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The investigations of slot film outflow used on the laminated cooling configuration
International Journal of Heat and Mass Transfer 141 (2019) 1078–1086
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
The investigations of slot film outflow used on the laminated cooling configuration Xiao-Dong Zhang ⇑, Jian-Jun Liu, Bai-Tao An University of Chinese Academy of Sciences, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e
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Article history: Received 15 September 2018 Received in revised form 17 June 2019 Accepted 8 July 2019 Available online 16 July 2019 Keywords: Laminated configuration Film cooling Cooling effectiveness Resistance coefficient Blowing ratio
a b s t r a c t The discrete film hole is the most common form of film cooling configurations in the turbine vane and blade. To enhance the film cooling effect, the improved hole, such as expanding-shape hole, is being used to replace the traditional cylindrical hole in the vane and blade cooling design. However the slot film outflow is been seen as the best form of film cooling when compared to the discrete holes. The slot film cooling configuration is usually used in the trailing edge of turbine vane and blade, but cannot be used in the mid-body of turbine vane and blade, with be drawback of lower mechanical strength. The present paper used the slot film outflow on the laminated cooling configuration. With the ribs in the laminated cooling configuration, the novel configuration can remarkably overcome the mechanical drawback of the simple slot film cooling, and can enhance the film cooling effect of the laminated cooling configuration. To investigate the cooling effect of laminated configuration with slot film outflow, four kinds of specimens are designed, including the traditional design with discrete film hole (baseline), the rearrangement design with discrete film hole (case A), the novel design with discrete slot (case B), and the novel design with continuous slot (case C). The Conjugate heat transfer (CHT) computations and the Pressure Sensitive Paint (PSP) test methods are used to assess the overall cooling performance (gov erall ) and the adiabatic film cooling effectiveness (gfilm ). The results show the two slot design cases (case B and case C) have higher film cooling effectiveness with more covered surface areas of film outflow, while performs lower flow resistance due to the lower flow velocity of the coolants in the slot. With the increase of Br, the film cooling effectiveness of two slot design cases (case B and case C) can keep increase, but the two hole design case (baseline and case A) cannot increase at area of Br > 0.55. At the blowing ratio near 0.96, for the baseline case, case A, case B, and case C, the area-averaged film cooling effectiveness is 0.26, 0.20, 0.68, and 0.50 respectively; and area-averaged the overall cooling effectiveness is 0.72, 0.81, 0.89, and 0.85 respectively; the flow frictions coefficients is 1.78, 2.15, 1.37, and 2.01 respectively. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Increasing the gas temperature of turbine inlet is the most effective method to improve gas turbine performance. With the increase of gas temperature, advanced cooling technologies need to be developed to protect the turbine vane and blade working under critical temperature. The previous gas turbines commonly use compound cooling method with convective cooling, film cooling and impingement cooling. With the current cooling method, the overall cooling effectiveness can reach up to 0.4–0.6, and the metal temperature of inlet guide vane can decrease up to 400–650 K, consuming about 5–10% (ratio of coolant mass flow rate to gas mass flow rate) coolants. The gas temperature of next ⇑ Corresponding author. E-mail address: [email protected] (X.-D. Zhang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.045 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
generation gas turbine will reach to 1970 K, and the needed cooling effectiveness of IGV is above 0.65. So if we don’t hope to consume more coolants, it is inevitable to develop the advanced cooling method. According to the work of Alexander et al. [1] and Funazaki et al. [8], the laminated cooling with integrated impingement, ribroughed and film cooling can result in a high overall cooling effectiveness and is believed to be a promising cooling method for the next generation gas turbines. As show in Fig. 1, the technology employs two walls which are separated small passage within which ribs may be present to increase coolant wetted area and to promote turbulence. Within the walls impingement cooling occurs, by film of coolants over the external surface, the cooler air insulates the hot gas and the outer wall. Many advanced cooling configurations based on a double wall cooling structure have been developed for last several decades.
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Nomenclature Tg T w;g Tc BR Re Pin coolant Pout C f Tw S
qci
v ci
qin;g
temperature at main flow inlet area-averaged wall temperature temperature at coolant inlet blowing ratio Reynolds number static pressure at coolant inlet static pressure at outlet surface flow resistance coefficient average wall temperature length of laminated element coolant density in impingement hole coolant velocity in impingement hole inlet gas density
Fig. 1. An example of blade with laminated cooling configuration.
Alexander et al. [1] develop an approach to assess both the aerothermal cooling performance of double-wall geometries along with the resulting thermomechanical stress field. The simulations indicates that reducing pedestal diameter and increasing their edge-to-edge spacing improved cooling performance, mechanical performance was adversely affected. DENG et al. [7] investigated the optimal film injection angle and blowing ratio for laminate cooling with different surface curvatures. For convex surface, shallower injection angle and higher blowing ratio promote the cooling effectiveness without regard to pressure loss. About 14.4% improvement of overall cooling effectiveness gains from 15° injection angle compared to 90° injection angle at high blowing ratio, while the pressure loss rises up to 2.1%. Funazaki and BinSalleh [8] researches on the cooling performance of two different integrated impingement cooling structure via the measurements based on (transient thermochromic liquid crystal) transient TLC technique as well as numerical simulation. It is indicated that the pin arrangement around the impingement jet is an important factor in order to attain higher cooling performance of the proposed integrated impingement cooling system. The hole/rib arrangement is main influenced factor for laminated cooling configuration. Cho and Rhee [6] described heat transfer studies for impingement/effusion configuration with three different hole arrangements, including staggered arrangement, shifted arrangement, and in-line array. The computation and experimental results showed the staggered arrangement leads to the highest Nusselt number. Nakamate et al. [16] investigated cooling configuration integrated impingement and pin-fin. Six amplified specimens were designed and tested in a facility with
v in;g
a gfilm gov erall c IGV CHT LED
inlet gas velocity injection angle in the streamwise direction adiabatic film cooling effectiveness overall cooling effectiveness injection angle in the spanwsie direction inlet guide vane conjugate heat transfer light emitting diode
Subscripts 1 film hole 2 rib 3 impingement hole
gas temperature of 673 K and Reynolds number of 3.8 105. The area-averaged cooling effectiveness of (each cooling unit consists of one impingement hole, two pins and one film hole) BASI arrangement and (each cooling unit consists of one impingement hole, three pins and one film hole) STAG arrangement was compared. The results showed BASI arrangement has the higher cooling effectiveness in the region of BR > 0.5 and the cooling effectiveness is lower in the region of BR < 0.5. Wang et al. [22] and Marc et al. [14] investigated the influences of coolant injection angle along the streamwise direction on the cooling effectiveness of laminated configuration using a fluid-thermal-structure coupling method. The results showed that the angled injection design is benefit to enhancing the overall cooling effectiveness and reducing the thermal stress. Li et al. [10] and Quan [20] tested laminated configuration in turbine blade on a liner cascade rig. Through comparing four kinds of configurations, the cooling performance of the B-type configuration (as shown in Fig. 2) is the best. The cooling effectiveness can reach up to 0.75 at blowing ratio 1.0, and if keeping increasing blowing ratio, the cooling effectiveness can reach up to 0.85. It was found the area ratio of film hole to cooling area has a clear impact to the cooling effectiveness and flow resistance. Panda et al. [11] performed transient conjugate heat transfer of a flat plate using an impinging jet with large eddy simulation. The computations show excellent agreement between the computational and the experimental data. Karim and Lamyaa [9] performed CFD investigation on three forms of film cooling configurations, including the standard cylindrical, rectangular slot, and oval slot. The results show rectangular slots have an increase in film cooling effectiveness for the same blowing ratio of coolant when compared to the standard circular hole, which is due to the minor counter rotating vortex pair effect. An oval slot design showed higher film cooling effectiveness and more spreading, covering more surface area. Bunker [4] investigated the potential improvement in adiabatic film effectiveness that can be achieved through the use of mesh-fed surface slot film
Fig. 2. Layout of staggered arrangement of laminated cooling configuration.
