An experimental investigation of secondary flow characteristics in a linear turbine cascade with upstream converging slot-holes using TR-PIV

Experimental Thermal and Fluid Science 59 (2014) 56–71

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An experimental investigation of secondary flow characteristics in a linear turbine cascade with upstream converging slot-holes using TR-PIV Jian Pu a, Jun Yu a, Jian-hua Wang a,⇑, Wen-shuo Yang a, Zhi-qiang Zhang b, Lei Wang b a b

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road No. 96, Hefei 230027, Anhui, PR China Aero-engine Institute of Aviation Industry Corporation of China, Wanlian Road No. 1, Shenyang 110015, Liaoning, PR China

a r t i c l e

i n f o

Article history: Received 7 May 2014 Received in revised form 20 July 2014 Accepted 23 July 2014 Available online 1 August 2014 Keywords: Time-Resolved PIV Secondary flow End-wall film cooling Converging slot-hole Free-stream turbulence level

a b s t r a c t To study the time-mean and temporal characteristics of secondary flow within a linear GE-E3 high pressure turbine cascade, a planar Time-Resolved Particle Image Velocimetry (TR-PIV) system is used. In the double-passage cascade, a row of six converging slot-holes is placed upstream of center blade to generate film cooling effect, and different turbulence grids are replaced to create various free-stream turbulence (Tuin) levels. In this experiment, the time-mean characteristics of secondary flow, the fast switch process of unsteady leading edge horseshoe vortex (LEHV), and the temporal characteristics of corner vortices (CVs) are completely exhibited by the TR-PIV technique. The influences of the upstream coolant injection and Tuin level on the flow characteristics of LEHV and passage vortex (PV) are discussed. The discussion reveals that: (1) in the case of no coolant injection, a high Tuin level slightly moves the LEHV toward the blade, changes the shape of the PV, increases the fluctuations of the LEHV and PV, and reduces the frequency of the LEHV switch process; (2) at various Tuin levels, the coolant injections suppress the formation of the LEHV, and the LEHV disappears at a high coolant-to-mainstream blowing ratio (BR) of 1.5; (3) a high BR of 1.5 can greatly weaken the PV at various Tuin levels, and relative to the case of low Tuin, the high Tuin level induces a larger reduction; (4) for a low BR, at various Tuin levels, a slight change in the LEHV results in a distinct difference of the PV characteristics; (5) for a high BR, since the LEHV disappears, the Tuin effect on the secondary flow characteristics is slight. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Secondary flow, as a common phenomenon in turbine cascades, usually is defined as any flow, which is not in primary or streamwise flow direction. Secondary flow usually causes aerodynamic loss and high convective heat transfer coefficient at end-wall [1–3]. As Langston [1] reviewed, understanding, analysis, prediction and control of the secondary flow are conducive to improve the performances of turbine cascades. Currently, a detailed measurement of the secondary flow features in a real turbine blade row is still a challenge due to several complicated factors, such as blade geometry, rotation, high Mach number, and high free-stream turbulence level, just to name a few [1–2]. To provide turbine designers with a relatively comprehensive understanding of the secondary flow structures in blade rows, linear turbine cascades have been extensively used in previous investigations ⇑ Corresponding author. Tel.: +86 551 63600945; fax: +86 551 63606459. E-mail address: [email protected] (J.-h. Wang). http://dx.doi.org/10.1016/j.expthermflusci.2014.07.014 0894-1777/Ó 2014 Elsevier Inc. All rights reserved.

[4–20], due to simple geometries and better performances of optical measurement under limited experimental capacities. Generally, to ensure flow periodicity, the cascades were consisted of more than three passages [4–12], but to reduce the required flow-rate and improve optical access, the cascades were also made of only one or two passages in previous investigations [13–20]. Up to date, several typical secondary flow patterns [1] in linear turbine cascades have been developed through flow visualizations. Wang et al. [4] presented a transient multi-vortex structure in a linear cascade through multiple smoke wires and laser light sheet. Ma et al. [5] studied the unsteady characteristics of the secondary vortices near the end-wall of a linear cascade with different incidence angles using hydrogen bubble technique, and their results indicated that a fluctuation HV system appears near the junction of the LE and end-wall, and a PV forms due to the interaction between the HVs on the both sides. Besides qualitative flow visualizations, some quantitative measurement techniques, such as fivehole pressure probe, hot-wire probe, Laser-Doppler Velocimetry (LDV) and PIV, have been widely used to understand the secondary

J. Pu et al. / Experimental Thermal and Fluid Science 59 (2014) 56–71

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Nomenclature Cxy c d Tuin Uin U u V v x, y z

xz

time-mean velocity contour in plane x  y = sqrt(U2+V2), m/s scaled-up blade chord length, m boundary layer thickness, m free-stream turbulence intensity inlet mean velocity of blade passage, m/s time-mean velocity in the x direction, m/s fluctuation velocity in the y direction, m/s time-mean velocity in the x direction, m/s fluctuation velocity in the y direction, m/s in-plane coordinates of measurement planes out-of-plane coordinate of measurement planes time-mean out-of-plane vorticity contour, 1/s

