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Advances in Mechanical Engineering
Volume 2012 (2012), Article ID 950452, 12 pages
Experimental Visualization of the Flow Structure for Jet in Crossflow with a Curved Hole Passage
Key Laboratory of Condition Monitor and Control for Power Plant Equipments, Power and Mechanical Engineering, School of Energy, North China Electric Power University, Beijing 102206, China
Received 4 July 2012; Accepted 19 September 2012
Academic Editor: C. T. Nguyen
Copyright © 2012 Jun Yu Liang and Shun Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The objective of this paper is to investigate the influence of a hole curvature on the flow structure and characteristics downstream of JICF (jet in cross-Flow) by means of smoke visualization and particle image velocimetry (PIV). The experiment was performed in a low speed wind tunnel with Reynolds numbers of about 480 and 1000, based on the hole diameter and main flow speed. Two geometries were tested: a circular hole with 90° curvature and a circular straight hole for comparison, under blowing ratios 0.5 and 1.0. The measurements were done in the symmetric plane and four cross-sections. The results show that the curved hole could decrease the mixing behavior of jet flow with the main flow as the hole leading edge also increases the chance of transportingthecoolant to the wall surface and the transverse coverage. The curved hole shows a high potential to increase the cooling effectiveness once it is applied to the turbine blades.
In order to raise the cycle efficiency, today’s gas turbine is heading towards high pressure ratio and high turbine inlet temperature. Consequently, thermal and mechanical loads of the turbine components exposed to the hot gas will be increased, leading to the necessity of applying efficient cooling techniques in order to guarantee the lifetimes. One of the often used cooling techniques is film cooling, in which coolant air extracted from the compressor is transferred into the cava of turbine blades and then ejected out through discrete holes or slots, arranged in a certain way, around the blades into the blade flow passage. The air forms a thin and low temperature film covering the blade and/or endwall surfaces for protecting them from the hot main flow. Since the extraction of air from the compressor incurs a penalty to the thermal efficiency and the ejection of coolant air into the blade passage and its mixing with the hot gas as well, introduce additional energy losses, it is therefore necessary to get more insight into the local flow field and then find a way to optimize the cooling hole design.
The essential features of such film-cooling flow are present in a more generic flow situation of JICF. Extensive investigations on this fundamental flow field by experimental and numerical methods have been done for many years [1–7]. Margason  and many others had given a detailed summary on the earlier studies. A detailed review on the recent progress in the study of JICF can be found from Karagozian .
Interaction of the jet flow with the main cross-flow creates a localized, very complex large-scale vortex structure near a jet hole, as shown in Figures 1 and 2 from Fric and Roshko  and New et al. . It is known that the near-field entrainment in the vicinity of the jet exit is influenced by these vortices , while the far-field entrainment is dominated by the CVP system .
In film cooling applications, one of the targets in JICF investigation is reducing the coolant jet penetration and making it as close adherence to the wall over a long distance as possible, which is of crucial importance for achieving higher effectiveness of film cooling. As the rotation sense of a CVP is such that it lifts the jet flow off the blade surface, a certain research work has been done to weaken the CVP. Haven and Kurosaka  introduced a vortex pair inside the jet hole passage, by installing two microvanes within the jet hole, which creates a vortex pair with a rotation sense opposite to the kidney vortices. Peterson and Plesniak  reported that interaction of in-hole vorticity created by turning of plenum flow direction could weaken the CVP, resulting in a lower trajectory and increased spanwise spreading. Kang  proposed another way to weaken the strength and scale of CVP by shaping the jet hole to create a secondary passage vortex pair (PVP) inside the jet hole. The PVP, rotating in the opposite sense to CVP, would be formed due to the centrifugal force acting on the low speed flow inside the boundary layer of hole a surface, as sketched in Figure 3. Stregth and scale of PVP will be increased with the hole curvature and boundary layer thickness. The PVP in curved channels was first observed by Dean, so that it is also named as Dean vortex pair characterized by the Dean number . Liang et al. [17–19] made a further numerical investigation in a curved hole with a square and circular cross-section by RANS and DES methods and confirmed that the curved hole weakens the counter-rotating vortex pair. However, there are still issues which remained unclear in the detailed mechanisms, which request further experiment and numerical work. Hence, this paper is to investigate the influences of hole curvature on the characteristics and structure of the vortex flow downstream in the JICF with a curved hole by means of PIV apparatus. The film cooling application will be taken as a background in the analysis and discussions. In addition, the experimental results may form an additional reference and database for CFD validation.
