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Heat transfer in a rectangular duct with perforated blockages and dimpled side walls
International Journal of Heat and Mass Transfer 97 (2016) 224–231
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer in a rectangular duct with perforated blockages and dimpled side walls Jung Shin Park, Young Hwa Jo, Jae Su Kwak ⇑ School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang 412-729, Republic of Korea
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 15 December 2015 Accepted 25 January 2016
Keywords: Heat transfer Gas turbine blade Trailing edge cooling Compound cooling Perforated blockages
a b s t r a c t Heat transfer and pressure drop in a duct with three serial perforated blockages equipped with staggered jets were experimentally investigated. Eight types of jet holes and three types of side walls, including dimpled walls, were tested. For heat transfer measurements, the transient liquid crystal technique was used. Reynolds numbers based on the hydraulic diameter of the duct and inlet velocity ranged from about 10,000–30,000. Experimental results showed that the Nusselt number ratios decreased as the Reynolds number increased, and the friction factor ratios increased as the Reynolds number increased. The heat transfer coefficient and the pressure loss were strongly affected by the number and the configuration of jets. Compared to the smooth side wall case, the cases with dimpled side walls showed large increases in heat transfer with slight increments in pressure loss. Therefore, it was determined that the thermal performance factor could be enhanced by up to 25% by using a dimpled side wall in the duct with perforated blockages. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Modern gas turbines are designed to allow for turbine inlet temperatures that exceed allowable material temperatures in order to improve turbine performance and power output. High temperature combustion gas and complex flow phenomena near the blade aggravate the heat transfer problem of the gas turbine blade. As such, various cooling techniques have been applied to blade cooling designs. Fig. 1 shows commonly used internal cooling techniques for a gas turbine blade. Impingement cooling, rib turbulated cooling, dimple cooling, and pin-fin cooling techniques have been widely applied to gas turbine cooling designs, and many studies have been conducted in order to improve the heat transfer performance of those techniques [1]. Some researchers have proposed new concepts with respect to internal cooling techniques for the blade trailing edge. For example, Moon and Lau [3] investigated the pressure drop and heat transfer on a rectangular duct with two perforated blockage configurations. They showed that the number of walls and the configuration of holes did not significantly affect the heat transfer augmentation level. Lau et al. [4] investigated the heat transfer for the flow moving through blockages with holes in an internal cooling passage near the trailing edge region by using naphthalene
⇑ Corresponding author. E-mail address: [email protected] (J.S. Kwak). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.01.081 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
sublimation. They studied the effects of inlet and exit geometry configurations and showed that the effects of the entrance channel and exit slot geometries were not significant to the average heat (mass) transfer or the distribution of the local heat (mass) transfer. Saha et al. [5] looked at the heat transfer and friction factor of a converging matrix structure with orthogonal ribs representing a gas turbine blade trailing-edge cooling passage. They showed that the matrix structure could result in an averaged Nusselt number enhancement factor of 3–4. Armellini et al. [6] and Coletti et al. [7] conducted experimental and numerical investigations of a trapezoidal cross-section model simulating a trailing edge cooling cavity with one rib-roughened wall and crossing jets. The interaction between the jets and ribs increased the heat transfer coefficient on both the bottom and upper wall. Shin and Kwak [8] measured the heat transfer coefficient in a turbine blade internal cooling passage model with five types of blockages. They showed that staggered impingement jets increased the heat transfer. However, the pressure drop also increased greatly. They concluded that the thermal performance for the perforated blockage could be improved by optimizing the hole shape. Kan et al. [9] investigated the combined effects between perforated blockages and pin fins in a cooling passage. Six different blockage configurations were investigated using both experimental and numerical methods. They showed that the hole-to-channel area ratio is the most important factor for heat transfer enhancement. Smaller area ratio cases showed larger heat transfer enhancements and larger pressure
J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
225
Nomenclature Dh f h k p Pr Re T
hydraulic diameter, mm friction factor heat transfer coefficient, W/m2 K thermal conductivity, W/m K pressure, pa Prandtl number of air Reynolds number temperature, °C or K
drops. Ahn et al. [10] studied the turbulent forced convective mass transfer downstream of blockages with round and elongated holes in a rectangular channel using naphthalene sublimation. They investigated the effects of the hole aspect ratios, for each holeto-channel area ratio, on the exposed channel wall. They found that the elongated holes showed a higher overall mass transfer on the channel wall than the round holes. Chung et al. [11] investigated the effects of the array pattern, hole size, and hole direction for the heat transfer and pressure loss on the side wall of a rectangular channel. They showed that the proposed inclined holes array presented improved cooling performance over a conventional configuration. Previous research [3,4,8–11] has explored the possibility of improving the thermal performance of the internal cooling with perforated blockages. In this study, a compound internal cooling technique for the turbine blade trailing edge with repeated perforated blockages and dimpled side walls is proposed. Eight types of blockage holes were considered, and two of them were selected to be tested with the dimpled side walls. The effects of the jet hole and side wall configurations on the heat transfer and pressure loss were experimentally investigated.
