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Effect of discrete-hole arrangement on film-cooling effectiveness for the endwall of a turbine blade cascade
Applied Thermal Engineering 91 (2015) 507e514
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Research paper
Effect of discrete-hole arrangement on film-cooling effectiveness for the endwall of a turbine blade cascade Francesca Satta*, Giovanni Tanda degli Studi di Genova, via Montallegro 1, I-16145 Genova, Italy DIME/MASET, Universita
h i g h l i g h t s Film cooling in a turbine cascade endwall with discrete holes was investigated. Two different discrete-hole configurations have been considered. The adiabatic film-cooling effectiveness was measured by liquid crystal thermography. Maps of effectiveness were used to compare the performance of two hole arrangements. Effectiveness was selectively averaged in regions at the largest heat transfer need.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 April 2015 Accepted 24 July 2015 Available online 12 August 2015
This paper investigates film cooling in a turbine cascade endwall for two discrete-hole configurations using liquid crystal thermography. The discrete holes, arranged in rows aligned in the pitchwise direction, gave rise to relative maxima of film-cooling effectiveness downstream of each row, followed by a marked decrease of effectiveness along the gap between adjacent rows of holes. This resulted in a not efficient coverage of the endwall surface, with succession of over- and under-cooled regions. The redesign of discrete-hole configuration, based on knowledge of the heat transfer coefficient map on the endwall without film cooling, enabled the redistribution of the coolant to provide a better coverage of the endwall and a significant increase of the area-averaged film-cooling effectiveness. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Film cooling Endwall Turbine cascade Liquid crystals
1. Introduction Film cooling has been widely used in high-performance gas turbine to protect turbine blades and endwalls from being damaged by hot gases [1]. It is based on the introduction of a secondary fluid (the coolant) through injection holes or slots placed in the blade and endwall material to form a protective layer between the surface and the hot mainstream gas. Endwall film cooling and associated heat transfer are strongly influenced by the secondary flow effects. Thus, locating filmcooling holes requires a deep understanding of secondary flow behaviour and associated heat transfer. Blair [2] was the first to measure the film-cooling effectiveness and convective heat transfer coefficient distributions on the endwall of a large-scale turbine vane passage. A cooling slot upstream of the passage channel
* Corresponding author. E-mail address: [email protected] (F. Satta). http://dx.doi.org/10.1016/j.applthermaleng.2015.07.082 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
leading edge was employed and results, obtained from several thermocouples embedded in the wall material, were presented for a range of blowing ratios. One of the key findings was that the effectiveness distributions showed extreme variations across the vane passage with much of the coolant from the upstream injection slot being swept across the endwall toward the suction side corner. Takeishi et al. [3] measured the film-cooling effectiveness distributions on the blade and endwall surfaces of a low speed, fully annular, low aspect ratio vane cascade, using surface-mounted thermocouples. Film-cooling holes were placed on the model vanes and on the inner and outer endwalls. They found that passage secondary flows strongly affect heat transfer and film cooling on the suction surface of the vane and the endwalls. Film-cooling performance for injection through discrete holes in a turbine blade endwall was investigated by Jabbari et al. [4] by using a mass transfer technique based on ammoniumediazo-paper. Visualization experiments revealed the paths and interaction of the jets, which changed with blowing and density ratios. Friedrichs et al. [5e7] conducted aerodynamic and film-cooling measurements for
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a cascade endwall; the ammonia and diazo technique was employed to measure the film-cooling effectiveness. They indicated a marked influence of the secondary flows on the film cooling and, at the same time, an influence of the film cooling on the secondary flows. An improved endwall film-cooling configuration was tested experimentally and results were compared with those obtained for a baseline cooling configuration, consisting of rows of holes at four axial positions [7]. More recently, Kost and Nicklas [8] and Nicklas [9] investigated the aero-thermal behaviour of a transonic cascade with endwall film cooling. Similar investigations, but on different endwall cooling schemes, were also performed by Knost and Thole [10,11]. In Refs. [8e11], a combination of cooling from an upstream slot with film-cooling holes in the passage of the vane was considered; filmcooling effectiveness results were obtained by using the infrared thermography as diagnostic tool. Significant improvement can be achieved in cooling characteristics of the film by using cooling holes with appropriately designed expanded exits, which are able to provide better lateral coverage and better centreline effectiveness. Barigozzi et al. [12] and Colban et al. [13] experimentally studied (by liquid-crystal and infra-red thermography, respectively) the effect of fan-shaped film-cooling holes for a vane endwall. Fan-shaped holes were found to give a superior cooling performance compared to that of cylindrical holes, but with the drawback of increased manufacturing cost and difficulty, particularly for the vane platform region. The aim of the present study is to investigate the film-cooling effectiveness improvement gained by the re-design of the cooling configuration, based on knowledge of the heat transfer coefficient map with no film cooling measured in Ref. [14], without introducing any larger complexity in the real machine manufacturing (hence avoiding fan-shaped holes, for example, or very expensive micro-holed surfaces).
2. Experimental facility The experiments were performed in a blow-down type wind tunnel housing a large-scale high-pressure turbine blade cascade (Fig. 1). An auxiliary apparatus was used to inject a secondary fluid
for the film-cooling of the cascade endwall. For practical reasons, the experiments were conducted with a cold air mainstream as primary fluid and a hot “coolant” air flow as secondary fluid according to a common practice followed in similar investigations. The coolant air flow, controlled by a variable speed fan and measured by means of a Venturi flowmeter, was heated by an electric heater and delivered to a plenum located underneath the cascade endwall. This process resulted in temperature differences between the coolant and mainstream in the 9e35 K range. 2.1. Test section and film-cooling geometry The linear cascade, shown in Fig. 1, is characterized by a blade chord of 312.5 mm, a height of 210.2 mm and a cascade pitch of 339.4 mm. The flow entered at a zero angle. The Zweifel coefficient of the cascade was 1.01. The endwall boundary layer at the cascade inlet was 18 mm thick with a displacement thickness of 2.22 mm, a momentum thickness of 1.92 mm, and a shape factor of 1.16. Fillets with a round profile extending for 10 mm along the endwall and blade surfaces were used for contouring. Since periodicity attainment required at least three passages, cascade consisted of four blades; measurements were performed in the central passage, where the heated endwall was located. The cascade periodicity, imposed by the modification of the flexible tailboards installed at the exit of the external blades, has been then checked by comparing the aerodynamic loadings measured over the two central blades. The investigated blade cascade has been previously aerodynamically tested without film cooling in Ref. [15]; similarly, endwall heat transfer without film cooling was experimentally studied in Ref. [14]. For the film-cooling experiments, the filmcooled endwall region was made of a 19 mm-thick layer of balsa wood having a low thermal conductivity (¼0.065 W/mK), in order to provide a nearly adiabatic surface, suitable to allow adiabatic film-cooling effectiveness measurements. The endwall regions immediately upstream and in the passage of the cascade featured discrete holes, arranged according to the two different layouts shown in Fig. 2. Regardless of the discretehole geometry, all the holes were cylindrical in shape, had a diameter of 5 mm (length to diameter ratio of 7.6) and ejected at a
Fig. 1. Schematic of the experimental facility and of the turbine cascade. Dimensions in [mm].
