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vanes on the heat transfer enhancement of a trapezoidal channel
Applied Thermal Engineering 102 (2016) 570–585
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
CFD analysis of the influence of guide ribs/vanes on the heat transfer enhancement of a trapezoidal channel Muiz Ur Rehman a, Waseem Siddique a,⇑, Inamul Haq b, Naqash Ali b, Zaryab Farooqi b a b
Department of Mechanical Engineering, Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad, Pakistan Department of Nuclear Engineering, Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad, Pakistan
h i g h l i g h t s CFD of influence of ribs/vanes in a trapezoidal channel was performed using Fluent. Arc-like vane is the best with 21% rise in overall performance at tip wall. Re No. increase results in heat transfer decrease but rise in pressure drop. Heat transfer is more for a trapezoidal channel compared to a rectangular one.
a r t i c l e
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Article history: Received 14 April 2015 Accepted 10 March 2016 Available online 6 April 2016 Keywords: Gas turbine Trapezoidal channel Heat transfer Blade trailing edge Computational Fluid Dynamics (CFD)
a b s t r a c t Gas turbines are used to generate mechanical power using the thermal energies of working fluid. Turbine thermal efficiency and power output both increases by letting high temperature combustion gasses at the turbine inlet. Combustion technology has advanced to such an extent that it can create hot gases having temperatures greater than the melting points of turbine built materials. Gas turbine blades are an important turbine part and they come in direct contact with combustion gases. To have a longer safe operation life of gas turbine blades, different configurations are designed to bring blade surface temperatures down to safe working limits. One way of accomplishing this is by the internal cooling of the gas turbine blades. Gas turbine blade trailing edge is designed to be thin and sharp. Usually pin slots are provided on its surface to eject a cooler air out for its cooling purposes, but if an internal cooling serpentine channel has to be placed inside it, it will have a shape of trapezoid. The channel inside can be modeled as a two-pass trapezoidal channel with a 180° turn. Gas turbine blade tip is an important region to be cooled. Clearance gap between blade and casing causes secondary leakage flow with high tip wall heat fluxes and local high blade temperatures. To increase the blade tip region heat extracting capacity of the internal cooling trapezoidal channel, different geometry designed ribs and vanes are placed at the channel turn. Together they make up six different cases to be analyzed for their heat transfer enhancement characteristics. Numerical based CFD technique is utilized to investigate different channels heat transfer enhancements. Channels pressure drops and overall performance is evaluated and compared. It is found that by placing ribs/vanes at the trapezoidal channel turn region, we can increase channel walls heat transfers up to 40%. A vane type design suggested that overall thermal performance for the channel tip wall region can be improved up to 21% as compared to a channel with no rib or vane attached. Rib/vane cases affect local flow fields to gain improved heat transfers at different regions of the trapezoidal channel. It is also concluded that with increase in Reynolds number, heat transfer decreases while pressure drop increases in a trapezoidal channel, regardless of presence or absence of vane/ribs in the turn region. This eventually results in decrease in the thermal performance of the channel with increase in Reynolds number. Finally, it is found that for same thermal and flow conditions, heat transfer is more at the tip wall for a trapezoidal channel compared to a rectangular channel. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
⇑ Corresponding author. http://dx.doi.org/10.1016/j.applthermaleng.2016.03.043 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Gas turbine plays a vital role in the current industrialized society, and as the demand for power increases, the power output
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Nomenclature Ac dh f L _ m Nu Nuo Nus P Pr R
cross sectional area at the turn of the channel [m2] hydraulic diameter of the channel at turn [m] friction factor length of the channel [m] mass flow rate [kg/s] Nusselt number Nusselt number based on Dittus Boelter correlation Nusselt number of a channel with smooth turn pressure [N/m2] Prandtl number rib
and thermal efficiency of gas turbine must also increase. One method of increasing both the power output and thermal efficiency of the engine is to increase the temperature of the gas entering the turbine. Thermodynamic efficiency increases as the temperature of working fluid at the turbine inlet increases. The combustion technology has increased to an extent that it can produce high temperate gasses, having temperatures above the gas turbine materials. This can result in gas turbine blade melt down, creeping and the triple point failures. Thus keeping the advantage of higher efficiencies at one hand, the gas turbine components must be cooled effectively during operations to work safely. Two-pass rectangular channels with 180° bend are used as cooling configurations in internal cooling of the gas turbine blades. A lot of research has been carried out both experimentally and numerically to develop and optimize different cooling techniques [1–4]. In the combined power plant cycle, steam is bled which act as a coolant. In such case only internal cooling of the blade is possible. This requires complete internal cooling design of gas turbine blade including its trailing edge [5]. The cooling of the blade should include all regions that are exposed to high-temperature gasses and thermal load. Among such regions, particularly for high-pressure turbines, is the blade tip area, which is shown in Fig. 1. The leakage flow associated with tip-shroud clearance gap is undesirable, not only because it generates secondary flows resulting in the reduction of the work done but also because it results in higher heating at the blade tip, from mid-chord to trailing edge, leading to high local temperatures. Therefore, it is essential to cool the turbine blade tip and near the tip regions [7]. Researchers focused attention on enhancing heat transfer at the inlet and outlet
Re Tb T(i) V
Reynolds number bulk fluid temperature [K] wall temperature [K] vane
Greek symbols D difference q density [kg/m3] g performance factor gs performance factor of a channel with smooth turn
pass of two-pass channels where the turn region was kept smooth [8–12]. Later several investigators performed experimental as well as numerical research to figure out ways to improve heat transfer at the tip region of the blade by installing vanes in the turn region. The effect of installing guide vanes in the two-pass channels on heat transfer was studied where it was found that guide vanes helped in eliminating the separation zone in the curved path which is helpful in enhancing heat transfer and reducing pressure drop [13]. Experimental investigations were performed to study the effects of guide vanes on pressure drop in smooth or roughened two-pass channels [14]. It was concluded that the shape and position of the guide vanes effects pressure losses and properly shaped guide vanes can decrease the overall pressure drop by 14–20%. The experimental and numerical results of local heat transfer and pressure distribution of the ribbed two-pass channels suggests that by introducing the turning vane the whole pressure loss was reduced up to 66% and the combination of a rib and a turning vane in the turn region could improve heat transfer in this region, about 10–15% [15]. RANS method was used to simulate the turbulent flows inside several 2D and 3D 180° U-ducts with and without guide vanes [16]. Simulations show that due to presence of vane, weaker secondary-flow vortices and smaller separation results in a substantial reduction in pressure loss. The trailing edge of the gas turbine blades is an important region as it affects the aerodynamics of the flow. Turbine blade is squeezed at the trailing side in order to accelerate the flow, as well as to redirect it. The aerodynamics of blade demands a sharp and thin trailing edge to reduce profile losses. The conventional method to cool this part of blade is to release a lot of cooling air though the slots along the airfoil trailing edge. However in the case
Fig. 1. Gas turbine blade clearance gap between casing and blade tip [6].
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of internal cooling designs, the coolant is not allowed to leave the channel except from the root section to avoid mixing of the gas in the main flow path. The release of air into the main gas flow path reduces the temperature and enthalpy of hot working fluid gasses thus reducing the thermal efficiency of the gas turbine. Thus trailing edge tip region also needs to be cooled properly [4,17]. The objective of this research is to model the cooling configuration for the tip region of the gas turbine blade trailing edge. It has been modeled as two-pass trapezoidal channel. The influence of the guide vanes/ribs on heat transfer in the turn region of two-pass rectangular cross-section channel was studied [18]. In the current study, the influence of similar vanes/ribs have been studied but for a channel with trapezoidal cross-section. The analysis has been performed using CFD technique to study heat transfer enhancement and the pressure drop in the trapezoidal channel. To the knowledge of the authors, such a study has not already been performed. This research work will give designers an opportunity to design better cooling schemes for gas turbine blades.