Acronyms BR

CV HV LE PV PS PHV PCV SS SHV SCV SV TKE TEV TV WV

corner vortex horseshoe vortex leading edge passage vortex pressure side pressure side leg horseshoe vortex pressure side corner vortex suction side suction side leg horseshoe vortex suction side corner vortex secondary vortex turbulent kinetic energy trailing edge wake vortex tertiary vortex wall vortex

blowing ratio

flow characteristics in linear cascades. For example, Senoo et al. [6] measured the time-mean characteristics of the secondary flow in a water tunnel of a linear ultra-highly loaded turbine cascade using PIV; Mahmood and Acharya [14] studied the secondary flow in a low speed linear cascade with different leading edge fillets using the five-hole pressure probe; Kang and Thole [15], and Radomsky and Thole [16] used LDV to measure the mean and fluctuating velocities of the secondary flow in a linear cascade with three scaled-up, first-stage stator vanes. Although a large number of experimental investigations on the secondary flow characteristics have been carried out in linear turbine cascades, it is difficult to capture some important transient-phenomena, such as the fast variation process of the unsteady HV, the appearance probability of the CV, and temporal development of the PV, using the measurement techniques with low time resolution rate. Therefore, in this work, a TR-PIV system with high time resolution rate is chosen to quantitatively study the time-mean and temporal behaviors of the secondary flow. To cool the turbine cascade end-wall, discrete film-cooling holes or slots are usually placed upstream of the junction of the end-wall and blade LE [7–13]. Rehder and Dannhauer [13] discussed the effect of tangential and perpendicular injections through a slot placed upstream of a linear double-passage cascade, and their results indicated that the tangential injection reduces the strength of the HV and PV, and removes the HV at higher mass flow rates, whereas the perpendicular injection strengthens the HV and PV, which cause a larger aerodynamic loss. Thrift and Thole [12] discussed the influence of injection angle for a slot placed upstream of a vane LE on the unsteadiness of the LEHV using a TR-PIV system, and their results indicated that the LEHV can be turned away from end-wall for 45° and 30° high momentum injections. Takeishi et al. [21] investigated the effect of upstream coolant injection from a fan-shaped hole on end-wall film cooling and the formation of a LEHV, and their results indicated that the suitable distance and blowing ratio can not only decrease high end-wall heat flux, but also weaken the strength of the HV; however, an insufficient injection actually reinforces the growth of the HV. Based on the above-mentioned discussions, it is concluded that the hole or slot geometry and coolant flow rate are two important factors of the end-wall film-cooling performance and the formation of the LEHV. Through the comparison with the performances of the slot, fan-shaped hole and cylindrical hole in flat plate tests conducted by Sargison et al. [22–23], converging

slot-hole (or console) was demonstrated to be the structure with higher film cooling effectiveness and lower aerodynamic loss. Generally, the converging slot-hole structure transits from circular hole into a slot with convergence in axial direction and divergence laterally, which results in an accelerated flow with lower jet turbulence and more stability due to the reduction of hole-area [24]. However, the influence of film-cooling injection from the converging slot-holes placed upstream of blade LE on the secondary flow, including the LEHV and PV, has not been reported by previous works. It is well known that free-stream turbulence (Tuin) level is an important factor of the fluid flow and end-wall heat transfer in the cascades with or without film-cooling injections [2]. The linear cascades generally were tested at a low Tuin level below 5 percent [4,10,15], but true turbine cascades actually operate at high Tuin levels from 8 percent to 40 percent [16–17]. Therefore, a detailed understanding of the secondary features at various Tuin levels is quite important in the optimization of cascade designs. Simon and Piggush [2] summarized the past investigations about the Tuin effect on the heat transfer and fluid flow in cascades, and they concluded that a higher Tuin can promote an earlier transition of endwall boundary layer into turbulence, and causes an increase in end-wall heat transfer [2]. Radomsky and Thole [16] used LDV to measure the flow characteristics at various Tuin levels in a vane cascade, and their results indicated that a high Tuin level increases the end-wall heat transfer and fluctuation of the LEHV. Unfortunately, so far, the experimental investigations of the Tuin effect on the secondary flow characteristics in a cascade with upstream film-cooling injection from the converging slot-holes have not been carried out. In this experiment, the secondary flow characteristics in a linear turbine cascade with three scaled-up GE-E3 high pressure blades are captured using an in-house TR-PIV system. In the cascade, a row of six converging slot-holes is placed upstream of the center blade to generate film cooling effect, and different turbulence grids are replaced to create various Tuin levels. This experimental investigation focuses on the following three objectives: firstly, quantitatively analyzing the time-mean and temporal characteristics of the secondary flow in the cascade without upstream coolant injection at a low Tuin level in Section 3; secondly, investigating the Tuin level effect on the secondary flow in the case without coolant injection in Section 4; thirdly, discussing the effect of upstream injection on the secondary flow characteristics at various Tuin levels in

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Section 5. The primary contributions of this work are to help designers to understand the influences of the film-cooling injection from the converging slot-holes and Tuin level on the secondary flow characteristics for optimizing the cascade design, as well as to provide numerical investigators with a relatively comprehensive database to validate numerical methods. 2. Experimental facilities and methodology 2.1. Experimental system A closed re-circulating facility with a transparent test section, which is manufactured by Plexiglas with a thickness of 15 mm, is designed for this TR-PIV experiment, and pure water is used as working medium, instead of air. The geometry and dimension of the test section are exhibited in Fig. 1(a). To improve optical access, the geometry of the turbine cascade used in this experiment is scaled up to three times of true GE-E3 high pressure turbine blade row as introduced in Wang et al. [20]. As shown in Fig. 1(a), the scaled-up cascade consists of three blades to form a double-passage, and a row of six converging slot-holes (or consoles) is placed upstream of the center blade. The blade and cooling-hole models are designed by help of SolidWorks program, and made of Acrylonitrile Butadiene