2. Test Facility and Experimental Procedure
2.1. Test Rig
The experiments were performed in a low speed open-loop wind tunnel as sketched in Figure 4. The main flow is supplied by a centrifugal fan with a capacity of maximum total pressure rise of 2200 kPa. The test section is 1600 mm long with a cross-section of mm2 (). A PT100 thermal resistance and a pitot tube are located at 500 mm downstream of the test section inlet to measure the main flow conditions. The free stream turbulence was measured with HWFA (Hot-Wire/Film Anemometer). Sampling frequency is about 2 kHz. A flat plate with jet hole is placed at half height of the tunnel with its leading edge at 950 mm from the test section inlet and extended to the tunnel sides in the transverse direction and to the tunnel exit in the streamwise direction. Air with particles goes through the flowmeter and enters a plenum, with a cross section of 80 mm 55 mm, placed inside the plate with a maximum thickness of 85 mm, as sketched in Figure 5. The plate is comprised of a rectifier cone at the leading edge, an injection plate, made of wood. Center of the hole exit is located at 393 mm downstream of the leading edge. A camera is placed on one side of the wind tunnel to measure the symmetric plane. For measuring the cross sections, the camera is placed at downstream of the wind tunnel outlet, with a distance from the hole center of about 550 mm.
The light source is supplied by Nd:YAG laser from BIG SKY with the highest repetition rate of 20 Hz. The type of CCD camera is POWERVIEW Plus 4 MP from TSI with resolution of pixel. The photo data captured by camera will be transported through a cable to PC. In order to get the time averaged results, 50–100 pairs of two-frame photo for one case were captured to quantify the flow field.
2.2. Hole Configuration
Two types of hole configurations, straight and curved with 90° curvature, as sketched in Figure 6, were investigated. Hole diameter is 6 mm. The length of straight hole . Direction of the exit flow of both geometries is upwards and normal to the main flow.
2.3. Test Settings
The smoke was only seeded for jet fluids to visualize the jet; while in PIV measurements, the smoke was seeded both for jet and main flow fluids. Because of the limitation of the sampling frequency of the PIV apparatus used and safety of the camera placed at downstream of the wind tunnel outlet, the main flow velocity is set to 1.2 m/s and 2.5 m/s, which corresponds to Reynolds number , based on the hole diameter and mainstream velocity, of about 480 and 1000. Velocity profile over the flat plate was measured at 393 mm downstream of the plate leading edge. Blowing ratios (BR), ranged from 0.5 and 1.5, were tested and they are defined as the ratios of the averaged jet speed against the main flow speed. However, discussions in this paper will be mainly focused on the results of BR 0.5 and 1.0 for both straight and curved holes. The measurements were done in the symmetric plane and four cross-sections , with the origin of the coordinate system at the hole exit center. Eight test cases with the detail parameters such as the Reynolds number , boundary thickness , turbulent intensity , and the Dean number for curved hole are listed in Table 1, where is defined as .
2.4. Experimental Uncertainties
The Kline-McClintock  method is applied to estimate the uncertainties of the measurements. In this way, the uncertainties of time averaged velocity can be decided with confidence of 95%. In the near-region downstream of the hole exit, the relative uncertainty of time averaged velocity is ranged from 6% to 15% under flow condition of , . In the rest of the region, the relative uncertainty is less than 5%. The uncertainty of the rest seven flow conditions should be smaller than 5%.
3. Results and Discussions
3.1. Symmetric Plane
3.1.1. Instantaneous Visualization
Figures 7 and 8 are instantaneous visualization pictures in the symmetric plane under and 1 and and 1000 for straight and curved holes, respectively. The pictures cover about downstream of the exit in the main flow direction marked with an arrow and in the normal direction. It can be clearly seen first from these pictures that in any of the conditions, the flow leaves the jet exit upwards to a certain distance from the exit without visible vortex motion and then turns towards the mainstream direction. Afterwards, the smoke trace is oscillating due to the Kelvin-Helmholtz instability of the annular shear layer which separates from the edge of the jet flow, resulting in a series of jet shear-layer vortices in the initial portion of the jet flow trajectory and a wake vortex system under the trajectory, which is similar to what reported by Fric and Roshko . It is seen that is height of the trajectory reduces with increasing Reynolds number and decreasing blowing ratio.