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(mainly downstream of the cascade throat); moderate-to-high heat transfer coefficients (region B) were found at the endwall entrance (as a result of the thin inlet thermal boundary layer), in the vicinity of blade pressure and suction sides, and around an imaginary line probably representing the footprint of the horseshoe vortex travelling along the lift-off line. Region A is featured by relatively low heat transfer coefficients. Therefore, discrete holes for configuration No.2 were placed in order to provide the necessary coolant coverage of regions B and C, as dictated by the actual heat transfer conditions. 2.2. Measurement technique and procedure
Fig. 2. Film-cooling layout and specifications; (a) configuration No.1, (b) configuration No.2. Black ellipses indicate hole exit locations on the blade passage side of the endwall; exit angles are indicated too.
30 inclination angle to the endwall surface. These geometric parameters are typical of endwall film-cooling configurations [6]. The exit angle is indicated in the respective figures. The number of filmcooling holes for both geometries was 29, in order to fix the same overall passage surface area. The first discrete-hole configuration (No.1, Fig. 2a), was designed according to a standard arrangement of holes and consisted of four rows of holes, aligned in the pitchwise direction, and located at different axial positions: immediately upstream of the cascade and at 30%, 60% and 90% of axial chord Cx. The second configuration (No.2, Fig. 2b), has been designed in this study for the purpose of improving the cooling performance on the basis of heat transfer experiments performed without film cooling [14], which indicated the endwall regions at the highest heat transfer coefficients requiring the highest coolant coverage (Fig. 3). Basically, a high heat transfer coefficient was recorded in region C
Fig. 3. Map of the endwall regions characterized by different values of the heat transfer coefficient without film cooling [14].
Various experimental methods have been used in the literature for the film-cooling effectiveness measurement: heating foils and thermocouples [2,3,16], the mass-transfer analogy [4,5,7], and thermal imaging techniques [9e13,17e21]. In the present work, liquid crystal (LC) thermography was used due to its ease of application and low cost. Detailed full field surface information can be obtained by heat transfer and film-cooling LC experiments performed according to steady-state or transient procedures [22]. In principle, the steadystate method is more time-consuming since each experiment can last several hours against few minutes required by the transient method. However, transient method may pose some difficulties when applied to a real cascade due to 3-D conduction effects in the endwall material, especially in the vicinity of the ejection holes. In this research the film-cooling effectiveness was deduced by LC measurements (and mainstream and coolant temperature measurements) taken at the end of a steady-state experiment. A pre-packaged LC sheet (Hallcrest R30C5W, bandwidth 5 C, red start at 30 C and blue start at 35 C), was used to detect the surface temperature of the endwall. The LC sheet, 0.15 mm thick, consisted of a thin LC layer laid on a thin transparent Mylar film and backed with a black background paint and a pressure-sensitive adhesive. The relationship between the colour (hue) and temperature of the LCs was obtained by means of a calibration experiment, described in Ref. [14] and performed in situ (i.e., same camera, illumination and viewing conditions as in the real experiment). In particular, for both calibration and film-cooling experiments, the colour distribution of the LCs was taken by a Nikon D-70 camera (through a Plexiglas optical window opposite to the endwall surface). A set of LED (light emitting diodes)-based light sources was used to provide a uniform lighting of the test section. LC images were transformed from the RGB (Red, Green, Blue) to the HSI (Hue, Saturation, Intensity) colour domain and processed to obtain the wall temperature from the hue distribution. Sheathed, 0.5 mm-dia, type-T thermocouples, with exposed junctions, were employed to measure the mainstream air temperature and the coolant temperature in the hole passage (for a limited number of holes) and in the plenum. Variations of coolant temperature between the plenum and the hole exit were typically registered due to the expected convective heat transfer between the coolant and the hole passage internal surface. A simple theoretical model has been developed to predict the coolant temperature drop from the plenum to the hole exit. The calculated temperature drop was always in very good agreement with the spot thermocouple measurements at the inlet/outlet hole sections and its extent was found to increase with the coolant-to-mainstream temperature difference and to decrease with the coolant mass flow rate. Calculated coolant temperature variations within the hole passages were generally equal to 7% of the plenum-tomainstream air temperature difference, irrespective of the blowing ratio and the discrete-hole configuration. These calculated values were adopted to correct the measured coolant temperature
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in the plenum and achieve a more realistic evaluation of Tc at the hole exit. The adiabatic film-cooling effectiveness is introduced as:
h¼
Tw T∞ Tc T∞
(1)
where T∞ is the mainstream air temperature, Tw is the endwall surface temperature and Tc is the coolant temperature. To support the assumption of adiabatic endwall conditions, the uncooled effectiveness has been calculated by a heat balance, at each point of the endwallemainstream interface, between the heat conducted through the balsa wood layer and the heat transferred by convection to the mainstream, by applying a given temperature difference between the coolant in the plenum and the mainstream air flow without coolant ejection. The uncooled effectiveness was found to be related to the conductive thermal resistance of the balsa layer and to the endwall heat transfer coefficient h, here taken as that measured for the endwall without film cooling [14]. In the regions far from hole exits, the uncooled effectiveness, deduced by a simple 1-D conduction model, was found to be in the range from 0.015 to 0.048. A special care was taken to evaluate the uncooled effectiveness immediately upstream of each injection hole where the thermal resistance of the material is lower and not uniform (due to the presence of the inclined holes and the reduction in the material thickness) and tangential conductive heat transfer tends to markedly affect the results; for this reason a 3-D conduction model has been adopted over these specific areas. The calculated values of the local uncooled effectiveness were finally used to correct the measured values of film-cooling effectiveness. 2.3. Test conditions During each test, the cascade was operating with a Reynolds number of 960,000, based on the chord length (¼0.3125 m) and the isentropic exit velocity (¼48 m/s). The mainstream air was taken at ambient temperature (about 27 C) with an average inlet velocity of about 13.5 m/s and an inlet turbulence intensity of 1%. The Mach number and turbulence intensity are low as compared with the actual engine conditions but deemed sufficient to understand the 3-D flow effect on film cooling as the discrete-hole cooling arrangement is modified. A nominal blowing ratio M based on the coolant and mainstream mass velocities was defined as:
M¼
. mc Aholes r∞ U∞
hole. In order to infer local characteristics for each cooling hole, the following equation can be used:
Mlocal
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi po;plenum p rc ¼ rinlet po;inlet p
(4)
where p is the local static pressure at the exit of the cooling hole, measured at the endwall without film cooling. Experiments were performed for three values of the nominal blowing ratio M, namely for M ¼ 2.5, 3.0 and 3.5 (which correspond to Minlet ¼ 1.0, 1.5, 2.0, respectively). The minimum blowing ratio value tested was the one for which the total pressure in the plenum was slightly larger than that at the mainflow inlet, this in order to avoid a reverse flow and consequently suction instead of blowing through the first row of holes. The jet-to-mainstream density ratio was in the 0.9e0.97 range. A representative example of the calculated local blowing ratios Mlocal is shown in Fig. 4, for the largest nominal blowing ratio investigated. For both configurations, local blowing ratio variations up to 50e60% were found, with maximum values near the front of blade pressure side and minimum values near the rear of the blade suction side and close to the passage exit. As the nominal blowing ratio is reduced, a more uniform distribution of Mlocal is progressively achieved. 2.4. Experimental uncertainty The uncertainty (at the 95% confidence level) in the film-cooling effectiveness measurement was evaluated according to the procedure outlined by Moffat [23]. The random uncertainty was determined by taking the standard deviation of measurements repeated under the same operating conditions. The fixed uncertainty was evaluated by taking into account errors associated with temperature (by LCs and thermocouples) readings and conceptual errors associated with the evaluation of the coolant exit temperature and the correction done to take into account the heat conduction in the
(2)
where mc is the total coolant mass flow, Aholes is the total injection area, while r∞ and U∞ are density and mean velocity of mainstream air at inlet conditions. An alternative definition of blowing ratio based on pressure differences has been considered, too:
Minlet ¼
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi po;plenum pinlet rc rinlet po;inlet pinlet
(3)
where (rc/rinlet) is the jet-to-mainstream density ratio, po,plenum and po,inlet are the plenum and inlet stagnation pressures, respectively, while pinlet is the inlet static pressure. Minlet is the blowing ratio that an idealized loss free coolant hole would have when ejecting to inlet conditions. The blowing ratios introduced by Eqs. (2) and (3) are different from the local blowing ratio, which is defined individually for each
Fig. 4. Local blowing ratio evaluated from static pressures at the endwall without film cooling.