Styrene plastic by a 3D rapid prototyping machine with a machining accuracy of 0.1 mm. During the experiment, pure water is ejected from a reservoir by a diving pump with 1.1 kW power. A part of the ejected water as mainstream flows into the test section, and the flow rate is controlled by a turbo flow meter with a maximal scale of 20 m3/h and an accuracy of 0.2%. Prior to entering the test section, water flows through a large developing zone, and a square-hole turbulence grid with a stream-wise length of 40 mm is set downstream of the zone to assure spatially uniform and undisturbed inlet flow. The other portion of the ejected water from the pump as coolant flows into a large developing zone prior to draining out of the cooling holes, and the flow rate is controlled by a rotameter with a maximal scale of 5 m3/h and an accuracy of 0.5%. Fig. 1(b) shows the dimension of the turbulence grids which are replaced to generate various turbulence levels of the free-stream. A fine grid possesses a hydraulic diameter of 5 mm, and a coarse grid possesses a hydraulic diameter of 15 mm. Fig. 1(c) illustrates the blade layout and the turbine cascade geometry data. The ratio of the blade span (l) to chord length (c) is equal to 0.85, and mid-span is defined as a plane of l = 0. Fig. 1(d) describes the configuration of the converging slot-holes used in this study. The hole diameter (D), slot width, and distance between the slot and the blade LE is equal to D = 4 mm, 0.5D = 2 mm, and 8D = 32 mm, respectively.

Fig. 1. Schematic diagram of linear cascade geometry.

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Fig. 2. Physical map of the experimental system.

2.2. TR-PIV system and data processing As shown in Fig. 2, when the inlet flow rate is steady, a planar TR-PIV system, which is consisted by a 2.0W semi-conductor continuous laser with 532 nm wavelength and a Photron FASTCAM SA5 1000K-M3 high-speed photographic camera with a full frame rate of 7000 fps (frame per second), is used to measure the velocity fields of interested planes in this experiment. Hollow glass spheres with an average size of 10 micrometers and a very good performance of light scattering are used as tracer particles in this experiment. The density ratio of the spheres to water is 1.05 and the Stokes number of the spheres is much smaller than 1; thus, these particles have a faithful following behavior. Illumination is provided by the continuous laser, and the light sheet with a maximum thickness of 1 mm is produced by the appropriate combination of cylindrical lenses. The high-speed camera is perpendicularly positioned to the light sheet, to capture the light scattered by the tracer particles. The image distortion is suppressed by means of a Nikon

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lens, whose focal length varies from 24 to 85 mm and aperture number is 2.8. Frame rate and shutter speed of the camera are adjusted sufficiently by Photron FASTCAM Viewer to carry out the TR-PIV experiment. The schematic layout of the interested planes, planes 1–15, is shown in Fig. 3. It can be seen that all the measured planes are nearly perpendicular to the hub-side end-wall, and the secondary flows in the zone from mid-span to hub-side end-wall are investigated. In the planar TR-PIV experiment, all reflective surfaces, including blade surface and hub-side end-wall, are blackened with gloss paint to reduce the optical reflection from curved and rough boundaries. Planes 1 and 2 as shown in Fig. 3(a) are used to study the secondary flow characteristics at the LE. Planes 3–10 as shown in Fig. 3(b) and (c) are chosen to study the secondary flow characteristics in the passage. When the velocity fields in planes 3–6 are captured, to assure camera is perpendicularly set to light sheet, a triangular transparent box as shown in Fig. 1(a) is filled with water/glycerol mixture to reduce the reflection in the process of image acquisition. Planes 11–15 as shown in Fig. 3(d) are chosen to study the secondary flow characteristics downstream of the passage exit. To quantitatively measure the velocity fields in the planes of focus, the first step of the TR-PIV processing is the camera calibration. A real dimension is marked on the surface of the blades to calculate camera magnification M = LO/LI, where LO is the size of the real object plane (in units of mm), and LI is the pixel number in digital images. Through calculation, M = 0.053 mm/pixel in planes 1–2, M = 0.063 mm/pixel in planes 3–6, and M = 0.071 mm/pixel in planes 7–15. When the velocity fields in planes 1 and 2 are measured, the high-speed camera is operated at a frame rate of 125 fps and a shutter speed of 1/300 s. When the velocity fields in planes 3–15 are measured, the frame rate and shutter speed is respectively set as 60 fps and 1/200 s. The raw images of the fifteen planes are processed by software, MatPIV [25], into vector maps. Firstly, the displacement vector of the particles is determined by Fourier-based cross correlation

Fig. 3. Schematic layout of measured planes.