The shear-layer vortices viewed in the symmetric plane corresponds to the cut-off view of the hairpin vortices as shown in Figure 9 which presents a snapshot of the coherent structure of isosurface obtained with the DES method by Liang and Kang  under blowing ratio 0.5 and Reynolds number 4000 for straight and 90° curved holes. The is defined as
It is seen from Figure 9(a) that when a hairpin vortex is well formed and shaded downstream, a next hairpin vortex starts to be formed in series. These results may suggest that the development of hairpin vortices is the underlying mechanism of coolant liftup. For the curved hole as shown in Figure 9(b), the PVP (or Dean vortex pair) issued from the curved hole exit could be clearly observed and it has a great influence on the formation and evolution of the hairpin vortices. The hairpin downstream was skewed and weakened due to the interaction of PVP with shear layer vortices, so the liftup of jet fluids would be suppressed and then increase the cooling effectiveness.
A horseshoe vortex is seen upstream of the jet in Figure 9 which could not be resolved by the experimental visualization. Streamwise vorticity component of the hairpin vortices will form the CVP which is evolving in a periodic unsteady manner with intermittent vortex structures as viewed from DES results. The wake vortices in Figures 7 and 8 extend upright from the wall towards the trajectory, which could be the normal vorticity component of the hairpin vortices. The wake vortices allow fluid to be drawn from the boundary layer into the jet itself, with an efficient entrainment of the boundary layer fluid into the downstream and the wake region of the jet, as indicated by Fric and Roshko .
The shear-layer vortices with coherent counter-rotating vortex pairs, named as wind-ward vortices and lee-ward vortices observed by New et al.  along the trajectory for blowing ratios from 2.3 to 5.8 for straight hole could not be observed from Figures 7 and 8 for blowing ratios 0.5 and 1.0. However, this vortex structure could be clearly observed under higher blowing ratio in this study as shown in Figure 10 which presents an instantaneous smoke visualization in the symmetric plane for a straight hole under blowing ratio 1.3 and Reynolds number 240. In Figure 10 a chain of vortex pairs with coherent counter-rotating wind-ward vortices and lee-ward vortices is observed.
It was believed that the curved hole could weaken the streamwise vorticity due to the secondary vortex pair, generated by the hole curvature, which is rotating in the opposite sense with CVP. As one can observe by comparing the height of the trajectory from the wall is reduced by the curved hole configuration under all the blowing ratios and Reynolds numbers. The number of the hairpin vortex under the same flow conditions is reduced by the curved hole, such as from 7 to 4 by comparing Figures 7(a) and 8(a). Even the less visible vortex structure could be observed at the higher Reynolds number condition in Figures 8(c) and 8(d). The jet flow breaks up in a short distance into small scale vortices. These behaviors could enhance the transportation of jet fluids towards the wall surface and lead to greater adherence.
Besides, care should be taken in concluding the vortex structure presented in Figures 7 to 10. Since they are instantaneous visualizations, the structure observed may be strongly associated with the time when a snapshot is taken. Hence, discussions on the time-averaged parameter are necessary which are given below.