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cooling. The mesh-fed film effectiveness was as much as 25% higher than that for shaped holes. PSP technique has been widely used to measure adiabatic film cooling effectiveness distributions on the surfaces of interest based on a mass transfer analog. Natsui et al. [18], Caciolli et al. [5] and Johnson et al. performed detailed analysis to evaluate the effects of various associated uncertainties in the PSP measurements on the measured film cooling effectiveness distributions over the surfaces of interest. The measurement uncertainty is estimated as high as 5% at the near field behind the coolant holes Conjugate heat transfer computation showed the excellent potential of CFD for analyzing complex structures. According the investigations of Bohn et al. [3], Sean [12], Toshihiko et al. [21], William et al. [23] and Panda et al. [19], the predictions produced by the conjugate heat transfer analysis compared favorably to measured results, falling within experimental tolerances and consistent both in trend and value. Montomoli et al. [15], Ni et al. [17] and Sidewell et al. [13] recommend to maintain for all the first three layers y+ lower than 3.5 to enhance the computation of the temperature derivative. The scope of the current work is to investigate a novel laminated cooling configuration with slot film outflow using CHT computation and PSP experiment. By assessing the adiabatic film cooling effectiveness, overall cooling effectiveness, and the flow resistance, the potential of laminated cooling configuration with slot film outflow is validated.
Table 1 Geometry parameters values. Parameter
Meaning
Value
D1, mm D2, mm D3, mm H1, mm H2, mm H3, mm L1, mm L2, mm L3, mm
Diameter of film hole Diameter of Rib Diameter of impingement hole Height of outer wall Height of middle space Height of inner wall Spacing of film hole Spacing of rib Spacing of impingement hole
1.1 1.2 1.2 0.8 0.8 1.0 6.0 3.0 6.0
2. Geometry models The laminated configuration with staggered arrangement presented in many papers is investigated as the baseline scheme. As shown in Fig. 2, the inner wall and outer wall are connected with ribs, and the impingement hole, film hole and rib are arranged in a beeline in the baseline scheme. When coolants flow from the impingement hole to the film hole, the coolants must pass the cylindrical ribs, so the convection cooling effect can be well achieved for the configurations with staggered arrangement. The geometry parameters of the baseline case is illustrated in Fig. 3, including the diameters of film hole, the diameter of rib, the diameter of impingement hole, the height of outer wall, the height of middle space, the height of inner wall, the spacing of film hole, the spacing of rib, the spacing of impingement hole. The relevant parameter values are shown in Table 1. As shown in Fig. 4, to increase the film cooling effectiveness of the baseline case, three improved cases were proposed and investigated, including the Case A, Case B and Case C. The film holes are rearranged with increased spacing along the streamwise direction and decrease the spacing along the transverse direction in the Case A. Replacing the discrete film holes in the Case A with continuous slot, the Case B was designed, which can results in the best film cooling effects. To overcome the possible mechanical drawback of Case B, the Case C was designed by replacing the continuous slot with the discrete slots. The width of the above slots is 0.3 mm and the inclined angle is 45°along the streamwise direction.
Fig. 3. Illustration of geometry parameters.
Fig. 4. Investigated schemes.
3. Experimental facilities and methods Experiments were carried out in the flat-plate film-cooling experimental rig at the Advanced Industrial Gas Turbine Technology Laboratory, Institute of Engineering Thermophysics, Chinese Academy of Sciences. As shown in Fig. 5, the experimental rig is a low-speed wind tunnel test device using PSP measurement method. The mainstream sequentially flows through the transition section, a settling section, and a contraction section, and eventually enters into the test section. The mainstream air speed entranced to the test section is 25 m/s and the mainstream air temperature is about 35 °C. The PSP measurement is used to test the adiabatic film cooling effectiveness. The excitation wavelength range was 380– 520 nm, and the emitting wavelength range was 620–750 nm. The PSP was excited by two 400 nm light-emitting diode (LED) lights. A 670 nm filter was mounted in front of the camera lens to prevent any reflected light from the illumination source from filtering into it. The calibration was conducted at three temperatures, which were 23.0 °C, 35.4 °C, and 47.8 °C, respectively. In order to validate the experimental accuracy of film-cooling effectiveness,
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Fig. 5. Experiment rig using PSP measurement.
a typical fan-shaped hole was tested using the same experimental facilities and measurement methods. In the investigation of An et al. [2], the comparison results show good agreement and the present experiment facilities and methods are reliable. The operating conditions in the present investigations are shown in Table 2. For machining convenience, the laminated film configuration specimen is combined with an outer board and an inner board as shown in Fig. 6. The ribs and the film holes are located on the outer board, while the impingement holes and rib-pits are located on the inner wall. In the combined state, the ribs of outer wall stretch into the rib-pits of inner wall. Eight topology periods along the streamwise direction and five topology periods along the spanwise direction are formed in the test specimen of the baseline design. The test specimens are manufactured using the stainless steel, which thermal conductivity is about 12 W/mK on 35 °C. Fig. 6. Test specimen model.