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Table 1 Flow conditions for experiment. Flow conditions

Type of grid

Blowing ratio (BR)

Measured planes

Condition Condition Condition Condition Condition Condition Condition

Fine grid Coarse grid Fine grid Fine grid Fine grid Coarse grid Coarse grid

0 0 0.5 1.0 1.5 0.5 1.5

Planes Planes Planes Planes Planes Planes Planes

1 2 3 4 5 6 7

1–15 1 and 1 and 1 and 1 and 1 and 1 and

10 10 10 10 10 10

and window shifting technique. The calculation starts off with a large interrogation window of 64  64 pixels and 50% overlap of the each interrogation region is used, and then ends with 32  32 pixels after 4 iterative calculations. Subsequently, spurious vectors in the raw vector maps are validated using, successively, a S/N ratio filter, a peak-height filter, a global filter, and a local filter. Finally, a nearest neighbor interpolation is used to smooth the vectors in the whole flow field. 2.3. Experimental conditions In this experiment, a fixed inlet Reynolds number Rein, based on the inlet mean velocity of the test section Uin, scaled-up blade chord length c, and physical parameters of water at 290 K, is chosen in the order of 104 (i.e. Rein = 4.0  104), which can be also observed in the past interrelated studies of Wang et al. [4] and Thrift and Thole [12]. In the case of no upstream coolant injection, the exit Reynolds number Reex, based on the exit mean velocity Uex, scaled-up chord length c and physical parameters of water at 290 K, is Reex = 1.2  105. Table 1 tabulates the experimental conditions. The effect of coolant-to-mainstream blowing ratio (BR = (qcUc)/(qinUin)) on the secondary flow characteristics is studied at a constant density ratio (DR = qc/qin) of 1.0. Uc, qc and qin respectively represents the mean velocity at the inlet of converging slot-hole, density of the coolant and density of the mainstream. The influence of Tuin level on the secondary flow characteristics is also studied through using different grids. 2.4. Incoming flow condition Flow in plane 0, which locates at a symmetrical plane as shown in Fig. 4, is measured to study the incoming flow condition. As

observed in Fig. 4, when a fine grid is used, the distribution of the dimensionless velocities U/U1 in plane 0 is almost symmetrical about the line of y = 0 (i.e. the mid-span). U1 is defined as the stream-wise velocity at the mid-span. By calculation using the velocities at the line of x = 50 mm, the ratio of the boundary layer thickness (d) to half-span (1/2l) is equal to 0.247; boundary layer shape factor (H) is 1.514; and highest turbulence intensity (Tuin) is equal to 2.67%. When a coarse grid is used, by calculation using the velocities at the same line in plane 0, the ratio of d to 1/2l is equal to 0.311; H is 1.257; and highest Tuin is equal to 10.02%. 2.5. Periodicity of passage flow Flow in plane 10 of the two designed passages is measured when a fine grid is used, to validate the periodicity of passage flow. As shown in Fig. 5(a), the time-mean velocity distributions in plane 10 of two passages are qualitatively similar. The values of Cxy/Uin at four lines of Lines 1, 2, 3 and 4 in planes 10 are quantitatively compared. As listed in Fig. 5(b), the absolute values of relative error of Cxy/Uin at all sampling points are less than 5%, which reflects a quite good periodicity in the two passages. Therefore, the following measurements are carried out only in the passage between the center blade and pressure side blade (i.e. passage 1 as shown in Fig. 5(a)). 2.6. Measurement uncertainty Generally, the total uncertainty of arbitrary variable can be estimated by the bias uncertainty and precision uncertainty. For the instantaneous velocity obtained by the TR-PIV system, the bias uncertainty is caused by camera calibration (M = LO/LI), particle displacement vector (Ds) detection and time interval of recording (Dt) [26]. In this experiment, the bias uncertainties of LO, LI, and Dt are 0.0001 m, 0.50 pixels, and 0.0000001 s, respectively. The pixel locking error in the PIV estimation can be reduced to an accuracy of 0.05–0.15 pixels, and thus the bias uncertainty of Ds can be estimated to be about 0.05 pixels. The random uncertainty on the instantaneous velocity measurement is primarily due to cross-correlation error and the typical value of the error is about 0.1 pixels [27]. The time-mean velocities in the measured planes are calculated by a sequence of N instantaneous PIV vector maps at each point. The selection of N is generally based on the examination of the data convergence with the sampling time. Fig. 6 shows the influence of

Fig. 4. Incoming flow condition at plane 0 when a fine grid is used.

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Fig. 5. Validation of periodicity in the two passages when a fine grid is used.

Fig. 6. Influence of sampling time on time-mean flow characteristics in plane 1 at Condition 1.

the sampling time on the time-mean flow characteristics in plane 1 at Condition 1. As shown in Fig. 6(a)–(f), the shape of the vortex and the distribution of velocities (Cxy/Uin) are similar, when N is larger than 600. Based on time averaging over N successive samples at three points listed in Fig. 6(g) and (h), Points A (x = 11.43 mm,

y = 37.31 mm), B (x = 26.85 mm, y = 29.71 mm) and C (x = 60.00 mm, y = 20.00 mm), if N = 1200, the absolute values of relative errors of the mean stream-wise velocity U, mean span-wise velocity V, fluctuating stream-wise velocity u, fluctuating span-wise velocity v from a sequence of 2560 samples are less

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Fig. 7. Time-mean velocity fields in planes 1 and 2 at Condition 1.