by Siddique et al. [17]. Fig. 2 shows dimensions for the smooth two-pass trapezoidal channel which acts as reference for all other modifications, causing increase or decrease of heat transfer at different regions of the channel, especially the tip-wall region. In addition to that it also acts as the reference for pressure drop across the channels. A 571.19 mm long inlet pass is connected to an outlet pass with 180° bend. The divider-to-tip wall distance is equal to the width of the inlet channel of 38.1 mm, while the thickness of the divider wall is 19.1 mm. The outlet pass extended after to avoid reverse flow effects is 349.29 mm long. The maximum height of the inlet pass is 76.2 mm while the minimum height of the outlet pass is 38.1 mm. This makes the angle between the top and bottom wall equal to 21.8°. Fig. 3 shows the two pass smooth channel which is modeled in the current study. It shows the tip-wall, inlet and outlet of trapezoidal channel along with the flow directions. The inlet is kept longer to make flow fully developed. The outlet is given additional length to compensate for reverse flows in the CFD simulation. 4. Geometry augmentations
2. Methodology The method used in current study is primarily numerical. Computational Fluid Dynamics (CFD) helps in designing of cooling configurations in a gas turbine blade with predictions about the trends of flow and heat transfer. The added advantage in using CFD is the 3D flow results compared to single measured points in experiments, which is useful in designing more efficient augmented heat transfer channels. ANSYS Workbench 14.0 is used as pre-processing, solution and post-processing software. ANSYS Design Modeler is used to create geometries, ANSYS ICEM CFD is used to generate mesh and ANSYS FLUENT 14.0 is used as a solver to solve fluid mechanics and heat transfer problem. Post processing is done using CFD Post 14.0. The low-Re k-epsilon model can be used with acceptable accuracy to predict the flow and heat transfer behavior in a trapezoidal channel [17]. In the current study the same model has been used for predicting the heat transfer and pressure drop in a trapezoidal channel with different configurations of vans and ribs at the turn region. Mesh independency is also necessary to have desired level of accuracy in answers along with the balance amount of computer resources utilized. CFD analysis results can be used to check the performance of different postulated Ribs and Vanes and for the further research work in future. 3. Description of the physical model The channel dimensions used by Lee et al. [19] are selected for the current study. This trapezoidal channel has been used in experimental setup by Lee et al. [19] and numerical simulations
In order to enhance heat transfer at the tip-wall region of gas turbine blade, different augmentations are suggested in the 180° turn of a rectangular channel [18]. The augmentations are classified as ribs and vanes cases. The difference between ribs and vanes is such that ribs are present up to certain height while the vanes are present with full height from bottom to top wall. Similar augmentations have been implemented in a channel with trapezoidal cross-section, in current study. Following is the detail of these augmentations: Case 1R: In this case two ribs of different lengths are attached at the bottom wall at the turn region. The geometry detail is given in Fig. 4. Width of these ribs is 3 mm, height is selected to be 6 mm hence an aspect ratio of height to width is 2:1. Case 2R: As shown in Fig. 5, this is a symmetric arc like rib which is attached to the bottom surface of the turn region; its aspect ratio height to width is 2:1. Its height is 6 mm and its width is 3 mm. Case 3R: As shown in Fig. 6, this configuration consists of two ribs on the bottom wall at the turn region but with the different geometry. Ribs thickness is 3 mm and height is 6 mm. Height to width aspect ratio is 2:1. Case 1V: It is same as Case 1R but the rib height is not limited to 6 mm, but the vane is connected from bottom to top wall. The other dimensions of this model are same as Case 1R. This case is shown in Fig. 7. Two vanes are attached at the turn region, one directs the flow toward the tip wall, and other brings flow inside the outlet pass.
Fig. 2. Dimensions of the two-pass trapezoidal channel used in the current research study.
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agreement between the experimental and numerical data for the smooth trapezoidal channel [17]. Therefore same validated turbulence model is selected for simulations of ribs and vanes at the turn region in current study. 7. Mesh independency
Fig. 3. Two-pass smooth channel showing flow directions.
Case 2V: This is generated from the Case 2R. The vane height connects between channel bottom and top walls. This case is shown in Fig. 8. Vane dimension values are same as of the Case 2R. This vane type is design to push part of the flow along the tip wall, and rests back into the outlet pass channel. Case 3V: It reflects the geometry and dimensions of Case 3R. Vanes are extended from bottom wall to the top wall of the channel turn region, as shown in Fig. 9. There are two vanes present, both directing flow in the same direction. 5. Computational details Finite Volume based CFD technique is used to solve fluid mechanics and heat transfer problem. Flow inside the trapezoidal channel is considered steady, incompressible, turbulent, and 3-dimensional. Dry air is selected as a working fluid with constant thermodynamic physical properties. All walls are kept at a constant temperature of 350 K and air enters the inlet at 310 K. Mass flow rate inside the channel is calculated based on the Reynolds number of 9400 at the turn region. Standard k-epsilon turbulence model with enhanced wall treatment is selected for the turbulent flow, as it shows smallest deviation in Nusselt number calculations based on experimental and numerical results for the smooth turn trapezoidal channel [17]. 6. Selection of turbulence model In previous work done [17], numerical validations of the experiment perform in a smooth channel [19] has been done successfully. The low-Re k-epsilon model showed the best
Mesh independent study has been performed to check the effect of changing mesh size on the CFD solution results. In current study, Case 2V has been used for the grid independence study. Statistics of mesh sizes is given in Table 1. To keep y+ value near to the wall equal to unity, calculations show that for Reynolds number of 9400 and hydraulic diameter of 45.72 mm, the minimum first layer height of the elements near wall should be 0.07 mm. Inflation growth rate of 1.2 is selected and total number of 11 layers are added to give inflation layers total height of 2.25 mm. All the cases selected for mesh independency have inflation layers with the same height and total number of layers. Fig. 10 shows mesh sizes for the inlet pass, from course to fine. Section wise area weighted average Nusselt numbers were calculated at the bottom wall of the trapezoidal channel. It was normalized by Nusselt number calculated from Dittus-Boelter correlation. The normalized Nusselt number is plotted and variation in the results is observed for all the mesh sizes. Average Nusselt number based on the bulk fluid temperatures of different zones at the bottom wall for different mesh sizes can be seen in Fig. 11. The trapezoidal channel is divided in 16 regions. The inlet pass is represented by 0–7, 8 is the turn region, while 9–16 shows outlet pass bottom wall regions. The difference in Nu/Nuo value for 1.96 million mesh size and 2.4 million mesh size is almost negligible with a maximum deviation of 1.5% at the turn region. Thus it is concluded that mesh element size of 1.25 mm (which resulted in 1.96 million mesh size) is the correct choice to perform all other simulations. Fig. 12 shows the mesh at the turn region of the three cases studied. 8. Analysis tools Heat transfer on different walls can be calculated by means of a dimensionless Nusselt number (Nu). This parameter directly reflects the heat transfer characteristics. Area averaged Nusselt number can be calculated at different walls of the channel to compare heat transfer performances for different augmented channels compared to case smooth turn channel. Addition to that, local Nusselt number values can be plotted as contours. This gives heat transfer variation at different regions of the wall. This section covers the details of analysis tools that are required to compare heat transfer characteristics of different ribs and vanes cases.
Fig. 4. Case 1R where two ribs are attached on the bottom wall (all dimensions are in mm).
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Fig. 5. Case 2R where a symmetric rib is attached on the bottom wall (all dimensions are in mm).
Fig. 6. Case 3R where two ribs on the bottom wall at the turn region but with the different geometry are attached (all dimensions are in mm).
Fig. 7. Case 1V where two vanes are attached on the bottom wall.
Fig. 8. Case 2V where a symmetric vane is attached on the bottom wall.
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Fig. 9. Case 3V where two vanes on the bottom wall at the turn region but with the different geometry are attached.
Table 1 Statistics of mesh sizes used in the study. Global mesh size (mm)
Total number of elements (million)
3 2 1.5 1.25 1.1
0.4 0.8 1.4 1.96 2.4
9.1. Velocity fields
The calculated Nusselt number has been normalized by DittusBoelter correlation which is given by Eq. (1).
Nuo ¼ 0:023 Re0:8 Pr0:3
pressure drops. The best case scenario would be the one where rib/vane augmentation causes high heat transfer along with low or suitable pressure drop across the channel.
ð1Þ
Further, nodal values of Nusselt number (Nu) can also be normalized with the corresponding values of the Nusselt number for the smooth turn channel (Nus). 9. Results and discussions Different ribs and vanes cases, have been designed in order to enhance heat transfer in the trapezoidal channel. The gas turbine blade tip region is an important region to be cooled effectively. Different cases are compared with smooth turn trapezoidal channel. Heat transfer enhancement is investigated in terms of walls Nusselt number. Heat transfer can be increased by changing the flow field inside the channel. Velocity fields are analyzed by the inspection of velocity contours. This helps in judging the kind of rib or vane case that increase or decrease local fluid velocities and favors the heat transfer. The increase in turbulence and nature of flow flied in the channel is also accompanied by corresponding
Velocity field for different cases can be analyzed with the help of velocity contours and velocity vectors. Mid plane is selected along the height of the channel to plot such contours and vectors. Velocity contours are plotted for the regions which are most influenced by the tuning effect and are important to be analyzed for velocity field changes among various ribs and vanes cases. Hence two inlet pass blocks before the turn region, seven outlet pass blocks after the turn region and the turn region itself is selected to plot the velocity contours. Velocity vectors are shown only at the turn region to show the effect of different ribs and vanes installed in this region on the flow field. The velocity contours for the vane cases and the smooth turn channel at mid plane are shown in Fig. 13 while velocity vectors for the same cases are shown in Fig. 14 which supports and explains the physics of the flow. Flow enters the inlet pass, passes though the turn region, and leaves from the outlet pass. No slip boundary condition is applied on all the walls, hence flow on the wall attains zero velocity. For the smooth turn, low velocity region at the corners of the turn region are formed. This is because of the local flow recirculation where flow gets trapped for instant and then moves away. There is a low velocity region at the beginning of the outlet pass and also some high velocity flow on the side wall of the outlet pass. The low velocity is due to separation of flow caused by the turning effect. The high velocity is because of the turning effect of flow but
Fig. 10. Mesh sizes for the inlet pass, from course to fine.
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Fig. 11. Average Nusselt number of different zones at the bottom wall for different mesh sizes.
Fig. 12. Mesh at the turn region of three different cases.
Fig. 13. Velocity contours for the vane cases and the smooth turn channel at mid plane.