3.1.2. Time-Averaged Presentation
All the time-averaged quantities to be presented hereafter are obtained over 50 to 100 sequential shots, with the sampling frequency 7.24 Hz, of the PIV measurement results. Figures 11–13 show time-averaged smoke photography, contours of the time averaged velocity magnitude and vorticity , in the symmetric plane for both holes under blowing ratios of 0.5 and 1.0 for Reynolds number 1000. It is seen from Figure 11 that, instead of the obviously observed vortices in the instantaneous smoke visualizations (Figures 7 and 8), jet smoke fluid in white is diffused along the main flow direction without visible vortices. A dark area close to the wall downstream of the jet exit is clearly observed in the pictures for straight hole cases but not for the curved hole cases. This indicates that the jet fluids issued from the curved hole could well adhere to the wall surface and could definitely improve the cooling effectiveness. It is seen from Figure 12, velocity contour with vectors, that the coming boundary layer flow is disturbed by the jet flow. Thickness of the boundary layer downstream the hole exit increases with the mainstream due to the motion of CVP and the blowing ratio. Compared to the straight hole cases, the thickness is reduced in the curved hole cases due to the passage vortex pair, generated in the curved hole passage, with an opposite rotation sense to the CVP. Location of maximum velocity near the hole exit deviates from the hole center towards the main flow direction due to the shearing action of cross-flow. It can be observed that the maximum velocity near the jet exit is increased with blowing ratio and reduced in the curved hole case, which can also be seen from Figure 13. Figure 13 shows the normal velocity component profile, extracted from Figure 12, at the location of above the hole exit. It can be seen additionally that the location of the maximum velocity is hardly affected by blowing ratio and is closer to the hole trailing edge at in the curved cases, instead of in the straight cases. Haven and Kurosaka  studied the effects of jet velocity profiles in top-hat and parabolic shapes under blowing ratios from 2.3 to 5.8 by using laser-induced fluorescence and digital particle-image velocimetry techniques. They found that the thicker shear layer associated with the parabolic profile is able to delay the formation of leading-edge and lee-side vortices, compared to the top-hat profile with thinner shear layer under the corresponding blowing ratio. As a result, there is an increase in jet penetration and a reduction in the near-field entrainment of cross-flow fluid by the parabolic profile. In the current study, the exit profile is more three-dimensional, especially for the curved hole cases. The thinner boundary thickness at the lee side of jet flow will definitely decrease the jet penetration and consequently the lower jet trajectory, as viewed from Figures 7, 8, and 11.
Figure 14 shows the contours of time averaged vorticity in the symmetric plane, with positive vorticity turning in the counter clockwise. It is seen that vorticity near the wall for both holes is negative, associated with the boundary layer, except for a small range, a short distance downstream of the hole exit under blowing ratio of 0.5. Along the jet trajectory, vorticity is positive at the wind-ward side and negative at the lee-ward side. The value of the vorticity increases with blowing ratio for both straight and curved holes and reduces from the straight hole to the curved hole for the same blowing ratio, which is consistent with the velocity profiles in Figure 14. It can be seen that the wind-ward side vorticity cannot be maintained as far as the lee-ward vorticity towards downstream, which is consistent with the instantaneous smoke visualization observations in Figures 7 and 8 in which only vortices in clockwise could be clearly visible along the trajectory. Zones, with positive vorticity, located between the wall and the jet trajectory may indicate the wake vortisity.
In order to further understand the jet flow structure in its cross sections, the smoke is again seeded only in the jet fluid and four cross sections were visualized and measured for both hole configurations under the studied Reynolds numbers and blowing ratios.
3.2.1. Instantaneous Visualization
Figures 15 and 16 present the instantaneous visualization pictures of the jet flow in the four cross sections for straight and curved holes, respectively, at Reynolds number and blowing ratios of 0.5 and 1.0. Scale of the space occupied by each of the pictures and their resolution are the same. It is seen that the jet flow is expanding in both vertical and transverse directions with distance towards downstream from (hole exit center) to for both straight and curved holes. With increasing blowing ratio, that is, more coolant fluids are injected, the expanding area becomes larger and shifts farther away from the wall, especially for the straight hole case (Figure 15). The expanded area is larger for the curved hole than that for straight hole in each of the sections, which lead to a favorable effect on the cooling effectiveness by the curved hole. It is further seen from Figure 15 that the “kidney shaped” vortex structure is well observed in the cross sections of jet flow, which has been reported by many researchers, such as [4–6]. In the current visualizations, it is found that the structure of the jet flow from the exit till is quite stable and symmetric at all the studied flow conditions for a straight hole. In section , the jet flow oscillates in both of the normal and transverse directions and is very unstable in the section of .