4. Experimental results and discussions For describing the cooling performance of laminated cooling configuration, the adiabatic film cooling effectiveness and the blowing ratio are defined as follows:
gfilm ¼ BR ¼
T g T w;g Tg Tc
ð1Þ
qci v ci qin;g v in;g
ð2Þ
Fig. 7 shows the adiabatic film cooling effectiveness distribution of the four cases under the blowing ratio of 0.55. For the baseline case, the peak cooling effectiveness appeared on the centerline of film hole, and the peak cooling effectiveness reaches about 0.5. Moreover, the film outflow laterally diffused along the streamwise direction and nearly stabilized at the sixth hole. For the Case A, due to the spacing of hole is shorten along the spanwise direction, the film covered area is increased and the film cooling effectiveness is better than the baseline Case. For the Case B, the film outflow can cover all
Table 2 Operating Conditions. Parameter
Range
Mainstream velocity, Vm Mainstream temperature, Tm Mainstream Reynolds number, ReD Turbulent intensity of mainstream, Tu Momentum thickness, Density ratio, DR
25 m/s 310 K 7200 3.5% 0.27 mm 1.38
the downstream surface area, so the film cooling effectiveness seems very uniform along the spanwise direction. However the cooling effectiveness distribution shows unstable flow phenomenon. The peak cooling effectiveness reaches up to 0.9 at the outlet of the three slots. Due to the effect of film coolants superposition, the cooling effectiveness appears augment trend from the first slot to the third slot. For the Case C, the peak film cooling effectiveness seems comparable with the Case B. Although the spacing along the streamwise direction of near two slots is increased when it is compared to the Case B, the film cooling effect can also keep effective to the downstream of the slot. At the same time, the mechanical feasibility of Case C is better than the Case B with continuous slots. For quantitatively assessing the cooling performance of the baseline case with discrete holes and the Case B with continuous slots, the comparisons of lateral averaged adiabatic film cooling effectiveness at BR = 0.19, 0.55, and 0.95 are shown in Fig. 8. It is obvious that the Case B with slot film outflow results in higher adiabatic film cooling effectiveness at all blowing ratios. The averaged film cooling effectiveness of Case B reaches above 0.6 at blowing ratio of 0.55, while the baseline case is below 0.3. It means the film cooling effectiveness can be doubled by replacing the discrete cylindrical film holes with continuous slot outflow. The distinction between the crests and troughs in film cooling effectiveness distribution of Case B is very large, which indicated the film cooling effectiveness along the streamwise direction is very nonuniform while the baseline case shows more smooth distribution. The comparison of lateral averaged adiabatic film cooling effectiveness at BR = 0.55 for the four cases is shown in Fig. 9. It
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Fig. 8. Comparisons of laterally averaged adiabatic film cooling effectiveness between the baseline case and Case B.
Fig. 9. Laterally averaged effectiveness comparison of the four cases (BR = 0.55).
Fig. 7. Adiabatic film cooling effectiveness distributions of the 4 cases on test surface (BR = 0.55).
is obvious that the Case B and the Case C with slots film outflow have higher adiabatic film cooling effectiveness than the baseline Case and Case A with ordinary film holes. The distribution pattern
is similar between Case B and Case C. But the film cooling effectiveness of Case B is larger than Case C, and the film cooling effectiveness of Case C is larger than Case A. Although the film cooling effectiveness of Case B is very high, but distinction between the peak value and trough value is very large, i.e., very nonuniform along the streamwise direction. Although the film cooling effectiveness of baseline case and the Case A is relatively low, but its distribution along the streamwise direction is the most uniform. Compared the baseline case and Case A, it is shown the film cooling effectiveness of Case A is slight higher than the baseline case at blowing ratio of 0.55. Fig. 10 shows the comparisons of the area-averaged film effectiveness for the four test cases at blowing ratios of 0.19, 0.55, and 0.96. The film cooling effectiveness trends are relatively similar for both the baseline case and the Case A. With the increase of blowing ratio, the film cooling effectiveness of the baseline case and the Case A finally decrease due to the film outflow lift-off at high blowing ratio conditions. However at the higher blowing ratio of 0.96, the film cooling effectiveness of Case A is lower than the baseline
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Fig. 10. Area-averaged film effectiveness comparison of the four Case.
case, which means the film outflow of Case A is easier to lift-off. The Case B and Case C show significant higher film cooling effectiveness than the baseline Case and Case A. For instance, at the blowing ratio of 0.96, the area-averaged film cooling effectiveness is 0.26, 0.20, 0.68, and 0.50 respectively for baseline case, Case A, Case B, and Case C. The results show that the laminated film configurations with slot film outflow have obvious advantages over the configurations with holes film outflow at all the tested conditions.
5. Conjugate heat transfer results Conjugate heat transfer computations are performed for assessing the overall cooling effectiveness and the resistance coefficient. ANSYS CFX is used to perform the steady 3D RANS computations. The governing equations used for simulation are the Reynolds averaged continuity, momentum, and the energy equations along with the full-turbulent SST turbulence model. As shown in Fig. 11, the computation model is composed by 7 cooling units along the streamwise direction for the baseline case. Translation periodic boundary conditions are used on the spanwise boundary. For getting a fully developed boundary layer of fluid flow, the inlet duct with a length of 4 cooling unit is connected. ICEM-CFD commercial software is employed to generate the computation mesh. As shown in Fig. 12, the structured mesh is used in the fluid domain, and the unstructured mesh is used in the solid domain. The initial height of the first layer is 0.002 mm on the outer solid walls and 0.004 mm on the inner walls. The overall grid in the fluid domain is about 3.5 million elements, and the grid in the solid domain is about 2.0 million. This grid can give dimensionless wall spacing y+ below 2.0 at the first wall cell, which is needed in the Shear Stress Transport (SST) turbulence model. At the gas inlet, the total temperature is set to 1800 K, the
Fig. 11. Diagram of computation model.