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Fig. 14. Velocity vectors for the vane cases and the smooth turn channel at mid plane.
also as it is the region where height of the channel is minimum and area of flow is also minimum, so for same mass flow rate, flow tries to attain high velocity. Later in the downstream the flow again tries to adjust its velocity. Near the tip wall, velocity having range of about 4.5 m/s covers most of the region. For the Case 1V, the wake that was observed in the smooth turn channel at the inner side wall of the outlet pass channel has been recovered, as the flow is directed back in. High velocity region in the side wall of outlet has been increased. Similar region is also observed near the divider wall of the inlet–outlet pass. A small wake region is observed behind the two vanes as the flow is very slow there. At the tip wall, majority of flow is slower than the smooth turn case, but a little high speed region is observed in the later part of the turn region near the tip wall. For Case 2V, a big high velocity region is observed near the tip wall region. The region also contains maximum of the flow velocity for this case. There is no wake region behind the vane and inner side wall of the outlet pass. There is a slower flow at the side wall of the outlet pass, majority of the flow here is in 5 m/s velocity range, but objectively high velocity is obtained near the tip wall. For Case 3V, a huge high velocity region is visible at the side wall outlet, later part of the tip wall and near the divider wall. More wakes are formed behind the first vane, ahead of the second vane and near inner side wall outlet pass. Most of the high velocity region is found after the half pass length of the turn region tip wall. In
the downstream of the outlet pass, a high velocity region is found at the inner side wall outlet. Case 3V has blocked more of the flow as compared to other cases. Compared to vanes, ribs are only attached on the bottom wall. They should have major influence near the bottom wall, but it is useful to observed flow field patterns caused by the ribs cases away from the bottom wall, so velocity contours of rib cases are also plotted on the mid plane. Velocity contours for rib cases on the mid plane are shown in Fig. 15 while velocity vectors for the same cases are shown in Fig. 16 which supports and explains the physics of the flow. It is observed that ribs cases have little influence on the velocity field away from the bottom wall as expected. The velocity contours have small changes as compared to smooth turn. For Case 1R, high velocity region at side wall outlet is little longer, flow is more attached at the inner side wall outlet, a higher velocity near the divider wall. On the tip wall flow is almost similar. For Case 2R flow is similar to case smooth turn. A small increase in velocity at the side wall outlet. For Case 3R, flow has higher velocity at side wall outlet. At the tip wall 4.2 m/s velocity field is broader and cover more length. Small wake is found in the early length of inner side wall outlet. As ribs are attached on the bottom wall, they have more influence at the vicinity of bottom wall only. Another plane is selected which is 4 mm above the bottom wall and velocity contours for the rib cases are plotted at it which are shown in
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Fig. 15. Velocity contours for rib cases on the mid plane.
Fig. 16. Velocity vectors for the rib cases and the smooth turn channel at mid plane.
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Fig. 17. Velocity contours for the rib cases at a plane 4 mm above the bottom wall.
Fig. 17. At the tip wall region some changes are visible. At the later part of the turn length slow velocity region in the case smooth turn is observed, but the rib cases have tried to minimize this and a faster flow is present in this region for the rib cases. Similarly for smooth turn, there is a slow flow region at the mid portion of tip wall vicinity, but in rib cases it is not present. From Fig. 17, Ribs cases have gained speed of flow in the later length of turn region at the tip wall. Case 1R and Case 3R are in more favor of this as compared to Case 2R. At the outlet pass, same differences are found as in the case of mid-plane velocity contours of rib cases. The effect of placing different types of ribs and vanes in the turn region is shown by velocity vectors at the turn region of the two-pass channel. Such vectors have been shown in Fig. 18. At the turn, centrifugal forces results in counter rotating vortices which can be seen in Smooth turn case. These strong vortices enhance the mixing of fluid thus cold fluid is transported to the heated walls more efficiently. Placing one rib at the bottom surface does not effects these vortices to a great extent so enhancement in heat transfer in the rib cases is not significantly enhanced. Far case 1V and 3V, the vane is blocking the flow, thus reducing the velocity near the tip wall, resulting in lesser mixing of fluid. For case 2V, the vane results in enhancement in velocity near the tip wall which results in higher heat transfer at the tip wall. 9.2. Channel heat transfer In order to study heat transfer of the trapezoidal channel, three walls are selected (Tip Wall, Bottom Wall outlet and Side Wall outlet). The locations of the channel walls are shown in Fig. 19. Tip wall heat transfer enhancement is the main objective of this study, but the bottom wall and side wall outlet are also important for the trailing edge of gas turbine blade. Local Nusselt number is calculated for each mesh point using Eq. (2).
NuðiÞ ¼
qw dh TðiÞ T b k
ð2Þ
Fluid bulk temperatures are required for the wall Nusselt number calculations. For tip wall, volume average temperature of the turn region has been taken as the bulk fluid temperature, ‘Tb’. For
side wall and bottom wall outlet, the volume average temperature of turn region and the outlet pass has been used as the bulk fluid temperature. T(i) is the local wall temperature. The normalized Nusselt number at three selected walls for all cases is shown in Fig. 20. Smooth turn channel results provide a reference platform to analyze the results of other ribs and vanes cases. For the tip wall region it can be seen that Case 2V has performed best with the normalized Nusselt number to be 3.42 which is 24% increase in heat transfer as compared to the smooth turn channel. For the side wall outlet Case 3V has increased a lot of heat transfer with normalized Nu of 3.83 as compared to the 2.67 for smooth turn, which is a total amount of 43% increase. All the rib cases have also contributed in heat transfer enhancement of the side wall, Case 1R increased 2.6%, Case 2R about 1.9% and Case 3-R showed 2.3% increase in heat transfer for the side wall outlet. For the bottom wall outlet only Case 3R and 3V are contributing in the heat transfer enhancement. Case 3V has increased 36% of the heat transfer while Case 3R increased 8.5% of heat transfer as compared to smooth turn trapezoidal channel. It can be seen that, Case 3V and Case 3R has contributed in all three regions of the channel while the increase in heat transfer by Case 3V is proportionally higher than that by the corresponding rib case. Case 1R and 2R have contributed in enhancement of heat transfer at side wall outlet region only. Case 2V has participated for significant amount of heat transfer increase at tip wall only. Case 1V has not participated in enhancing heat transfer at any region and is not suitable for heat transfer enhancement of the trapezoidal channel. 9.3. Tip wall heat transfer In previous section heat transfer was compared on the basis of average values of Nu/Nuo on three walls of the channel. In this section, local values of Nu/Nuo on the tip wall region has been discussed. In a two pass trapezoidal channel with a 180° turn, flow has to change its direction very sharply. The high speed fluid coming in the inlet pass strikes the tip wall region, change its direction, then strikes the side wall of outlet pass and finally leaves through the
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Fig. 18. Velocity vectors for the rib and vane cases at the turn region of the two-pass channel.
Fig. 19. Locations of three walls (Tip Wall, Bottom Wall outlet and Side Wall outlet) selected to present results.
outlet pass of trapezoidal channel. Hence lot of flow with high kinetic energy strikes the tip wall and enforce forced convection. But this phenomena only dominates on the wall region that is just ahead of the inlet pass, tip wall region attached to the outlet pass has low flow velocities hence have low heat transfer. An attempt is made by putting ribs/vanes at the turn region to homogenies and accelerate the flow along the tip wall to enhance heat transfer. The comparison of vane cases based on the Nusselt number contours on tip wall is shown in Fig. 21. For Case 1V, which is not suitable for heat transfer enhancement, has tried to homogenies the heat transfer at the longer length of turn but net amount of heat transfer is lesser than the case-ST. Case 2V which is the most successful heat transfer candidate at the tip wall, has not only
homogenized the heat transfer to the longer length of turn but also has increased heat transfer at the left and right side of the tip wall. More high heat transfer zones are observed due to more impingement and laminated flows because of this vane design type. Heat transfer area at the tip wall region attached to inlet pass and wall area near the side wall outlet, now has higher heat transfer values. Nu/Nuo values ranging between 3.7 and 4, covers most of these regions. Top and bottom areas for the outlet pass tip wall region also has an increase in heat transfer. Case 3V has a completely different heat transfer configuration than the case-ST. Good heat transfer is present along most of the turn length. There is more heat transfer at the later part of the turn as compared to left, region attached to inlet pass. Amount of concentrated heat transfer is less than the Case 2V and more spread in heat transfer is found, but Case 2-V showed maximum area averaged heat transfer. Comparison of rib cases with the case-ST is presented in Fig. 22. Small differences can the seen in the bottom right side of the tip wall. Ribs are attached to the bottom wall of the turn only, hence they have little influence in flow field and heat transfer at the higher levels of the tip wall. Case 3R shows highest heat transfer at the bottom right corner of tip wall hence it has the highest average heat transfer than other ribs cases. Case 1R shows a slight higher heat transfer than case ST for the same reason. Case 2R shows a little increase in heat transfer in the same zone as compared to case-St but the intensity is slight weaker. Hence overall, Case 2R shows the same average heat transfer as is found in case ST. 9.4. Channel pressure drop Friction factor ‘f’ is a measure of pressure drop across the channel and it can be calculated for different ribs and vanes cases using Eq. (3).
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Fig. 20. Normalized Nusselt number comparison in three regions of the channel for all cases.
