PERFORMANCE ANALYSIS OF A TURBINE STAGE HAVING COOLED NOZZLE BLADES WITH TRAILING EDGE EJECTION

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1 THE AMERCAN SOCETY OF MECHANCAL ENGNEERS 35 E. 7th St., New York. N.Y TA-12 The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy material for internal or personal use under ciraanstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of $0.30 per page is paid directly to the CCC, 27 Congress Street Salem MA Requests for special permission or bull( reproduction should be addressed to the AWE Technical Polishing Department Copyright Cl996 by ASME All Rights Reserved Printed in USA PERFORMANCE ANALYSS OF A TURBNE STAGE HAVNG COOLED NOZZLE BLADES WTH TRALNG EDGE EJECTON J. H. Kim, T. S. Kim, J. S. Lee and S. T. Ro Turbo and Power Machinery Research Center Seoul National University Seoul, Korea ) ABSTRACT This work presents an aerothermodynamic modeling of a cooled turbine blade and the performance analysis of a turbine stage having cooled nozzle blades with trailing edge coolant ejection. A mean line analysis, based on the well-known Ainley- Mathieson scheme, is adopted for the basic loss prediction of the blade rows without cooling. A unique model regarding the interaction between coolant and main gas is proposed. The interactions considered are the heat transfer from main gas to coolant and the temperature and pressure losses by the mixing of two streams due to the trailing.edge coolant ejection. For a model turbine stage with nozzle cooling, parametric analyses are carried out Co investigate the effect of main design variables (amount of coolant flow, coolant temperature and coolant ejection area) on the stage performance. The influences of coolant mass flow ratio and temperature on the mixing loss and specific work are investigated. The results are also rearranged to investigate the effect of blade temperature on the specific work. Analysis is also carried out by varying the ejection area, which may give useful criteria in determining the coolant condition and ejection hole size of real gas turbine engines. static pressure PR total-to-total pressure ratio R gas constant St Stanton number total temperature Tb average temperature of gas side blade surface Ter a average temperature of coolant side blade surface total temperature ratio between coolant and gas static temperature velocity pressure loss coefficient mixing pressure loss coefficient flow angle heat exchange effectiveness cooling effectiveness asymptotic cooling effectiveness specific heat ratio density mass flow ratio between coolant and gas NOMENCLATURE A area C cooling effectiveness parameter C constant-pressure specific heat fraction of trailing edge area, see equation (10) fraction of coolant ejection area, see equation (10) dh, specific work of rotor expansion M Mach number mass flow rate P. total pressure P mass averaged total pressure, see equation (12) SUBSCRPTS nozzle inlet 2 nozzle exit 3 rotor exit blade coolant main gas nr o blade row inlet state after mixing beide row outlet beide row exit annulus space Presented at the 1996 ASME Turbo Asia Conference November 5-7, 1996 Jakarta, ndonesia

2 te tic trailing edge uncooled condition axial station 1. NTRODUCTON Numerous analyses have demonstrated the influence of turbine cooling on the overall performance of gas turbine engines (Kawaike et al, 198, El-Masri, 1986, Kim and Ro, 1995). To predict the performance of an engine, however, there should be a clear understanding of the phenomena in cooled turbines. Accordingly, it is required to evaluate the interactions between main gas and coolant precisely, which usually result in the temperature dilution and the pressure loss. Especially, it is quite important to investigate the aerodynamics of mixing process which causes the main fluid dynamic loss in a cooled turbine. Up to now, lots of studies have been executed both experimentally and analytically about the secondary fluid ejection into the main stream of turbine blade rows. Yamamoto et al. (1991) experimentally investigated the flows in a linear cascade with secondary air ejection at various locations of Wade surface. Willett and Fottner (199) performed an experiment about the mixing process at turbine blades, especially on the suction side. to et al. (1980) measured the local pressure losses in a cascade with air ejection in order to simulate the film cooling. They also predicted the mixing pressure loss analytically by assuming a mixing at constant static pressure and made a comparison between experiment and prediction. Schobeiri (1989) made a semianalytical study concerning the mixing characteristics with trailing edge ejection and presented the behavior of the mixing pressure loss coefficient. Most of the previous studies mentioned above are focused only on the aerodynamic interaction between the main stream and the ejected flow in a blade row. Moreover, there have been few researches about the influence of thermal and fluid dynamic interactions on the stage performance. n this regard, it is quite necessary to fully recognize