Fig. 12. Local views of computation grids.
velocity is 500 m/s and the Reynolds number is 4.9 104. At the flow outlet, the static pressure is set to 101,325 Pa. At the inlet of coolant plenum, coolant total temperature is set to 800 K. The velocity of coolant changes with blowing ratio, and the Reynolds number Rec varies from to 1.0 104 to 6.0 104. The Rec is defined by using the diameter of film hole and the velocity of film flow. The heat conductivity of the solid is set to 10 W/(mK) and the resultant Biot number is about 0.1, which is similar with the turbine blade in the gas turbines. A monitor point was set up in the solid body to inspect the temperature convergence history in the CHT computation. The overall cooling effectiveness and flow resistance coefficient of coolant flow are discussed in detail. Overall cooling effectiveness coefficient and flow resistance coefficient of coolant are defined as:
gov erall ¼ cf ¼
T g T w;g Tg Tc
Pin;coolant Pout 0:5qin;g v 2in;g
ð3Þ
ð4Þ
The computational method is also validated by the experimental data. The test model and the experimental data can be found in literature [16]. The comparisons of computational results and the experimental data for cooling effectiveness are shown in Fig. 13. Good agreement was noticed in the area of BR > 0.4, but a distinction appeared in the area of BR < 0.4. To validate the mesh independence, three kinds of computation grids with different amounts of element are used for simulating the baseline case. The total element number of ‘‘coarser mesh”, ‘‘used mesh”, and the ‘‘finer mesh is respectively about 2.2 million, 5.0 million and 7.5 million, Fig. 14 shows the temperature at inner wall along spanwise direction between the tenth rib and the fifth impingement hole. The comparison indicates the used mesh is claimed to be fine enough. The comparison of overall cooling effectiveness contours at outer wall surface are shown in Fig. 15 at the blowing ratio of 0.5. It is clear that the Case A has higher overall cooling effective-
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Fig. 13. Comparisons of computed and measured cooling effectiveness at different blowing ratios.
Fig. 15. Overall cooling effectiveness contours on the outer surface (BR = 0.55).
Fig. 14. Comparisons with different computation mesh.
ness than the baseline case and the Case B has higher overall cooling effectiveness than the Case A, while Case C have a slight lower overall cooling effectiveness than the Case B. The peak cooling effectiveness is appeared downstream of the film holes or slots. At the blowing ratio of 0.5, the peak overall cooling effectiveness reached above 0.75 for the Case B and Case C. For assessing the cooling performance quantitatively, the averaged cooling effectiveness coefficients are computed with the ‘‘Averaged-post area” as shown in Fig. 15. Fig. 16 shows the relationships of overall cooling effectiveness and the blowing ratios for the four cases. It is presented that the overall cooling effectiveness of Case B and the C is larger than the baseline case and Case A at the computed blowing ratios. For the Case B and the Case C with slot film outflow, the overall cooling effectiveness is very close while the BR is less than 0.6. Case B results in slightly higher overall cooling effectiveness than Case C while BR is larger than 0.6. The baseline case has the higher overall cooling effectiveness when BR is less than 0.45, while has the lower overall cooling effectiveness while BR is larger than 0.45. The overall cooling effectiveness at
Fig. 16. Comparison of area-averaged overall cooling effectiveness at different blowing ratios.
BR = 0.19 is 0.56, 0.50, 0.59, and 0.57 respectively for the four cases. While the overall cooling effectiveness at BR = 0.96 is 0.72, 0.81, 0.89, and 0.85 respectively. Through synthetically considering the film cooling effectiveness and the overall cooling effectiveness of the baseline case and Case A, it can be concluded that the internal convection cooling effect of Case A is stronger than the baseline case. Fig. 17 shows the relationship between the flow resistances coefficient and the blowing ratio for the four cases. It is presented that the Case A has the highest flow resistance coefficient, while the Case B has the lowest flow resistances coefficient. The baseline case and the Case C have the middle resistances coefficient. For
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hole/slot for the four cases. It is shown the obvious flow separation phenomenon appeared at the downstream of film hole for the Case A and Case B, but without separation in the Case B and Case C. It is due to the different inclined angle of the film hole/slot and different coolants momentum for the four cases. The baseline case and the Case A used uninclined discrete film hole, which enable the film coolants easier to lift-off the outer wall. Moreover, the film outflow with slots can cover more outer wall areas along spanwise direction, which can lead to the higher film cooling effectiveness too. 6. Conclusions
Fig. 17. Comparison of flow resistance coefficient vs blowing ratio.
instance, the flow resistance coefficients are respectively 1.78, 2.15, 1.37, and 2.01 near blowing ratio of 0.96 for the baseline case, Case A, Case B, and Case C. It can also be found that the flow resistance coefficient is influenced by the area of film hole/slot and the distance from the impingement hole to the film hole of /slot in the cooling configurations. The lowest flow resistances coefficient of Case B benefits from the largest flow area of continuous slots among the four cases. Fig. 18 shows the comparison of temperature contour and velocity vector at the streamwise direction plane through the film
For investigating the potential of slot film outflow used in the laminated film cooling configuration, four cases are designed, including the baseline case, Case A with rearrangement film holes, Case B with continuous slot film outflow, and Case C with discrete slot film outflow. The pressure-sensitive paint measurement technique test is performed to assess the adiabatic film cooling performance and the conjugate heat transfer computation by ANSYS CFX 16.0 is performed to assess the overall cooling performance. The results show that the three improved cases perform better than the baseline case. The main conclusions are as following: (1) The Case B and Case C with slot film outflow achieved obvious higher film cooling effectiveness than the baseline case and Case A with film holes at all tested blowing ratios. The adiabatic film cooling effectiveness at BR = 0.96 is 0.26, 0.20, 0.68, and 0.50 for the baseline case, Case A, Case B, and Case C respectively. (2) The Case B and Case C with slot film outflow have higher overall cooling effectiveness than the baseline case and Case A with film holes. The overall cooling effectiveness at BR = 0.19 are 0.56, 0.50, 0.59, and 0.57 for the baseline case, Case A, Case B, and Case C, respectively. For higher blowing ratio, the overall cooling effectiveness at BR = 0.96 is 0.72, 0.81, 0.89, and 0.85 for the baseline case, Case A, Case B, and Case C, respectively. (3) The baseline case presents the highest flow resistance, while the Case B with continuous slot film outflow presents the lowest flow resistance for coolants. The flow resistance coefficients at blowing ratio of 0.96 are 1.78, 2.15, 1.37, and 2.01 for the baseline case, Case A, Case B, and Case C respectively. (4) Generally, slot has better cooling performance than the discrete film hole. However, the uniformity of the coolant outflow at the outlet face must be put much more emphasizes due to the non-uniform pressure distribution. So the Case 4 with discrete slot is much more feasible in the turbine blade cooling.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement The authors wish to acknowledge the financial support from the National Natural Science Foundation of China through Grant No. 51506197. Appendix A. Supplementary material Fig. 18. Comparison of temperature contour (left) and velocity vector (right) at BR = 0.5.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.045.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
The investigations of slot film outflow used on the laminated cooling configuration Xiao-Dong Zhang ⇑, Jian-Jun Liu, Bai-Tao An University of Chinese Academy of Sciences, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China
a r t i c l e
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Article history: Received 15 September 2018 Received in revised form 17 June 2019 Accepted 8 July 2019 Available online 16 July 2019 Keywords: Laminated configuration Film cooling Cooling effectiveness Resistance coefficient Blowing ratio
