to calculate the mean heat transfer coeffi-
15
xlO 2 tO
Io0 IZ
Nus = 0.0903 Re °'72 Prs 1/3 7
Presentdata Steam-heating Steam-cooling
-
]~F "
~7 Air-cooling O Calculated
2 0.5
'0.7
i
2
[
I
3
4
=
5
6
Res x 105
I
8
Figure 9. Relation between gas-side mean Nusselt number l~ug and Reg.
330
M. Obata et al.
1.0
cients of the present test blade for Reg = 0.7 × 105-5.0 × 10 ~ as lqUg= 0.0903 Re °'72gPr~/3
~b% In-coming
(29)
Comparison o f Calculations and Experiments on Relative Temperatures
:
:I
....
II
The accuracy of the present analysis has been examined in terms of the mean blade metal temperature at midspan and the coolant temperature at the outlet of the outgoing passage by applying the experimentally confirmed Eq. (29). An example is shown in Fig. 10 for three cases of ~ in terms of the root-totip distribution of relative temperatures ~/m (solid lines) and ~/~ (broken lines) to represent the nondimensional temperature Tm and T~, along with experimental values obtained from the mean metal temperature at a blade midspan section (for ~/m) and those obtained from the steam outlet temperature (for ~/c). It will be noted that calculations agree with experiments to within 5 %, and this agreement has also been confirmed for other test conditions. Calculated values and experimental values of ~/m are compared as a function of ~b in Fig. 11, although only for steam-cooling test conditions. Thus, it has been concluded that, even for superheated steam near saturation, which suffers a comparatively large change in fluid properties as temperature changes, cooling performance can well be calculated by means of values estimated on the temperature basis as in Eq. (21). Also, it is to be appreciated that other essential assumptions included in the present analytical method are not too critical in a quantitative sense.
:..(----
Out-going passage
~ [~
- -
Tim
Estimated icp= 1.70 , jcP = - 0 . 250 curve ip =0.719 , jp =1.10 - - - - - - i ~ =0.709, jA =1.16
, ~ 0.5
0.4
~ Present data /7c r/rn ~ %
0.3
O
• • •
[3
0.2
5.29 2.72 1.25
I 0.2
0
T~ = 623 K To.in=383 K Re8 =1.94Xl0 s
0.4
0.6
0.8
.0
~/L
~p
Figure 10. Comparison of calculations and experimental results for ~m and ~c.
Since steam cooling and air cooling differ in the experimental conditions, comparison was made on the values normalized to an operating condition selected as a reasonable gas turbine cycle [1], that is, Tg = 1473 K, Tc,in 473 K, R% = 3.37 x 105, and Prg = 0.705, by means of the following formula:
right-hand side is obtained as a constant value in the present analytical method and that ~.... g is obtained for empirically determined r/m,~. Figure 12 compares calculated and experimental values for steam cooling and air cooling for blade relative temperature ~m as a function of mass flow ratio ~. For both cases of cooling, agreement between calculation and experiment is fairly good. It will be noted, furthermore, that the way ~/m increases as 4) increases testifies to the superiority of steam cooling. To achieve 7/,, = 0.5, for example, as much as ~b = 5.6% of air is
:
~m,eng=f en~(Tc/ Ts, Tc/ Tm, Reg, Prg) ~I. . . . A~s(T~/T#, T~/Tm, Ree,Prg)
.~1.25
Steam-cooling
Root Comparison o f Cooling Characteristics between Steam and Air
--
(30)
where ~/m,e,g and l~m.cas denote the blade metal relative temperature in the operating condition and in the experiments, respectively. It will be noted that the function ratio on the
1.0 0.8 I** 0.6
I II
E
0.4 0.2
--Steam-cooling test
~ /
o A
Estimated
0 Figure 11. Comparison of calculations and experimental values of ~m as a function of ~b.
Present data
I
I
2
3
0.74 ! .40 1.94 [3, 4.58, 4
5
813 573 623 503A 6
383 383 383 383, 7
A Return-Flow Steam-Cooled Gas Turbine Blade 331 1.0
,
compared with those of an air-cooled blade and that the present method is capable of designing such blades to attain high efficiency cooling. Although the present method involves many assumptions, they are not critical in a quantitative sense. In particular, the method should enable designers to predict the influence of geometric and aerodynamic variables that affect the cooling performance of closed return-flow steam-cooled blades with a useful degree of accuracy and without a great deal of effort, and might be equally applicable to other gaseous coolants and to more complex cooling arrangements.
j Present data
Estimated
O Steam-heating
0.8--
Z~ Steam-cooling
E
~7 Air-cooling O.
