Flow field analysis inside a gas turbine trailing edge cooling channel under static and rotating conditions

International Journal of Heat and Fluid Flow 32 (2011) 1147–1159

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Flow field analysis inside a gas turbine trailing edge cooling channel under static and rotating conditions A. Armellini, L. Casarsa ⇑, C. Mucignat Dipartimento di Ingegneria Elettrica Gestionale e Meccanica, University of Udine, Via delle Scienze 208, 33100 Udine, Italy

a r t i c l e

i n f o

Article history: Received 10 March 2011 Received in revised form 19 September 2011 Accepted 21 September 2011 Available online 11 October 2011 Keywords: Internal cooling Trailing edge Rotating channel PIV Coriolis Rotational effects

a b s t r a c t The flow field inside a modern internal cooling channel specifically designed for the trailing edge of gas turbine blades has been experimentally investigated under static and rotating conditions. The passage is characterized by a trapezoidal cross-section of high aspect-ratio and coolant discharge at the blade tip and along the wedge-shaped trailing edge, where seven elongated pedestals are also installed. The tests were performed under engine similar conditions with respect to both Reynolds (Re = 20,000) and Rotation (Ro = 0, 0.23) numbers, while particular care was put in the implementation of proper pressure conditions at the channel exits to allow the comparison between data under static and rotating conditions. The flow velocity was measured by means of 2D and Stereo-PIV techniques applied in the absolute frame of reference. The relative velocity fields were obtained through a pre-processing procedure of the PIV images developed on purpose. Time averaged flow fields inside the stationary and rotating channels are analyzed and compared. A substantial modification of the whole flow behavior due to rotational effects is commented, nevertheless no trace of rotation induced secondary Coriolis vortices has been found because of the progressive flow discharge along the trailing edge. For Ro = 0.23, at the channel inlet the high aspect-ratio of the cross section enhances inviscid flow effects which determine a mass flow redistribution towards the leading edge side. At the trailing edge exits, the distortion of the flow path observed in the channel central portion causes a strong reduction in the dimensions of the 3D separation structures that surround the pedestals. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Gas turbine engines are used in many fields of engineering, ranging from land based power generation systems to aircraft propulsion. The research conducted on gas turbines over the past several decades has led to the design of engines able to operate at ever increasing temperatures with a consequent significant augmentation of performance. The improvements in turbine blade cooling techniques developed through research have been the major contribution to this. Several cooling approaches are normally employed in high pressure turbines. In general, turbine blades are cooled by a combination of external film cooling and internal impingement and convection cooling, Bunker (2007). In the latter case, the blade is provided with internal cooling passages inside which the heat from the blade material is extracted through a forced convection process that is enhanced by the use of turbulence promoters installed on the passages internal surfaces. The design of such devices must

⇑ Corresponding author. Tel.: +39 0432 558010; fax: +39 0432 558027. E-mail address: [email protected] (L. Casarsa). 0142-727X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2011.09.007

be optimized to achieve the greatest reduction in blade temperature with the lowest pressure losses as possible, Bunker (2007). Therefore, a detailed knowledge about the involved flow features is essential to understand the resulting heat-transfer mechanisms and to guide the design process. When looking at the available literature, it is possible to realize that the majority of the studies deals with cooling schemes normally used for the blades’ central body, i.e. square or rectangular rib-roughened channels, where the coolant flows along the main blade axis (i.e. along the radial direction), eventually in multiple passages configuration. Moreover, some characteristics of real turbine blade cooling passages, in terms of channel geometry and working conditions, are often omitted in an attempt to ease the investigation by adopting idealized channel geometries of lower complexity. In the specific case of cooling systems applied to the trailing edge (TE), a special effort is required for a close examination. Indeed, the TE region is one of the most critical, due to quite strict aerodynamic, thermal and structural requirements that oblige to use cooling channels characterized by cross sections of high aspect-ratio (AR), single flow pass, and coolant discharge through multiple exits, Bunker (2008). In particular, in order to conform

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Nomenclature AR b C ~ C Dh ~ Fc h r.m.s. Re Ro x, y, z U, V, W

b/h, channel aspect ratio (–) channel width (m) mean velocity modulus (m/s) velocity vector (m/s) hydraulic diameter (m) Coriolis force vector per unit of volume (kg/s2 m2) channel height (m) root mean square value =UbDh/t, Reynolds number (–) =XDh =U b , Rotation number (–) radial, axial and cross-wise coordinates mean velocity components along x, y, and z directions (m/s)

to the thin edge of the airfoil, the TE exhaust sections are usually shaped as rectangular openings of high AR from which the coolant is discharged along the axial direction (i.e. the direction perpendicular the radial one). Moreover, the TE exit slots are often provided with elongated pin–fins, usually named pedestals, which enhance the turbulence level and guarantee the necessary blade structural solidity. In view of the complexity of real TE passages, it appears essential to investigate engine-similar geometries which, on the other hand, must be sufficiently generic that the results can be widely applied. Recently, computational fluid dynamics became a valuable tool for the investigation of the aero-thermal behavior of these complex devices, Felten and Laskowski (2007). However, the employed turbulence models still rely on the validation with experimental data in order to be applied with the accuracy required by a reliable design, Andreini et al. (2011a). At present, the majority of the contributions concerning the aero-thermal analysis of TE passages comes from studies dealing with channels for stator blades. Taslim et al. (1998) and, more recently, Armellini et al. (2010) and Coletti et al. (2011), experimentally investigated ribbed radial channels with axial outlet through slots. In these studies, high heat transfer was achieved by coupling the effects of rib-roughened surfaces and axial crossing-jets generated from a perforated wall that divided the passage along the radial direction. Armellini et al. (2010) and Coletti et al. (2011) provided also a comparison with the numerical predictions obtained by a Reynolds Averaged Navier Stokes simulation, that highlights the difficulties they encountered in achieving accurate numerical solutions of both thermal and flow fields. A TE channel geometry provided with coolant ejection through slots and lands was investigated in the experimental work of Choi et al. (2008). The coolant enters in a radial channel of constant cross section and it is forced through a 90° bend before to enter two rows of perforated blockage inserts used to generate flow impingement on the channel walls. Finally, the coolant is discharged outside through a wedge-shaped TE section. The thermal field was measured by means of liquid crystal thermography at varying Reynolds number and blockage configuration. Besides valuable information about the effect of different geometries and working conditions on the heat transfer performance, their data showed also a non-uniform distribution of the heat transfer coefficient along the radial direction. The cause of this behavior must be probably found in the design of the passage entrance, which configuration determines an uneven flow velocity distribution along the TE. A detailed flow field analysis would be useful to confirm these results. Facchini et al. (2009a, 2009b) made use of a flow redirecting wall at the channel leading side, coupled with coolant purging at the blade tip in an attempt to provide a quasi-uniform flow along the TE exit of their