a b s t r a c t The discrete film hole is the most common form of film cooling configurations in the turbine vane and blade. To enhance the film cooling effect, the improved hole, such as expanding-shape hole, is being used to replace the traditional cylindrical hole in the vane and blade cooling design. However the slot film outflow is been seen as the best form of film cooling when compared to the discrete holes. The slot film cooling configuration is usually used in the trailing edge of turbine vane and blade, but cannot be used in the mid-body of turbine vane and blade, with be drawback of lower mechanical strength. The present paper used the slot film outflow on the laminated cooling configuration. With the ribs in the laminated cooling configuration, the novel configuration can remarkably overcome the mechanical drawback of the simple slot film cooling, and can enhance the film cooling effect of the laminated cooling configuration. To investigate the cooling effect of laminated configuration with slot film outflow, four kinds of specimens are designed, including the traditional design with discrete film hole (baseline), the rearrangement design with discrete film hole (case A), the novel design with discrete slot (case B), and the novel design with continuous slot (case C). The Conjugate heat transfer (CHT) computations and the Pressure Sensitive Paint (PSP) test methods are used to assess the overall cooling performance (gov erall ) and the adiabatic film cooling effectiveness (gfilm ). The results show the two slot design cases (case B and case C) have higher film cooling effectiveness with more covered surface areas of film outflow, while performs lower flow resistance due to the lower flow velocity of the coolants in the slot. With the increase of Br, the film cooling effectiveness of two slot design cases (case B and case C) can keep increase, but the two hole design case (baseline and case A) cannot increase at area of Br > 0.55. At the blowing ratio near 0.96, for the baseline case, case A, case B, and case C, the area-averaged film cooling effectiveness is 0.26, 0.20, 0.68, and 0.50 respectively; and area-averaged the overall cooling effectiveness is 0.72, 0.81, 0.89, and 0.85 respectively; the flow frictions coefficients is 1.78, 2.15, 1.37, and 2.01 respectively. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Increasing the gas temperature of turbine inlet is the most effective method to improve gas turbine performance. With the increase of gas temperature, advanced cooling technologies need to be developed to protect the turbine vane and blade working under critical temperature. The previous gas turbines commonly use compound cooling method with convective cooling, film cooling and impingement cooling. With the current cooling method, the overall cooling effectiveness can reach up to 0.4–0.6, and the metal temperature of inlet guide vane can decrease up to 400–650 K, consuming about 5–10% (ratio of coolant mass flow rate to gas mass flow rate) coolants. The gas temperature of next ⇑ Corresponding author. E-mail address: [email protected] (X.-D. Zhang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.045 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
generation gas turbine will reach to 1970 K, and the needed cooling effectiveness of IGV is above 0.65. So if we don’t hope to consume more coolants, it is inevitable to develop the advanced cooling method. According to the work of Alexander et al. [1] and Funazaki et al. [8], the laminated cooling with integrated impingement, ribroughed and film cooling can result in a high overall cooling effectiveness and is believed to be a promising cooling method for the next generation gas turbines. As show in Fig. 1, the technology employs two walls which are separated small passage within which ribs may be present to increase coolant wetted area and to promote turbulence. Within the walls impingement cooling occurs, by film of coolants over the external surface, the cooler air insulates the hot gas and the outer wall. Many advanced cooling configurations based on a double wall cooling structure have been developed for last several decades.
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Nomenclature Tg T w;g Tc BR Re Pin coolant Pout C f Tw S
qci
v ci
qin;g
temperature at main flow inlet area-averaged wall temperature temperature at coolant inlet blowing ratio Reynolds number static pressure at coolant inlet static pressure at outlet surface flow resistance coefficient average wall temperature length of laminated element coolant density in impingement hole coolant velocity in impingement hole inlet gas density
Fig. 1. An example of blade with laminated cooling configuration.
Alexander et al. [1] develop an approach to assess both the aerothermal cooling performance of double-wall geometries along with the resulting thermomechanical stress field. The simulations indicates that reducing pedestal diameter and increasing their edge-to-edge spacing improved cooling performance, mechanical performance was adversely affected. DENG et al. [7] investigated the optimal film injection angle and blowing ratio for laminate cooling with different surface curvatures. For convex surface, shallower injection angle and higher blowing ratio promote the cooling effectiveness without regard to pressure loss. About 14.4% improvement of overall cooling effectiveness gains from 15° injection angle compared to 90° injection angle at high blowing ratio, while the pressure loss rises up to 2.1%. Funazaki and BinSalleh [8] researches on the cooling performance of two different integrated impingement cooling structure via the measurements based on (transient thermochromic liquid crystal) transient TLC technique as well as numerical simulation. It is indicated that the pin arrangement around the impingement jet is an important factor in order to attain higher cooling performance of the proposed integrated impingement cooling system. The hole/rib arrangement is main influenced factor for laminated cooling configuration. Cho and Rhee [6] described heat transfer studies for impingement/effusion configuration with three different hole arrangements, including staggered arrangement, shifted arrangement, and in-line array. The computation and experimental results showed the staggered arrangement leads to the highest Nusselt number. Nakamate et al. [16] investigated cooling configuration integrated impingement and pin-fin. Six amplified specimens were designed and tested in a facility with
v in;g
a gfilm gov erall c IGV CHT LED
inlet gas velocity injection angle in the streamwise direction adiabatic film cooling effectiveness overall cooling effectiveness injection angle in the spanwsie direction inlet guide vane conjugate heat transfer light emitting diode
Subscripts 1 film hole 2 rib 3 impingement hole
gas temperature of 673 K and Reynolds number of 3.8 105. The area-averaged cooling effectiveness of (each cooling unit consists of one impingement hole, two pins and one film hole) BASI arrangement and (each cooling unit consists of one impingement hole, three pins and one film hole) STAG arrangement was compared. The results showed BASI arrangement has the higher cooling effectiveness in the region of BR > 0.5 and the cooling effectiveness is lower in the region of BR < 0.5. Wang et al. [22] and Marc et al. [14] investigated the influences of coolant injection angle along the streamwise direction on the cooling effectiveness of laminated configuration using a fluid-thermal-structure coupling method. The results showed that the angled injection design is benefit to enhancing the overall cooling effectiveness and reducing the thermal stress. Li et al. [10] and Quan [20] tested laminated configuration in turbine blade on a liner cascade rig. Through comparing four kinds of configurations, the cooling performance of the B-type configuration (as shown in Fig. 2) is the best. The cooling effectiveness can reach up to 0.75 at blowing ratio 1.0, and if keeping increasing blowing ratio, the cooling effectiveness can reach up to 0.85. It was found the area ratio of film hole to cooling area has a clear impact to the cooling effectiveness and flow resistance. Panda et al. [11] performed transient conjugate heat transfer of a flat plate using an impinging jet with large eddy simulation. The computations show excellent agreement between the computational and the experimental data. Karim and Lamyaa [9] performed CFD investigation on three forms of film cooling configurations, including the standard cylindrical, rectangular slot, and oval slot. The results show rectangular slots have an increase in film cooling effectiveness for the same blowing ratio of coolant when compared to the standard circular hole, which is due to the minor counter rotating vortex pair effect. An oval slot design showed higher film cooling effectiveness and more spreading, covering more surface area. Bunker [4] investigated the potential improvement in adiabatic film effectiveness that can be achieved through the use of mesh-fed surface slot film
Fig. 2. Layout of staggered arrangement of laminated cooling configuration.