6
Stelam
O. 4
~x,
CONCLUSIONS
Tg = 1473K To. in=473 K
0.2
0
I
0
,
2
~
From the results of this investigation, the following conclusions have been drawn:
I
4
,
6
8
¢% Figure 12. Comparison of cooling characteristics of steam and with those of air.
needed, whereas ck = 2.3% is ample enough for steam, a saving of about 60% in the mass flow ratio for a given cooling blade and operating condition. This is shown in Fig. 13 in terms of the ratio of blade relative temperature of steam cooling to that of air cooling, "Om.s/'Om,o,as a function of the mass flow ratio 0. It will be observed that the superiority of steam cooling over air cooling is more apparent for smaller mass flow ratios, and that at q~ = 2% or thereabouts, the blade relative temperature, or the cooling efficiency, of steam cooling can be as much as 1.5 times that of air cooling.
1. A one-dimensional analytical method that calculates the spanwise metal temperatures and the coolant temperatures for a closed return-flow type of gas turbine blade cooled by a gaseous coolant has been developed. 2. The metal temperature in the blade midspan section and the coolant temperature at the cooling passage outlet have been predicted for the experimental conditions with reasonable accuracy, thus confirming the reliability of the present analytical method. The range of validity is Re~ = 0.74 x 105-5.0 x 105, Tg/Tc.in = 0.8-2.1, and 0 = 1-8%. 3. In comparing the cooling characteristics of steam and air for the same blade configuration and operating condition, it has been ascertained that steam is superior to air and that when a coolant/gas flow ratio is about 2%, steam is - 1.5 times more effective than air. We wish to acknowledge the support extended to us by IshikawajimaHarima Heavy Industries Co., Ltd. NOMENCLATURE A
PRACTICAL SIGNIFICANCE The analytical method and experimental data of the present work are restricted to stationary return-flow blades that are internally cooled by forcing steam through a number of incoming and outgoing passages of constant cross section laid spanwise from root to tip. Nevertheless, it has been shown that such a steam-cooled blade has attractive cooling characteristics
1.8
Tg = 1473 K
\
Tc,in =473 K
Res = 3 . 3 7 x 10s t~
-.~~0.~5
1.4
~.0
I
0
I
2
I
I
4
I
6
8
¢% Figure 13. Relation between ratio of ~m of steam cooling to that of air cooling and ~.
cross-sectional area, m 2 Bi Biot number ( = ~gC/hm), dimensionless C chord length, m Cp specific heat at constant pressure, J/(kg K) D hydraulic diameter, m h enthalpy, J i~p, i~, ix multiple in Eq. (21), dimensionless ic., j~, jx exponent in Eq. (21), dimensionless K defined by Eq. (6), dimensionless 1 distance from blade root, m L, L* blade span length and effective length, m m, n exponent in Eq. (19), dimensionless Nu Nusselt number ( = oLD/h or o~c/X), dimensionless Pr Prandfl number ( = Cp#/h), dimensionless Re Reynolds number ( = puD/# or puc/p.), dimensionless S distance along blade surface, m S peripheral length, m t blade pitch, m T temperature, K U velocity, m/s W mass flow rate, kg/s
332
M. Obata et al. x X Z
nondimensionai span length ( = I/L), dimensionless defined by Eq. (6), dimensionless defined by Eq. (26), dimensionless
# p 7
Greek Symbols heat transfer coefficient, W/(m 2 K) gas outlet angle, rad cooling flow ratio ( = wc/wg), dimensionless thermal conductivity, W/(m K) relative temperature, dimensionless viscosity, Pa s density, kg/m 3 multiple in Eq. (19), dimensionless
a b c f g
air cooling outgoing passage coolant flow or cooling-side incoming passage main gas flow or gas-side
c~ /~2 ~b X
Subscripts
in m out s
cooling passage inlet blade metal cooling passage outlet steam cooling REFERENCES
1. Obata, M., and Taniguchi, H., Steam Cooling of Gas Turbine Blades, J. JSME, 87-788, 690-695, 1984. 2. Louis, J. F., Hiraoka, K., and EI-Masari, M. A., A Comparative Study of the Influence of Different Means of Turbine Cooling Performance, ASME Paper No. 83-GT-180, 1983. 3. Ainley, D. G., Internal Air Cooling for Turbine Blades--A General Design Survey, ARC R&M No. 3013, 1957. 4. Moffat, R. J., Describing the Uncertainties in Experimental Results, Exper. Thermal Fluid Sci., 1, 3-17, 1988. 5. Wilson, D. G., and Pope, J. A., Convective Heat Transfer to Gas Turbine Blade Surface, PIME, 168, 861-874, 1954.
Received April 15, 1988; revised January 17, 1989