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endwall material. The total uncertainty in the h measurement turned out to be ±12% at h ¼ 0.15 and ±8% at h ¼ 0.6.
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Contours of film-cooling effectiveness, for all of the blowing ratios, are shown in Fig. 5 (configuration No.1) and 6 (configuration No.2). Generally speaking, the majority of the cooling footprints showed individual jets, displaying little lateral spreading downstream of most of the holes. Holes placed directly upstream of other holes seemed to increase the cooling benefit from the downstream hole since the upstream cooling prevented the natural jet lift-off
that would occur otherwise, as observed in previous literature studies (for instance [12]). Upstream of the leading edge, the effect of the horseshoe vortex is visible, especially for configuration No.1 (Fig. 5), where the ejected coolant was not able to efficiently cover the endwall region downstream of the first row of holes and close to the pressure surface. This finding is consistent with results presented in Refs. [5,11] under similar operating and geometry conditions. For configuration No.2 (Fig. 6), holes upstream of the leading edge were mainly placed on the front of turbine blades; as a consequence, a large endwall region, triangular in shape, appears to be virtually unprotected. As inferred from Fig. 3, in this region the need for cooling is relatively small; therefore, the solution adopted in the
Fig. 5. Contours of film-cooling effectiveness for configuration No.1 and different blowing ratios.
Fig. 6. Contours of film-cooling effectiveness for configuration No.2 and different blowing ratios.
3. Results and discussion
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Configuration No.1
-0.4 -0.2
-0.2
M = 2.5 M=3 M = 3.5
0 0.2
0.2 0.4
x/Cx
x/Cx
M = 2.5 M=3 M = 3.5
0
0.4 0.6
0.6
0.8
0.8
1
1
1.2
1.2
1.4
1.4
1.6
Configuration No.2
-0.4
0
0.1
0.2
0.3
η
0.4
0.5
1.6
0.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Fig. 7. Axial variations of pitchwise-averaged film-cooling effectiveness at different blowing ratios, for the two discrete-hole configurations.
design of configuration No.2 permitted to save coolant that otherwise would feed regions not requiring film cooling. In the first half of the blade passage, the fluid ejected near the suction side was clearly swept in the direction of the streamlines for both discrete-hole configurations. Conversely, near the pressure side region, a different behaviour was observed: for the configuration No.1, the trajectories coming from the second and third holes from the pressure surface located on the second row (at 30% of axial chord) are turned toward the suction surface despite their orientation angles in the direction of mainstream line. This local deflection resulted in an uncooled region between the second and the third rows of holes close to the pressure surface. This effect is mitigated for the configuration No.2, where the holes are not displaced in-line but fitted close to the pressure surface and along the line approximately lying halfway between the pressure and suction surfaces. Attention is now given to the region in the middle of the blade passage: for configuration No.1, at 60% of axial chord, the traces of jets emerging from the second to fourth hole from the pressure surface merge downstream of the holes, while the first hole (close to the pressure surface) and the last two holes (close to the suction surface) provided individual coolant jets whose trajectories are
M = 2.5
-0.4 -0.2
-0.2
-0.2
0.2
0.4
0.4
x/Cx
0.2
0.4
0.6 0.8
0.8
0.6 0.8
1
1
1
1.2
1.2
1.2
1.4
1.4
1.4
1.6
1.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Config. No.1 Config. No.2
0
0.2
0.6
M = 3.5
-0.4
Config. No.1 Config. No.2
0
x/Cx
x/Cx
M=3
-0.4
Config. No.1 Config. No.2
0
approximately in the inviscid streamline direction. In the same endwall region, the pattern of film-cooling effectiveness for configuration No.2, where holes are aligned in the mainstream direction, reflects the position of cooling holes: a strip at low effectiveness, parallel to the pressure side is generated in correspondence of a region at low heat transfer coefficients. Contrary to what observed by Friedrichs [7], the ejected jets from holes located in the midline between suction and pressure surfaces are not significantly affected by crossflow, but appear to be mainly directed along the inviscid streamline direction. Due to the relative vicinity of holes in this area, the traces merge to form a region at a relatively high level of cooling effectiveness. Finally, the cooling holes located close to the blade passage outlet display again different patterns of h depending on the specific configuration. When the holes are aligned at 90% axial chord (configuration No.1), the coolant jets merge at a high film-cooling effectiveness, extending from the hole exits to the vicinity of the suction side trailing edge. The different hole placement for configuration No.2 provides, on the same endwall region, lower h values immediately downstream of the hole exits as compared to those for configuration No.1, but a coolant coverage on a markedly larger endwall area of potentially high heat transfer.
0
0.1
0.2
0.3
η
0.4
0.5
0.6
1.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Fig. 8. Comparisons between pitchwise-averaged film-cooling effectiveness distributions for configuration No.1 and No.2, at different blowing ratios. Only endwall regions at mediumehigh heat transfer coefficient were considered in each pitchwise average.