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cooling. The mesh-fed film effectiveness was as much as 25% higher than that for shaped holes. PSP technique has been widely used to measure adiabatic film cooling effectiveness distributions on the surfaces of interest based on a mass transfer analog. Natsui et al. [18], Caciolli et al. [5] and Johnson et al. performed detailed analysis to evaluate the effects of various associated uncertainties in the PSP measurements on the measured film cooling effectiveness distributions over the surfaces of interest. The measurement uncertainty is estimated as high as 5% at the near field behind the coolant holes Conjugate heat transfer computation showed the excellent potential of CFD for analyzing complex structures. According the investigations of Bohn et al. [3], Sean [12], Toshihiko et al. [21], William et al. [23] and Panda et al. [19], the predictions produced by the conjugate heat transfer analysis compared favorably to measured results, falling within experimental tolerances and consistent both in trend and value. Montomoli et al. [15], Ni et al. [17] and Sidewell et al. [13] recommend to maintain for all the first three layers y+ lower than 3.5 to enhance the computation of the temperature derivative. The scope of the current work is to investigate a novel laminated cooling configuration with slot film outflow using CHT computation and PSP experiment. By assessing the adiabatic film cooling effectiveness, overall cooling effectiveness, and the flow resistance, the potential of laminated cooling configuration with slot film outflow is validated.
Table 1 Geometry parameters values. Parameter
Meaning
Value
D1, mm D2, mm D3, mm H1, mm H2, mm H3, mm L1, mm L2, mm L3, mm
Diameter of film hole Diameter of Rib Diameter of impingement hole Height of outer wall Height of middle space Height of inner wall Spacing of film hole Spacing of rib Spacing of impingement hole
1.1 1.2 1.2 0.8 0.8 1.0 6.0 3.0 6.0
2. Geometry models The laminated configuration with staggered arrangement presented in many papers is investigated as the baseline scheme. As shown in Fig. 2, the inner wall and outer wall are connected with ribs, and the impingement hole, film hole and rib are arranged in a beeline in the baseline scheme. When coolants flow from the impingement hole to the film hole, the coolants must pass the cylindrical ribs, so the convection cooling effect can be well achieved for the configurations with staggered arrangement. The geometry parameters of the baseline case is illustrated in Fig. 3, including the diameters of film hole, the diameter of rib, the diameter of impingement hole, the height of outer wall, the height of middle space, the height of inner wall, the spacing of film hole, the spacing of rib, the spacing of impingement hole. The relevant parameter values are shown in Table 1. As shown in Fig. 4, to increase the film cooling effectiveness of the baseline case, three improved cases were proposed and investigated, including the Case A, Case B and Case C. The film holes are rearranged with increased spacing along the streamwise direction and decrease the spacing along the transverse direction in the Case A. Replacing the discrete film holes in the Case A with continuous slot, the Case B was designed, which can results in the best film cooling effects. To overcome the possible mechanical drawback of Case B, the Case C was designed by replacing the continuous slot with the discrete slots. The width of the above slots is 0.3 mm and the inclined angle is 45°along the streamwise direction.
Fig. 3. Illustration of geometry parameters.
Fig. 4. Investigated schemes.
3. Experimental facilities and methods Experiments were carried out in the flat-plate film-cooling experimental rig at the Advanced Industrial Gas Turbine Technology Laboratory, Institute of Engineering Thermophysics, Chinese Academy of Sciences. As shown in Fig. 5, the experimental rig is a low-speed wind tunnel test device using PSP measurement method. The mainstream sequentially flows through the transition section, a settling section, and a contraction section, and eventually enters into the test section. The mainstream air speed entranced to the test section is 25 m/s and the mainstream air temperature is about 35 °C. The PSP measurement is used to test the adiabatic film cooling effectiveness. The excitation wavelength range was 380– 520 nm, and the emitting wavelength range was 620–750 nm. The PSP was excited by two 400 nm light-emitting diode (LED) lights. A 670 nm filter was mounted in front of the camera lens to prevent any reflected light from the illumination source from filtering into it. The calibration was conducted at three temperatures, which were 23.0 °C, 35.4 °C, and 47.8 °C, respectively. In order to validate the experimental accuracy of film-cooling effectiveness,
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Fig. 5. Experiment rig using PSP measurement.
a typical fan-shaped hole was tested using the same experimental facilities and measurement methods. In the investigation of An et al. [2], the comparison results show good agreement and the present experiment facilities and methods are reliable. The operating conditions in the present investigations are shown in Table 2. For machining convenience, the laminated film configuration specimen is combined with an outer board and an inner board as shown in Fig. 6. The ribs and the film holes are located on the outer board, while the impingement holes and rib-pits are located on the inner wall. In the combined state, the ribs of outer wall stretch into the rib-pits of inner wall. Eight topology periods along the streamwise direction and five topology periods along the spanwise direction are formed in the test specimen of the baseline design. The test specimens are manufactured using the stainless steel, which thermal conductivity is about 12 W/mK on 35 °C. Fig. 6. Test specimen model.