the operational characteristics of the turbine stages with blade cooling and to analyze the influence of cooling on the aerodynamic performance. Accordingly, the main purpose of this work is to suggest models which can describe the characteristics of cooled turbine stages and to investigate the influence of cooling on the overall performance for a model turbine stage. n this study, models for the blade cooling process including the mixing of two streams (main gas and coolant) at trailing edge are suggested. A cooling effectiveness equation is introduced to represent the relation among total temperature, mass flow rates of two streams and average blade surface temperature. The conditions after the mixing of two streams are determined by solving coupled governing equations for mass, momentum and energy. The cooling models are incorporated into a mean line performance prediction method and a calculation routine for predicting the characteristics of turbines with blade cooling is developed. The performance of a turbine stage having cooled nozzle blades with trailing edge ejection is analyzed by the routine. nozzle rotor Fig.1 Schematic blade profile at mean radius 2. ANALYSS ROUTNE 2.1 Basic Loss Prediction Method The mean line analysis has been widely used to predict the performance of uncooled turbines. n this study, the well-known method by Ainley and Mathieson (1951) is adopted for the basic aerodynamic analysis routine and the cooling process models are added to the routine as will be explained in the following sections. Shown in Fig. 1 is the schematic blade profile. The pressure loss coefficient defined by the following equation is of prime importance in calculating the aerodynamic loss. P P y o Po Po where the subscripts i and o represent the blade row inlet and outlet respectively. The pressure loss consists of the profile loss, the secondary loss and the tip clearance loss of a blade row. Adopted in this study is the correlations of pressure loss coefficients suggested by Dunham and Came (1970), which were formulated by modifying the Ainley-Mathieson correlations (1951). Since they are so well acknowledged, the detailed equations need not be shown in this paper. 2.2 Thermodynamic Modeling for Blade Cooling The convective cooling is characterized by blade internal cooling followed by trailing edge coolant ejection. Flow pattern through a stage is assumed as follows. While the main gas flows through a coolde blade row, its total temperature drops by heat transfer to the coolant. After the heat exchange, mixing of two streams occurs at the row exit plane, and the fully mixed gas enters the next blade row. Cooling effectiveness is defined as follows: r Th 0 T --T where T ed and rci are the row inlet average total temperatures of gas and coolant and Th is the average gas side blade surface temperature. The cooling effectiveness is related to the mass flow ratio between coolant and main gas. Adopted in this study is an effectiveness equation that was derived theoretically by ( ) (2) 2

3 C 0/70,r, Vg trailing edge continuity equation: p & lig COS agag + pe Ve cosara, = x-direction momentum equation: plicos2agag + pc tie2 cos 2 aca, + pga, = p m d cos2 a,a, + pa, y-direction momentum equation: (5) (6) Fig.2 Model for flow mixing at blade row exit Pg Vg2 cosag sin agag + pe lt! cosa, sin atel, p,v,2 cosa, sin aa, energy equation: pg Vg cos agagcpgrg + pc Ve coscrearcpc Tc (7) (8) considering energy balance among coolant, wall and gas (Kim and Ro,995). The equation appears as follows: " = C C = St An g C Pg co -0 A c where the parameter C represents the cooling technology level and qs. means the asymptotic cooling effectiveness which is less than 1.0 for typical convective cooling schemes. The ratio between the blade surface area and the gas flow area can be estimated from given geometric data. The heat exchange effectiveness inside the cooling passage is defined as follows: (3) () equation of state: p= prt for each working fluid (gas, coolant, mixed gas) (9) Above equations are rearranged in non-dimensional forms and solved with the aid of a non-linear equation solving technique. The properties (Cp. R) after mixing are corrected. n the equations, the annulus area of blade row exit A, and the gas flow area Ag may be given from the blade geometric data. The coolant flow area Ac can be determined as follows by introducing area parameters d and/ Ac 1 = fd and A = - d, where Ale = d and = f (10) A, A, A, Ate where Ted and 7; denote the coolant total temperatures supplied to the row and at the ejection plane (after heat exchange) respectively and Th i represents the blade inside (coolant side) temperature. 