2. Experimental setup and measurement methods Fig. 2 shows the schematic of the test setup. The test setup consisted of a blower, a Venturi flow meter, an electrical heater (12 kW), two pneumatic valves with solenoid valves, a plenum
t
a
transient time, s thermal diffusivity of blade material, m2/s
Subscripts 0 for fully developed turbulent flow in a smooth duct i initial condition m mainstream w wall of test surface
chamber, and a rectangular duct with perforated blockages. Air was heated by the electrical heater and bypassed until a predetermined air temperature was reached. Then, the heated air was diverted toward the test section via the two pneumatic valves. A 280-mm wide, 35-mm high duct was connected to the plenum chamber, and three perforated blockages were installed in the duct. Fig. 3 presents a detailed view of the heat transfer measurement region. The heat transfer coefficient was measured on the side walls between the perforated blockages. Liquid crystals (35C1W, Hallcrest) were sprayed on the side wall, and black paint was sprayed over the liquid crystal coating. The color change of the liquid crystals was recorded using a digital CCD camera (AVT Stingray F033C) from the back of the liquid crystal coated surface, as shown in Fig. 2. Before conducting the heat transfer tests, the relation between the hue of the liquid crystals and the temperature was calibrated. Black paint and liquid crystals were sprayed on the 5-mm thick aluminum plate, and the temperature of the plate was controlled by a temperature controller. At each temperature step, the hue value was calculated from the color of the liquid crystals. Fig. 4 presents the liquid crystal calibration results. In order to measure the mainstream temperature for each heat transfer measurement plane, a total of five T-type thermocouples for each measurement plane were installed, as shown in Fig. 3. The pressure drop through the perforated blockages was measured from a total of ten pressure taps installed upstream and downstream of the heat transfer measurement planes. Fig. 5 presents the perforated blockages used in this study. The configuration of the blockages was selected by referring to results from the authors’ previous study [8], in which the case with wider holes and the case with the greater number of holes showed better performance. Each blockage set consisted of three perforated blockages with the same configuration except for the hole locations. Holes for each blockage were fabricated so that the jet from the upstream blockage impinged to the downstream blockage between the jets. Hole sizes were determined so that the flow area for each blockage was the same for all blockages. Table 1 lists the configuration of each perforated blockage. Fig. 6 shows the three types of side walls considered in this study. Fig. 6(a) shows the smooth side wall, and Fig. 6(b) and (c) show the dimpled cases with 15-mm and 7.5-mm diameter dimples, respectively. For both dimpled cases, the ratios of the dimple depth and dimple-to-dimple distance to the dimple diameter were 0.2 and 1.33, respectively. The transient liquid crystal technique was used to measure the heat transfer coefficient. For this technique, the test model was assumed to be a one-dimensional semi-infinite model with a convective boundary condition. The governing equation, initial, and boundary conditions are as follows:
@ 2 T 1 @T ¼ @x2 a @t Fig. 1. Commonly used internal cooling techniques for a gas turbine blade [2].
ð1Þ
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Fig. 2. Schematic of the experimental setup.
Fig. 4. Relation between the temperature and hue value.
Fig. 3. Detailed view of the heat transfer measurement region.
at t ¼ 0; T ¼ T i at x ¼ 0; k
ð2Þ
@T ¼ hðT w T m Þ @x
at x ! 1; T ¼ T i
ð3Þ ð4Þ
During the heat transfer test, the mainstream temperature varied with time due to the thermal inertia of the test section, and the variation of the mainstream temperature was assumed as a series of step changes. For the varying mainstream temperature case, the solution for the above equations at the surface are as follows [12].
" # pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! pffiffiffiffiffi X n h aðt si Þ h at T w T i ¼ ðT m;0 T i Þ F F DT m;i þ k k i¼1 where, FðxÞ ¼ 1 expðx ÞerfcðxÞ. 2
ð5Þ
In Eq. (5), the transient time (t) between the initial temperature (Ti) and the predetermined wall temperature (Tw) was calculated using the hue history of the liquid crystals at every pixel of the recorded images. The mainstream temperature (Tm) was the averaged temperature measured by the five thermocouples shown in Fig. 4. During the heat transfer measurement tests, the color of the liquid crystals was recorded using a digital CCD camera (Stingray F033C, AVT) and stored in a computer at a rate of 30 frames per seconds. From every image pixel, the hue was calculated and the transient time from the initial condition to the predetermined hue value was also calculated. This procedure was conducted using a Matlab-based image processing program. The details of the procedure were explained in Shin and Kwak [8]. The test duration time was limited in order to keep the temperature of the opposite side of the test section at its initial value. Wagner et al. [13] suggested a maximum test duration time by using Eq. (6).
attest duration 2
thickness
<
1 4
ð6Þ
For the current study, tduration time was about 190 s, and the transient test duration time was kept below 60 s. The averaged heat transfer coefficient was compared with that for the smooth duct with the same hydraulic diameter and Reynolds number. The Nusselt number (Nu) is defined by Eq. (7), and the Nusselt number for a fully developed turbulent flow in a smooth duct (Nu0) is calculated using Eq. (8) [14]:
Nu ¼
hDh ka
ð7Þ
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J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
Fig. 6. Side wall configurations.