Fig. 21. The comparison of vane cases based on the Nusselt number contours on tip wall.
f ¼2q
2 DP Ac dh _ L m
ð3Þ
where ‘q’ is the fluid density, ‘Ac’ is the cross sectional area of the _ is the mass flow turn where the Reynolds number is calculated, ‘m’ rate in the channel, ‘Dp’ is the pressure drop across the channel and ‘L’ is the length across the stations on which ‘Dp’ is measured. In Eq. (2) all the parameters are constant, except the ‘Dp’, which varies for different ribs and vane cases. Hence friction factor ‘f’, directly reflects the pressure drop across the channel. Location of the station planes at which this pressure difference is measured for different cases is given in Fig. 23. The length across the two planes ‘L’ is also shown. Area average value of pressure at the two planes are calculated to find their ‘Dp’. Friction factor ‘f’ calculated based on the pressure difference can be normalized by ‘fo’, which is the friction factor for the fully developed turbulent flow in a smooth channel and is calculated by a correlation given by Eq. (4).
f o ¼ ½0:79 lnðReÞ 1:64
2
ð4Þ
The normalized friction factor ‘f/fo’ is helpful in establishing a pressure drop parameter in trapezoidal channel for different ribs and vanes cases. Results for the normalized friction factors ‘f/fo’ for each case except case 3V is shown in Fig. 24. Case 3V showed almost 10 times more pressure drop and therefore is not included in Fig. 24. For the augmented channels, cases 2V/R are showing the least pressure drop and cases 3V/R are showing most of the pressure drop. 9.5. Overall comparison The performance factor ‘g’ has been defined by Eq. (5), which signifies the effect of both heat transfer and pressure drop across the channels. Higher value of performance factor means that there is higher proportions of heat transfer as compared to the corresponding pressure drop across the channel, which is desirable.
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Fig. 22. The comparison of rib cases based on the Nusselt number contours with case-ST.
Fig. 24. Normalized friction factors ‘f/fo’ for different cases calculated at Re = 9400.
Fig. 23. The location of the station planes at which this pressure difference is measured for different cases.
g¼
Nu=Nuo 1=3
f =f o
ð5Þ
Performance factors are presented for the tip wall, side wall outlet and bottom wall outlet for the trapezoidal channels and are shown in Fig. 25. Case 2V has showed 21% better performance factor at the tip wall than the case smooth turn. Case 1R showed 1.4% better performance at the side wall outlet and Case 3R is showing 1.7% better heat transfer at the bottom wall outlet. Case
3V is a good configuration for heat transfer but does not show good results because of huge pressure drops as compared to Case ST. The detail comparison in different regions of the channel for different cases can be made if the performance factors for different cases are normalized with the corresponding values of smooth turn channel. The overall comparison for all the cases is shown in Fig. 26. Case 2V is the most successful configuration at the tip wall, and the increase in performance factor is significant as compared to other configurations for side and bottom wall outlet. It has a decrease of about 12% of performance factor at the side and bottom wall, but this problem can be solved by putting suitable rib tabulators at side and bottom wall of outlet pass channel. Case 1V is not
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Fig. 25. Performance factors for the tip wall, side wall outlet and bottom wall outlet for all cases.
Fig. 26. The overall comparison of all the cases.
desirable in any mentioned region of the trapezoidal channel. Case 3V has some significant efforts for heat transfer enhancement but due to its huge pressure drop it has a drop in overall performance for all walls. Rib cases are showing comparable similar results among themselves, but neither of these is showing better performance for the tip wall region. 9.6. Effect of Reynolds number Performance of different vanes and ribs at the turn region of the trapezoidal channel at various Reynolds number has been studied. Fig. 27 shows the effect of Reynolds number on Nusselt number for different vane and rib cases. It is observed that for all cases, heat transfer increases by 2.2–2.4 times with increase in Reynolds number from 9400 to 57,200. The effect is more pronounced in case 2V compared to other cases. Fig. 28 shows the effect of Reynolds number on normalized Nusselt number for different vane and rib cases. With increase in Reynolds number, all the cases shows 24–27% decrease in normalized Nusselt number. This is because at higher Reynolds number the value of Nusselt number calculated by using Eq. (1) also increases. This increase is more compared to increase in Nusselt number shown in Fig. 26, thus it decreases the normalized value. Fig. 29 shows the effect of Reynolds number on pressure drop for different vane and rib cases (excluding case 3V). Increasing trends in pressure drop are found at higher Reynolds numbers
Fig. 27. Effect of Reynolds number on Nusselt number for different vane and rib cases.
for all cases. Also, at higher Reynolds number, pressure drop in case 3R surpasses the other cases where the pressure drop almost doubles with increase in Reynolds number from 9400 to 57,200.
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Fig. 28. Effect of Reynolds number on normalized Nusselt number for different vane and rib cases.
Fig. 30. Effect of Reynolds number on performance factor for different vane and rib cases.
Fig. 31. Comparison of tip-wall heat transfer for different channel cross-section. Fig. 29. Effect of Reynolds number on pressure drop for different vane and rib cases.
Fig. 30 shows the effect of Reynolds number on performance factor for different vane and rib cases. Performance factor decreases by almost 40% with increase in Reynolds number. These deceasing trends are due to increase in pressure drop as well as decrease in normalized Nusselt number with increase in Reynolds number. The effect of ribs/vanes on tip wall heat transfer. at turn region of a rectangular channel were previously studied [18]. Similar effects are studied in current study for a trapezoidal channel. Fig. 31 compares the heat transfer variation with Reynolds number for both channels with different vanes and ribs. It is observed that a trapezoidal channel enhances more heat transfer compared to the rectangular channel. So at tip-wall of the trailing edge, heat transfer is more compared to that at mid-span of the blade. This might be considered as inherent advantage as at trailing edge, heat flux is more which requires more cooling. Further, it is noted that for rectangular channel, the heat transfer is mostly not affected by change in Reynolds number, but in case of a trapezoidal channel, it reduces as discusses earlier. Also, case 1V gives maximum heat
transfer advantage in rectangular channel but in trapezoidal channel, case 2V proved to be the best among the studied cases. 10. Conclusions In the current work, different internal cooling trapezoid serpentine channels with and without rib or vane at the turn region are analyzed using CFD technique. Study is carried out to determine heat transfer at three important channel walls and to examine corresponding channels pressure drops. Overall performance of channels is evaluated and compared. Based on the results, following important conclusions are drawn: Heat transfer capacity of the channel tip wall can be enhanced by placing a suitable kind of rib or vane at the trapezoidal channel turn region. The rib/vane design changes the flow field, causing rise or fall of the local heat transfer coefficient ‘h’. Case 2V has been analyzed to be most successful configuration, affecting 24% better heat transfer and 21% rise in overall performance at the channel tip wall.
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Case 2V has caused some heat transfer drop at side and bottom wall outlet, but this can be overcome by installing a very well designed rectangular rib tabulators at side and bottom walls of the outlet pass of the channel. Case 3V has showed about 10–40% rise in channel heat transfer, but due to its severe channel pressure drop, its overall performance has decreased between 40% and 50%. Hence it is not a desirable case for channel heat transfer enhancement. Case 1V shows drop in both channel heat transfer and overall performance, making it most unattractive. Rib cases have increased small amount of heat transfer between 2% and 9% and overall performance ranging less than 2% on channel walls. But neither of them showed better heat transfer for the tip wall region. Thermal performance decreases with increase in Reynolds number for a trapezoidal case regardless of the augmentation in the turn region. For the same Reynolds number, heat transfer depends on the cross-section of the channel. Acknowledgement The authors acknowledge the computational support by the Advance Computational Research Laboratory, Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan. References [1] S. Mochizuki, A. Murata, R. Shibata, Wen-Jei Yang, Detailed measurements of local heat transfer coefficients in turbulent flow through smooth and ribroughened serpentine passages with a 180° sharp bend, Int. J. Heat Mass Transfer 42 (11) (1998) 1925–1934. [2] M. Hirota, H. Fujita, A. Syuhada, S. Araki, T. Yoshida, T. Tanaka, Heat/mass transfer characteristics in two-pass smooth channels with a sharp 180-deg turn, Int. J. Heat Mass Transfer 42 (20) (1999) 3757–3770. [3] M. Hirota, H. Fujita, L. Cai, H. Nakayama, M. Yanagida, A. Syafa’at, Heat (mass) transfer in rectangular cross-sectioned two-pass channels with an inclined divider wall, Int. J. Heat Mass Transfer 45 (5) (2002) 1093–1107.