2.3 Modeling for Mixing Process As mentioned in 2.2, the mixing of gas and coolant streams is assumed to occur at the blade row exit after heat exchanging. The temperatures of two streams before mixing are calculated by using the energy balance equation and the heat exchange effectiveness as described in 2.2. Of course, the main stream pressure before mixing is determined by applying the loss models mentioned in 2.1. Figure 2 shows the mixing plane to be analyzed. n this work, also assumed are a mixing at constant static pressure. With the state values before mixing, the states (temperature, pressure, velocity, etc.) of gas after mixing are determined by solving the following coupled governing equations. A uniform velocity profile for each stream is assumed, which means that the boundary layer is neglected. The existence of shear layer between two streams is also neglected. 2. Calculation Conditions The influence of blade cooling on the perforinance of a model turbine stage is analyzed. The geometric data of the turbine stage are summarized in Table. The model stage is the first stage of a gas turbine engine under development (Kim et at,995). The nominal design parameters are as follows: design parameters : rotational speed rpm inlet total temperature K inlet total pressure kpa inlet mass flow kg/s (without cooling) The properties used are as follows: 'specific heat ratio : yg = 1.333, ye = 1.00 gas constant : R g = R = cifkgk c Only the nozzle cooling is considered Following cooling parameters are used for equation(3). 3

4 item chord' (mm) pitch' (mm) Table 1 Stage geometric data maximum thickness' (mm) blade inlet angle' (deg.) blade outlet angle' (deg.) trailing edge thickness" (mm) hub diameter (mm) tip diameter (mm) tip clearance (mm) a: at mean line b: normal to blade angle nozzle rotor o: 1.0 re f = OS , 2 / / Ah/Ag = 3.80, c = 0.5, St = 0.005, O. = RESULTS AND DSCUSSONS 3.1 General Description n this work, analyses are performed by using the following three non-dimensional parameters, which describe coolant thermal condition (total temperature), mass flow and ejection area, respectively. T A Tv mg A, Since the purpose of this study is to investigate the influence of above parameters on the stage performance, the stage inlet temperature and the rotor speed are kept constant as the design values. Morover, all the calculations are made to result in the constant total-to-total pressure ratio as follows: total-to-total pressure ratio, PR,, (stage inlet to outlet) = 2.2 First, analyses are carried out to show the effect of in c / Agana r for a fixed value off Then, the effect off is investigated with the / As as a parameter for a fixed value of T. Fig.3 Coolant total pressure at ejection plane as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio (PR= 2.2) S f = Fig. Mixed-out total temperature as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio (PR= 2.2) 32 Effect of Coolant Flow Rate and Temperature Calculations are made by varying and 7- for a fixed ejection area (/=0.333). Shown in Fig. 3 is the calculated coolant total pressure Pe at the ejection plane, which is normalized by the stage inlet total pressure P i. Calculations are made until the coolant choking condition. n this calculation, choking occurs beyond the maximum (0.12) in the figure except for the case of T=. For a given a higher r leads to a higher coolant Mach number and thus a higher total pressure. Figure presents the mixed-out total temperature rm. which is normalized by the stage inlet total temperature Tr As the coolant mass flow increases and the coolant temperature decreases, the temperature loss increases. The pressure loss through both the nozzle and rotor does not much depend upon the coolant mass flow ratio. The mixing pressure loss, however, must be directly affected by the magnitude of th e hiig. To analyze the mixing process, a mixing pressure loss coefficient is defined as follows, which has been frequently used in basic fluid dynamic studies (Schobeiri, 1989, Wilfert etal., 199): - P. - Pn, Pm - Pm p. titgpg + thg + Ate (12) As shown in Fig. 5, increasing the coolant mass flow ratio initially accompanies the increase of Yrn. The non-zero value of Y. even without ejection =0) is due to the existence of the finite trailing edge thickness, which can be acknowledged when

5 f = b E Fig.5 Mixing pressure loss coefficient as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio (PR= 2.2) Fig.7 Stage specific work as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio f=0.333 (PR,t = 2.2) ci:" E f = , / / / Therefore, with sufficiently large coolant addition, the mixed-out flow may become more pressurized than the flow before mixing. For a cooled stage, it is not easy to define a stage efficiency. n this work, it seems quite reasonable to evaluate the specific rotor expansion work that is defined in equation (13) as the stage performance parameter, since the total-to-total pressure ratio is maintained constant for all cases. AhR = Cp,(T, - T3) (13) Fig.6 Mixed-out total pressure as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio (PR if = 2.2) we look into the formulation of the conservation equations of 2.3. Ejection of coolant, however, does not always cause the total pressure loss. That is, when the momentum contribution of the coolant is significant, Y,,, decreases. After reaching a local minimum. Y,,, increases again with increasing mass flow ratio. This phenomenon is qualitatively similar to the