F. Satta, G. Tanda / Applied Thermal Engineering 91 (2015) 507e514 Table 1 Mean h-values obtained averaging the film cooling effectiveness in the different zones identified by the convective heat transfer coefficient map reported in Fig. 3. Configuration
No.1 No.1 No.1 No.2 No.2 No.2
M
2.5 3.0 3.5 2.5 3.0 3.5
Minlet
1.0 1.5 2.0 1.0 1.5 2.0
Region A
B
C
BþC
AþBþC
0.167 0.133 0.111 0.107 0.090 0.073
0.200 0.180 0.166 0.210 0.179 0.163
0.076 0.107 0.147 0.151 0.169 0.197
0.141 0.146 0.157 0.182 0.174 0.179
0.148 0.142 0.145 0.163 0.153 0.152
3.1. Effect of blowing ratio Fig. 7 reports the pitchwise-averaged distributions of h along the dimensionless axial coordinate x/Cx, at different blowing ratios, for both configurations. Generally speaking, in the blade passage region, the pitchwise-averaged effectiveness for configuration No.1 shows a relative maximum immediately downstream of each row of holes and the extent of the relative maximum increases with the distance in the axial direction (as found in Refs. [5,12]). However, due to the shortness of the ejected jet trajectories, the pitchwiseaveraged h distribution rapidly decays downstream of hole exits, originating large regions of relatively low cooling effectiveness. Conversely, configuration No.2 provides a more uniform h distribution along the streamwise direction and, at the same time, the cooling effect is more persistent for a larger distance downstream of the last row of holes. It is apparent from Fig. 7 that the best cooling performance was achieved, for both configurations, at the lowest blowing ratio (M ¼ 2.5), except for the endwall region immediately downstream of the cascade passage (x/Cx > 1). Indeed, within the vane passage, as the blowing ratio is increased, the increased jet lift-off from the holes is probably responsible for the attenuation of relative maxima in h displayed by config. No.1 and for the generalized, slight reduction in h observed for config. No.2. Conversely, for x/Cx > 1, the augmentation of the coolant coverage, especially for config. No.2, as M is increased can be due to the fact that local blowing ratios for the last row of holes are lower than elsewhere (and probably below the lift-off limit), even for the largest injection, as can be inferred from Fig. 4. 3.2. Effect of the film-cooling geometry The comparison of film-cooling effectiveness provided by the two discrete-hole configurations has to take into account the local need for cooling, far from being uniform over the endwall in real applications. Therefore, only local h data included in the endwall region B and C of Fig. 3, where the need for cooling is significant, were considered in the pitchwise averages reported in Fig. 8. The comparison shows that the holes of configuration No.2, which do not feed the low heat transfer regions located in the first half of the blade passage, provide a better coverage where the demand for cooling is higher. Moreover, the pitchwise-averaged film-cooling effectiveness for configuration No.2 is more evenly distributed along the axial direction, thus providing a fairly uniform coolant coverage over the endwall regions featured by a relatively high cooling need. 3.3. Area-averaged film-cooling effectiveness The mean h values obtained by averaging the film-cooling effectiveness over regions A, B, and C are reported in Table 1. Data averaged over individual areas show that mean h values for
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configuration No.1 are larger in region A, where the demand for cooling is the smallest, while configuration No.2 provides better results in region C, where the convective heat transfer is the largest. Here the film-cooling effectiveness is as higher as the blowing ratio is increased, which is the opposite of what occurs within the two other regions, as outlined in the comment to Fig. 7. Of particular relevance are the mean values obtained averaging h over the entire endwall area (A þ B þ C) and over the mediumehigh heat transfer area (B þ C). The h values averaged over the entire endwall area indicate a better performance of the configuration No.2; this is much more evident when only the area interested by high heat transfer values (region B þ C) is considered, with relative enhancements from þ14% (at M ¼ 3.5) to þ29% (at M ¼ 2.5). This finding is consistent with results presented in Ref. [7] for similar cascade and operating conditions, where an improved cooling configuration, designed according to a different criterion (based on the computed aerodynamic losses, rather than on the heat transfer coefficient distribution as in the present case), provided a better performance as compared to a standard cooling configuration, especially at the lowest inlet blowing ratio investigated. 4. Conclusions The arrangement of discrete holes for the film cooling of a turbine cascade endwall has a marked effect on the distribution of the film-cooling effectiveness and on the coolant coverage on the endwall surface. A standard arrangement provided by rows of holes aligned along the pitchwise direction leads to overcooled regions just immediately downstream of each hole row and to undercooled regions in the space between hole rows. A different distribution of coolant through holes located where the cooling demand is expected to be higher has been found to allow a more uniform cooling of the endwall and a larger coolant coverage. An increase in the film-cooling effectiveness, averaged over endwall regions where the heat transfer coefficient is relatively high (and the need for cooling too), of up to 29% is provided by the configuration having hole location re-designed on the basis of the heat transfer coefficient distribution. References [1] J.C. Han, S. Dutta, S. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, second ed., CRC Press, Taylor & Francis, 2013. [2] M.F. Blair, An experimental study of heat transfer and film cooling on largescale turbine endwalls, ASME J. Heat Transf. 96 (1974) 524e529. [3] K. Takeishi, M. Matsuura, S. Aoki, T. Sato, An experimental study of heat transfer and film cooling on low aspect ratio turbine nozzles, ASME J. Turbomach. 112 (1990) 488e496. [4] M.Y. Jabbari, K.C. Marston, E.R.G. Eckert, R.J. Goldstein, Film cooling of the gas turbine endwall by discrete-hole injection, ASME J. Turbomach. 118 (1996) 278e284. [5] S. Friedrichs, H.P. Hodson, W.N. Dawes, Distribution of film-cooling effectiveness on a turbine endwall measured with the ammonia and diazo technique, ASME J. Turbomach. 118 (1996) 613e621. [6] S. Friedrichs, H.P. Hodson, W.N. Dawes, Aerodynamic aspects of endwall filmcooling, ASME J. Turbomach. 119 (1997) 786e793. [7] S. Friedrichs, H.P. Hodson, W.N. Dawes, The design of an improved endwall film-cooling configuration, ASME J. Turbomach. 121 (1999) 772e780. [8] F. Kost, M. Nicklas, Film-cooled turbine endwall in a transonic flow field: part I e aerodynamic measurements, ASME J. Turbomach. 123 (2001) 709e719. [9] M. Nicklas, Film-cooled turbine endwall in a transonic flow field: part II e heat transfer and film-cooling effectiveness, ASME J. Turbomach. 123 (2001) 720e729. [10] D.G. Knost, K.A. Thole, Adiabatic effectiveness measurements of endwall filmcooling for a first stage vane, in: Proceedings of ASME Turbo Expo Conf., 2004. Vienna, Austria, ASME Paper No. GT-2004e53326. [11] K.A. Thole, D.G. Knost, Heat transfer and film-cooling for the endwall of a first stage turbine vane, Int. J. Heat Mass Transf. 48 (2005) 5255e5269. [12] G. Barigozzi, G. Benzoni, G. Franchini, A. Perdichizzi, Fan-shaped hole effects on the aero-thermal performance of a film-cooled endwall, ASME J. Turbomach. 128 (2006) 43e52.
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[13] W. Colban, K.A. Thole, M. Haendler, A comparison of cylindrical and fan-shaped film-cooling holes on a vane endwall at low and high freestream turbulence levels, ASME J. Turbomach. 130 (2008), 0310071/031007-9. [14] F. Satta, G. Tanda, Measurement of local heat transfer coefficient on the endwall of a turbine blade cascade by liquid crystal thermography, Exp. Therm. Fluid Sci. 58 (2014) 209e215. [15] M. Sacchi, D. Simoni, M. Ubaldi, P. Zunino, S. Zecchi, Endwall effusion cooling system behaviour within a high-pressure turbine cascade. Part 1: aerodynamic measurements, in: Proceedings of ASME Turbo Expo Conf., 2010. Glasgow, U.K., ASME Paper GT2010e22931. [16] C.S. Yang, C.L. Lin, C. Gau, Film cooling performance and heat transfer over an inclined film-cooled surface at different convergent angles with respect to highly turbulent mainstream, Appl. Therm. Eng. 29 (2009) 167e177. [17] E. Lutum, J. von Wolfersdorf, B. Weigand, K. Semmler, Film cooling on a convex surface with zero pressure gradient flow, Int. J. Heat Mass Transf. 43 (2000) 2973e2987.