u0 , v0 , w0 r.m.s. velocity fluctuations along x, y, and z directions (m/s) Ub bulk velocity (m/s) Greek symbols a =atan(U/V), incidence angle (°) Dt separation time between two PIV samples (s) q density (kg/m3) t kinematic viscosity (m2/s) X angular velocity (rad/s)

wedge-shaped channel. Heat transfer coefficient distributions obtained by liquid crystal thermography were reported for channel configurations characterized by different turbulence promoters installed along the TE and for an outlet tip mass flow rate ranging from 0% to 25% of the inlet mass flow. The results were compared with those obtained for a channel without inlet turning flow, i.e. with an axial flow at the inlet of the trailing edge test section. Their data showed a quasi-uniform heat transfer field upstream of the TE exit, in particular when the 25% of the coolant was discharged at the tip. However the flow configuration (pure axial or axial-radial) significantly influenced the heat transfer coefficient distribution in the region close to the blade hub and inside the TE exit section. The differences were partially justified by means of surface flow visualizations. It has to be noted that, in all the aforementioned contributions, a constant pressure condition was imposed along the TE exit. This choice, surely justified by the need to use simple and replicable conditions, does not fully match real engine conditions, where the pressure radial distribution is far from being constant and depends upon the airfoil design (Dixon, 1998). However, no mention is made about this point by all the cited authors. If rotor blade cooling channels are considered, the rotational effects on the fluid flow and on the heat transfer distribution must be taken into account as well. Unfortunately, the main contributions found in literature concern stereotyped rotating channels which results do not apply straight forward to the TE cooling problem. Moreover, only few of them analyze the rotational effects on the flow field. The most relevant contributions come from the experimental campaigns performed by Bons and Kerrebrock (1999), Elfert et al. (2008), Gallo et al. (2008), Iacovides et al. (1999) and Servouze et al. (2003). They all confirmed the relevance of Coriolis induced secondary flows on the development of the relative flow field. A detailed experimental thermal analysis in a two-pass rotating ribbed duct can be found in the work of Chang et al. (2010). They show the influences of Reynolds, Rotation and buoyancy numbers on the local heat transfer. On a similar geometry, Liou et al. (2007) investigated also the effects of different channel orientations. Recently, a complete thermal analysis of a blade cooling system was achieved taking into account the different cooling schemes employed at the blade leading edge Liu et al. (2008a), central body Huh et al. (2008) and trailing edge Liu et al. (2008b) regions. This latter contribution, together with the works of Rallabandi et al. (2010) and Chang et al. (2007) are to the author’s knowledge the only examples available in literature referring to cooling schemes with axial flow discharge, so resembling modern TE cavities. They all investigated the thermal field inside a rotating channel of trapezoidal cross section with flow ejection at the TE through holes (Chang et al., 2007) or slots (Liu et al., 2008b; Rallabandi et al., 2010). In these experiments, the pressure boundary conditions are controlled by confining the outlet

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flow from the main channel in a radial duct used as return passage. By doing so, the centrifugal forces act on the flow inside both the main and return channels, so producing similar radial pressure gradients. This assures pressure conditions across the channel exits that can be considered fairly rotation independent. Nevertheless, the adopted return passages appear to be downsized in order to exclude a priori their influence on the flow developing inside the test section. Based on the open literature review, the objective of the current work is to study the effect of rotation on the flow field inside a cooling channel for blade trailing edge. The channel geometry resembles those of current interest, i.e. a cross-section of high aspect ratio, radial inlet flow, and axial and radial flow discharge through exhaust sections located at blade trailing edge and tip, respectively. The tests were conducted under engine similar conditions with respect to the selected Reynolds (Re) and rotation (Ro) numbers, while particular care was put in the implementation of proper pressure conditions at the channel exits in order to allow the comparison between the data under static and rotating conditions. The aerodynamic flow field has been investigated by means of Particle Image Velocimetry (PIV). In order to retrieve the relative velocity fields from PIV data acquired in the absolute reference frame, a particular experimental procedure has been developed. The aerodynamic analysis highlights flow features that are specific characteristics of modern TE internal cooling schemes and leads to a better understanding of the flow mechanisms responsible for heat transfer augmentation under static and rotating conditions.

In order to provide an almost uniform flow at the entrance of the TE exit section, the channel width is reduced progressively form hub to tip by means of a redirecting wall. At the model tip, a short channel with rectangular cross section (having the same height of the main channel but AR = 3.625) guides the flow towards the tip exit made of five equally spaced holes of 7 mm radius. Inside the TE section, seven elongated pedestals are installed to ensure structural rigidity and to promote flow turbulence. At the channel exits, a polyester fibers filter is placed, Fig. 2b. As it will be explained in Section 3.4, the filter has been used to control the pressure boundary conditions in a way to guarantee a meaningful comparison between the data acquired under static and rotating conditions. The test section is connected to a settling chamber (Figs. 1 and 2), which has been designed to provide identical inlet flow distribution under both static and rotating conditions. The counter balanced settling chamber and the channel, are connected by means of a flange to the slow shaft of a gear reduction unit. The system is installed on a metallic frame and driven by an electric motor. Flexible aluminum tubes connect the settling chamber to a 3 m long, 97 mm internal diameter steel pipe in the middle of which a calibrated orifice flow meter is placed. The steel pipe is finally connected to the outlet duct of a 4 kW centrifugal fan, the rotational speed of which can be varied by means of an inverter to control the air flow rate. The plant instrumentation allows the flow rate, and hence the Reynolds number, to be measured with a maximum error of less than 1.5%.