than 0.60%, 0.30%, 2.00%, and 1.50%, respectively. Accordingly, 1200 successively measured samples are chosen to calculate the time-mean velocities in this experiment. 3. Results of secondary flow development for BR = 0 at a low Tuin level In this section, the time-mean and temporal characteristics of the secondary flow from planes 1 to 15 at Condition 1 (i.e. Tuin = 2.67% and BR = 0) are captured and analyzed. 3.1. Secondary vortices at leading edge When incoming fluid stagnates onto a rounded blade LE, due to the span-wise pressure gradient, a roll-up horseshoe vortex (HV) generally forms in the vicinity of the LE. The flow characteristics of the LEHV are dependent on inlet Reynolds number, boundary layer thickness, Tuin level, and LE diameter [28–32]. In this

experiment at Condition 1, the time-mean velocity fields in planes 1 and 2 are shown in Fig. 7. As observed in plane 1, a clock-wise rotated LEHV appears at the end-wall LE junction, and the vortex core locates at point (x = 12.06 mm, y = 37.18 mm). Subsequently, the HV essentially begins to split near the blade LE. From plane 1 to plane 2, the HV core moves away from the end-wall, and locates at point (x = 11.87 mm, y = 34.71 mm) in plane 2. In fact, according to the collective conclusion from past studies [12,28–32], the movement of the LEHV is unsteady due to high turbulence intensities. In this experiment, the TR-PIV system with a frame rate of 125 fps is used to quantitatively study the temporal behaviors of the LEHV in plane 1. At Condition 1, the stream-wise fluctuating velocities (u) with time at three points slightly upstream of the time-mean LEHV core, i.e. (x = 18.00 mm, y = 38.00 mm), (x = 18.00 mm, y = 34.00 mm), and (x = 18.00 mm, y = 30.00 mm), are processed by Fourier transformation. Fig. 8(a) shows the relations of dimensionless power (G) to Strouhal number (Str), which is obtained from the Fourier

Fig. 8. Temporal behaviors of LEHV in plane 1 at Condition 1: (a) power spectral densities (PSD) of stream-wise fluctuating velocities, u, at three points upstream the timemean HV; (b) temporal sequence of representative instantaneous patterns.

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frequency (f), scaled-up chord length (c) and Uin, i.e. Str = f  c/Uin. It can be observed that the Strouhal numbers of u at the three points are about Str = 0.597, which represents that the periodic time of the HV movement in plane 1 at Condition 1 is about T = 5.877t+ = 5.877  (d/Uin). Fig. 8(b) illustrates a sequence of six instantaneous flow patterns with vorticity distributions in plane 1. The time interval of two patterns is about 1t+. It can be observed that the LEHV switches between two modes (i.e. backflow and zero-flow modes) from t = 1t+ to t = 6t+. In general, the backflow mode (e.g. at t = 2t+) generates when a large negative stream-wise velocity occurs directly beneath the HV, while the zero-flow mode (e.g. at t = 6t+) is engendered when a near-zero stream-wise velocity appears beneath the HV [30–32]. At t = 1t+, only a HV appears at the end-wall LE junction and near-wall reverse flow passes under the HV. Subsequently, at t = 2t+, a secondary vortex (SV) and a tertiary vortex (TV) form upstream of the HV, due to the pressure gradient between the incoming fluid and near-wall reverse flow. At t = 3t+, an inrush of fluid above the TV occurs and the SV erupts away from the end-wall. The eruptive process is nearly completed up to t = 4t+, by this time, the SV disappears from the near-wall region, and is completely caught by the HV. With an enhancement

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of the HV, the TV gradually becomes weak at t = 5t+, and only the HV is left in the near-wall region at t = 6t+. The analysis of the successive flow patterns reveals that the fluid inrush and eruption of SV play an important role in the switch of the two modes. This conclusion is not obtained by the previous studies of Wang et al. [4] and Ma et al. [5], where the two modes were also found, but the fast development process of the switch between the two modes was not captured by the measurement technique with low time resolution rate. 3.2. Secondary vortices in the passage The LEHV splits near the blade LE, and enters into the passage along both sides of the blade to form two horseshoe vortices, i.e. pressure side leg HV and suction side leg HV (PHV and SHV). Fig. 9(a) describes the time-mean velocity fields from planes 3 to 6. In plane 3, two small vortices (i.e. PHV and SHV) rotate opposite to each other. Farther downstream, the PHV immediately is swept toward the SS due to the pressure gradient from the PS to the SS, and mixes with the SHV. In plane 4, it can be observed that a large vortex with the same rotation direction as the PHV mixes with a

Fig. 9. Flow characteristics from planes 3 to 6 at Condition 1: (a) time-mean velocity fields from planes 3 to 6; and (b) instantaneous vorticity fields in planes 5 and 6.

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Fig. 10. Flow characteristics from planes 7 to 10 at Condition 1: (a) time-mean velocity fields from planes 7 to 10; (b) three representative instantaneous patterns in plane 10; and (c) Representative instantaneous patterns in planes 7 and 8.

Fig. 11. Characteristics of corner vortices from planes 7 to 10.

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small vortex. Up to plane 5, the large vortex absorbs the small vortex, and a large passage vortex (PV) forms adjacent to the SS. The rotation direction of the PV is the same as the PHV, therefor it is deemed that the PHV is stronger than the SHV in the mixing process and the PHV is a major part of the PV [4]. From plane 5 to plane 6, the PV core approaches the SS and slightly lifts above the end-wall. Although the patterns of the time-mean flow fields in planes 5 and 6 represent a single-vortex structure, a mixing process of a multi-core PHV and a single-core SHV actually occurs in the instantaneous flow fields of the two planes, as observed in Fig. 9(b). Fig. 10(a) illustrates the variation in the time-mean velocity fields from planes 7 to 10. It can be observed that a counter-clockwise rotating PV occupies in all planes, and the position of the core is almost invariable, while the size gradually increases. According to the flow visualization of Wang et al. [4], the SHV wraps around the PV, and the both vortices travel along the SS toward the passage exit. However, in this experiment, only a small SHV is clearly observed in plane 9, as observed the time-mean velocity fields from planes 7 to10. In plane 10, the streamlines adjacent to the SS seem to be clockwise, which indicates the presence of the SHV. Three representative instantaneous flow patterns in plane 10 are shown in Fig. 10(b), and it can be found that an instantaneous SHV occurs at t = t0 + 0.2 s. According to statistics of the sequence of 1200 instantaneous patterns in plane 10, the appearance probability of the SHV is about 30 percent. Therefore, it is reasonable that the SHV is too weak to be clearly observed in the time-mean velocity field of plane 10. In addition, as observed in Fig. 10(c), the instantaneous SHVs can be also observed in the instantaneous velocity fields of planes 7 and 8.