Nu0 ¼
ðf 0 =8ÞðReDh 1000ÞPr ½1 þ 12:7ðf 0 =8Þ
1=2
ð8Þ
ðPr2=3 1Þ
Here, Dh is the hydraulic diameter of the test section, ka is the thermal conductivity of the air, and h is the heat transfer coefficient. f0 (the friction factor for a fully developed turbulent flow in a smooth duct), f (the Darcy friction factor), and the thermal performance factor (TP) are defined by Eqs. (9)–(11), respectively.
f 0 ¼ ½0:79ðReDh Þ 1:642 f ¼
ð9Þ
ðDp=DxÞDh qa u2 =2
TP ¼
ð10Þ
Nu=Nu0 ðf =f 0 Þ
ð11Þ
1=3
The measurement uncertainties [15,16] for the Nusselt number, Reynolds number, friction factor, and the thermal performance factor for a typical test case are estimated as 7.7%, 6.3%, 5.5%, and 8.2%, respectively. 3. Results and discussions Fig. 5. Perforated blockages: (a) 7 circular, (b) 7 wide, (c) 7 narrow, (d) 9 circular, (e) 11 circular, (f) 7 wide top–bottom, (g) 7 wide-45, (h) 7 wide-45/135.
Fig. 7 presents the Nusselt number distribution on the smooth side wall with various perforated blockages. The arrows in the fig-
Table 1 Perforated blockage configurations. Hole configuration
Hole diameter
Hole-to-hole distance
Hole length
Number of holes
Hole angle
7 circular 7 wide 7 narrow 9 circular 11 circular 7 wide top–bottom 7 wide – 45 7 wide – 45/135
20 mm 12 mm 12 mm 17.6 mm 16 mm 12 mm 12 mm 12 mm
40 mm 40 mm 40 mm 31.11 mm 25.45 mm 40 mm/17.5 mm 40 mm 40 mm
– 28.8 mm 28.8 mm – – 28.8 mm 28.8 mm 28.8 mm
7 7 7 9 11 7 7 7
– 0° 90° – – 0° 45° 45°/135°
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Fig. 7. Nusselt number distribution on the smooth side wall (Re = 10,000).
ures indicate the location of the jet holes. All cases showed traces of the jets and jet impingements. After the jets impinged to the downstream blockage, the flow turned toward the side walls and resulted in a high Nusselt number on the side wall near the downstream blockage. The increasing Nusselt number toward the downstream blockage is a trend that has been observed in previous studies [4,8]. Comparing Fig. 7(a), (b), and (c), the wide hole case (Fig. 7(b)) showed a more uniform Nusselt number distribution. This was followed by the 7 circular hole case (Fig. 7(a)) and the 7 narrow hole case (Fig. 7(c)). Therefore, it was concluded that the jet hole shape was able to significantly alter the Nusselt number distribution. The effects of the jet hole shape on the Nusselt number distribution were more significant at the first measurement plane. The effects of the number of holes can be observed by comparing Fig. 7(a), (d), and (e). As the number of circular holes increased from seven (Fig. 7(a)) to eleven (Fig. 7(e)), the Nusselt number distribution became more uniform in the spanwise direction. Closely located jets were able to easily merge with one another, and this resulted in a nearly two-dimensional Nusselt number distribution on the side walls. In order to investigate the effects of hole location, the wide holes were located near the top and bottom side wall, and Fig. 7
(f) shows the resulting Nusselt number distribution. Since some of the wide holes were placed near the side wall, the jets were able to enhance the heat transfer on the side wall, and this resulted in higher Nusselt numbers than in the case with middle height jet holes (Fig. 7(b)). However, the Nusselt number distribution was less uniform than it was for the 7 wide hole case (Fig. 7(b)). The effects of the wide hole orientation were also considered. Fig. 7(g) and (h) are the heat transfer measurement results for the angled wide hole cases. For the 45 degree case (Fig. 7(g)), the traces of the high Nusselt number shifted along the angle of the jet hole. For the 45/135 degree case (Fig. 7(h)), the Nusselt number was higher where two jets were located close to one another. However, the Nusselt number distribution was less uniform than that for the 45 degree case (Fig. 7(g)). Comparing Fig. 7(b), (c), and (g), the 45 degree case (Fig. 7(g)) showed greater uniformity than the narrow hole case (90 degrees, Fig. 7(c)). However, it showed less uniformity than the wide hole case (0 degrees, Fig. 7(b)). When the angled holes were placed in a cross pattern (Fig. 7(h)), the Nusselt number distribution was less uniform than it was for the 45 degree case (Fig. 7(g)). For the quantitative comparison of heat transfer augmentation via different perforated blockages, the Nusselt numbers on the first and second side walls were averaged, and Fig. 8 shows the overall
J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
Fig. 8. Averaged Nusselt number ratio for smooth side wall cases.
229
Fig. 10. Thermal performance factor for smooth side wall cases.
Fig. 9. Friction factor ratio for smooth side wall cases.
averaged Nusselt number ratio with smooth side walls. The overall averaged Nusselt number ratio was the highest for the 7 wide topbottom and 7 narrow hole cases, for which the jets were relatively close to the side walls. For the circular hole cases, the overall averaged Nusselt number ratio decreased as the number of holes increased. The angled wide hole cases – particularly the 7 wide 45/135 case – showed a relatively low Nusselt number augmentation since the jets for those cases were relatively far from the side walls. Fig. 9 shows the friction factor ratio for the smooth side wall cases calculated by Eqs. (8) and (9). For all cases, the friction factor ratio increased as the Reynolds number increased. Cases showing a high Nusselt number ratio presented a high friction factor. The 7 narrow and 7 wide top-bottom cases showed high pressure losses, while the 7 wide 45/135 case resulted in the lowest friction factor ratio. Fig. 10 presents the thermal performance factor for the smooth side wall cases calculated using Eq. (10). For all cases, the thermal performance factor decreased as the Reynolds number increased, and the thermal performance factor was less than 0.5. The cases with 7 wide angled holes showed the lowest thermal performance factors, and the other cases did not show a constant trend with the Reynolds number. Generally, cases with circular holes, the case with 7 wide holes, and the case with 7 wide top-bottom holes presented a high thermal performance factor. Among the tested perforated blockages, blockages showing the highest Nusselt number
Fig. 11. Nusselt number distribution on the dimpled side wall (Re = 10,000).
ratio and the highest thermal performance factor – the 7 wide top-bottom hole and 7 circular hole cases – were applied to the channel with dimpled side walls.