1.1. Test rig

2. Experimental methodology

The present channel geometry is sketched in Fig. 1a. The flow enters the channel along the radial direction and it is exhausted at both tip and TE. The inlet section is rectangular with high AR (equal to 7.25), while the TE exit portion has a wedge-shaped cross section.

2.1. Particle image velocimetry measurement chain Two-dimensional and Stereo PIV techniques were used to perform flow field measurements. The systems set-up included a

Fig. 1. Schematic of the experimental facility (a) and nomenclature and positions of the PIV measurement planes (b).

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Fig. 2. Test rig (a) and detail of the model trailing edge equipped with the fibers filter (b).

125 mJ double cavity Nd:Yag laser, two 12-bit CCD cameras with a resolution of 1024  1280 pixels and the related synchronization and acquisition systems. The seeding was provided by a Laskin nozzle type seeding generator operated with vegetable oil, which guarantees a very narrow particles size distribution with a mean diameter of 1.2 lm. For the 2D measurements, the particles were imaged with a lens of 60 mm focal length set at f# 4, at a nominal magnification of 10 pixels/mm. The laser sheet thickness was about 1.2 mm and the separation time was set to 100 ls in order to limit the outof-plane displacement of the tracer particles. To perform StereoPIV measurements the cameras, mounted on Scheimpflug adapters, have been placed on the same side of the laser sheet, at angles equal to 0° and 45° with respect to the direction normal to the measurement planes. This choice was due to optical access constraints, which were quite severe especially in the rotating tests. The particles were imaged by means of two lenses with 105 mm focal length, set at f# 4 and 8 for the backward and forward scattering camera, respectively. The stereo images were processed performing image back-projection and then stereo reconstruction. A disparity correction was used to minimize the misalignment errors, as suggested by Willert (1997). The measurement chain calibration was realized by means of 6 exposures of a calibration target acquired at different off-plane positions. The target was made of an orthogonal grid of black dots of 0.8 mm diameter on white background. The grid spacing was 2  2 mm, which resulted in more than 200 dots on each exposure, sufficient for an accurate

image dewarping. The nominal magnification of the dewarped images was 30 pixels/mm. The separation time was considerably shorter (10–30 ls) than in the 2D measurements in order to minimize the number of lost particles due to the high cross-plane velocity component. For all measurements, the PIV images were processed using the commercial software PIVview from PIVTEC GmbH, with a first interrogation window of 64  64 pixels, a single step of window size refinement and 50% of window overlapping. Two steps of window distortion–displacement were used for each step of the refinement procedure. Finally, a Gaussian peak-fitting was adopted to perform the sub-pixel interpolation. With these settings, a field of 80  64 displacement vectors was defined in each measurement area with a spatial resolution of 1.5 and 0.5 mm for the 2D and Stereo measurements, respectively. Vector validation was performed with tests based on a normalized median filter and on criteria of primary to secondary correlation peak and minimum signal-to-noise ratio. The percentage of invalid vectors was typically low, less than 3%, and only the valid vectors were sampled to obtain the time averaged vector fields. For technical reasons, it was chosen to perform the experiments under rotation with the measurement chain arranged outside the test rig. Consequently, the PIV samples were acquired in phase locked mode, i.e. the measurements were performed at a specified circumferential position of the test model. For this purpose, the TTL signal from a photodiode periodically screened by a target integral to the test section, was sampled by a counter board at a frequency of 20 MHz. The time lapse occurred between two successive rising edges of the photodiode signal is used to get in real time the mean angular velocity for each revolution, X, with a relative error that can be estimated equal to @ X=X ¼ 3:5  107 . Thanks to the highly accurate measurement of X and to the high momentum of inertia of the test rig that limits its angular velocity fluctuations, the circumferential position of the rotor was resolved with an accuracy of about 0.007° which leads to a remarkable image positioning stability. Indeed, at the model tip, with a magnification factor of 10 pixels/mm, the uncertainty in the angular position leads to image shifts of about ±1 pixel along both x and y image axes. These values are by far smaller than the actual interrogation windows size, so reducing to negligible values the spatial averaging error in the computation of the time-averaged velocity fields. Nomenclature and localization of the flow planes selected for the PIV measurements are reported in Fig. 1b. Depending on the orientation of the measurement plane, 2D or Stereo-PIV was used in an attempt to minimize the measurement error. Twodimensional measurements have been performed in the horizontal planes xy, xy1, and xy2, located at z = 0 mm, z = 14.55 mm, and z = 14.55 mm, respectively and in the symmetry planes xz of the five jets at the tip exhaust section (xz  F1, . . . , xz  F5 in Fig. 1b). For a better characterization of the inlet flow, 2D data were also acquired in the xz-in plane located inside the channel entry section at y = 0 mm. More detailed information about the interpedestal flow structure have been obtained with Stereo-PIV measurements acquired inside the inter-pedestal passage P4 (see Fig. 1b) in the yz (located at x = 262.5 mm) and xz (located at y = 165 mm) planes. The Stereo-PIV method was applied in order to reduce the parallax error due to the strong cross-plane velocity component that characterizes the yz and xz measurement planes. The flow planes were divided into smaller measurement windows, that were acquired successively, in order to meet the required spatial resolution. For every measurement window, 1000 samples have been acquired and then averaged to compute the time averaged velocity fields and the related turbulent statistics.