[18] S. Ou, R.B. Rivir, Leading edge film cooling heat transfer with high free stream turbulence using a transient liquid crystal image method, Int. J. Heat Fluid Flow 22 (2001) 614e623. [19] G. Vogel, A.B.A. Graf, J. von Wolfersdorf, B. Weigand, A novel transient heaterfoil technique for liquid crystal experiments on film-cooled surfaces, ASME J. Turbomach. 125 (2003) 529e537. [20] C. Zhang, B. Song, Y. Lin, Q. Xu, G. Liu, Cooling effectiveness of effusion walls with deflection hole angles measured by infrared imaging, Appl. Therm. Eng. 29 (2009) 966e972. [21] M.G. Ghorab, Film cooling effectiveness and net heat flux reduction of advanced cooling schemes using thermochromic liquid crystal, Appl. Therm. Eng. 31 (2011) 77e92. [22] P.T. Ireland, T.V. Jones, Liquid crystal measurements of heat transfer and surface shear stress, Meas. Sci. Technol. 11 (2000) 969e986. [23] R.J. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3e17.
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Research paper
Effect of discrete-hole arrangement on film-cooling effectiveness for the endwall of a turbine blade cascade Francesca Satta*, Giovanni Tanda degli Studi di Genova, via Montallegro 1, I-16145 Genova, Italy DIME/MASET, Universita
h i g h l i g h t s Film cooling in a turbine cascade endwall with discrete holes was investigated. Two different discrete-hole configurations have been considered. The adiabatic film-cooling effectiveness was measured by liquid crystal thermography. Maps of effectiveness were used to compare the performance of two hole arrangements. Effectiveness was selectively averaged in regions at the largest heat transfer need.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 April 2015 Accepted 24 July 2015 Available online 12 August 2015
This paper investigates film cooling in a turbine cascade endwall for two discrete-hole configurations using liquid crystal thermography. The discrete holes, arranged in rows aligned in the pitchwise direction, gave rise to relative maxima of film-cooling effectiveness downstream of each row, followed by a marked decrease of effectiveness along the gap between adjacent rows of holes. This resulted in a not efficient coverage of the endwall surface, with succession of over- and under-cooled regions. The redesign of discrete-hole configuration, based on knowledge of the heat transfer coefficient map on the endwall without film cooling, enabled the redistribution of the coolant to provide a better coverage of the endwall and a significant increase of the area-averaged film-cooling effectiveness. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Film cooling Endwall Turbine cascade Liquid crystals
1. Introduction Film cooling has been widely used in high-performance gas turbine to protect turbine blades and endwalls from being damaged by hot gases [1]. It is based on the introduction of a secondary fluid (the coolant) through injection holes or slots placed in the blade and endwall material to form a protective layer between the surface and the hot mainstream gas. Endwall film cooling and associated heat transfer are strongly influenced by the secondary flow effects. Thus, locating filmcooling holes requires a deep understanding of secondary flow behaviour and associated heat transfer. Blair [2] was the first to measure the film-cooling effectiveness and convective heat transfer coefficient distributions on the endwall of a large-scale turbine vane passage. A cooling slot upstream of the passage channel
* Corresponding author. E-mail address: [email protected] (F. Satta). http://dx.doi.org/10.1016/j.applthermaleng.2015.07.082 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
leading edge was employed and results, obtained from several thermocouples embedded in the wall material, were presented for a range of blowing ratios. One of the key findings was that the effectiveness distributions showed extreme variations across the vane passage with much of the coolant from the upstream injection slot being swept across the endwall toward the suction side corner. Takeishi et al. [3] measured the film-cooling effectiveness distributions on the blade and endwall surfaces of a low speed, fully annular, low aspect ratio vane cascade, using surface-mounted thermocouples. Film-cooling holes were placed on the model vanes and on the inner and outer endwalls. They found that passage secondary flows strongly affect heat transfer and film cooling on the suction surface of the vane and the endwalls. Film-cooling performance for injection through discrete holes in a turbine blade endwall was investigated by Jabbari et al. [4] by using a mass transfer technique based on ammoniumediazo-paper. Visualization experiments revealed the paths and interaction of the jets, which changed with blowing and density ratios. Friedrichs et al. [5e7] conducted aerodynamic and film-cooling measurements for
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a cascade endwall; the ammonia and diazo technique was employed to measure the film-cooling effectiveness. They indicated a marked influence of the secondary flows on the film cooling and, at the same time, an influence of the film cooling on the secondary flows. An improved endwall film-cooling configuration was tested experimentally and results were compared with those obtained for a baseline cooling configuration, consisting of rows of holes at four axial positions [7]. More recently, Kost and Nicklas [8] and Nicklas [9] investigated the aero-thermal behaviour of a transonic cascade with endwall film cooling. Similar investigations, but on different endwall cooling schemes, were also performed by Knost and Thole [10,11]. In Refs. [8e11], a combination of cooling from an upstream slot with film-cooling holes in the passage of the vane was considered; filmcooling effectiveness results were obtained by using the infrared thermography as diagnostic tool. Significant improvement can be achieved in cooling characteristics of the film by using cooling holes with appropriately designed expanded exits, which are able to provide better lateral coverage and better centreline effectiveness. Barigozzi et al. [12] and Colban et al. [13] experimentally studied (by liquid-crystal and infra-red thermography, respectively) the effect of fan-shaped film-cooling holes for a vane endwall. Fan-shaped holes were found to give a superior cooling performance compared to that of cylindrical holes, but with the drawback of increased manufacturing cost and difficulty, particularly for the vane platform region. The aim of the present study is to investigate the film-cooling effectiveness improvement gained by the re-design of the cooling configuration, based on knowledge of the heat transfer coefficient map with no film cooling measured in Ref. [14], without introducing any larger complexity in the real machine manufacturing (hence avoiding fan-shaped holes, for example, or very expensive micro-holed surfaces).
2. Experimental facility The experiments were performed in a blow-down type wind tunnel housing a large-scale high-pressure turbine blade cascade (Fig. 1). An auxiliary apparatus was used to inject a secondary fluid
for the film-cooling of the cascade endwall. For practical reasons, the experiments were conducted with a cold air mainstream as primary fluid and a hot “coolant” air flow as secondary fluid according to a common practice followed in similar investigations. The coolant air flow, controlled by a variable speed fan and measured by means of a Venturi flowmeter, was heated by an electric heater and delivered to a plenum located underneath the cascade endwall. This process resulted in temperature differences between the coolant and mainstream in the 9e35 K range. 2.1. Test section and film-cooling geometry The linear cascade, shown in Fig. 1, is characterized by a blade chord of 312.5 mm, a height of 210.2 mm and a cascade pitch of 339.4 mm. The flow entered at a zero angle. The Zweifel coefficient of the cascade was 1.01. The endwall boundary layer at the cascade inlet was 18 mm thick with a displacement thickness of 2.22 mm, a momentum thickness of 1.92 mm, and a shape factor of 1.16. Fillets with a round profile extending for 10 mm along the endwall and blade surfaces were used for contouring. Since periodicity attainment required at least three passages, cascade consisted of four blades; measurements were performed in the central passage, where the heated endwall was located. The cascade periodicity, imposed by the modification of the flexible tailboards installed at the exit of the external blades, has been then checked by comparing the aerodynamic loadings measured over the two central blades. The investigated blade cascade has been previously aerodynamically tested without film cooling in Ref. [15]; similarly, endwall heat transfer without film cooling was experimentally studied in Ref. [14]. For the film-cooling experiments, the filmcooled endwall region was made of a 19 mm-thick layer of balsa wood having a low thermal conductivity (¼0.065 W/mK), in order to provide a nearly adiabatic surface, suitable to allow adiabatic film-cooling effectiveness measurements. The endwall regions immediately upstream and in the passage of the cascade featured discrete holes, arranged according to the two different layouts shown in Fig. 2. Regardless of the discretehole geometry, all the holes were cylindrical in shape, had a diameter of 5 mm (length to diameter ratio of 7.6) and ejected at a
Fig. 1. Schematic of the experimental facility and of the turbine cascade. Dimensions in [mm].