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In previous literature, the time-mean and transient characteristics of the CVs in the passage were rarely studied, since the sizes of the CVs are too extremely small to be viewed by general flow visualizations [4–5] and time-mean measurements [6,14–16]. Just like in Fig. 10, the CVs do not appear in the time-mean velocity fields. However, the existence of the PCV and SCV can be verified in the instantaneous flow fields captured by the TR-PIV system. Fig. 11(a) shows the representative contours of instantaneous vorticity from planes 7 to 10. It can be seen that an instantaneous PCV is clearly shown in planes 7, 8 and 9 and an instantaneous SCV in plane 10. Fig. 11(b) lists the appearance probabilities of the CVs from planes 7 to 10, according to statistics of 1200 instantaneous patterns in each plane. It can be found that, for each measured plane, the appearance probability of the instantaneous PCV is higher than that of the instantaneous SCV. 3.3. Secondary vortices downstream of the passage exit Fig. 12(a) exhibits the time-mean velocity fields from planes 11 to 15, which are chosen to investigate the secondary flow characteristics downstream of the passage exit. The PV with counterclockwise rotation is successfully captured. It can be found that the size of the PV gradually increases, and the PV core gradually moves away from the end-wall from plane 11 to 15, except in plane 12. The reason may be that the PV in plane 12 is suppressed by the above counter-rotated wall vortex (WV), which generally is difficult to be captured in time-mean velocity fields [4,33]. Just like in Fig. 12, a WV is clearly identified near the SS only in plane 12, while the WV is invisible in other planes. In general, the WV is considered to be formed by the induction of the PV and originates at

Fig. 12. Flow characteristics from planes 11 to 15 at Condition 1: (a) time-mean velocity fields from planes 11 to 15; (b) a representative instantaneous pattern in plane 12; and (c) TEV characteristics in plane 11 of different passages.

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the same location as the PV, while the SHV is independent of the PV [4,33]. In Fig. 12(a), the time-mean SHV is not apparent, which means that the time-mean SHV becomes weak downstream of the passage exit, whereas the instantaneous SHV can be observed near the SS, as described in Fig. 12(b) which shows a representative instantaneous pattern in plane 12. In addition, the time-mean SCV can be clearly observed in planes 11, 13 and 14. Unlike the flow features in the passage, a trailing edge wake vortex (TEV) caused by trailing edge wake appears in time-mean velocity fields from planes 11 to 15 as shown in Fig. 12(a). The TEV is rather unsteady, since the shape, location and rotation direction of the TEV from plane 11 to 15 are variable. In the double-passage cascade, the flow in the passage is validated to be periodic as discussed in Section 2.5, but the TEV possesses a poor periodicity, since as described in Fig. 12(c), the shapes of TEVs downstream of the two passage exits are different. Therefore, in the following, the influences of the Tuin and coolant injection on the secondary flow only in the passage are analyzed. In a word, the experiment using the TR-PIV technique can obtain not only the spatial development of the secondary flow in

the cascade, which is similar with the main flow features reported by the past investigations of Wang et al. [4], Mahmood and Acharya [14] and Kang and Thole [15], but also some important temporal-phenomena, e.g. the fast switch process between the two modes of the LEHV, and the appearance probability of the CVs in the passage, which are difficult to be captured by the time-mean measurements. 4. Results of Tuin effect on secondary flow characteristics for BR=0 In this section, the influence of Tuin level on the secondary flow characteristics is discussed for BR = 0 (i.e. no upstream coolant injection). A low Tuin of 2.67% is generated by a fine grid, whereas a high Tuin of 10.02% by a coarse grid. 4.1. Effect of Tuin on flow characteristics of LEHV Fig. 13(a)–(c) illustrate the variations in the time-mean velocity fields and vorticity fields, as well as turbulent kinetic energy (TKE)

Fig. 13. Influence of free-stream turbulence level on the flow characteristics in plane 1 at BR = 0: (a) time-mean velocity fields, (b) time-mean vorticity fields, and (c) turbulent kinetic energy distributions in Region A.

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Fig. 14. Influence of free-stream turbulence level on the flow characteristics in plane 10 at BR = 0: (a) time-mean velocity fields, (b) time-mean vorticity fields, (c) TKE distributions and (d) appearance probabilities of the CVs.

Fig. 15. Influence of upstream film-cooling injection on the LEHV in plane 1 at a low Tuin level.

distributions in plane 1 at various Tuin levels, respectively. As shown in Fig. 13(a), comparison of the position of the HV core at both Tuin levels reveals that the HV core is more closer to the LE

at the higher Tuin level. This phenomenon is also captured by Radomsky and Thole [16] in a linear cascade with three scaledup, first-stage stator vanes. In Region A (i.e. the LEHV region), the

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Fig. 16. Influence of upstream film-cooling injection on the time-mean vorticity fields in plane 10 at a low Tuin level.