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2.2. Determination of the relative velocity fields Since the PIV data have been acquired in the absolute reference frame, to determine the relative velocity fields it is necessary to know the peripheral velocity. The latter can be computed provided that the angular velocity and the radii of rotation of the measurement points inside the channel are known. Concerning the angular velocity X, in Section 3.1 it has already been explained how its value is accurately measured at every channel revolution. On the contrary, the position of the measurement points with respect to the center of rotation cannot be retrieved with sufficient accuracy by means of a direct measurement, therefore an indirect method has been developed for this purpose. A target similar to the one used for Stereo-PIV calibrations is placed inside the test section at the position of the laser sheet. Then, the test section is put in rotation and two images of the target are acquired with a separation time (Dt) that guarantees a target displacement of about 200 pixels between the two images. For both the images the marker centers are determined by means of a cross-correlation with a sample signal. Afterwards, since the rotation angle between the two images is known (the latter being XDt), the center of rotation of every marker can be determined. Because the center of rotation must obviously be the same for every marker, all the calculated values (>100) can be ensemble averaged, providing the definition of the center of rotation with an accuracy of about ±0.5 pixels. The subtraction of the peripheral velocity was performed with two different procedures for the 2D or Stereo data, once again with the aim to ensure the best accuracy of the results. For the 2D data in the xy planes, the component of tracer particle displacement due to the peripheral velocity was subtracted directly from the PIV samples before the cross correlation was performed. In this way, the PIV experimental parameters could be set in accordance with the requirements of the relative flow field. This strategy is essential to guarantee a satisfactory accuracy in situations where the magnitude of the peripheral velocity is much higher than the relative one, as it occurs in some region of the present flow field. This approach requires in practice to de-rotate the second frame of the PIV image pairs (frame B) with respect to the center of rotation of the test section by an angle equal to XDt, which is actually the angle swept by the test section during the separation time Dt (i.e. the elapsed time between frames A and B of a PIV image pair). The de-rotated frame, frame B⁄, is reconstructed from frame B with the procedure described in the following. For every pixel of frame A, the displacement due to the solid body rotation of the test section is calculated. This displacement vector defines from which points of frame B the light intensity signal must be interpolated to reconstruct the pixel value belonging to frame B⁄. The choice of a suitable interpolation scheme is a key point for the accuracy of the procedure. In the present case the image reconstruction is performed by means of a in-house developed software based on the SINC-8 interpolation scheme that performs the interpolation on 8  8 pixels stencils and guarantees accurate image reconstructions with associated errors of less than 0.01 pixels (Astarita and Cardone, 2005). In order to provide an estimate of the pre-processing procedure uncertainty (definition of the center of rotation and de-rotation of frame B), sequences of image pairs of the target used for Stereo-PIV calibration have been acquired and then de-rotated. The markers of frames B⁄ showed an almost perfect superimposition with respect to the corresponding ones of each frame A, the differences on the centers position turned out to be below 0.05 pixels. Therefore, it can be concluded that the de-rotation procedure has a limited impact on the PIV error made in the determination of the relative velocity field. If particle relative displacements of 6–10 pixels are measured, the de-rotation error is responsible for an increase of the velocity uncertainty of less than 1% with respect to a standard

static measurement. Considering the characteristics of the pre-processing procedure here adopted, the de-rotation error is mainly due to the error in the estimate of the image center of rotation. Therefore, it is actually a bias that applies to all the instantaneous velocity fields of each measurement set. A completely different approach was used to retrieve the relative velocity from the absolute data acquired in Stereo-PIV mode. In this case, the subtraction of the peripheral velocity from the PIV images with the same procedure used for the 2D data, would require to use the information from the Stereo calibration (i.e. camera viewing angles). Since in Stereo-PIV the calibration is the most important source of error (Willert et al., 2007), the use of calibration data for an image manipulation additional to the standard image back projection would result in an even lower accuracy. For this reason, the authors preferred to adopt a post-processing procedure, where the peripheral velocity was removed the from the instantaneous absolute velocity fields. This was done for every instantaneous velocity field before to compute the time averaged one, in a way to account also for small drifts in the angular velocity. 2.3. Error analysis The results that will be presented in Section 4, refer only to statistical quantities, such as the time averaged velocity fields. Due to the limited number of samples (1000) used to compute the flow statistics, the sampling error tends to be larger than other error sources and therefore it was chosen as the overall upper bound estimate for the PIV data uncertainty. For the 2D measurement acquired in planes xy under static conditions, the normalized r.m.s. errors in the statistical quantities are computed as in Armellini et al. (2009):

eU ¼

r½U

1 u0 ¼ pffiffiffiffi ; jUj N jUj

e0u ¼

r½u0  u0

1 ¼ pffiffiffiffiffiffiffi 2N

ð1Þ

where r is the standard deviation, U is the mean velocity, u0 is the r.m.s. velocity fluctuation and N is the number of independent samples. The uncertainties in the measured values of U and u0 are simply obtained by multiplying the errors in Eq. (1) by a confidence coefficient, Zc. Assuming values Zc = 1.96 (corresponding to a 95% confidence level) and N = 1000, the overall upper bound estimate of the uncertainty in the mean velocities turns out to be less than 2%. This value applies to the largest part of the velocity fields, with the exception of those limited regions affected by very low velocities and high fluctuations, namely inside zones of separated flow. Under the same assumptions, the maximum uncertainty in the estimate of the r.m.s. velocities is less than 5%. If the data under rotation are considered, the error introduced by the image pre-processing procedure has also to be taken into account. Consequently, based on the error estimate of the image de-rotation procedure (see Section 3.2), the upper bound of the velocity uncertainty rises up to 3%. Moreover, phase-averaging errors can be neglected due to the high image positioning stability obtained in the present experiments, as already reported in Section 3.1. The reliability of Stereo-PIV data mainly resides on the accuracy of the measurement chain calibration, which errors lead to biases in the image back-projection and in the Stereo reconstruction of the velocity components, especially in the out-of-plane one. These biases will obviously affect the time averaged vector fields. A possible method to diagnose and eventually correct these errors is based on a procedure that uses the information from the disparity vector fields (Scarano et al., 2005). However, since accurate data acquired by means of standard 2D-PIV are available, the authors prefer to assess the Stereo data accuracy with a cross-comparison. As an example, Fig. 3 shows time averaged U and V velocity

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Fig. 3. Comparison of time averaged U (a) and V (b) velocity profiles extracted along the intersection line of planes xy (2D-PIV data) and xz (Stereo-PIV data) for both Ro = 0 and 0.23.

component profiles extracted along the intersection line between measurement planes xy and xz, obtained by means of 2D and Stereo PIV, respectively. It can be observed that in both test conditions (Ro = 0 and 0.23) the Stereo data are almost superimposed to the 2D ones. The differences are within 0.05 Ub, for both in-plane (U) and out-of-plane (V) velocity components of the Stereo data, so revealing a satisfactory accuracy of the Stereo-PIV measurements. It has to be observed that for the measurement along the yz and xz planes, the channel rotation determines a misalignment between the laser sheet (image plane) and the actual geometrical plane of the channel. This inconvenience could lead to a significant spatial averaging error. However, in the present experiments the very small separation time required to avoid tracer particles loss, limits the image/geometrical planes misalignment within the laser sheet thickness.