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509
(mainly downstream of the cascade throat); moderate-to-high heat transfer coefficients (region B) were found at the endwall entrance (as a result of the thin inlet thermal boundary layer), in the vicinity of blade pressure and suction sides, and around an imaginary line probably representing the footprint of the horseshoe vortex travelling along the lift-off line. Region A is featured by relatively low heat transfer coefficients. Therefore, discrete holes for configuration No.2 were placed in order to provide the necessary coolant coverage of regions B and C, as dictated by the actual heat transfer conditions. 2.2. Measurement technique and procedure
Fig. 2. Film-cooling layout and specifications; (a) configuration No.1, (b) configuration No.2. Black ellipses indicate hole exit locations on the blade passage side of the endwall; exit angles are indicated too.
30 inclination angle to the endwall surface. These geometric parameters are typical of endwall film-cooling configurations [6]. The exit angle is indicated in the respective figures. The number of filmcooling holes for both geometries was 29, in order to fix the same overall passage surface area. The first discrete-hole configuration (No.1, Fig. 2a), was designed according to a standard arrangement of holes and consisted of four rows of holes, aligned in the pitchwise direction, and located at different axial positions: immediately upstream of the cascade and at 30%, 60% and 90% of axial chord Cx. The second configuration (No.2, Fig. 2b), has been designed in this study for the purpose of improving the cooling performance on the basis of heat transfer experiments performed without film cooling [14], which indicated the endwall regions at the highest heat transfer coefficients requiring the highest coolant coverage (Fig. 3). Basically, a high heat transfer coefficient was recorded in region C
Fig. 3. Map of the endwall regions characterized by different values of the heat transfer coefficient without film cooling [14].
Various experimental methods have been used in the literature for the film-cooling effectiveness measurement: heating foils and thermocouples [2,3,16], the mass-transfer analogy [4,5,7], and thermal imaging techniques [9e13,17e21]. In the present work, liquid crystal (LC) thermography was used due to its ease of application and low cost. Detailed full field surface information can be obtained by heat transfer and film-cooling LC experiments performed according to steady-state or transient procedures [22]. In principle, the steadystate method is more time-consuming since each experiment can last several hours against few minutes required by the transient method. However, transient method may pose some difficulties when applied to a real cascade due to 3-D conduction effects in the endwall material, especially in the vicinity of the ejection holes. In this research the film-cooling effectiveness was deduced by LC measurements (and mainstream and coolant temperature measurements) taken at the end of a steady-state experiment. A pre-packaged LC sheet (Hallcrest R30C5W, bandwidth 5 C, red start at 30 C and blue start at 35 C), was used to detect the surface temperature of the endwall. The LC sheet, 0.15 mm thick, consisted of a thin LC layer laid on a thin transparent Mylar film and backed with a black background paint and a pressure-sensitive adhesive. The relationship between the colour (hue) and temperature of the LCs was obtained by means of a calibration experiment, described in Ref. [14] and performed in situ (i.e., same camera, illumination and viewing conditions as in the real experiment). In particular, for both calibration and film-cooling experiments, the colour distribution of the LCs was taken by a Nikon D-70 camera (through a Plexiglas optical window opposite to the endwall surface). A set of LED (light emitting diodes)-based light sources was used to provide a uniform lighting of the test section. LC images were transformed from the RGB (Red, Green, Blue) to the HSI (Hue, Saturation, Intensity) colour domain and processed to obtain the wall temperature from the hue distribution. Sheathed, 0.5 mm-dia, type-T thermocouples, with exposed junctions, were employed to measure the mainstream air temperature and the coolant temperature in the hole passage (for a limited number of holes) and in the plenum. Variations of coolant temperature between the plenum and the hole exit were typically registered due to the expected convective heat transfer between the coolant and the hole passage internal surface. A simple theoretical model has been developed to predict the coolant temperature drop from the plenum to the hole exit. The calculated temperature drop was always in very good agreement with the spot thermocouple measurements at the inlet/outlet hole sections and its extent was found to increase with the coolant-to-mainstream temperature difference and to decrease with the coolant mass flow rate. Calculated coolant temperature variations within the hole passages were generally equal to 7% of the plenum-tomainstream air temperature difference, irrespective of the blowing ratio and the discrete-hole configuration. These calculated values were adopted to correct the measured coolant temperature
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in the plenum and achieve a more realistic evaluation of Tc at the hole exit. The adiabatic film-cooling effectiveness is introduced as:
h¼
Tw T∞ Tc T∞
(1)
where T∞ is the mainstream air temperature, Tw is the endwall surface temperature and Tc is the coolant temperature. To support the assumption of adiabatic endwall conditions, the uncooled effectiveness has been calculated by a heat balance, at each point of the endwallemainstream interface, between the heat conducted through the balsa wood layer and the heat transferred by convection to the mainstream, by applying a given temperature difference between the coolant in the plenum and the mainstream air flow without coolant ejection. The uncooled effectiveness was found to be related to the conductive thermal resistance of the balsa layer and to the endwall heat transfer coefficient h, here taken as that measured for the endwall without film cooling [14]. In the regions far from hole exits, the uncooled effectiveness, deduced by a simple 1-D conduction model, was found to be in the range from 0.015 to 0.048. A special care was taken to evaluate the uncooled effectiveness immediately upstream of each injection hole where the thermal resistance of the material is lower and not uniform (due to the presence of the inclined holes and the reduction in the material thickness) and tangential conductive heat transfer tends to markedly affect the results; for this reason a 3-D conduction model has been adopted over these specific areas. The calculated values of the local uncooled effectiveness were finally used to correct the measured values of film-cooling effectiveness. 2.3. Test conditions During each test, the cascade was operating with a Reynolds number of 960,000, based on the chord length (¼0.3125 m) and the isentropic exit velocity (¼48 m/s). The mainstream air was taken at ambient temperature (about 27 C) with an average inlet velocity of about 13.5 m/s and an inlet turbulence intensity of 1%. The Mach number and turbulence intensity are low as compared with the actual engine conditions but deemed sufficient to understand the 3-D flow effect on film cooling as the discrete-hole cooling arrangement is modified. A nominal blowing ratio M based on the coolant and mainstream mass velocities was defined as:
M¼
. mc Aholes r∞ U∞
hole. In order to infer local characteristics for each cooling hole, the following equation can be used:
Mlocal
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi po;plenum p rc ¼ rinlet po;inlet p
(4)