Fig. 17. Influence of free-stream turbulence level on: (a) time-mean vorticity fields for BR = 0.5 and time-mean velocity fields for BR = 1.5 in plane 1.

variation of velocity distribution is slight at various Tuin levels. Upstream of Region A, especially in the region near the end-wall, the influence of the incoming fluid turbulence level is intensive; therefore, the variations of the velocity fields and streamlines are obvious. As shown in Fig. 13(b), the vorticity in the HV core is slightly enhanced with an increase in the Tuin level. In addition, relative to the case of the lower Tuin level, at the high Tuin level, the vorticity distribution in plane 1 is disordered. As described in Fig. 13(b), the dimensionless TKE distributions in enlarged Region A indicate that higher TKE levels occur with higher Tuin levels.

Compared with the lower Tuin case, the peak TKE levels are located closer to the blade LE, since the LEHV core is closer to the LE at higher Tuin level. To verify the unsteadiness of the LEHV in plane 1 at a high Tuin of 10.02%, the stream-wise fluctuating velocities (u) with time at three points slightly upstream of the time-mean LEHV core, i.e. (x = 12.00 mm, y = 38.00 mm), (x = 12.00 mm, y = 34.00 mm), and (x = 12.00 mm, y = 30.00 mm), are processed using Fourier transformation. By calculation, the Strouhal numbers (Str = f  c/Uin) of u at the three points are about

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Str = 0.471. Compared with the case of lower Tuin level (Str = 0.597), the frequency of the oscillation between two modes is lower at the high Tuin level. 4.2. Effect of Tuin on flow characteristics of PV Besides the LEHV, the flow characteristics of the PV are also affected by the Tuin levels. Fig. 14(a)–(c) illustrate that, at various Tuin levels, the variations of the time-mean velocity fields and vorticity fields, as well as dimensionless TKE distributions in plane 10, respectively. As shown in Fig. 14(a), compared with the low Tuin case, at the high Tuin level, the PV enlarges in size, and the PV core moves away from the end-wall, and the SHV disappears. In addition, the distinctly different time-mean velocity distributions directly induce a change in the time-mean vorticity distributions as described in Fig. 14(b). Comparison of the vorticity distributions at various Tuin levels reveals that the increased Tuin induces an enhancement of the vorticty in PV core. As shown in Fig. 14(c), comparison of the TKE distributions at the two Tuin levels indicates that higher TKE levels appear at the higher Tuin levels. Fig. 14(d) lists the appearance probabilities of the CVs in plane 10 at the two Tuin levels, according to statistics of 1200 instantaneous patterns. It can be found that the appearance probability of the instantaneous PCV is higher than that of the instantaneous SCV at various Tuin levels. In short, for BR = 0, the Tuin level causes a slight variation in the time-mean velocity field near the LEHV region and a large change in the time-mean velocity field of the PV. The LEHV core moves closer to the LE at higher Tuin level. A high Tuin level increases the fluctuations of the LEHV and PV and the vorticities in LEHV and PV cores, while reduces the frequency of the LEHV movement.

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coolant injection. For low momentum injections of BR = 0.5 and 1.0, comparing to the case of BR = 0, the variation of the PV is inapparent. From BR = 0 to 0.5, the upstream coolant injection exhibits a small effect on the PV, since the shape of the PV and the vorticity of the PV core almost keep unchanged. With an increase of the BR from 0.5 to 1.0, the PV gradually enlarges in size, the vortex core slowly move away from the end-wall, and the vorticity of the PV core begins to decrease. For a high momentum injection of BR = 1.5, the LEHV disappears, therefore, the characteristics of the PV are acutely changed by the coolant injection. Comparison of the PV characteristics at the four BRs of BR = 0, 0.5, 1.0, and 1.5 reveals that,

5. Results of upstream film-cooling injection effect at various Tuin levels A row of six converging slot-holes upstream of the LE is used to supply film coolant, suppress the formation of the LEHV and weaken the PV. In Section 5.1, at a low Tuin of 2.67%, the effect of upstream coolant injection on the secondary flow characteristics is discussed. In Section 5.2, the influence of Tuin level on the secondary flow characteristics in the cascade with upstream film-cooling injections is investigated. 5.1. Effect of upstream film-cooling injection at a low Tuin level Fig. 15 shows the time-mean velocity fields in plane 1 for BR = 0, 0.5, 1.0, and 1.5, at the Tuin of 2.67%. It can be found that the coolant injection from converging slot-holes can suppress the formation of the LEHV. For a low momentum injection of BR = 0.5, relative to the case of BR = 0, the LEHV still forms at the end-wall LE junction whereas the LEHV is descreased by the coolant injection. The LEHV core locates at point (x = 12.06 mm, y = 37.18 mm) for BR = 0 but changes the location at point (x = 7.97 mm, y = 41.57 mm) for BR = 0.5, which indicates that the LEHV begins to approach the end-wall with an increase of BR from 0 to 0.5. For BR = 1.0, the LEHV cannot be observed, but the streamlines adjacent to the LE and end-wall seem to be clockwise, which indicates the presence of an extremely small vortex near the junction of the end-wall and LE. For a high momentum injection of BR = 1.5, the LEHV disappears. Since the PV is caused by the mixing of the HVs as introduced in Section 3.2, the variation of the LEHV will change the PV characteristics. Fig. 16 exhibits the time-mean vorticity fields in plane 10 for BR = 0, 0.5, 1.0, and 1.5, at the Tuin of 2.67%. It can be found that the size, shape and vorticity distributions of the PV are changed by the

Fig. 18. Influence of Tuin level on the time-mean vorticity fields in plane 1 for: (a) BR = 0, (b) BR = 0.5, and (c) BR = 1.5.