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Fig. 11 presents the Nusselt number distribution on the dimpled side wall. For all cases, the Nusselt number increased as the Reynolds number increased, and the heat transfer augmentation induced by the dimples was clearly observed. Compared to the smooth side wall case (Fig. 7), the dimpled side wall case did not show clear traces of the jets or impingements due to the flow disturbance caused by the dimples. Fig. 12 is the averaged Nusselt number ratio for the dimpled side wall cases with selected perforated blockages. The smooth side wall cases were also included for comparison. For both types of blockages, the dimpled side wall cases showed higher Nusselt number ratios than the smooth side wall cases, and all cases showed a decreasing Nusselt number ratio trend as the Reynolds number increased. The results also showed that the Nusselt number ratios for the small dimpled side wall were higher than those for the large dimpled side wall cases for both blockage configurations. Therefore, it could be concluded that dimples on side walls, especially smaller dimples, effectively increased the Nusselt number because of the enhanced flow disturbance created by the dimples. Small dimples were able to increase the Nusselt number up to16% for the 7 circular case and 22% for the 7 wide top-bottom case. As seen in Figs. 12 and 13, the dimpled side wall cases showed higher Nusselt number ratios, but the pressure loss was also larger
Fig. 14. Thermal performance factor for dimpled side wall cases.
than that for the smooth side wall cases. In order to confirm the advantages of using a dimpled side wall, the thermal performance factors for the dimpled and smooth side wall cases were calculated and presented in Fig. 14. For all cases, the thermal performance factor decreased as the Reynolds number increased. In Fig. 14, the side wall with small dimples showed the highest thermal performance factor, followed by the cases with large dimples. Small dimples on the side wall resulted in a 25% improvement in the thermal performance factor for the circular hole case and an 18% improvement for the 7 wide top-bottom hole case. Therefore, it can be said that dimples on the side wall in a duct with a perforated blockage are able to significantly improve thermal performance. 4. Conclusions In this study, the effects of perforated blockage and side wall configurations of a turbine blade trailing edge model on the heat transfer augmentation and pressure loss were experimentally investigated. A total of eight blockage types and three side wall types were considered. Based on the experimental results, the following conclusions have been derived.
Fig. 12. Averaged Nusselt number ratio for dimpled side wall cases.
(1) For all cases, the Nusselt number ratio and the thermal performance factor decreased as the Reynolds number increased. The friction factor ratio increased with the Reynolds number. (2) As the number of circular holes on the blockage increased, the distribution of the Nusselt number became more uniform. However, the overall averaged Nusselt number ratio and the thermal performance factor decreased. (3) The cases with jet holes close to the side walls showed high Nusselt number ratios. Generally, the cases with high Nusselt number ratios showed high pressure losses. (4) Dimpled side wall cases resulted in increased Nusselt numbers, but the pressure losses also increased slightly. The thermal performance factors for the dimpled side wall cases were higher than that for the smooth side wall case by up to 25%.
Acknowledgments
Fig. 13. Friction factor ratio for dimpled side wall cases.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A2A2A01002636).
J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
References [1] J.C. Han, S. Dutta, S.V. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, second ed., Taylor & Francis, New York, 2013. [2] J.S. Kwak, J.C. Han, Heat transfer coefficients and film-cooling effectiveness on a gas turbine blade tip, J. Heat Transfer 125 (3) (2003) 494–502. [3] S.W. Moon, S.C. Lau, Heat transfer between blockages with holes in a rectangular channel, J. Heat Transfer 125 (3) (2003) 587–594. [4] S.C. Lau, J. Cervantes, J.C. Han, R.J. Rudolph, Internal cooling near trailing edge of a gas turbine airfoil with cooling airflow through blockage with holes, in: Proc. of ASME Turbo Expo, Barcelona, Spain, GT2006-91230, 2006. [5] K. Saha, S. Guo, S. Acharya, C. Nakamata, Heat transfer and pressure measurements in a lattice-cooled trailing edge of a turbine airfoil, in: Proc. of ASME Turbo Expo, Berlin, Germany, GT2008-51324, 2008. [6] A. Armellini, F. Coletti, T. Arts, C. Scholtes, Aero-thermal investigation of a ribroughened trailing edge channel with crossing-jets. Part I: flow field analysis, in: Proc. of ASME Turbo Expo, Berlin, Germany, GT2008-50694, 2008. [7] F. Coletti, A. Armellini, T. Arts, C. Scholtes, Aero-thermal investigation of a ribroughened trailing edge channel with crossing-jets. Part II: heat transfer analysis, in: Proc. of ASME Turbo Expo, Berlin, Germany, GT2008-50695, 2008. [8] S. Shin, J.S. Kwak, Effect of hole shape on the heat transfer in a rectangular duct with perforated blockage walls, J. Mech. Sci. Technol. 22 (10) (2008) 1945– 1951.