where p is the local static pressure at the exit of the cooling hole, measured at the endwall without film cooling. Experiments were performed for three values of the nominal blowing ratio M, namely for M ¼ 2.5, 3.0 and 3.5 (which correspond to Minlet ¼ 1.0, 1.5, 2.0, respectively). The minimum blowing ratio value tested was the one for which the total pressure in the plenum was slightly larger than that at the mainflow inlet, this in order to avoid a reverse flow and consequently suction instead of blowing through the first row of holes. The jet-to-mainstream density ratio was in the 0.9e0.97 range. A representative example of the calculated local blowing ratios Mlocal is shown in Fig. 4, for the largest nominal blowing ratio investigated. For both configurations, local blowing ratio variations up to 50e60% were found, with maximum values near the front of blade pressure side and minimum values near the rear of the blade suction side and close to the passage exit. As the nominal blowing ratio is reduced, a more uniform distribution of Mlocal is progressively achieved. 2.4. Experimental uncertainty The uncertainty (at the 95% confidence level) in the film-cooling effectiveness measurement was evaluated according to the procedure outlined by Moffat [23]. The random uncertainty was determined by taking the standard deviation of measurements repeated under the same operating conditions. The fixed uncertainty was evaluated by taking into account errors associated with temperature (by LCs and thermocouples) readings and conceptual errors associated with the evaluation of the coolant exit temperature and the correction done to take into account the heat conduction in the
(2)
where mc is the total coolant mass flow, Aholes is the total injection area, while r∞ and U∞ are density and mean velocity of mainstream air at inlet conditions. An alternative definition of blowing ratio based on pressure differences has been considered, too:
Minlet ¼
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi po;plenum pinlet rc rinlet po;inlet pinlet
(3)
where (rc/rinlet) is the jet-to-mainstream density ratio, po,plenum and po,inlet are the plenum and inlet stagnation pressures, respectively, while pinlet is the inlet static pressure. Minlet is the blowing ratio that an idealized loss free coolant hole would have when ejecting to inlet conditions. The blowing ratios introduced by Eqs. (2) and (3) are different from the local blowing ratio, which is defined individually for each
Fig. 4. Local blowing ratio evaluated from static pressures at the endwall without film cooling.
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endwall material. The total uncertainty in the h measurement turned out to be ±12% at h ¼ 0.15 and ±8% at h ¼ 0.6.
511
Contours of film-cooling effectiveness, for all of the blowing ratios, are shown in Fig. 5 (configuration No.1) and 6 (configuration No.2). Generally speaking, the majority of the cooling footprints showed individual jets, displaying little lateral spreading downstream of most of the holes. Holes placed directly upstream of other holes seemed to increase the cooling benefit from the downstream hole since the upstream cooling prevented the natural jet lift-off
that would occur otherwise, as observed in previous literature studies (for instance [12]). Upstream of the leading edge, the effect of the horseshoe vortex is visible, especially for configuration No.1 (Fig. 5), where the ejected coolant was not able to efficiently cover the endwall region downstream of the first row of holes and close to the pressure surface. This finding is consistent with results presented in Refs. [5,11] under similar operating and geometry conditions. For configuration No.2 (Fig. 6), holes upstream of the leading edge were mainly placed on the front of turbine blades; as a consequence, a large endwall region, triangular in shape, appears to be virtually unprotected. As inferred from Fig. 3, in this region the need for cooling is relatively small; therefore, the solution adopted in the
Fig. 5. Contours of film-cooling effectiveness for configuration No.1 and different blowing ratios.
Fig. 6. Contours of film-cooling effectiveness for configuration No.2 and different blowing ratios.
3. Results and discussion
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Configuration No.1
-0.4 -0.2
-0.2
M = 2.5 M=3 M = 3.5
0 0.2
0.2 0.4
x/Cx
x/Cx
M = 2.5 M=3 M = 3.5
0
0.4 0.6
0.6
0.8
0.8
1
1
1.2
1.2
1.4
1.4
1.6
Configuration No.2
-0.4
0
0.1
0.2
0.3
η
0.4
0.5
1.6
0.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Fig. 7. Axial variations of pitchwise-averaged film-cooling effectiveness at different blowing ratios, for the two discrete-hole configurations.
design of configuration No.2 permitted to save coolant that otherwise would feed regions not requiring film cooling. In the first half of the blade passage, the fluid ejected near the suction side was clearly swept in the direction of the streamlines for both discrete-hole configurations. Conversely, near the pressure side region, a different behaviour was observed: for the configuration No.1, the trajectories coming from the second and third holes from the pressure surface located on the second row (at 30% of axial chord) are turned toward the suction surface despite their orientation angles in the direction of mainstream line. This local deflection resulted in an uncooled region between the second and the third rows of holes close to the pressure surface. This effect is mitigated for the configuration No.2, where the holes are not displaced in-line but fitted close to the pressure surface and along the line approximately lying halfway between the pressure and suction surfaces. Attention is now given to the region in the middle of the blade passage: for configuration No.1, at 60% of axial chord, the traces of jets emerging from the second to fourth hole from the pressure surface merge downstream of the holes, while the first hole (close to the pressure surface) and the last two holes (close to the suction surface) provided individual coolant jets whose trajectories are
M = 2.5
-0.4 -0.2
-0.2
-0.2
0.2
0.4
0.4
x/Cx
0.2
0.4
0.6 0.8
0.8
0.6 0.8
1
1
1
1.2
1.2
1.2
1.4
1.4
1.4
1.6
1.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Config. No.1 Config. No.2
0
0.2
0.6
M = 3.5
-0.4
Config. No.1 Config. No.2
0
x/Cx
x/Cx
M=3
-0.4
Config. No.1 Config. No.2
0
approximately in the inviscid streamline direction. In the same endwall region, the pattern of film-cooling effectiveness for configuration No.2, where holes are aligned in the mainstream direction, reflects the position of cooling holes: a strip at low effectiveness, parallel to the pressure side is generated in correspondence of a region at low heat transfer coefficients. Contrary to what observed by Friedrichs [7], the ejected jets from holes located in the midline between suction and pressure surfaces are not significantly affected by crossflow, but appear to be mainly directed along the inviscid streamline direction. Due to the relative vicinity of holes in this area, the traces merge to form a region at a relatively high level of cooling effectiveness. Finally, the cooling holes located close to the blade passage outlet display again different patterns of h depending on the specific configuration. When the holes are aligned at 90% axial chord (configuration No.1), the coolant jets merge at a high film-cooling effectiveness, extending from the hole exits to the vicinity of the suction side trailing edge. The different hole placement for configuration No.2 provides, on the same endwall region, lower h values immediately downstream of the hole exits as compared to those for configuration No.1, but a coolant coverage on a markedly larger endwall area of potentially high heat transfer.
0
0.1
0.2
0.3
η
0.4
0.5
0.6
1.6
0
0.1
0.2
0.3
η
0.4
0.5
0.6
Fig. 8. Comparisons between pitchwise-averaged film-cooling effectiveness distributions for configuration No.1 and No.2, at different blowing ratios. Only endwall regions at mediumehigh heat transfer coefficient were considered in each pitchwise average.