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[4] L. Cai, H. Ota, M. Hirota, H. Nakayama, H. Fujita, Influence of channel aspect ratio on heat transfer characteristics in sharp-turn connected two-pass channels with inclined divider wall, Exp. Therm. Fluid Sci. 28 (6) (2004) 513–523. [5] W. Siddique, L. El-Gabry, T. Fransson, Design improvement of internally cooled trailing edge at engine-similar conditions – a conjugate heat transfer problem, ASME Turbo Expo 2012, Copenhagen, Denmark, 2012. [6] B. Sunden, X. Gongnan, Gas turbine blade tip heat transfer and cooling: a literature survey, Heat Transfer Eng. (2011) 527–554. [7] R.S. Bunker, Axial turbine blade tips: function, design and durability, AIAA J. Propul. Power 22 (2006) 271–285. [8] R.J. Boyle, Heat transfer in serpentine passages with turbulence promoters, ASME Paper No. 84-HT-24, 1984. [9] J.C. Han, P.R. Chandra, S.C. Lau, Local heat/mass transfer distributions around sharp 180° turns in two-pass smooth and rib-roughened channels, ASME J. Heat Transfer 110 (1988) 91–98. [10] P.R. Chandra, S.C. Lau, J.C. Han, Effect of rib angle on local heat/mass transfer distribution in a two-pass rib-roughened channel, ASME J. Turbomach. 110 (1988) 233–241. [11] J.C. Han, P. Zhang, Effect of rib angle on local heat/mass transfer distribution in a three-pass rib-roughened channel, ASME J. Turbomach. 113 (1991) 123–130. [12] S.V. Ekkad, J.C. Han, Detailed heat transfer distributions in two-pass square channels with rib turbulators, Int. J. Heat Mass Transfer 40 (1997) 2523–2537. [13] L. Rathjen, D.K. Hennecke, S. Bock, R. Kleinstueck, Detailed heat/mass transfer distributions in a rotating two-pass coolant channel with engine-near cross section and smooth wall, Heat Transfer Gas Turbine Syst. 934 (2001) 432–439. [14] S.C. Babu, D.V. Ratna Rao, S.V. Prabhu, Effect of guide vanes on pressure drop in a rib roughened square channel with a sharp cornered 180° bend, in: AIAA 41st Aerospace Sciences Meeting and Exhibit Reno, Paper No. AIAA 2003-1145, 2003. [15] W. Chen, J. Ren, H.D. Jiang, Effect of turning vane configurations on heat transfer and pressure drop in a ribbed internal cooling system, ASME J. Turbomach. 133 (2011). Paper No. 041012. [16] J. Luo, E.H. Razinsky, Analysis of turbulent flow in 180° turning ducts with and without guide vanes, ASME J. Turbomach. 131 (2009). Paper No. 021011. [17] W. Siddique, L. El-Gabry, I.V. Shevchuk, T.H. Fransson, Validation and analysis of numerical results for a two-pass trapezoidal channel with different cooling configurations of trailing edge, J. Turbomach. 135 (1) (2013) 0110271– 0110278. [18] G. Xie, W. Zhang, B. Sunden, Computational analysis of the influences of guide ribs/vanes on enhanced heat transfer of a turbine blade tip-wall, Int. J. Therm. Sci. 51 (2012) 184–194. [19] S.W. Lee, H.S. Ahn, S.C. Lau, Heat (mass) transfer distribution in a two-pass trapezoidal channel with a 180° turn, ASME J. Heat Transfer 129 (2007) 1529– 1536.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
CFD analysis of the influence of guide ribs/vanes on the heat transfer enhancement of a trapezoidal channel Muiz Ur Rehman a, Waseem Siddique a,⇑, Inamul Haq b, Naqash Ali b, Zaryab Farooqi b a b
Department of Mechanical Engineering, Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad, Pakistan Department of Nuclear Engineering, Pakistan Institute of Engineering & Applied Sciences, Nilore, Islamabad, Pakistan
h i g h l i g h t s CFD of influence of ribs/vanes in a trapezoidal channel was performed using Fluent. Arc-like vane is the best with 21% rise in overall performance at tip wall. Re No. increase results in heat transfer decrease but rise in pressure drop. Heat transfer is more for a trapezoidal channel compared to a rectangular one.
a r t i c l e
i n f o
Article history: Received 14 April 2015 Accepted 10 March 2016 Available online 6 April 2016 Keywords: Gas turbine Trapezoidal channel Heat transfer Blade trailing edge Computational Fluid Dynamics (CFD)
a b s t r a c t Gas turbines are used to generate mechanical power using the thermal energies of working fluid. Turbine thermal efficiency and power output both increases by letting high temperature combustion gasses at the turbine inlet. Combustion technology has advanced to such an extent that it can create hot gases having temperatures greater than the melting points of turbine built materials. Gas turbine blades are an important turbine part and they come in direct contact with combustion gases. To have a longer safe operation life of gas turbine blades, different configurations are designed to bring blade surface temperatures down to safe working limits. One way of accomplishing this is by the internal cooling of the gas turbine blades. Gas turbine blade trailing edge is designed to be thin and sharp. Usually pin slots are provided on its surface to eject a cooler air out for its cooling purposes, but if an internal cooling serpentine channel has to be placed inside it, it will have a shape of trapezoid. The channel inside can be modeled as a two-pass trapezoidal channel with a 180° turn. Gas turbine blade tip is an important region to be cooled. Clearance gap between blade and casing causes secondary leakage flow with high tip wall heat fluxes and local high blade temperatures. To increase the blade tip region heat extracting capacity of the internal cooling trapezoidal channel, different geometry designed ribs and vanes are placed at the channel turn. Together they make up six different cases to be analyzed for their heat transfer enhancement characteristics. Numerical based CFD technique is utilized to investigate different channels heat transfer enhancements. Channels pressure drops and overall performance is evaluated and compared. It is found that by placing ribs/vanes at the trapezoidal channel turn region, we can increase channel walls heat transfers up to 40%. A vane type design suggested that overall thermal performance for the channel tip wall region can be improved up to 21% as compared to a channel with no rib or vane attached. Rib/vane cases affect local flow fields to gain improved heat transfers at different regions of the trapezoidal channel. It is also concluded that with increase in Reynolds number, heat transfer decreases while pressure drop increases in a trapezoidal channel, regardless of presence or absence of vane/ribs in the turn region. This eventually results in decrease in the thermal performance of the channel with increase in Reynolds number. Finally, it is found that for same thermal and flow conditions, heat transfer is more at the tip wall for a trapezoidal channel compared to a rectangular channel. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
⇑ Corresponding author. http://dx.doi.org/10.1016/j.applthermaleng.2016.03.043 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Gas turbine plays a vital role in the current industrialized society, and as the demand for power increases, the power output
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Nomenclature Ac dh f L _ m Nu Nuo Nus P Pr R
cross sectional area at the turn of the channel [m2] hydraulic diameter of the channel at turn [m] friction factor length of the channel [m] mass flow rate [kg/s] Nusselt number Nusselt number based on Dittus Boelter correlation Nusselt number of a channel with smooth turn pressure [N/m2] Prandtl number rib
and thermal efficiency of gas turbine must also increase. One method of increasing both the power output and thermal efficiency of the engine is to increase the temperature of the gas entering the turbine. Thermodynamic efficiency increases as the temperature of working fluid at the turbine inlet increases. The combustion technology has increased to an extent that it can produce high temperate gasses, having temperatures above the gas turbine materials. This can result in gas turbine blade melt down, creeping and the triple point failures. Thus keeping the advantage of higher efficiencies at one hand, the gas turbine components must be cooled effectively during operations to work safely. Two-pass rectangular channels with 180° bend are used as cooling configurations in internal cooling of the gas turbine blades. A lot of research has been carried out both experimentally and numerically to develop and optimize different cooling techniques [1–4]. In the combined power plant cycle, steam is bled which act as a coolant. In such case only internal cooling of the blade is possible. This requires complete internal cooling design of gas turbine blade including its trailing edge [5]. The cooling of the blade should include all regions that are exposed to high-temperature gasses and thermal load. Among such regions, particularly for high-pressure turbines, is the blade tip area, which is shown in Fig. 1. The leakage flow associated with tip-shroud clearance gap is undesirable, not only because it generates secondary flows resulting in the reduction of the work done but also because it results in higher heating at the blade tip, from mid-chord to trailing edge, leading to high local temperatures. Therefore, it is essential to cool the turbine blade tip and near the tip regions [7]. Researchers focused attention on enhancing heat transfer at the inlet and outlet
Re Tb T(i) V
Reynolds number bulk fluid temperature [K] wall temperature [K] vane
Greek symbols D difference q density [kg/m3] g performance factor gs performance factor of a channel with smooth turn
pass of two-pass channels where the turn region was kept smooth [8–12]. Later several investigators performed experimental as well as numerical research to figure out ways to improve heat transfer at the tip region of the blade by installing vanes in the turn region. The effect of installing guide vanes in the two-pass channels on heat transfer was studied where it was found that guide vanes helped in eliminating the separation zone in the curved path which is helpful in enhancing heat transfer and reducing pressure drop [13]. Experimental investigations were performed to study the effects of guide vanes on pressure drop in smooth or roughened two-pass channels [14]. It was concluded that the shape and position of the guide vanes effects pressure losses and properly shaped guide vanes can decrease the overall pressure drop by 14–20%. The experimental and numerical results of local heat transfer and pressure distribution of the ribbed two-pass channels suggests that by introducing the turning vane the whole pressure loss was reduced up to 66% and the combination of a rib and a turning vane in the turn region could improve heat transfer in this region, about 10–15% [15]. RANS method was used to simulate the turbulent flows inside several 2D and 3D 180° U-ducts with and without guide vanes [16]. Simulations show that due to presence of vane, weaker secondary-flow vortices and smaller separation results in a substantial reduction in pressure loss. The trailing edge of the gas turbine blades is an important region as it affects the aerodynamics of the flow. Turbine blade is squeezed at the trailing side in order to accelerate the flow, as well as to redirect it. The aerodynamics of blade demands a sharp and thin trailing edge to reduce profile losses. The conventional method to cool this part of blade is to release a lot of cooling air though the slots along the airfoil trailing edge. However in the case
Fig. 1. Gas turbine blade clearance gap between casing and blade tip [6].