As anticipated in Section 2, a polyester fibers filter is placed at the channel exits in order get similar pressure boundary conditions for both static and rotating tests. In view of the filter pressure drop, the mean pressure inside the test section is significantly higher than the ambient value. For the test at Ro = 0 the duct relative pressure is almost uniform with a mean value of about 1200 Pa. When the channel is put into rotation, the centrifugal forces will act on the coolant flow determining a positive radial pressure gradient from hub to tip. The experimental evidence of this is the variation of the static pressure signal acquired upstream of the orifice flow meter when switching from static to rotating conditions. Under system rotation, a drop of about 180 Pa is observed in that pressure value. Since the mass flow rate is the same for both Ro = 0 and 0.23 conditions, the experimentally observed pressure drop is only due to the centrifugal forces. Further support to this observation comes from an estimation made by applying the momentum equation to the PIV data obtained in plane xy. The positive excess pressure from hub to tip turned out to be about 160 Pa, in good agreement with the measured value. At this point it has to be observed that the centrifugal excess pressure is only about 15% of the filter pressure losses. Consequently, the radial pressure ratio distribution between inside/outside the channel is about the same between static and rotating conditions, although still different from real engine applications. Nevertheless, the selected strategy used to control the pressure boundary conditions has the definitive advantage to be of easy implementation, it can be well reproduced both numerically and experimentally and it assures almost comparable conditions at varying the Ro number with a negligible effect on the channel fluid dynamic. Therefore, in the present comparison between static and rotating data, the effect of the pressure boundary conditions can be neglected and, conversely, other rotational effects will be put in greater evidence. 3. Results and discussion 3.1. Static channel The inlet flow to the test section for Ro = 0 is characterized by the velocity and turbulent statistics distributions reported in Fig. 4. The profiles in the figures have been extracted from planes

2.4. Test conditions The experiments have been performed at Re = 20,000 and Ro = 0, 0.23 defined on bulk velocity (Ub about 5.22 m/s) and hydraulic diameter (Dh = 58.18 mm), both computed at the channel entry section. The working fluid was air at ambient temperature, the mean rotational speed was about 200 rpm, corresponding to a tip-speed of 22 m/s. Mach number similarity does not need to be fulfilled, since the Mach number is normally below the value for air compressibility effects, as also demonstrated in the recent work from Facchini and Tarchi (2008). Also the channel eccentricity (namely Rm/Dh, where Rm is the mean radius of rotation) is not a significant similarity parameter, being the experiments run in isothermal conditions. The tests under rotation have been conducted with the channel y axis aligned with the direction of the peripheral velocity, (see Fig. 1). This channel orientation does not differ substantially from a real application, where the blade metal angle at the trailing edge can be as low as 30°, and it has the definitive advantage to simplify the results analysis. Indeed, it maximizes the effects on the flow field due to the channel AR and Coriolis forces in view of the orthogonality between the axis of rotation and the flow principal directions (radial and axial, x and y axis, respectively).

Fig. 4. Inlet flow characteristics in the channel symmetry planes at x = 69.8 mm for Ro = 0: U velocity in plane xy (a), U velocity in plane xz (b), r.m.s. velocity fluctuations u0 and v0 in plane xy (c) and r.m.s. velocity fluctuations u0 and w0 in plane xz (d).

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xy and xz-in at position x = 68.9 mm. In both the horizontal (Fig. 4a) and vertical (Fig. 4b) channel symmetry planes the mean radial velocities profiles, U, and those pertaining to the r.m.s. velocities (Fig. 4c and d) are typical of a turbulent flow under development, as expected in view of the limited entry length. In plane xy, the inlet flow is slightly imbalanced towards the trailing edge of the duct (y < 0) as a consequence of the blockage effect of the redirecting wall at the channel leading side. The small local perturbations that are measured in the profiles reported in Fig. 4 are due to the honeycomb filter placed at the channel entry section, which use is however essential to prevent flow separation and to promote flow turbulence. An estimation of the mass flow split between the channel exits was obtained by the numerical integration over the tip’s holes areas of the streamwise velocity profiles extracted from planes xy and xz  F1/F5. The mass flow discharged at the tip turned out to be about 10% of the inlet one. In Fig. 5a, time averaged in-plane velocity contour, Cxy, and stream-tracers in the channel central plane xy are reported. The flow velocity decreases along the radial direction (x axis), as a consequence of the gradual coolant discharge at the trailing edge. At the blade tip, close to the leading side of the channel, a small region of separated flow is observed. This is a consequence of the geometrical discontinuity between tip and redirecting walls, coupled with flow diffusion evidenced by the diverging path of the stream-tracers. Inside the TE region, flow separation occurs downstream of every pedestal, generating recirculation bubbles which dimension reduces progressively from hub to tip. Indeed, as the fluid flows towards higher radii, it assumes a more axial direction and therefore