result obtained by the previous study (Schobeiri, 1989). However, if we consider the mixing process from the view point of the mainstream gas flow, we can get quite a different trend. Shown in Fig. 6 is the mixed-out total pressure Pm normalized by the main stream total pressure P, just before mixing. After reaching a minimum value, the mixed-out total pressure increases with the increasing coolant mass fraction. The specific work is normalized by the value of uncooled case and shown in Fig. 7. As can be easily imagined, a lower coolant temperature leads to a smaller specific work due to the lower total temperature and pressure at rotor inlet (i.e., at mixed-out plane). As clearly shown in the figure, for the coolant flow ratio above a certain value, the specific work increases, which seems to be very interesting. Even though the mixed-out total temperature always decreases as the coolant flow ratio increases, the mixedout total pressure increases for the higher mass flow ratio range as in Fig. 6. Therefore, for the higher mass flow ratio range, the rotor expansion work increases again because the pressure rise compensates for the temperature dilution. When we look into the results from Fig. 5 to Fig. 7, we can find out an important fact Y,,, is usually considered as an important parameter in mixing process, which plays a key role in a cooled turbine (Schobeiri, 1989). From the result of this study, however, it should be admitted that the variation of Y,,, does not have a close relationship with the specific work variation and thus it can not sufficiently explain the variation of the stage overall performance. n conclusion, the total pressure difference (or ratio) between upstream main flow and mixed-out flow is more suitable as a parameter that accounts for the behavior of performance variation. Up to now, we considered the loss and specific work as a 5

6 (Tbfr i ) (Tb/Ti =0.768), =0.09 (Tr 1 =0.730) 1 1, M e =1 ',, ', / r = Fig.8 Blade temperature as a function of coolant mass flow ratio with temperature ratio as a parameter and constant ejection area ratio (Plitt = 2.2) Fig.10 Mixing pressure loss coefficient as a function of ejection area ratio with coolant mass flow ratio as a parameter and constant temperature ratio (PRier. 2.2) ct (T ba ) =0.06(T b/t,=0.768) =0.09(T b/ti a0.230) Me Tb 7; r = J _ 10 Fig.9 Stage specific work as a function of blade temperature with temperature ratio as a parameter and constant ejection area ratio (PRit = 2.2) function of mass flow ratio. t is also required to investigate the results from the view point of the real engine environment. in a real engine, the performance absolutely depends upon the blade operating. temperature. Therefore, it is important to have information about the turbine performance variation with the blade temperature. The blade temperature variation with the coolant mass flow ratio is depicted in Fig. 8, which shows the result according to the equation (3). Figure 9 shows the specific work variation with the blade temperature. For an arbitrary r, the specific work usually decreases as the blade temperature drops because more coolant is required and higher mixing pressure and temperature losses occur. For the sufficiently lower blade temperature range, however, the specific work increases due to the fact mentioned above for Fig.11 Mixed out total pressure as a function of ejection area ratio f with coolant mass flow ratio as a parameter and constant temperature ratio (Pf7n = 2.2) Fig. 7. For the Th /Ti values higher than 0.82 and with the 7* range considered here, larger specific work can be obtained with lower coolant temperature. 3.3 Effect of Election Area Calculations are carried out to see the influence of the ejection area on the mixing loss and specific work. The pressure loss coefficient Yn, is shown in Fig. 10 as a function f with the mass flow ratio as a parameter and for a fixed temperature ratio T. of 0.5. f the mass flow ratio is constant, the blade temperature is kept constant as indicated in the figure. The coolant velocity increases with the decreasing ejection 6

7 k 1.00 ` 0.98 cc c Ts =0.5 te0.03(t,-0.837) - =0.06(T/7 1 =0.768) S Mel tc0.09(tt =0.730) OA &6. OA 10 leads to the optimum design in the aspect of the overall stage performance. A Similar result to Fig. 10 was obtained from a previous study (Schobeiri, 1989) and it was concluded that the loss coefficient may be used as a major guide to the determination of ejection hole size. From the result of our study, however, Y. has only a nominal meaning in the aspect of stage performance and the mixed-out total pressure itself is important. Figure 0 shows the calculated total pressure of coolant at the ejection plane. The coolant pressure P c in the figure may conservatively represent the coolant source condition. Accordingly, this analysis routine may be utilized as a design guide in choosing the ejection geometry when the blade temperature and the coolant source condition are detennincd in advance. Flg.12 Stage specific work as a function of ejection area ratio with coolant