4. Experimental results and discussions For describing the cooling performance of laminated cooling configuration, the adiabatic film cooling effectiveness and the blowing ratio are defined as follows:
gfilm ¼ BR ¼
T g T w;g Tg Tc
ð1Þ
qci v ci qin;g v in;g
ð2Þ
Fig. 7 shows the adiabatic film cooling effectiveness distribution of the four cases under the blowing ratio of 0.55. For the baseline case, the peak cooling effectiveness appeared on the centerline of film hole, and the peak cooling effectiveness reaches about 0.5. Moreover, the film outflow laterally diffused along the streamwise direction and nearly stabilized at the sixth hole. For the Case A, due to the spacing of hole is shorten along the spanwise direction, the film covered area is increased and the film cooling effectiveness is better than the baseline Case. For the Case B, the film outflow can cover all
Table 2 Operating Conditions. Parameter
Range
Mainstream velocity, Vm Mainstream temperature, Tm Mainstream Reynolds number, ReD Turbulent intensity of mainstream, Tu Momentum thickness, Density ratio, DR
25 m/s 310 K 7200 3.5% 0.27 mm 1.38
the downstream surface area, so the film cooling effectiveness seems very uniform along the spanwise direction. However the cooling effectiveness distribution shows unstable flow phenomenon. The peak cooling effectiveness reaches up to 0.9 at the outlet of the three slots. Due to the effect of film coolants superposition, the cooling effectiveness appears augment trend from the first slot to the third slot. For the Case C, the peak film cooling effectiveness seems comparable with the Case B. Although the spacing along the streamwise direction of near two slots is increased when it is compared to the Case B, the film cooling effect can also keep effective to the downstream of the slot. At the same time, the mechanical feasibility of Case C is better than the Case B with continuous slots. For quantitatively assessing the cooling performance of the baseline case with discrete holes and the Case B with continuous slots, the comparisons of lateral averaged adiabatic film cooling effectiveness at BR = 0.19, 0.55, and 0.95 are shown in Fig. 8. It is obvious that the Case B with slot film outflow results in higher adiabatic film cooling effectiveness at all blowing ratios. The averaged film cooling effectiveness of Case B reaches above 0.6 at blowing ratio of 0.55, while the baseline case is below 0.3. It means the film cooling effectiveness can be doubled by replacing the discrete cylindrical film holes with continuous slot outflow. The distinction between the crests and troughs in film cooling effectiveness distribution of Case B is very large, which indicated the film cooling effectiveness along the streamwise direction is very nonuniform while the baseline case shows more smooth distribution. The comparison of lateral averaged adiabatic film cooling effectiveness at BR = 0.55 for the four cases is shown in Fig. 9. It
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Fig. 8. Comparisons of laterally averaged adiabatic film cooling effectiveness between the baseline case and Case B.
Fig. 9. Laterally averaged effectiveness comparison of the four cases (BR = 0.55).
Fig. 7. Adiabatic film cooling effectiveness distributions of the 4 cases on test surface (BR = 0.55).
is obvious that the Case B and the Case C with slots film outflow have higher adiabatic film cooling effectiveness than the baseline Case and Case A with ordinary film holes. The distribution pattern
is similar between Case B and Case C. But the film cooling effectiveness of Case B is larger than Case C, and the film cooling effectiveness of Case C is larger than Case A. Although the film cooling effectiveness of Case B is very high, but distinction between the peak value and trough value is very large, i.e., very nonuniform along the streamwise direction. Although the film cooling effectiveness of baseline case and the Case A is relatively low, but its distribution along the streamwise direction is the most uniform. Compared the baseline case and Case A, it is shown the film cooling effectiveness of Case A is slight higher than the baseline case at blowing ratio of 0.55. Fig. 10 shows the comparisons of the area-averaged film effectiveness for the four test cases at blowing ratios of 0.19, 0.55, and 0.96. The film cooling effectiveness trends are relatively similar for both the baseline case and the Case A. With the increase of blowing ratio, the film cooling effectiveness of the baseline case and the Case A finally decrease due to the film outflow lift-off at high blowing ratio conditions. However at the higher blowing ratio of 0.96, the film cooling effectiveness of Case A is lower than the baseline
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Fig. 10. Area-averaged film effectiveness comparison of the four Case.
case, which means the film outflow of Case A is easier to lift-off. The Case B and Case C show significant higher film cooling effectiveness than the baseline Case and Case A. For instance, at the blowing ratio of 0.96, the area-averaged film cooling effectiveness is 0.26, 0.20, 0.68, and 0.50 respectively for baseline case, Case A, Case B, and Case C. The results show that the laminated film configurations with slot film outflow have obvious advantages over the configurations with holes film outflow at all the tested conditions.
5. Conjugate heat transfer results Conjugate heat transfer computations are performed for assessing the overall cooling effectiveness and the resistance coefficient. ANSYS CFX is used to perform the steady 3D RANS computations. The governing equations used for simulation are the Reynolds averaged continuity, momentum, and the energy equations along with the full-turbulent SST turbulence model. As shown in Fig. 11, the computation model is composed by 7 cooling units along the streamwise direction for the baseline case. Translation periodic boundary conditions are used on the spanwise boundary. For getting a fully developed boundary layer of fluid flow, the inlet duct with a length of 4 cooling unit is connected. ICEM-CFD commercial software is employed to generate the computation mesh. As shown in Fig. 12, the structured mesh is used in the fluid domain, and the unstructured mesh is used in the solid domain. The initial height of the first layer is 0.002 mm on the outer solid walls and 0.004 mm on the inner walls. The overall grid in the fluid domain is about 3.5 million elements, and the grid in the solid domain is about 2.0 million. This grid can give dimensionless wall spacing y+ below 2.0 at the first wall cell, which is needed in the Shear Stress Transport (SST) turbulence model. At the gas inlet, the total temperature is set to 1800 K, the
Fig. 11. Diagram of computation model.