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reduces its angle of attack to the obstacle, as shown by the streamtraces path in Fig. 5 and, more clearly, by the plot in Fig. 6. The flow angle a with respect the axial direction (y axis) reported in Fig. 6 has been computed by the velocity components extracted from plane xy, along a line at y = 132 mm. This location has been selected because it is half way between the pedestals leading edges (y = 144 mm) and the beginning of the inclined wall (y = 120 mm). Moreover, it is close to the pedestals but sufficiently upstream that the flow does not feel the deviation imposed by the obstacles, as it is possible to observe from the stream-tracers paths in Fig. 5. Turbulent statistics in the xy plane are provided in Figs. 5b-c, in terms of r.m.s. velocity fluctuations (radial, u0 , and axial, v0 ). The turbulent field turns out to be anisotropic, the radial fluctuations being in general higher than the axial one. The only exceptions are observed immediately downstream of every pedestals, where v0 reaches about 0.2Ub in the shear layers between the separation bubbles and the main inter-pedestal flow. The continuous flow development justifies the increase of the u0 fluctuations observed along the radial direction in Fig. 5b. With the aim to provide an exhaustive description of the complex three-dimensional flow structure inside the inter pedestal passages, Fig. 7 reports the time-averaged stream-tracers and contour plots of the flow velocity acquired in planes xy, xy1, and xz inside passage P4. The mean flow path in plane xy1 (Fig. 7b) highlights a behavior of the near wall flow substantially different from the one of the core flow (Fig. 7a). The deviation of the stream-tracers path found in plane xy1 (Fig. 7b) near the upstream face of the pedestal at x = 300 mm suggests the existence of a

Fig. 5. Time averaged stream-tracers and contour plots of the in-plane velocity modulus Cxy (a), radial velocity fluctuations u0 (b) and axial velocity fluctuations v0 (c) in the xy plane for Ro = 0.

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Fig. 6. Comparison of flow angles, a, for Ro = 0 and 0.23. Data extracted from measurement plane xy along a line at y = 132 mm.

Fig. 8. Time averaged stream-tracers and contour plots of radial u0 (a) and axial v0 (b) velocity fluctuations in plane xy1 and wall normal velocity fluctuations w0 (c) in plane xz inside the 4th inter-pedestal passage for Ro = 0.

Fig. 7. Time averaged stream-tracers and velocity contour plots inside the 4th inter-pedestal passage for Ro = 0.

horse-shoe vortex branch. This latter derives from the deviation of the boundary layer at the junction between pedestal and channel upper wall, and afterwards it is advected by the main stream towards the exhaust. A similar structure must develop also at the opposite pedestal/wall junction (z < 0). The data in the xz plane (Fig. 7c) allow to localize and to size up these vortical structures. On the lower channel side (z < 0) the time averaged foot-print of the horse-shoe vortex appears as a single structure that extends approximately over half of the passage height. On the contrary, on the upper side (z > 0) the stream-tracers suggest a horse-shoe structure made of more than one vortex cell. Indeed, a visual inspection of the instantaneous flow fields revealed that, at the lower junction a horse shoe made of a single and steady primary vortex is found in the majority of the samples. Conversely, an unsteady vortex system made of multiple cells, characterizes the flow at the upper junction, so that the time averaged stream-tracers in Fig. 7c are less representative of the actual flow topology. On the suction side of the pedestal at x = 225 mm, the strong flow separation that leads to the large recirculating structure does not allow the horse shoe vortices to develop inside the inter-pedestals

passage. Finally, the contour plot of the V velocity in the xz plane (Fig. 7c) shows a quasi-symmetric flow distribution with respect to the x axis. Turbulent statistics inside passage P4 in planes xy1 and xz are reported in Fig. 8. Differently from the channel central plane xy, in plane xy1 both u0 and v0 assume comparable values, with maxima localized in the shear layer between the passage through flow and the separation structure downstream of the obstacle (Fig. 8a and b). The trace of the advected branch of the horse-shoe vortex is highlighted by local increment of the u0 fluctuations in the region [260 < x < 285, 215 < y < 155] of Fig. 8a. The vertical (wall normal) fluctuations w0 , Fig. 8c, similarly to u0 and v0 in plane xy1, are higher inside the shear layer that bounds the separated flow region downstream the obstacle. Two other regions of high w0 are detected inside the horse-shoe structures, with a wider extension for the structure located on the lower channel side (z < 0). This difference in the w0 distribution inside the horse-shoe vortices is consequent to the different stability of the two structures commented above. The existence of the horse-shoe vortices on the pedestals upstream faces should guarantee an efficient flow renewal on the channel walls, as confirmed by the high values of the wall normal fluctuations, so determining high heat transfer rates. On the contrary, inside the recirculation regions, the heat and mass transfer mechanisms should be less effective. Consequently, the development of a non-uniform heat transfer field is expected to be found. These observations allow to provide a thorough explanation of the data reported in Andreini et al. (2011b), where a numerical simulation of the heat transfer field inside the present channel geometry under identical working conditions is performed. Inside the other inter-pedestal passages, according to results commented in Figs. 5 and 6, a similar flow behavior has been observed, with differences only in the dimensions of the separated flow structures. 3.2. Rotating channel The time-averaged relative velocity field measured in plane xy inside the rotating duct is presented in Fig. 9a. The comparison

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Fig. 9. Time averaged stream-tracers and contour plots of the in-plane velocity modulus Cxy (a), radial velocity fluctuations u0 (b) and axial velocity fluctuations v0 (c) in the xy plane for Ro = 0.23.

with the stationary data (Fig. 5a) shows large scale differences in the flow behavior: wider flow separation at the tip, more uniform flow velocity at the TE, and substantially different flow velocity distribution in the channel entry section. As expected, the estimate of the mass flow discharged at the tip, performed in the same manner as for the Ro = 0, shows that the mass flow split between the channel exits does not vary with respect to the static case (about 10% at the tip and 90% along the TE). In Fig. 10, inlet flow characteristics for the rotating channel are reported at position x = 69.8 mm. The U velocity profiles have to be compared with those for Ro = 0 in Fig. 4a-b. Under rotation, the inlet flow is strongly imbalanced toward the leading side of the channel (y > 0). Despite the relative low Reynolds number, this flow deviation has to be ascribed to inviscid flow effects, namely the conservation of angular momentum. When the flow enters the channel it tends to preserve its angular momentum and so a relative vorticity opposite to the one imposed by rotation must appear. This effect is maximum for the ideal case of a steady potential flow with constant entropy and rothalpy. Under these assumptions the analytical solution obtained by Vavra (1974) is:

~ ! DU ¼ 2Xb ðV; W  0Þ; r~ C ¼ 2X

ð2Þ

where b is the channel width (4.12 Dh) and DU is the velocity difference between the two channel sides. The experimental data agree qualitatively but not quantitatively with the ideal case, showing a lower velocity difference between channel’s leading and trailing sides. This is mainly due to the existence of not negligible viscous effects on the flow inside the settling chamber which make the assumption of irrotational flow no longer valid. Finally, the stream-

Fig. 10. Inlet flow characteristics in the channel symmetry planes at x = 69.8 mm for Ro = 0.23: U velocity in plane xy (a), U velocity in plane xz (b), r.m.s. velocity fluctuations u0 and v0 in plane xy (c) and r.m.s. velocity fluctuations u0 and w0 in plane xz (d).

wise velocity profile distribution in the vertical symmetry plane of the inlet channel for Ro = 0.23 is reported in Fig. 10b, the compari-

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son with the same data for Ro = 0 (Fig. 4b) does not show significant differences. In a relative flow field as the present one, Coriolis forces are often considered the only responsible for mass flow redistribution that derives from the appearance of secondary structures, acting on the channel cross section. In a channel with outwards radial flow as the present one, rotation induced Coriolis vortices yield a velocity profile skewed towards the trailing edge side (Bons and Kerrebrock, 1999). In the present case, this effect is overcome by the inviscid flow effect commented above, which is significantly enhanced by the high AR of the inlet duct cross-section and by the choice of a channel orientation that implies the alignment between the direction of the peripheral velocity and the duct width (see Fig. 1). This observation demonstrates the need for detailed experimental analysis in order to provide a reliable insight on the flow behavior and correct boundary conditions for the CFD analysis. Coriolis effects turn out to be more intense in the mean flow at higher radii. Fig. 11 shows the time averaged stream-tracers superimposed to the contour plots of the in-plane mean velocity in the xy, xy1, xy2, and yz planes. Different flow paths can be observed by comparing Fig. 11b with Figs. 11a and c. The Coriolis forces, ~ ~ ~ F c ¼ 2qX C, act in plane xy along the direction normal to the stream-tracers, towards y < 0, p and are proportional to the in-plane ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi flow velocity modulus, C xy ¼ U 2 þ V 2 . Therefore they are stronger on the core flow, so resulting in a significant change of the stream-tracers curvature when observed at different channel elevations, as shown also by the plots in Fig. 12. In this figure, the flow angles with respect to the y direction are computed along a line at x = 262.5 mm (the dashed white lines in Figs. 11a–c) from the data in the xy, xy1, and xy2 planes for both Ro = 0 and 0.23. In static conditions (Fig. 12a), the higher inertia of the core flow makes its redirection towards the TE exit less intense with respect to the slower boundary layer flow. Therefore, the flow angle in the xy plane is always bigger with respect to those detected in planes xy1 and xy2. For Ro = 0.23 (Fig. 12b), opposite trends are found: the smallest angles are detected in the core flow (plane xy) and slightly higher values than for Ro = 0 are found in planes xy1 and xy2. The commented deviation of the mean flow path has an impact on the flow distribution along the channel height. As an example, Fig 13 reports velocity profiles extracted from the yz plane at position

Fig. 12. Comparison of flow angles, a, for Ro = 0 (a) and 0.23 (b). Data extracted from measurement plane xy, xy1, and xy2 along a line at x = 262.5 mm.

y = 40 mm. Under rotation, Coriolis forces turn the velocity vector in the core flow towards y < 0. Consistently, an augmentation of the V velocity component and a reduction of the U one are observed about position z = 0 mm with respect to the static case (Fig. 13b and a). Because of momentum conservation, a pressure gradient normal to the core flow velocity vector and pointing towards y < 0 will arise. According to boundary layer theory, this pressure gradient acts also in the near wall region, where, in view of the lower intensity of Coriolis forces, it produces a flow acceleration along x direction, as clearly shown by the comparison of the U velocity profiles in Fig. 13a. The resulting streamwise velocity distribution is characterized by a twisted velocity profile (Fig. 13d and

Fig. 11. Time averaged stream-tracers and in-plane velocity modulus contour plots in the xy1 (a), xy (b), xy2 (c), and xz (d) planes for Ro = 0.23.

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Fig. 13. Comparison of velocity profiles characteristics for Ro = 0 and 0.23 extracted from plane yz at y = 40 mm: mean radial velocity U (a), mean axial velocity V (b), velocity modulus Cxyz (c), incidence angle a = atan(U/V) (d), velocity vectors distribution along the data extraction line (e).

e) with boundary layers far thinner than the ones observed for Ro = 0 (Fig. 13c). In the present case, because of the flow discharge along the TE, the mass flow redistribution due to rotation is not associated with the appearance of large and intense secondary vortices, as demonstrated by the stream-tracers path in Fig. 11d. It is important to notice that in this measurements set, a significant uncertainty in the W velocity is expected in view of its very low value (about 0.01 Ub). This explains, for example, the wavy path of the stream-tracers presented in Fig. 11d. Nevertheless, those data can still be used at least for a qualitative representation of the mean flow structure. Finally, the enhanced flow curvature commented in the central plane xy (Fig. 11b) justifies also the existence of a wider separation at the model tip with respect to the static case (see Figs. 5a and 8a). As a direct consequence of the rotational effects just commented, the flow angle of attack to the pedestals measured in the xy central plane (z = 0) is reduced when switching from static to rotating conditions, Fig. 6. This in turns makes the flow separation on the pedestals suction side less intense and smaller recirculation bubbles are observed in almost all the TE passages (Figs. 5a and 8a). A quantitative comparison is provided in Fig. 14, where V velocity profiles extracted from plane xy along a line at y = 150 mm for Ro = 0, 0.23 are shown. At this channel elevation (z = 0), a clear reduction of the extension of the recirculating flow region is reported for Ro = 0.23 in the first five inter-pedestal passages, together with a reduction of the V velocity values. For passages P6 and P7, the bubble size is about the same as for Ro = 0. Only for passage P8 a wider separation, and consistently an increased flow velocity, is detected with respect to the static case, in agreement with the higher angle of attack reported in Fig. 6. The rotational effects on the flow field just commented have also a remarkable impact on the flow turbulent statistics, provided