It is observed from Figure 16 (curved hole) that the structure of the jet flow is totally different from that in Figure 15 (straight hole) and exhibits completely different flow characteristics, caused from the passage vortex pair (PVP) generated by the curved hole passage. Interaction between PVP and CVP leads to form a new vortex structure, as observed, which is distinct from the kidney shaped vortex structure in the straight hole cases. At section (exit center), the jet fluids bifurcate in transverse direction since the PVP could provide a stronger transverse momentum. At the downstream sections , the PVP rotating in the opposite sense to the CVP can be clearly observed and located above the CVP. The PVP and CVP are seen to be coherent in all the sections, except for under in which the vortex structure shows high turbulence.
With increasing Reynolds number, the instantaneous smoke visualization pictures show highly unstable and less well-organized vortex structure for all the blowing ratios and hole geometries studied, especially for the curved hole cases, as one can see from Figure 17. Figure 17 shows the instantaneous smoke visualization pictures in the four sections of both straight and curved holes under for .
3.2.2. Time-Averaged Presentation
Figure 18 is the time-averaged smoke visualization pictures for both hole in the section of under blowing ratios of 0.5 and 1.0 for Reynolds numbers 480 and 1000. Although the vortex structure could not be obviously viewed from the averaged pictures as the instantaneous pictures in Figures 15 to 17, the CVP still can be clearly recognized, especially for the straight hole cases. It can be observed again that the jet issued from the curved hole present a flat-top shape at both Reynolds numbers and both blowing ratios, leading to a much wider transverse spreading, compared to the straight hole cases.
In order to further understand the evolution of PVP and CVP and their interaction along the jet trajectory, contours of time averaged vorticity in the four sections , 1, 2, 4 for both straight and curved hole are presented in Figure 19 for Reynolds number 1000 and BR 0.5. For the other flow conditions, the contours are essentially the same. The positive values of correspond to counter-clockwise vorticity. It is seen that two main isoline loops are observed in the sections of straight hole, corresponding to the CVP with positive vorticity at the left hand side of hole center and negative vorticity at the right hand side of hole center. Four main loops are observed in the sections of curved hole, corresponding to, except for CVP, the PVP with the sign opposite to CVP as indicated in the plot of section . At the sections of and 2, the PVP located above the CVP could be still observed. It is seen that the PVP attempts to push the CVP downwards towards the wall surface or, in other words, the PVP attempts to prevent CVP to elevate coolant away from the wall surface. It can be noticed from that the interaction of PVP with CVP accompanies with a momentum exchange between the two vortex pairs. Both the strength of PVP and CVP decrease gradually with distance. At the position of the vorticity from PVP has been completely transported into the CVP, resulting in mixing of PVP with CVP and a significant reduction of the strength of CVP. CVP is well symmetric with respect to the symmetric line in all the sections, while for PVP a good symmetry can only be observed in sections and 1.
Figure 20 shows the variation of CVP center height (), read from time-averaged section streamline patterns of one vortex due to its symmetry, with streamsiwe sections. As expected, the height is increasing with distance for all the conditions studied. Increasing blowing ratio and/or reducing of the Reynolds number will result in the increase of for both holes. It may be noticed that high Reynolds numbers correspond to low boundary layer thickness or displacement thickness. It then may be concluded that the evolution of CVP center height in the mainstream direction is affected not only by the blowing ratios but also the boundary layer thickness. It can also be seen again that the height of the curved hole is lower for all the flow conditions than that of straight holes.
The flow structure downstream of jet in cross-flow has been investigated by means of PIV. Instantaneous and time-averaged visualization pictures and quantities in the symmetric plane and four cross-sections are presented and discussed for different Reynolds numbers and blowing ratios, with the comparison of curved hole to straight hole.
The flow leaves the jet upwards to a certain distance from its exit without visible vortex motion and then turns towards the mainstream direction with a series of hairpin vortices along the jet trajectory and a wake vortex system under the trajectory. Height of the trajectory reduces with increasing Reynolds number and decreasing the blowing ratio. With increasing Reynolds number, the smoke traces become more unstable and disordered and break up into small scale vortices in a short distance downstream of the jet exit for all the blowing ratios and hole geometries studied, especially for the curved hole cases.
The PVP generated inside the curved hole rotating in a sense opposite to CVP downstream. PVP could weaken CVP due the interaction between them and enhance the transportation of jet fluids towards the wall surface and lead to greater adherence of the jet fluid to the wall in all conditions studied. The curved hole configuration shows its high potential in the film cooling applications.