Fig. 12. Local views of computation grids.
velocity is 500 m/s and the Reynolds number is 4.9 104. At the flow outlet, the static pressure is set to 101,325 Pa. At the inlet of coolant plenum, coolant total temperature is set to 800 K. The velocity of coolant changes with blowing ratio, and the Reynolds number Rec varies from to 1.0 104 to 6.0 104. The Rec is defined by using the diameter of film hole and the velocity of film flow. The heat conductivity of the solid is set to 10 W/(mK) and the resultant Biot number is about 0.1, which is similar with the turbine blade in the gas turbines. A monitor point was set up in the solid body to inspect the temperature convergence history in the CHT computation. The overall cooling effectiveness and flow resistance coefficient of coolant flow are discussed in detail. Overall cooling effectiveness coefficient and flow resistance coefficient of coolant are defined as:
gov erall ¼ cf ¼
T g T w;g Tg Tc
Pin;coolant Pout 0:5qin;g v 2in;g
ð3Þ
ð4Þ
The computational method is also validated by the experimental data. The test model and the experimental data can be found in literature [16]. The comparisons of computational results and the experimental data for cooling effectiveness are shown in Fig. 13. Good agreement was noticed in the area of BR > 0.4, but a distinction appeared in the area of BR < 0.4. To validate the mesh independence, three kinds of computation grids with different amounts of element are used for simulating the baseline case. The total element number of ‘‘coarser mesh”, ‘‘used mesh”, and the ‘‘finer mesh is respectively about 2.2 million, 5.0 million and 7.5 million, Fig. 14 shows the temperature at inner wall along spanwise direction between the tenth rib and the fifth impingement hole. The comparison indicates the used mesh is claimed to be fine enough. The comparison of overall cooling effectiveness contours at outer wall surface are shown in Fig. 15 at the blowing ratio of 0.5. It is clear that the Case A has higher overall cooling effective-
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Fig. 13. Comparisons of computed and measured cooling effectiveness at different blowing ratios.
Fig. 15. Overall cooling effectiveness contours on the outer surface (BR = 0.55).
Fig. 14. Comparisons with different computation mesh.
ness than the baseline case and the Case B has higher overall cooling effectiveness than the Case A, while Case C have a slight lower overall cooling effectiveness than the Case B. The peak cooling effectiveness is appeared downstream of the film holes or slots. At the blowing ratio of 0.5, the peak overall cooling effectiveness reached above 0.75 for the Case B and Case C. For assessing the cooling performance quantitatively, the averaged cooling effectiveness coefficients are computed with the ‘‘Averaged-post area” as shown in Fig. 15. Fig. 16 shows the relationships of overall cooling effectiveness and the blowing ratios for the four cases. It is presented that the overall cooling effectiveness of Case B and the C is larger than the baseline case and Case A at the computed blowing ratios. For the Case B and the Case C with slot film outflow, the overall cooling effectiveness is very close while the BR is less than 0.6. Case B results in slightly higher overall cooling effectiveness than Case C while BR is larger than 0.6. The baseline case has the higher overall cooling effectiveness when BR is less than 0.45, while has the lower overall cooling effectiveness while BR is larger than 0.45. The overall cooling effectiveness at
Fig. 16. Comparison of area-averaged overall cooling effectiveness at different blowing ratios.
BR = 0.19 is 0.56, 0.50, 0.59, and 0.57 respectively for the four cases. While the overall cooling effectiveness at BR = 0.96 is 0.72, 0.81, 0.89, and 0.85 respectively. Through synthetically considering the film cooling effectiveness and the overall cooling effectiveness of the baseline case and Case A, it can be concluded that the internal convection cooling effect of Case A is stronger than the baseline case. Fig. 17 shows the relationship between the flow resistances coefficient and the blowing ratio for the four cases. It is presented that the Case A has the highest flow resistance coefficient, while the Case B has the lowest flow resistances coefficient. The baseline case and the Case C have the middle resistances coefficient. For
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hole/slot for the four cases. It is shown the obvious flow separation phenomenon appeared at the downstream of film hole for the Case A and Case B, but without separation in the Case B and Case C. It is due to the different inclined angle of the film hole/slot and different coolants momentum for the four cases. The baseline case and the Case A used uninclined discrete film hole, which enable the film coolants easier to lift-off the outer wall. Moreover, the film outflow with slots can cover more outer wall areas along spanwise direction, which can lead to the higher film cooling effectiveness too. 6. Conclusions
Fig. 17. Comparison of flow resistance coefficient vs blowing ratio.
instance, the flow resistance coefficients are respectively 1.78, 2.15, 1.37, and 2.01 near blowing ratio of 0.96 for the baseline case, Case A, Case B, and Case C. It can also be found that the flow resistance coefficient is influenced by the area of film hole/slot and the distance from the impingement hole to the film hole of /slot in the cooling configurations. The lowest flow resistances coefficient of Case B benefits from the largest flow area of continuous slots among the four cases. Fig. 18 shows the comparison of temperature contour and velocity vector at the streamwise direction plane through the film
For investigating the potential of slot film outflow used in the laminated film cooling configuration, four cases are designed, including the baseline case, Case A with rearrangement film holes, Case B with continuous slot film outflow, and Case C with discrete slot film outflow. The pressure-sensitive paint measurement technique test is performed to assess the adiabatic film cooling performance and the conjugate heat transfer computation by ANSYS CFX 16.0 is performed to assess the overall cooling performance. The results show that the three improved cases perform better than the baseline case. The main conclusions are as following: (1) The Case B and Case C with slot film outflow achieved obvious higher film cooling effectiveness than the baseline case and Case A with film holes at all tested blowing ratios. The adiabatic film cooling effectiveness at BR = 0.96 is 0.26, 0.20, 0.68, and 0.50 for the baseline case, Case A, Case B, and Case C respectively. (2) The Case B and Case C with slot film outflow have higher overall cooling effectiveness than the baseline case and Case A with film holes. The overall cooling effectiveness at BR = 0.19 are 0.56, 0.50, 0.59, and 0.57 for the baseline case, Case A, Case B, and Case C, respectively. For higher blowing ratio, the overall cooling effectiveness at BR = 0.96 is 0.72, 0.81, 0.89, and 0.85 for the baseline case, Case A, Case B, and Case C, respectively. (3) The baseline case presents the highest flow resistance, while the Case B with continuous slot film outflow presents the lowest flow resistance for coolants. The flow resistance coefficients at blowing ratio of 0.96 are 1.78, 2.15, 1.37, and 2.01 for the baseline case, Case A, Case B, and Case C respectively. (4) Generally, slot has better cooling performance than the discrete film hole. However, the uniformity of the coolant outflow at the outlet face must be put much more emphasizes due to the non-uniform pressure distribution. So the Case 4 with discrete slot is much more feasible in the turbine blade cooling.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgement The authors wish to acknowledge the financial support from the National Natural Science Foundation of China through Grant No. 51506197. Appendix A. Supplementary material Fig. 18. Comparison of temperature contour (left) and velocity vector (right) at BR = 0.5.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.045.
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