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of internal cooling designs, the coolant is not allowed to leave the channel except from the root section to avoid mixing of the gas in the main flow path. The release of air into the main gas flow path reduces the temperature and enthalpy of hot working fluid gasses thus reducing the thermal efficiency of the gas turbine. Thus trailing edge tip region also needs to be cooled properly [4,17]. The objective of this research is to model the cooling configuration for the tip region of the gas turbine blade trailing edge. It has been modeled as two-pass trapezoidal channel. The influence of the guide vanes/ribs on heat transfer in the turn region of two-pass rectangular cross-section channel was studied [18]. In the current study, the influence of similar vanes/ribs have been studied but for a channel with trapezoidal cross-section. The analysis has been performed using CFD technique to study heat transfer enhancement and the pressure drop in the trapezoidal channel. To the knowledge of the authors, such a study has not already been performed. This research work will give designers an opportunity to design better cooling schemes for gas turbine blades.
by Siddique et al. [17]. Fig. 2 shows dimensions for the smooth two-pass trapezoidal channel which acts as reference for all other modifications, causing increase or decrease of heat transfer at different regions of the channel, especially the tip-wall region. In addition to that it also acts as the reference for pressure drop across the channels. A 571.19 mm long inlet pass is connected to an outlet pass with 180° bend. The divider-to-tip wall distance is equal to the width of the inlet channel of 38.1 mm, while the thickness of the divider wall is 19.1 mm. The outlet pass extended after to avoid reverse flow effects is 349.29 mm long. The maximum height of the inlet pass is 76.2 mm while the minimum height of the outlet pass is 38.1 mm. This makes the angle between the top and bottom wall equal to 21.8°. Fig. 3 shows the two pass smooth channel which is modeled in the current study. It shows the tip-wall, inlet and outlet of trapezoidal channel along with the flow directions. The inlet is kept longer to make flow fully developed. The outlet is given additional length to compensate for reverse flows in the CFD simulation. 4. Geometry augmentations
2. Methodology The method used in current study is primarily numerical. Computational Fluid Dynamics (CFD) helps in designing of cooling configurations in a gas turbine blade with predictions about the trends of flow and heat transfer. The added advantage in using CFD is the 3D flow results compared to single measured points in experiments, which is useful in designing more efficient augmented heat transfer channels. ANSYS Workbench 14.0 is used as pre-processing, solution and post-processing software. ANSYS Design Modeler is used to create geometries, ANSYS ICEM CFD is used to generate mesh and ANSYS FLUENT 14.0 is used as a solver to solve fluid mechanics and heat transfer problem. Post processing is done using CFD Post 14.0. The low-Re k-epsilon model can be used with acceptable accuracy to predict the flow and heat transfer behavior in a trapezoidal channel [17]. In the current study the same model has been used for predicting the heat transfer and pressure drop in a trapezoidal channel with different configurations of vans and ribs at the turn region. Mesh independency is also necessary to have desired level of accuracy in answers along with the balance amount of computer resources utilized. CFD analysis results can be used to check the performance of different postulated Ribs and Vanes and for the further research work in future. 3. Description of the physical model The channel dimensions used by Lee et al. [19] are selected for the current study. This trapezoidal channel has been used in experimental setup by Lee et al. [19] and numerical simulations
In order to enhance heat transfer at the tip-wall region of gas turbine blade, different augmentations are suggested in the 180° turn of a rectangular channel [18]. The augmentations are classified as ribs and vanes cases. The difference between ribs and vanes is such that ribs are present up to certain height while the vanes are present with full height from bottom to top wall. Similar augmentations have been implemented in a channel with trapezoidal cross-section, in current study. Following is the detail of these augmentations: Case 1R: In this case two ribs of different lengths are attached at the bottom wall at the turn region. The geometry detail is given in Fig. 4. Width of these ribs is 3 mm, height is selected to be 6 mm hence an aspect ratio of height to width is 2:1. Case 2R: As shown in Fig. 5, this is a symmetric arc like rib which is attached to the bottom surface of the turn region; its aspect ratio height to width is 2:1. Its height is 6 mm and its width is 3 mm. Case 3R: As shown in Fig. 6, this configuration consists of two ribs on the bottom wall at the turn region but with the different geometry. Ribs thickness is 3 mm and height is 6 mm. Height to width aspect ratio is 2:1. Case 1V: It is same as Case 1R but the rib height is not limited to 6 mm, but the vane is connected from bottom to top wall. The other dimensions of this model are same as Case 1R. This case is shown in Fig. 7. Two vanes are attached at the turn region, one directs the flow toward the tip wall, and other brings flow inside the outlet pass.
Fig. 2. Dimensions of the two-pass trapezoidal channel used in the current research study.
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agreement between the experimental and numerical data for the smooth trapezoidal channel [17]. Therefore same validated turbulence model is selected for simulations of ribs and vanes at the turn region in current study. 7. Mesh independency
Fig. 3. Two-pass smooth channel showing flow directions.
Case 2V: This is generated from the Case 2R. The vane height connects between channel bottom and top walls. This case is shown in Fig. 8. Vane dimension values are same as of the Case 2R. This vane type is design to push part of the flow along the tip wall, and rests back into the outlet pass channel. Case 3V: It reflects the geometry and dimensions of Case 3R. Vanes are extended from bottom wall to the top wall of the channel turn region, as shown in Fig. 9. There are two vanes present, both directing flow in the same direction. 5. Computational details Finite Volume based CFD technique is used to solve fluid mechanics and heat transfer problem. Flow inside the trapezoidal channel is considered steady, incompressible, turbulent, and 3-dimensional. Dry air is selected as a working fluid with constant thermodynamic physical properties. All walls are kept at a constant temperature of 350 K and air enters the inlet at 310 K. Mass flow rate inside the channel is calculated based on the Reynolds number of 9400 at the turn region. Standard k-epsilon turbulence model with enhanced wall treatment is selected for the turbulent flow, as it shows smallest deviation in Nusselt number calculations based on experimental and numerical results for the smooth turn trapezoidal channel [17]. 6. Selection of turbulence model In previous work done [17], numerical validations of the experiment perform in a smooth channel [19] has been done successfully. The low-Re k-epsilon model showed the best
Mesh independent study has been performed to check the effect of changing mesh size on the CFD solution results. In current study, Case 2V has been used for the grid independence study. Statistics of mesh sizes is given in Table 1. To keep y+ value near to the wall equal to unity, calculations show that for Reynolds number of 9400 and hydraulic diameter of 45.72 mm, the minimum first layer height of the elements near wall should be 0.07 mm. Inflation growth rate of 1.2 is selected and total number of 11 layers are added to give inflation layers total height of 2.25 mm. All the cases selected for mesh independency have inflation layers with the same height and total number of layers. Fig. 10 shows mesh sizes for the inlet pass, from course to fine. Section wise area weighted average Nusselt numbers were calculated at the bottom wall of the trapezoidal channel. It was normalized by Nusselt number calculated from Dittus-Boelter correlation. The normalized Nusselt number is plotted and variation in the results is observed for all the mesh sizes. Average Nusselt number based on the bulk fluid temperatures of different zones at the bottom wall for different mesh sizes can be seen in Fig. 11. The trapezoidal channel is divided in 16 regions. The inlet pass is represented by 0–7, 8 is the turn region, while 9–16 shows outlet pass bottom wall regions. The difference in Nu/Nuo value for 1.96 million mesh size and 2.4 million mesh size is almost negligible with a maximum deviation of 1.5% at the turn region. Thus it is concluded that mesh element size of 1.25 mm (which resulted in 1.96 million mesh size) is the correct choice to perform all other simulations. Fig. 12 shows the mesh at the turn region of the three cases studied. 8. Analysis tools Heat transfer on different walls can be calculated by means of a dimensionless Nusselt number (Nu). This parameter directly reflects the heat transfer characteristics. Area averaged Nusselt number can be calculated at different walls of the channel to compare heat transfer performances for different augmented channels compared to case smooth turn channel. Addition to that, local Nusselt number values can be plotted as contours. This gives heat transfer variation at different regions of the wall. This section covers the details of analysis tools that are required to compare heat transfer characteristics of different ribs and vanes cases.
Fig. 4. Case 1R where two ribs are attached on the bottom wall (all dimensions are in mm).
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Fig. 5. Case 2R where a symmetric rib is attached on the bottom wall (all dimensions are in mm).
Fig. 6. Case 3R where two ribs on the bottom wall at the turn region but with the different geometry are attached (all dimensions are in mm).
Fig. 7. Case 1V where two vanes are attached on the bottom wall.
Fig. 8. Case 2V where a symmetric vane is attached on the bottom wall.
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Fig. 9. Case 3V where two vanes on the bottom wall at the turn region but with the different geometry are attached.
Table 1 Statistics of mesh sizes used in the study. Global mesh size (mm)
Total number of elements (million)
3 2 1.5 1.25 1.1
0.4 0.8 1.4 1.96 2.4
9.1. Velocity fields
The calculated Nusselt number has been normalized by DittusBoelter correlation which is given by Eq. (1).
Nuo ¼ 0:023 Re0:8 Pr0:3
pressure drops. The best case scenario would be the one where rib/vane augmentation causes high heat transfer along with low or suitable pressure drop across the channel.
ð1Þ
Further, nodal values of Nusselt number (Nu) can also be normalized with the corresponding values of the Nusselt number for the smooth turn channel (Nus). 9. Results and discussions Different ribs and vanes cases, have been designed in order to enhance heat transfer in the trapezoidal channel. The gas turbine blade tip region is an important region to be cooled effectively. Different cases are compared with smooth turn trapezoidal channel. Heat transfer enhancement is investigated in terms of walls Nusselt number. Heat transfer can be increased by changing the flow field inside the channel. Velocity fields are analyzed by the inspection of velocity contours. This helps in judging the kind of rib or vane case that increase or decrease local fluid velocities and favors the heat transfer. The increase in turbulence and nature of flow flied in the channel is also accompanied by corresponding
Velocity field for different cases can be analyzed with the help of velocity contours and velocity vectors. Mid plane is selected along the height of the channel to plot such contours and vectors. Velocity contours are plotted for the regions which are most influenced by the tuning effect and are important to be analyzed for velocity field changes among various ribs and vanes cases. Hence two inlet pass blocks before the turn region, seven outlet pass blocks after the turn region and the turn region itself is selected to plot the velocity contours. Velocity vectors are shown only at the turn region to show the effect of different ribs and vanes installed in this region on the flow field. The velocity contours for the vane cases and the smooth turn channel at mid plane are shown in Fig. 13 while velocity vectors for the same cases are shown in Fig. 14 which supports and explains the physics of the flow. Flow enters the inlet pass, passes though the turn region, and leaves from the outlet pass. No slip boundary condition is applied on all the walls, hence flow on the wall attains zero velocity. For the smooth turn, low velocity region at the corners of the turn region are formed. This is because of the local flow recirculation where flow gets trapped for instant and then moves away. There is a low velocity region at the beginning of the outlet pass and also some high velocity flow on the side wall of the outlet pass. The low velocity is due to separation of flow caused by the turning effect. The high velocity is because of the turning effect of flow but
Fig. 10. Mesh sizes for the inlet pass, from course to fine.