F. Satta, G. Tanda / Applied Thermal Engineering 91 (2015) 507e514 Table 1 Mean h-values obtained averaging the film cooling effectiveness in the different zones identified by the convective heat transfer coefficient map reported in Fig. 3. Configuration
No.1 No.1 No.1 No.2 No.2 No.2
M
2.5 3.0 3.5 2.5 3.0 3.5
Minlet
1.0 1.5 2.0 1.0 1.5 2.0
Region A
B
C
BþC
AþBþC
0.167 0.133 0.111 0.107 0.090 0.073
0.200 0.180 0.166 0.210 0.179 0.163
0.076 0.107 0.147 0.151 0.169 0.197
0.141 0.146 0.157 0.182 0.174 0.179
0.148 0.142 0.145 0.163 0.153 0.152
3.1. Effect of blowing ratio Fig. 7 reports the pitchwise-averaged distributions of h along the dimensionless axial coordinate x/Cx, at different blowing ratios, for both configurations. Generally speaking, in the blade passage region, the pitchwise-averaged effectiveness for configuration No.1 shows a relative maximum immediately downstream of each row of holes and the extent of the relative maximum increases with the distance in the axial direction (as found in Refs. [5,12]). However, due to the shortness of the ejected jet trajectories, the pitchwiseaveraged h distribution rapidly decays downstream of hole exits, originating large regions of relatively low cooling effectiveness. Conversely, configuration No.2 provides a more uniform h distribution along the streamwise direction and, at the same time, the cooling effect is more persistent for a larger distance downstream of the last row of holes. It is apparent from Fig. 7 that the best cooling performance was achieved, for both configurations, at the lowest blowing ratio (M ¼ 2.5), except for the endwall region immediately downstream of the cascade passage (x/Cx > 1). Indeed, within the vane passage, as the blowing ratio is increased, the increased jet lift-off from the holes is probably responsible for the attenuation of relative maxima in h displayed by config. No.1 and for the generalized, slight reduction in h observed for config. No.2. Conversely, for x/Cx > 1, the augmentation of the coolant coverage, especially for config. No.2, as M is increased can be due to the fact that local blowing ratios for the last row of holes are lower than elsewhere (and probably below the lift-off limit), even for the largest injection, as can be inferred from Fig. 4. 3.2. Effect of the film-cooling geometry The comparison of film-cooling effectiveness provided by the two discrete-hole configurations has to take into account the local need for cooling, far from being uniform over the endwall in real applications. Therefore, only local h data included in the endwall region B and C of Fig. 3, where the need for cooling is significant, were considered in the pitchwise averages reported in Fig. 8. The comparison shows that the holes of configuration No.2, which do not feed the low heat transfer regions located in the first half of the blade passage, provide a better coverage where the demand for cooling is higher. Moreover, the pitchwise-averaged film-cooling effectiveness for configuration No.2 is more evenly distributed along the axial direction, thus providing a fairly uniform coolant coverage over the endwall regions featured by a relatively high cooling need. 3.3. Area-averaged film-cooling effectiveness The mean h values obtained by averaging the film-cooling effectiveness over regions A, B, and C are reported in Table 1. Data averaged over individual areas show that mean h values for
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configuration No.1 are larger in region A, where the demand for cooling is the smallest, while configuration No.2 provides better results in region C, where the convective heat transfer is the largest. Here the film-cooling effectiveness is as higher as the blowing ratio is increased, which is the opposite of what occurs within the two other regions, as outlined in the comment to Fig. 7. Of particular relevance are the mean values obtained averaging h over the entire endwall area (A þ B þ C) and over the mediumehigh heat transfer area (B þ C). The h values averaged over the entire endwall area indicate a better performance of the configuration No.2; this is much more evident when only the area interested by high heat transfer values (region B þ C) is considered, with relative enhancements from þ14% (at M ¼ 3.5) to þ29% (at M ¼ 2.5). This finding is consistent with results presented in Ref. [7] for similar cascade and operating conditions, where an improved cooling configuration, designed according to a different criterion (based on the computed aerodynamic losses, rather than on the heat transfer coefficient distribution as in the present case), provided a better performance as compared to a standard cooling configuration, especially at the lowest inlet blowing ratio investigated. 4. Conclusions The arrangement of discrete holes for the film cooling of a turbine cascade endwall has a marked effect on the distribution of the film-cooling effectiveness and on the coolant coverage on the endwall surface. A standard arrangement provided by rows of holes aligned along the pitchwise direction leads to overcooled regions just immediately downstream of each hole row and to undercooled regions in the space between hole rows. A different distribution of coolant through holes located where the cooling demand is expected to be higher has been found to allow a more uniform cooling of the endwall and a larger coolant coverage. An increase in the film-cooling effectiveness, averaged over endwall regions where the heat transfer coefficient is relatively high (and the need for cooling too), of up to 29% is provided by the configuration having hole location re-designed on the basis of the heat transfer coefficient distribution. References [1] J.C. Han, S. Dutta, S. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, second ed., CRC Press, Taylor & Francis, 2013. [2] M.F. Blair, An experimental study of heat transfer and film cooling on largescale turbine endwalls, ASME J. Heat Transf. 96 (1974) 524e529. [3] K. Takeishi, M. Matsuura, S. Aoki, T. Sato, An experimental study of heat transfer and film cooling on low aspect ratio turbine nozzles, ASME J. Turbomach. 112 (1990) 488e496. [4] M.Y. Jabbari, K.C. Marston, E.R.G. Eckert, R.J. Goldstein, Film cooling of the gas turbine endwall by discrete-hole injection, ASME J. Turbomach. 118 (1996) 278e284. [5] S. Friedrichs, H.P. Hodson, W.N. Dawes, Distribution of film-cooling effectiveness on a turbine endwall measured with the ammonia and diazo technique, ASME J. Turbomach. 118 (1996) 613e621. [6] S. Friedrichs, H.P. Hodson, W.N. Dawes, Aerodynamic aspects of endwall filmcooling, ASME J. Turbomach. 119 (1997) 786e793. [7] S. Friedrichs, H.P. Hodson, W.N. Dawes, The design of an improved endwall film-cooling configuration, ASME J. Turbomach. 121 (1999) 772e780. [8] F. Kost, M. Nicklas, Film-cooled turbine endwall in a transonic flow field: part I e aerodynamic measurements, ASME J. Turbomach. 123 (2001) 709e719. [9] M. Nicklas, Film-cooled turbine endwall in a transonic flow field: part II e heat transfer and film-cooling effectiveness, ASME J. Turbomach. 123 (2001) 720e729. [10] D.G. Knost, K.A. Thole, Adiabatic effectiveness measurements of endwall filmcooling for a first stage vane, in: Proceedings of ASME Turbo Expo Conf., 2004. Vienna, Austria, ASME Paper No. GT-2004e53326. [11] K.A. Thole, D.G. Knost, Heat transfer and film-cooling for the endwall of a first stage turbine vane, Int. J. Heat Mass Transf. 48 (2005) 5255e5269. [12] G. Barigozzi, G. Benzoni, G. Franchini, A. Perdichizzi, Fan-shaped hole effects on the aero-thermal performance of a film-cooled endwall, ASME J. Turbomach. 128 (2006) 43e52.
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