mass flow ratio as a parameter and constant temperature ratio (PRff = 2.2) =0.03(17T,=0.837) =0.06(TT,=0.768) ; 0.09(T/T i =0.730) Meal r t Fig.13 Coolant total pressure at ejection plane as a function of ejection area ratio f with coolant mass flow ratio as a parameter and constant temperature ratio (Miff = 2.2) area. The coolant choking limitation is shown in the figure. Y. has a minimum value at a certain value off However, the mixedout total pressure increases monotonically with the reduction in the ejection area as shown in Fig.. As shown in Fig. 12, the specific work variation is much affected by the variation of the mixed-out total pressure. The analysis of this section may be useful in determining the ejection geometry of real turbines once the required blade temperature ((hat is, required coolant mass flow) is known. t should be admitted that if we focus on the thermodynamic stage performance, the absolute value of mixed-out total pressure is important. That is, even though an optimum value off may be deduced from the mixing pressure loss coefficient Y., it does not. CONCLUDNG REMARKS A performance prediction method for cooled turbine stages are introduced, which is based on the mean line analysis and models for cooling process are incorporated in. The models for blade cooling take into account the blade temperature as a parameter. The mixing of main gas and coolant by trailing edge coolant ejection is modeled by the coupled governing equations. The performance of a model turbine stage with nozzle cooling is analyzed. The mixing process is analyzed in terms of nondimensional parameters for coolant mass flow ratio (1 coolant total temperature (7') and ejection area (f) and the influence of mixing on the stage performance is investigated. To maintain the. consistency of comparison, the stage inlet condition and the totalto-total pressure are kept constant. Analyses are carried out for a fixed value of trailing edge ejection area. The main stream total pressure loss increases with the initial increase of coolant mass flow ratio: However, further increase in mass flow ratio leads to the reversal increase of mixed-out total pressure due to the sufficiently large momentum transfer from the coolant flow. For the range of sufficiently large coolant mass flow ratio, the stage specific work is directly affected by the behavior of the mixed-out total pressure. The specific work is rearranged as a function of the blade temperature. For the calculation regime in this study, lower coolant temperature gives rise to slightly larger specific work at a given blade temperature for the higher blade temperature range. n addition, it is observed that the mixing pressure loss coefficient can not fully explain the behavior of the stage performance and an exact prediction of the mixed-out total pressure as well as total temperature is required. Analyses are also carried out by varying the coolant ejection area for a fixed coolant temperature ratio T. For a given coolant mass flow ratio, the reduction in ejection area always leads to specific work increase, which is explained by the increases of the mixed-out total pressure. The overall analysis can be expected to be applied to the parametric study of the cooling design including the determination of coolant mass flow and ejection hole size. 7

8 ACKNOWLEDGMENTS This work was supported by the Turbo and Power Machinery Research Center of Seoul National University. REFERENCES Ainley, D. G. and Mathieson, G. C. R., 1951, "A Method of Performance Estimation for Axial-Flow Turbines," British ARC, R&M 297. Dunham, J. and Came, P.M., 1970, "mprovement to the Ainley- Mathieson Method of Turbine Performance Prediction," ASME Journal of Engineering for Power, Vol.92, pp El-Masri, M. A., 1986, "On Thermodynamics of Gas-Turbine Cycles : Part 2 A Model for Expansion in Cooled Turbines," ASME Journal of Engineering for Gas Turbines and Power, Vol.108, pp to, S., Eckert, E. R. G., and Goldstein, R. J., 1980, "Aerodynamic Loss in a Gas Turbine Stage with Film Cooling," ASME Journal of Engineering for Power, Vol.' 02, pp Kawaike, K., Kobayashi, N., and lkeguchi, T., 198, "Effect of New Blade Cooling System With Minimized Gas Temperature Dilution on Gas Turbine Performance," ASME Journal of Engineering for Gas Turbines and Power, Vol.106, pp Kim, J.-C., Sohn, J.-L. and Cha, J.-H., 1995, "Development of 1.2 MW ndustrial Gas Turbine Engine," ASME paper 95-CTP Kim, T. S. and Ro, S. T., 1995, "Comparative Evaluation of the Effect.of Turbine Configuration on the Performance of Heavy- Duty Gas Turbines," ASME paper 95-GT-33 Schobeiri, T., 1989, "Optimum Trailing Edge Ejection for Cooled Gas Turbine Blades," ASME Journal of Turbomachincry, Vol.111, pp Wilfert, G. and Fottner, L., 199, "The Aerodynamic Mixing Effect of Discrete Cooling Jets with Mainstream Flow on a Highly Loaded Turbine Blade," ASME paper 9-GT-235. Yamamoto, A., Kondo, Y., and Murao, R., 1991, "Cooling-Air njection into Secondary Flow and Loss Fields Within a Linear Turbine Cascade," ASME Journal of Turbomachinery, Vol.113, pp