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Fig. 11. Average Nusselt number of different zones at the bottom wall for different mesh sizes.
Fig. 12. Mesh at the turn region of three different cases.
Fig. 13. Velocity contours for the vane cases and the smooth turn channel at mid plane.
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Fig. 14. Velocity vectors for the vane cases and the smooth turn channel at mid plane.
also as it is the region where height of the channel is minimum and area of flow is also minimum, so for same mass flow rate, flow tries to attain high velocity. Later in the downstream the flow again tries to adjust its velocity. Near the tip wall, velocity having range of about 4.5 m/s covers most of the region. For the Case 1V, the wake that was observed in the smooth turn channel at the inner side wall of the outlet pass channel has been recovered, as the flow is directed back in. High velocity region in the side wall of outlet has been increased. Similar region is also observed near the divider wall of the inlet–outlet pass. A small wake region is observed behind the two vanes as the flow is very slow there. At the tip wall, majority of flow is slower than the smooth turn case, but a little high speed region is observed in the later part of the turn region near the tip wall. For Case 2V, a big high velocity region is observed near the tip wall region. The region also contains maximum of the flow velocity for this case. There is no wake region behind the vane and inner side wall of the outlet pass. There is a slower flow at the side wall of the outlet pass, majority of the flow here is in 5 m/s velocity range, but objectively high velocity is obtained near the tip wall. For Case 3V, a huge high velocity region is visible at the side wall outlet, later part of the tip wall and near the divider wall. More wakes are formed behind the first vane, ahead of the second vane and near inner side wall outlet pass. Most of the high velocity region is found after the half pass length of the turn region tip wall. In
the downstream of the outlet pass, a high velocity region is found at the inner side wall outlet. Case 3V has blocked more of the flow as compared to other cases. Compared to vanes, ribs are only attached on the bottom wall. They should have major influence near the bottom wall, but it is useful to observed flow field patterns caused by the ribs cases away from the bottom wall, so velocity contours of rib cases are also plotted on the mid plane. Velocity contours for rib cases on the mid plane are shown in Fig. 15 while velocity vectors for the same cases are shown in Fig. 16 which supports and explains the physics of the flow. It is observed that ribs cases have little influence on the velocity field away from the bottom wall as expected. The velocity contours have small changes as compared to smooth turn. For Case 1R, high velocity region at side wall outlet is little longer, flow is more attached at the inner side wall outlet, a higher velocity near the divider wall. On the tip wall flow is almost similar. For Case 2R flow is similar to case smooth turn. A small increase in velocity at the side wall outlet. For Case 3R, flow has higher velocity at side wall outlet. At the tip wall 4.2 m/s velocity field is broader and cover more length. Small wake is found in the early length of inner side wall outlet. As ribs are attached on the bottom wall, they have more influence at the vicinity of bottom wall only. Another plane is selected which is 4 mm above the bottom wall and velocity contours for the rib cases are plotted at it which are shown in
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Fig. 15. Velocity contours for rib cases on the mid plane.
Fig. 16. Velocity vectors for the rib cases and the smooth turn channel at mid plane.
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Fig. 17. Velocity contours for the rib cases at a plane 4 mm above the bottom wall.
Fig. 17. At the tip wall region some changes are visible. At the later part of the turn length slow velocity region in the case smooth turn is observed, but the rib cases have tried to minimize this and a faster flow is present in this region for the rib cases. Similarly for smooth turn, there is a slow flow region at the mid portion of tip wall vicinity, but in rib cases it is not present. From Fig. 17, Ribs cases have gained speed of flow in the later length of turn region at the tip wall. Case 1R and Case 3R are in more favor of this as compared to Case 2R. At the outlet pass, same differences are found as in the case of mid-plane velocity contours of rib cases. The effect of placing different types of ribs and vanes in the turn region is shown by velocity vectors at the turn region of the two-pass channel. Such vectors have been shown in Fig. 18. At the turn, centrifugal forces results in counter rotating vortices which can be seen in Smooth turn case. These strong vortices enhance the mixing of fluid thus cold fluid is transported to the heated walls more efficiently. Placing one rib at the bottom surface does not effects these vortices to a great extent so enhancement in heat transfer in the rib cases is not significantly enhanced. Far case 1V and 3V, the vane is blocking the flow, thus reducing the velocity near the tip wall, resulting in lesser mixing of fluid. For case 2V, the vane results in enhancement in velocity near the tip wall which results in higher heat transfer at the tip wall. 9.2. Channel heat transfer In order to study heat transfer of the trapezoidal channel, three walls are selected (Tip Wall, Bottom Wall outlet and Side Wall outlet). The locations of the channel walls are shown in Fig. 19. Tip wall heat transfer enhancement is the main objective of this study, but the bottom wall and side wall outlet are also important for the trailing edge of gas turbine blade. Local Nusselt number is calculated for each mesh point using Eq. (2).
NuðiÞ ¼
qw dh TðiÞ T b k
ð2Þ
Fluid bulk temperatures are required for the wall Nusselt number calculations. For tip wall, volume average temperature of the turn region has been taken as the bulk fluid temperature, ‘Tb’. For
side wall and bottom wall outlet, the volume average temperature of turn region and the outlet pass has been used as the bulk fluid temperature. T(i) is the local wall temperature. The normalized Nusselt number at three selected walls for all cases is shown in Fig. 20. Smooth turn channel results provide a reference platform to analyze the results of other ribs and vanes cases. For the tip wall region it can be seen that Case 2V has performed best with the normalized Nusselt number to be 3.42 which is 24% increase in heat transfer as compared to the smooth turn channel. For the side wall outlet Case 3V has increased a lot of heat transfer with normalized Nu of 3.83 as compared to the 2.67 for smooth turn, which is a total amount of 43% increase. All the rib cases have also contributed in heat transfer enhancement of the side wall, Case 1R increased 2.6%, Case 2R about 1.9% and Case 3-R showed 2.3% increase in heat transfer for the side wall outlet. For the bottom wall outlet only Case 3R and 3V are contributing in the heat transfer enhancement. Case 3V has increased 36% of the heat transfer while Case 3R increased 8.5% of heat transfer as compared to smooth turn trapezoidal channel. It can be seen that, Case 3V and Case 3R has contributed in all three regions of the channel while the increase in heat transfer by Case 3V is proportionally higher than that by the corresponding rib case. Case 1R and 2R have contributed in enhancement of heat transfer at side wall outlet region only. Case 2V has participated for significant amount of heat transfer increase at tip wall only. Case 1V has not participated in enhancing heat transfer at any region and is not suitable for heat transfer enhancement of the trapezoidal channel. 9.3. Tip wall heat transfer In previous section heat transfer was compared on the basis of average values of Nu/Nuo on three walls of the channel. In this section, local values of Nu/Nuo on the tip wall region has been discussed. In a two pass trapezoidal channel with a 180° turn, flow has to change its direction very sharply. The high speed fluid coming in the inlet pass strikes the tip wall region, change its direction, then strikes the side wall of outlet pass and finally leaves through the
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Fig. 18. Velocity vectors for the rib and vane cases at the turn region of the two-pass channel.
Fig. 19. Locations of three walls (Tip Wall, Bottom Wall outlet and Side Wall outlet) selected to present results.
outlet pass of trapezoidal channel. Hence lot of flow with high kinetic energy strikes the tip wall and enforce forced convection. But this phenomena only dominates on the wall region that is just ahead of the inlet pass, tip wall region attached to the outlet pass has low flow velocities hence have low heat transfer. An attempt is made by putting ribs/vanes at the turn region to homogenies and accelerate the flow along the tip wall to enhance heat transfer. The comparison of vane cases based on the Nusselt number contours on tip wall is shown in Fig. 21. For Case 1V, which is not suitable for heat transfer enhancement, has tried to homogenies the heat transfer at the longer length of turn but net amount of heat transfer is lesser than the case-ST. Case 2V which is the most successful heat transfer candidate at the tip wall, has not only
homogenized the heat transfer to the longer length of turn but also has increased heat transfer at the left and right side of the tip wall. More high heat transfer zones are observed due to more impingement and laminated flows because of this vane design type. Heat transfer area at the tip wall region attached to inlet pass and wall area near the side wall outlet, now has higher heat transfer values. Nu/Nuo values ranging between 3.7 and 4, covers most of these regions. Top and bottom areas for the outlet pass tip wall region also has an increase in heat transfer. Case 3V has a completely different heat transfer configuration than the case-ST. Good heat transfer is present along most of the turn length. There is more heat transfer at the later part of the turn as compared to left, region attached to inlet pass. Amount of concentrated heat transfer is less than the Case 2V and more spread in heat transfer is found, but Case 2-V showed maximum area averaged heat transfer. Comparison of rib cases with the case-ST is presented in Fig. 22. Small differences can the seen in the bottom right side of the tip wall. Ribs are attached to the bottom wall of the turn only, hence they have little influence in flow field and heat transfer at the higher levels of the tip wall. Case 3R shows highest heat transfer at the bottom right corner of tip wall hence it has the highest average heat transfer than other ribs cases. Case 1R shows a slight higher heat transfer than case ST for the same reason. Case 2R shows a little increase in heat transfer in the same zone as compared to case-St but the intensity is slight weaker. Hence overall, Case 2R shows the same average heat transfer as is found in case ST. 9.4. Channel pressure drop Friction factor ‘f’ is a measure of pressure drop across the channel and it can be calculated for different ribs and vanes cases using Eq. (3).