The authors would like to acknowledge the financial support received from the National Natural Science Fundamental of China.
- R. Fearn and R. P. Weston, “Vorticity Associated with a jet in a cross flow,” AIAA Journal, vol. 12, no. 12, pp. 1666–1671, 1974.
- G. Bergeles, A. D. Gosman, and B. E. Launder, “The near-field character of a jet discharged normal to a main stream,” Journal of Heat Transfer, vol. 98, no. 3, pp. 373–378, 1976.
- Y. Kamotani and I. Greber, “Experiments on a turbulent jet in a cross flow,” AIAA Journal, vol. 10, no. 11, pp. 1425–1429, 1972.
- J. Andreopoulos and W. Rodi, “Experimental investigation of jets in a crossflow,” Journal of Fluid Mechanics, vol. 138, pp. 93–127, 1984.
- P. K. Snyder and K. L. Orloff, “Three-dimensional laser Doppler anemometer measurements of a jet in a crossflow,” NASA TM 85,997, 1984.
- T. F. Fric and A. Roshko, “Vortical structure in the wake of a transverse jet,” Journal of Fluid Mechanics, vol. 279, pp. 1–47, 1994.
- R. M. Kelso, C. Delo, and A. J. Smits, “Unsteady wake structures in transverse jets,” in Proceedings of the AGARD Symposium on Computational and Experimental Assessment of Jets in Cross Flow, Winchester, UK, April 1993, AGARD-CP-534.
- R. J. Margason, “Fifty years of jet in crossflow research,” in Proceedings of the AGARD Symposium on Computational and Experimental Assessment of Jets in Cross Flow, Winchester, UK, April 1993, AGARD-CP-534.
- A. R. Karagozian, “Transverse jets and their control,” Progress in Energy and Combustion Science, vol. 36, no. 5, pp. 531–553, 2010.
- T. H. New, T. T. Lim, and S. C. Luo, “Effects of jet velocity profiles on a round jet in cross-flow,” Experiments in Fluids, vol. 40, no. 6, pp. 859–875, 2006.
- S. L. V. Coelho and J. C. R. Hunt, “Dynamics of the near field of strong jets in crossflows,” Journal of Fluid Mechanics, vol. 200, pp. 95–120, 1989.
- S. H. Smith and M. G. Mungal, “Mixing, structure and scaling of the jet in crossflow,” Journal of Fluid Mechanics, vol. 357, pp. 83–122, 1998.
- B. A. Haven and M. Kurosaka, “Improved jet coverage through vortex cancellation,” AIAA Journal, vol. 34, no. 11, pp. 2443–2444, 1996.
- S. D. Peterson and M. W. Plesniak, “Short-hole jet-in-crossflow velocity field and its relationship to film-cooling performance,” Experiments in Fluids, vol. 33, no. 6, pp. 889–898, 2002.
- S. Kang, “Numerical investigation of the 3D flow structures nearby cooling hole,” Asian Joint Conference on Propulsion and Power, AJCPP2006-22084.
- W. R. Dean, “Note on the motion of fluid in a curved pipe,” Philosophical Magazine, vol. 20, pp. 208–223, 1927.
- J. Y. Liang, S. Kang, and L. Ma, “Numerical investigation of the flow over curved rectangular cooling hole,” Journal of Engineering Thermophysics, vol. 31, no. 2, pp. 251–255, 2010 (Chinese).
- J. Y. Liang and S. Kang, “Correlation and spectra analysis for jet in cross flow based on DES results,” in Proceedings of the 4th Symposium on Hybrid RANS-LES Methods, Beijing, China, September 2011.
- J. Y. Liang and S. Kang, “Detached eddy simulation of the single cooling hole in flat plate,” Journal of Engineering Thermophysics, vol. 32, no. 3, pp. 395–398, 2011 (Chinese).
- G. Haller, “An objective definition of a vortex,” Journal of Fluid Mechanics, vol. 525, pp. 1–26, 2005.
- S. J. Kline and F. A. McClintock, “Describing uncertainties in single-sample experiments,” Mechanical Engineering, vol. 75, pp. 3–8, 1953.