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for BR = 1.5, the size of the PV is the smallest, the vorticity of the PV core is the lowest, and the vortex core is closest to the end-wall. To sum up, at the Tuin of 2.67%, the coolant injection from the converging slot-holes located upstream of the LE is propitious to suppress the formation of the LEHV and weaken the PV. For the low momentum injections, a small vortex still forms near the LE and the injection has little effect on the PV. For the high momentum injection up to BR = 1.5, the LEHV is eliminated and the PV is significantly weakened, which may result in lower heat transfer and aerodynamic loss in the turbine cascade. 5.2. Effect of Tuin on secondary flow characteristics for BR = 0.5 and 1.5 Fig. 17(a) describes the variation of the time-mean vorticity fields at two Tuin levels for a low BR of 0.5. Small vortices form near the junction of the end-wall and LE. Comparison with the lower Tuin case, at the high Tuin level, the vortex core slightly approaches the end-wall, and the vorticity in vortex core enhances. Additionally, the various Tuin levels of incoming fluid cause more disordered vorticity distributions upstream of the cooling holes, whereas the variation of vorticity field in region downstream of the cooling holes (i.e. Region B in the figure) is slight. Fig. 17(b) exhibits the time-mean velocity fields at the two Tuin levels for a high BR of 1.5. It can be observed that the LEHV disappears and the distributions of velocity field in region downstream of the cooling holes (i.e. Region C as circled in the figure) is similar, whereas the various Tuin levels of incoming fluid cause distinctly different velocity fields upstream of the cooling holes, especially in the region near the end-wall. Fig. 18(a)–(c) respectively exhibit the influences of Tuin level on the time-mean vorticity fields in plane 10 for BR = 0, 0.5 and 1.5. It can be found that, for each Tuin level, the PV is weakened with an increase in the BR, and this effect on the PV is more obvious for the BR is larger than 1.5. From BR = 0 to 0.5, at lower Tuin, the shape and vorticity of the PV core almost keep unchanged; whereas at higher Tuin, the BR effect enhances, the PV core apporaches the SS and end-wall, and the vorticity in the PV core decreases, though the reduction of the vorticity is not markable. From BR = 0 to 1.5, relative to the case of lower Tuin, the high Tuin level induces a larger reduction of the vorticity in the PV core. For BR = 0 and 0.5 at the two Tuin levels in Fig. 18(a) and (b), the Tuin effect on the PV is obvious, since a new PV is generated by the mixture of HVs which are changed by the Tuin level as shown in Figs. 13 and 17(a). For BR = 0.5 as described in Fig. 18(b), compared with the low Tuin case, the PV core apporaches the SS, and the vorticity reduces at the high Tuin level. For BR = 1.5 at various Tuin levels as described in Fig. 18(c), the effect of Tuin level is slight, since the LEHV disappears at the two Tuin levels as shown in Fig. 17(b). Compared with the low Tuin case, at the high Tuin level, the PV core slightly apporaches the end-wall and the vorticity in the PV core slightly increases. In conclusion, at various Tuin levels, the upstream coolant injection can suppress the formation of the LEHV and a high momentum injection can greatly weaken the PV. For a low BR of 0.5, at various Tuin levels, a slight change of the LEHV results in a distinct difference of the PV. For a high BR of 1.5, the effect of Tuin level on the secondary flow characteristics is slight. 6. Conclusions An experimental investigation using the TR-PIV technique with high time resolution rate is conducted to capture the secondary flow characteristics in a linear scaled-up GE-E3 high pressure turbine cascade with and without upstream film-cooling injection from a row of converging slot-holes, at various free-stream

turbulence levels. The following important conclusions, which were not reported by previous literatures, can be drawn through the processing and analysis of the experimental data. 1. Secondary flow characteristics for BR = 0 at various Tuin levels  The frequency of the LEHV movement and fast switch process between two modes are successfully captured by the TR-PIV technique. An analysis of the successive transient patterns reveals that the fluid inrush and eruption of the SV play an important role in the switch of the two modes.  An increased Tuin level slightly moves the LEHV toward the blade, causes a large change in the shape of the PV, increases the vorticity in the PV core and the fluctuations of the LEHV and PV, and reduces the frequency of the LEHV movement.  The transient characteristics of the CVs in the passage are also obtained by the TR-PIV technique. At various Tuin level, the appearance probability of the instantaneous PCV is higher than that of the instantaneous SCV. 2. Secondary flow characteristics for BR > 0 at various Tuin levels  At various Tuin levels, the upstream coolant injections can suppress the formation of the LEHV, for a high BR of 1.5, the LEHV completely disappears, but for a low momentum injection, a small vortex still appears near the LE.  At various Tuin levels, compared with the case of BR = 0, a high BR of 1.5 can weaken the PV, whereas the effect of a lower BR on the PV is not obvious. Relative to the low Tuin case, the high Tuin level induces a larger reduction of the vorticity in the PV core.  For a low BR of 0.5, at various Tuin levels, a slight change of the LEHV characteristics results in a distinct difference of the PV.  For a high BR of 1.5, the effect of Tuin level on the secondary flow characteristics is slight, although the Tuin levels change the flow characteristics of the incoming fluid.

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