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[9] R. Kan, J. Ren, H. Jiang, Combined effects of perforated blockages and pin fins in a trailing edge internal cooling duct, in: Proc. of ASME Turbo Expo, Dusseldorf, Germany, GT2014-25767, 2014. [10] H.S. Ahn, S.W. Lee, S.C. Lau, D. Banerjee, Mass (heat) transfer downstream of blockages with round and elongated holes in a rectangular channel, J. Heat Transfer 129 (12) (2007) 1676–1685. [11] H. Chung, J.S. Park, H.S. Sohn, D.H. Rhee, H.H. Cho, Trailing edge cooling of a gas turbine blade with perforated blockages with inclined holes, in: Proc. of ASME Turbo Expo, San Antonio, Texas, USA, GT2013-95445, 2013. [12] J.S. Kwak, Comparison of analytical superposition solutions of the transient liquid crystal technique, J. Thermophys. Heat Transfer 22 (2) (2008) 290–295. [13] G. Wagner, M. Kotulla, P. Ott, B. Weigand, J. von Wolfersdorf, The transient liquid crystal technique: influence of surface curvature and finite wall thickness, J. Turbomach. 127 (1) (2005) 175–182. [14] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Introduction Heat Transfer, fifth ed., Wiley, New York, 2007, pp. 484–488. [15] R.B. Abernethy, B.P. Bendict, R.B. Dowdell, ASME measurement uncertainty, J. Fluids Eng. 107 (2) (1985) 161–164. [16] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 75 (1) (1953) 3–8.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer in a rectangular duct with perforated blockages and dimpled side walls Jung Shin Park, Young Hwa Jo, Jae Su Kwak ⇑ School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang 412-729, Republic of Korea
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 15 December 2015 Accepted 25 January 2016
Keywords: Heat transfer Gas turbine blade Trailing edge cooling Compound cooling Perforated blockages
a b s t r a c t Heat transfer and pressure drop in a duct with three serial perforated blockages equipped with staggered jets were experimentally investigated. Eight types of jet holes and three types of side walls, including dimpled walls, were tested. For heat transfer measurements, the transient liquid crystal technique was used. Reynolds numbers based on the hydraulic diameter of the duct and inlet velocity ranged from about 10,000–30,000. Experimental results showed that the Nusselt number ratios decreased as the Reynolds number increased, and the friction factor ratios increased as the Reynolds number increased. The heat transfer coefficient and the pressure loss were strongly affected by the number and the configuration of jets. Compared to the smooth side wall case, the cases with dimpled side walls showed large increases in heat transfer with slight increments in pressure loss. Therefore, it was determined that the thermal performance factor could be enhanced by up to 25% by using a dimpled side wall in the duct with perforated blockages. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Modern gas turbines are designed to allow for turbine inlet temperatures that exceed allowable material temperatures in order to improve turbine performance and power output. High temperature combustion gas and complex flow phenomena near the blade aggravate the heat transfer problem of the gas turbine blade. As such, various cooling techniques have been applied to blade cooling designs. Fig. 1 shows commonly used internal cooling techniques for a gas turbine blade. Impingement cooling, rib turbulated cooling, dimple cooling, and pin-fin cooling techniques have been widely applied to gas turbine cooling designs, and many studies have been conducted in order to improve the heat transfer performance of those techniques [1]. Some researchers have proposed new concepts with respect to internal cooling techniques for the blade trailing edge. For example, Moon and Lau [3] investigated the pressure drop and heat transfer on a rectangular duct with two perforated blockage configurations. They showed that the number of walls and the configuration of holes did not significantly affect the heat transfer augmentation level. Lau et al. [4] investigated the heat transfer for the flow moving through blockages with holes in an internal cooling passage near the trailing edge region by using naphthalene
⇑ Corresponding author. E-mail address: [email protected] (J.S. Kwak). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.01.081 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
sublimation. They studied the effects of inlet and exit geometry configurations and showed that the effects of the entrance channel and exit slot geometries were not significant to the average heat (mass) transfer or the distribution of the local heat (mass) transfer. Saha et al. [5] looked at the heat transfer and friction factor of a converging matrix structure with orthogonal ribs representing a gas turbine blade trailing-edge cooling passage. They showed that the matrix structure could result in an averaged Nusselt number enhancement factor of 3–4. Armellini et al. [6] and Coletti et al. [7] conducted experimental and numerical investigations of a trapezoidal cross-section model simulating a trailing edge cooling cavity with one rib-roughened wall and crossing jets. The interaction between the jets and ribs increased the heat transfer coefficient on both the bottom and upper wall. Shin and Kwak [8] measured the heat transfer coefficient in a turbine blade internal cooling passage model with five types of blockages. They showed that staggered impingement jets increased the heat transfer. However, the pressure drop also increased greatly. They concluded that the thermal performance for the perforated blockage could be improved by optimizing the hole shape. Kan et al. [9] investigated the combined effects between perforated blockages and pin fins in a cooling passage. Six different blockage configurations were investigated using both experimental and numerical methods. They showed that the hole-to-channel area ratio is the most important factor for heat transfer enhancement. Smaller area ratio cases showed larger heat transfer enhancements and larger pressure
J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
225
Nomenclature Dh f h k p Pr Re T
hydraulic diameter, mm friction factor heat transfer coefficient, W/m2 K thermal conductivity, W/m K pressure, pa Prandtl number of air Reynolds number temperature, °C or K
drops. Ahn et al. [10] studied the turbulent forced convective mass transfer downstream of blockages with round and elongated holes in a rectangular channel using naphthalene sublimation. They investigated the effects of the hole aspect ratios, for each holeto-channel area ratio, on the exposed channel wall. They found that the elongated holes showed a higher overall mass transfer on the channel wall than the round holes. Chung et al. [11] investigated the effects of the array pattern, hole size, and hole direction for the heat transfer and pressure loss on the side wall of a rectangular channel. They showed that the proposed inclined holes array presented improved cooling performance over a conventional configuration. Previous research [3,4,8–11] has explored the possibility of improving the thermal performance of the internal cooling with perforated blockages. In this study, a compound internal cooling technique for the turbine blade trailing edge with repeated perforated blockages and dimpled side walls is proposed. Eight types of blockage holes were considered, and two of them were selected to be tested with the dimpled side walls. The effects of the jet hole and side wall configurations on the heat transfer and pressure loss were experimentally investigated.