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Fig. 20. Normalized Nusselt number comparison in three regions of the channel for all cases.
Fig. 21. The comparison of vane cases based on the Nusselt number contours on tip wall.
f ¼2q
2 DP Ac dh _ L m
ð3Þ
where ‘q’ is the fluid density, ‘Ac’ is the cross sectional area of the _ is the mass flow turn where the Reynolds number is calculated, ‘m’ rate in the channel, ‘Dp’ is the pressure drop across the channel and ‘L’ is the length across the stations on which ‘Dp’ is measured. In Eq. (2) all the parameters are constant, except the ‘Dp’, which varies for different ribs and vane cases. Hence friction factor ‘f’, directly reflects the pressure drop across the channel. Location of the station planes at which this pressure difference is measured for different cases is given in Fig. 23. The length across the two planes ‘L’ is also shown. Area average value of pressure at the two planes are calculated to find their ‘Dp’. Friction factor ‘f’ calculated based on the pressure difference can be normalized by ‘fo’, which is the friction factor for the fully developed turbulent flow in a smooth channel and is calculated by a correlation given by Eq. (4).
f o ¼ ½0:79 lnðReÞ 1:64
2
ð4Þ
The normalized friction factor ‘f/fo’ is helpful in establishing a pressure drop parameter in trapezoidal channel for different ribs and vanes cases. Results for the normalized friction factors ‘f/fo’ for each case except case 3V is shown in Fig. 24. Case 3V showed almost 10 times more pressure drop and therefore is not included in Fig. 24. For the augmented channels, cases 2V/R are showing the least pressure drop and cases 3V/R are showing most of the pressure drop. 9.5. Overall comparison The performance factor ‘g’ has been defined by Eq. (5), which signifies the effect of both heat transfer and pressure drop across the channels. Higher value of performance factor means that there is higher proportions of heat transfer as compared to the corresponding pressure drop across the channel, which is desirable.
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Fig. 22. The comparison of rib cases based on the Nusselt number contours with case-ST.
Fig. 24. Normalized friction factors ‘f/fo’ for different cases calculated at Re = 9400.
Fig. 23. The location of the station planes at which this pressure difference is measured for different cases.
g¼
Nu=Nuo 1=3
f =f o
ð5Þ
Performance factors are presented for the tip wall, side wall outlet and bottom wall outlet for the trapezoidal channels and are shown in Fig. 25. Case 2V has showed 21% better performance factor at the tip wall than the case smooth turn. Case 1R showed 1.4% better performance at the side wall outlet and Case 3R is showing 1.7% better heat transfer at the bottom wall outlet. Case
3V is a good configuration for heat transfer but does not show good results because of huge pressure drops as compared to Case ST. The detail comparison in different regions of the channel for different cases can be made if the performance factors for different cases are normalized with the corresponding values of smooth turn channel. The overall comparison for all the cases is shown in Fig. 26. Case 2V is the most successful configuration at the tip wall, and the increase in performance factor is significant as compared to other configurations for side and bottom wall outlet. It has a decrease of about 12% of performance factor at the side and bottom wall, but this problem can be solved by putting suitable rib tabulators at side and bottom wall of outlet pass channel. Case 1V is not
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Fig. 25. Performance factors for the tip wall, side wall outlet and bottom wall outlet for all cases.
Fig. 26. The overall comparison of all the cases.
desirable in any mentioned region of the trapezoidal channel. Case 3V has some significant efforts for heat transfer enhancement but due to its huge pressure drop it has a drop in overall performance for all walls. Rib cases are showing comparable similar results among themselves, but neither of these is showing better performance for the tip wall region. 9.6. Effect of Reynolds number Performance of different vanes and ribs at the turn region of the trapezoidal channel at various Reynolds number has been studied. Fig. 27 shows the effect of Reynolds number on Nusselt number for different vane and rib cases. It is observed that for all cases, heat transfer increases by 2.2–2.4 times with increase in Reynolds number from 9400 to 57,200. The effect is more pronounced in case 2V compared to other cases. Fig. 28 shows the effect of Reynolds number on normalized Nusselt number for different vane and rib cases. With increase in Reynolds number, all the cases shows 24–27% decrease in normalized Nusselt number. This is because at higher Reynolds number the value of Nusselt number calculated by using Eq. (1) also increases. This increase is more compared to increase in Nusselt number shown in Fig. 26, thus it decreases the normalized value. Fig. 29 shows the effect of Reynolds number on pressure drop for different vane and rib cases (excluding case 3V). Increasing trends in pressure drop are found at higher Reynolds numbers
Fig. 27. Effect of Reynolds number on Nusselt number for different vane and rib cases.
for all cases. Also, at higher Reynolds number, pressure drop in case 3R surpasses the other cases where the pressure drop almost doubles with increase in Reynolds number from 9400 to 57,200.
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Fig. 28. Effect of Reynolds number on normalized Nusselt number for different vane and rib cases.
Fig. 30. Effect of Reynolds number on performance factor for different vane and rib cases.
Fig. 31. Comparison of tip-wall heat transfer for different channel cross-section. Fig. 29. Effect of Reynolds number on pressure drop for different vane and rib cases.
Fig. 30 shows the effect of Reynolds number on performance factor for different vane and rib cases. Performance factor decreases by almost 40% with increase in Reynolds number. These deceasing trends are due to increase in pressure drop as well as decrease in normalized Nusselt number with increase in Reynolds number. The effect of ribs/vanes on tip wall heat transfer. at turn region of a rectangular channel were previously studied [18]. Similar effects are studied in current study for a trapezoidal channel. Fig. 31 compares the heat transfer variation with Reynolds number for both channels with different vanes and ribs. It is observed that a trapezoidal channel enhances more heat transfer compared to the rectangular channel. So at tip-wall of the trailing edge, heat transfer is more compared to that at mid-span of the blade. This might be considered as inherent advantage as at trailing edge, heat flux is more which requires more cooling. Further, it is noted that for rectangular channel, the heat transfer is mostly not affected by change in Reynolds number, but in case of a trapezoidal channel, it reduces as discusses earlier. Also, case 1V gives maximum heat
transfer advantage in rectangular channel but in trapezoidal channel, case 2V proved to be the best among the studied cases. 10. Conclusions In the current work, different internal cooling trapezoid serpentine channels with and without rib or vane at the turn region are analyzed using CFD technique. Study is carried out to determine heat transfer at three important channel walls and to examine corresponding channels pressure drops. Overall performance of channels is evaluated and compared. Based on the results, following important conclusions are drawn: Heat transfer capacity of the channel tip wall can be enhanced by placing a suitable kind of rib or vane at the trapezoidal channel turn region. The rib/vane design changes the flow field, causing rise or fall of the local heat transfer coefficient ‘h’. Case 2V has been analyzed to be most successful configuration, affecting 24% better heat transfer and 21% rise in overall performance at the channel tip wall.
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Case 2V has caused some heat transfer drop at side and bottom wall outlet, but this can be overcome by installing a very well designed rectangular rib tabulators at side and bottom walls of the outlet pass of the channel. Case 3V has showed about 10–40% rise in channel heat transfer, but due to its severe channel pressure drop, its overall performance has decreased between 40% and 50%. Hence it is not a desirable case for channel heat transfer enhancement. Case 1V shows drop in both channel heat transfer and overall performance, making it most unattractive. Rib cases have increased small amount of heat transfer between 2% and 9% and overall performance ranging less than 2% on channel walls. But neither of them showed better heat transfer for the tip wall region. Thermal performance decreases with increase in Reynolds number for a trapezoidal case regardless of the augmentation in the turn region. For the same Reynolds number, heat transfer depends on the cross-section of the channel. Acknowledgement The authors acknowledge the computational support by the Advance Computational Research Laboratory, Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan. References [1] S. Mochizuki, A. Murata, R. Shibata, Wen-Jei Yang, Detailed measurements of local heat transfer coefficients in turbulent flow through smooth and ribroughened serpentine passages with a 180° sharp bend, Int. J. Heat Mass Transfer 42 (11) (1998) 1925–1934. [2] M. Hirota, H. Fujita, A. Syuhada, S. Araki, T. Yoshida, T. Tanaka, Heat/mass transfer characteristics in two-pass smooth channels with a sharp 180-deg turn, Int. J. Heat Mass Transfer 42 (20) (1999) 3757–3770. [3] M. Hirota, H. Fujita, L. Cai, H. Nakayama, M. Yanagida, A. Syafa’at, Heat (mass) transfer in rectangular cross-sectioned two-pass channels with an inclined divider wall, Int. J. Heat Mass Transfer 45 (5) (2002) 1093–1107.
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