2. Experimental setup and measurement methods Fig. 2 shows the schematic of the test setup. The test setup consisted of a blower, a Venturi flow meter, an electrical heater (12 kW), two pneumatic valves with solenoid valves, a plenum
t
a
transient time, s thermal diffusivity of blade material, m2/s
Subscripts 0 for fully developed turbulent flow in a smooth duct i initial condition m mainstream w wall of test surface
chamber, and a rectangular duct with perforated blockages. Air was heated by the electrical heater and bypassed until a predetermined air temperature was reached. Then, the heated air was diverted toward the test section via the two pneumatic valves. A 280-mm wide, 35-mm high duct was connected to the plenum chamber, and three perforated blockages were installed in the duct. Fig. 3 presents a detailed view of the heat transfer measurement region. The heat transfer coefficient was measured on the side walls between the perforated blockages. Liquid crystals (35C1W, Hallcrest) were sprayed on the side wall, and black paint was sprayed over the liquid crystal coating. The color change of the liquid crystals was recorded using a digital CCD camera (AVT Stingray F033C) from the back of the liquid crystal coated surface, as shown in Fig. 2. Before conducting the heat transfer tests, the relation between the hue of the liquid crystals and the temperature was calibrated. Black paint and liquid crystals were sprayed on the 5-mm thick aluminum plate, and the temperature of the plate was controlled by a temperature controller. At each temperature step, the hue value was calculated from the color of the liquid crystals. Fig. 4 presents the liquid crystal calibration results. In order to measure the mainstream temperature for each heat transfer measurement plane, a total of five T-type thermocouples for each measurement plane were installed, as shown in Fig. 3. The pressure drop through the perforated blockages was measured from a total of ten pressure taps installed upstream and downstream of the heat transfer measurement planes. Fig. 5 presents the perforated blockages used in this study. The configuration of the blockages was selected by referring to results from the authors’ previous study [8], in which the case with wider holes and the case with the greater number of holes showed better performance. Each blockage set consisted of three perforated blockages with the same configuration except for the hole locations. Holes for each blockage were fabricated so that the jet from the upstream blockage impinged to the downstream blockage between the jets. Hole sizes were determined so that the flow area for each blockage was the same for all blockages. Table 1 lists the configuration of each perforated blockage. Fig. 6 shows the three types of side walls considered in this study. Fig. 6(a) shows the smooth side wall, and Fig. 6(b) and (c) show the dimpled cases with 15-mm and 7.5-mm diameter dimples, respectively. For both dimpled cases, the ratios of the dimple depth and dimple-to-dimple distance to the dimple diameter were 0.2 and 1.33, respectively. The transient liquid crystal technique was used to measure the heat transfer coefficient. For this technique, the test model was assumed to be a one-dimensional semi-infinite model with a convective boundary condition. The governing equation, initial, and boundary conditions are as follows:
@ 2 T 1 @T ¼ @x2 a @t Fig. 1. Commonly used internal cooling techniques for a gas turbine blade [2].
ð1Þ
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Fig. 2. Schematic of the experimental setup.
Fig. 4. Relation between the temperature and hue value.
Fig. 3. Detailed view of the heat transfer measurement region.
at t ¼ 0; T ¼ T i at x ¼ 0; k
ð2Þ
@T ¼ hðT w T m Þ @x
at x ! 1; T ¼ T i
ð3Þ ð4Þ
During the heat transfer test, the mainstream temperature varied with time due to the thermal inertia of the test section, and the variation of the mainstream temperature was assumed as a series of step changes. For the varying mainstream temperature case, the solution for the above equations at the surface are as follows [12].
" # pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! pffiffiffiffiffi X n h aðt si Þ h at T w T i ¼ ðT m;0 T i Þ F F DT m;i þ k k i¼1 where, FðxÞ ¼ 1 expðx ÞerfcðxÞ. 2
ð5Þ
In Eq. (5), the transient time (t) between the initial temperature (Ti) and the predetermined wall temperature (Tw) was calculated using the hue history of the liquid crystals at every pixel of the recorded images. The mainstream temperature (Tm) was the averaged temperature measured by the five thermocouples shown in Fig. 4. During the heat transfer measurement tests, the color of the liquid crystals was recorded using a digital CCD camera (Stingray F033C, AVT) and stored in a computer at a rate of 30 frames per seconds. From every image pixel, the hue was calculated and the transient time from the initial condition to the predetermined hue value was also calculated. This procedure was conducted using a Matlab-based image processing program. The details of the procedure were explained in Shin and Kwak [8]. The test duration time was limited in order to keep the temperature of the opposite side of the test section at its initial value. Wagner et al. [13] suggested a maximum test duration time by using Eq. (6).
attest duration 2
thickness
<
1 4
ð6Þ
For the current study, tduration time was about 190 s, and the transient test duration time was kept below 60 s. The averaged heat transfer coefficient was compared with that for the smooth duct with the same hydraulic diameter and Reynolds number. The Nusselt number (Nu) is defined by Eq. (7), and the Nusselt number for a fully developed turbulent flow in a smooth duct (Nu0) is calculated using Eq. (8) [14]:
Nu ¼
hDh ka
ð7Þ
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Fig. 6. Side wall configurations.
Nu0 ¼
ðf 0 =8ÞðReDh 1000ÞPr ½1 þ 12:7ðf 0 =8Þ
1=2
ð8Þ
ðPr2=3 1Þ
Here, Dh is the hydraulic diameter of the test section, ka is the thermal conductivity of the air, and h is the heat transfer coefficient. f0 (the friction factor for a fully developed turbulent flow in a smooth duct), f (the Darcy friction factor), and the thermal performance factor (TP) are defined by Eqs. (9)–(11), respectively.
f 0 ¼ ½0:79ðReDh Þ 1:642 f ¼
ð9Þ
ðDp=DxÞDh qa u2 =2
TP ¼
ð10Þ
Nu=Nu0 ðf =f 0 Þ
ð11Þ
1=3
The measurement uncertainties [15,16] for the Nusselt number, Reynolds number, friction factor, and the thermal performance factor for a typical test case are estimated as 7.7%, 6.3%, 5.5%, and 8.2%, respectively. 3. Results and discussions Fig. 5. Perforated blockages: (a) 7 circular, (b) 7 wide, (c) 7 narrow, (d) 9 circular, (e) 11 circular, (f) 7 wide top–bottom, (g) 7 wide-45, (h) 7 wide-45/135.
Fig. 7 presents the Nusselt number distribution on the smooth side wall with various perforated blockages. The arrows in the fig-
Table 1 Perforated blockage configurations. Hole configuration
Hole diameter
Hole-to-hole distance
Hole length
Number of holes
Hole angle
7 circular 7 wide 7 narrow 9 circular 11 circular 7 wide top–bottom 7 wide – 45 7 wide – 45/135
20 mm 12 mm 12 mm 17.6 mm 16 mm 12 mm 12 mm 12 mm
40 mm 40 mm 40 mm 31.11 mm 25.45 mm 40 mm/17.5 mm 40 mm 40 mm
– 28.8 mm 28.8 mm – – 28.8 mm 28.8 mm 28.8 mm
7 7 7 9 11 7 7 7
– 0° 90° – – 0° 45° 45°/135°
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Fig. 7. Nusselt number distribution on the smooth side wall (Re = 10,000).
ures indicate the location of the jet holes. All cases showed traces of the jets and jet impingements. After the jets impinged to the downstream blockage, the flow turned toward the side walls and resulted in a high Nusselt number on the side wall near the downstream blockage. The increasing Nusselt number toward the downstream blockage is a trend that has been observed in previous studies [4,8]. Comparing Fig. 7(a), (b), and (c), the wide hole case (Fig. 7(b)) showed a more uniform Nusselt number distribution. This was followed by the 7 circular hole case (Fig. 7(a)) and the 7 narrow hole case (Fig. 7(c)). Therefore, it was concluded that the jet hole shape was able to significantly alter the Nusselt number distribution. The effects of the jet hole shape on the Nusselt number distribution were more significant at the first measurement plane. The effects of the number of holes can be observed by comparing Fig. 7(a), (d), and (e). As the number of circular holes increased from seven (Fig. 7(a)) to eleven (Fig. 7(e)), the Nusselt number distribution became more uniform in the spanwise direction. Closely located jets were able to easily merge with one another, and this resulted in a nearly two-dimensional Nusselt number distribution on the side walls. In order to investigate the effects of hole location, the wide holes were located near the top and bottom side wall, and Fig. 7
(f) shows the resulting Nusselt number distribution. Since some of the wide holes were placed near the side wall, the jets were able to enhance the heat transfer on the side wall, and this resulted in higher Nusselt numbers than in the case with middle height jet holes (Fig. 7(b)). However, the Nusselt number distribution was less uniform than it was for the 7 wide hole case (Fig. 7(b)). The effects of the wide hole orientation were also considered. Fig. 7(g) and (h) are the heat transfer measurement results for the angled wide hole cases. For the 45 degree case (Fig. 7(g)), the traces of the high Nusselt number shifted along the angle of the jet hole. For the 45/135 degree case (Fig. 7(h)), the Nusselt number was higher where two jets were located close to one another. However, the Nusselt number distribution was less uniform than that for the 45 degree case (Fig. 7(g)). Comparing Fig. 7(b), (c), and (g), the 45 degree case (Fig. 7(g)) showed greater uniformity than the narrow hole case (90 degrees, Fig. 7(c)). However, it showed less uniformity than the wide hole case (0 degrees, Fig. 7(b)). When the angled holes were placed in a cross pattern (Fig. 7(h)), the Nusselt number distribution was less uniform than it was for the 45 degree case (Fig. 7(g)). For the quantitative comparison of heat transfer augmentation via different perforated blockages, the Nusselt numbers on the first and second side walls were averaged, and Fig. 8 shows the overall
J.S. Park et al. / International Journal of Heat and Mass Transfer 97 (2016) 224–231
Fig. 8. Averaged Nusselt number ratio for smooth side wall cases.
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Fig. 10. Thermal performance factor for smooth side wall cases.
Fig. 9. Friction factor ratio for smooth side wall cases.
averaged Nusselt number ratio with smooth side walls. The overall averaged Nusselt number ratio was the highest for the 7 wide topbottom and 7 narrow hole cases, for which the jets were relatively close to the side walls. For the circular hole cases, the overall averaged Nusselt number ratio decreased as the number of holes increased. The angled wide hole cases – particularly the 7 wide 45/135 case – showed a relatively low Nusselt number augmentation since the jets for those cases were relatively far from the side walls. Fig. 9 shows the friction factor ratio for the smooth side wall cases calculated by Eqs. (8) and (9). For all cases, the friction factor ratio increased as the Reynolds number increased. Cases showing a high Nusselt number ratio presented a high friction factor. The 7 narrow and 7 wide top-bottom cases showed high pressure losses, while the 7 wide 45/135 case resulted in the lowest friction factor ratio. Fig. 10 presents the thermal performance factor for the smooth side wall cases calculated using Eq. (10). For all cases, the thermal performance factor decreased as the Reynolds number increased, and the thermal performance factor was less than 0.5. The cases with 7 wide angled holes showed the lowest thermal performance factors, and the other cases did not show a constant trend with the Reynolds number. Generally, cases with circular holes, the case with 7 wide holes, and the case with 7 wide top-bottom holes presented a high thermal performance factor. Among the tested perforated blockages, blockages showing the highest Nusselt number
Fig. 11. Nusselt number distribution on the dimpled side wall (Re = 10,000).
ratio and the highest thermal performance factor – the 7 wide top-bottom hole and 7 circular hole cases – were applied to the channel with dimpled side walls.
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Fig. 11 presents the Nusselt number distribution on the dimpled side wall. For all cases, the Nusselt number increased as the Reynolds number increased, and the heat transfer augmentation induced by the dimples was clearly observed. Compared to the smooth side wall case (Fig. 7), the dimpled side wall case did not show clear traces of the jets or impingements due to the flow disturbance caused by the dimples. Fig. 12 is the averaged Nusselt number ratio for the dimpled side wall cases with selected perforated blockages. The smooth side wall cases were also included for comparison. For both types of blockages, the dimpled side wall cases showed higher Nusselt number ratios than the smooth side wall cases, and all cases showed a decreasing Nusselt number ratio trend as the Reynolds number increased. The results also showed that the Nusselt number ratios for the small dimpled side wall were higher than those for the large dimpled side wall cases for both blockage configurations. Therefore, it could be concluded that dimples on side walls, especially smaller dimples, effectively increased the Nusselt number because of the enhanced flow disturbance created by the dimples. Small dimples were able to increase the Nusselt number up to16% for the 7 circular case and 22% for the 7 wide top-bottom case. As seen in Figs. 12 and 13, the dimpled side wall cases showed higher Nusselt number ratios, but the pressure loss was also larger
Fig. 14. Thermal performance factor for dimpled side wall cases.
than that for the smooth side wall cases. In order to confirm the advantages of using a dimpled side wall, the thermal performance factors for the dimpled and smooth side wall cases were calculated and presented in Fig. 14. For all cases, the thermal performance factor decreased as the Reynolds number increased. In Fig. 14, the side wall with small dimples showed the highest thermal performance factor, followed by the cases with large dimples. Small dimples on the side wall resulted in a 25% improvement in the thermal performance factor for the circular hole case and an 18% improvement for the 7 wide top-bottom hole case. Therefore, it can be said that dimples on the side wall in a duct with a perforated blockage are able to significantly improve thermal performance. 4. Conclusions In this study, the effects of perforated blockage and side wall configurations of a turbine blade trailing edge model on the heat transfer augmentation and pressure loss were experimentally investigated. A total of eight blockage types and three side wall types were considered. Based on the experimental results, the following conclusions have been derived.
Fig. 12. Averaged Nusselt number ratio for dimpled side wall cases.
(1) For all cases, the Nusselt number ratio and the thermal performance factor decreased as the Reynolds number increased. The friction factor ratio increased with the Reynolds number. (2) As the number of circular holes on the blockage increased, the distribution of the Nusselt number became more uniform. However, the overall averaged Nusselt number ratio and the thermal performance factor decreased. (3) The cases with jet holes close to the side walls showed high Nusselt number ratios. Generally, the cases with high Nusselt number ratios showed high pressure losses. (4) Dimpled side wall cases resulted in increased Nusselt numbers, but the pressure losses also increased slightly. The thermal performance factors for the dimpled side wall cases were higher than that for the smooth side wall case by up to 25%.
Acknowledgments
Fig. 13. Friction factor ratio for dimpled side wall cases.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A2A2A01002636).
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