Fig. 14. Comparison of V velocity profiles for Ro = 0 and 0.23 extracted from plane xy at y = 150 mm.

for plane xy in Fig. 9b and c. With respect to the stationary case (Fig. 5b and c), lower values of both radial and axial fluctuations are found almost at every location of plane xy. More in detail, in the channel central portion the flow deviation commented about Fig. 13 is responsible for the lower u0 values with respect to the case for Ro = 0. The reduced flow angle of attack to the pedestals makes the flow separations downstream of the obstacles less intense, with a consequent reduction of the flow turbulence levels. This, with the exception of passage P8, where the flow angle of attack is higher than for Ro = 0, as already commented. Details of the mean inter-pedestals flow structure for Ro = 0.23 are reported in Fig. 15. In comparison with the data for Ro = 0

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Fig. 17. Time averaged stream-tracers and contour plots of radial (a) and axial (b) velocity fluctuations in plane xy1 and wall normal velocity fluctuations (c) in plane xz inside the 4th inter-pedestal passage for Ro = 0.23. Fig. 15. Time averaged stream-tracers and velocity contour plots inside the 4th inter-pedestal passage for Ro = 0.23.

(Fig. 7a and b), the mean flow turns out to be more aligned along the passage axis (Fig. 15a and b). This different behavior results from the combination of multiple effects, namely the reduction of the flow angle of attack to the pedestals (Fig. 6) and the Coriolis forces that divert the inter-pedestals flow towards x < 0. Moreover, in the near wall flow no evident traces of horse shoe vortices are found on the upstream side of the pedestal, as highlighted by the stream-tracers in plane xz of Fig. 15c. The reason of this has to be found in the velocity distribution of the flow approaching the pedestal. Indeed, the horse-shoe dimension is proportional to the extension of the boundary layer that approaches the junction region, where the structure is generated, Ballio et al. (1998). Under rotation, because of the rotational effects on the flow inside the channel central portion, the approaching flow is characterized by a more uniform streamwise velocity distribution and thinner boundary layers with respect to the static conditions (Fig. 16), so leading to much smaller and hardly detectable horse-shoes vortices (in Fig. 16, position y = 120 mm has been chosen because it is about the point where the streamline that impinges onto the

obstacle crosses the measurement plane yz, see Fig. 9a). Also by the visual inspection of the instantaneous flow fields no evidence of horse-shoe structures was found. Dedicated and very high resolution measurements will be necessary to detected such small flow features. Again, as it was for the flow in the channel central portion (Fig. 11d), no traces of secondary vortical structures due to Coriolis forces are detected by the stream-tracers path in plane xz (Fig. 15c). All the above observations are supported and confirmed by the velocity fluctuations maps shown in Fig. 17. An overall reduction of the turbulent activity can be observed with respect to the stationary case, Fig. 8. Again, no trace of horse-shoe structures can be found in the wall normal fluctuations map of Fig. 17c. In conclusion, in the inter-pedestals region the rotational effects determine the development of a more uniform flow, characterized by a strong reduction of both the separated flow regions and horse shoe vortices dimensions. Even if this ensures a more uniform distribution of the heat transfer coefficient over the channel surfaces, the enhancement factor due to the turbulent mixing associated to the horse shoe vortices will be lost, as it is predicted by the numerical analysis of Andreini et al. (2011b). 4. Conclusions

Fig. 16. Comparison of streamwise velocity profiles for Ro = 0 and 0.23 extracted from plane yz at y = 120 mm.

In the present study, the effect of rotation on the flow field inside a cooling channel for blade trailing edge has been experimentally investigated. The selected geometry is characterized by a trapezoidal cross section of high AR and by axial/radial flow paths with coolant discharge at both the model tip (10% of the inlet mass flow) and TE (90% of the inlet mass flow). The wedge-shaped TE channel portion is provided with seven elongated pedestals equally spaced. The tests have been carried out at Re = 20,000, Ro = 0, 0.23, with the channel width aligned along the peripheral velocity direction. The use of a filter installed at the channel exits guaranteed the imposition of similar pressure boundary conditions for both static and rotating cases. This was essential to allow a meaningful comparison between Ro = 0 and 0.23 data and to

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highlight rotational effects. Flow field measurements have been performed by means of 2D and Stereo-PIV techniques, applied in the absolute frame of reference. For the rotating tests, the relative velocity field was accurately retrieved from the absolute one thanks to the implementation of a PIV image pre-processing procedure, described in the paper. The analysis of the data for Ro = 0.23, in comparison with the data for Ro = 0, allow to highlight remarkable rotational effects that can be summarized as follow:  At the channel inlet, inviscid flow effects cause the flow to be strongly imbalanced toward the upwind side of the duct, so opposed to the expected flow redistribution due to Coriolis forces only. The high AR of the channel cross-section is the main reason for this flow behavior.  Inside the channel central region, Coriolis effects, being stronger in the core flow, produce a twisted velocity profile along the channel height: the core flow is more diverted towards the channel TE while the near wall flow is accelerated along the radial direction with a consequent reduction of the boundary layer thickness.  Inside the TE region, local Coriolis effects coupled with those observed in the channel central portion, make the inter-pedestals flow more uniform and substantially aligned along the axial direction. The reduction of the separated flow region downstream of the pedestals is a direct consequence of the twisted velocity profile approaching the obstacles. On the pedestals upstream faces, the thinner boundary layers do not promote the development of the large horse shoe vortex branches found for Ro = 0.  Because of the flow discharge at the TE, rotation induced Coriolis vortices are not detected in the channel cross section. On the basis of the present results, rotational effects are expected to alter mainly the heat transfer field inside the TE channel portion, where a more uniform distribution of the heat transfer coefficient with lower maxima should be found. The results of this study, besides improving the overall understanding of the rotational effects inside innovative trailing edge cooling passages, provide also a useful data base for the validation of CFD codes on a challenging test case. Acknowledgment The present work has been supported by the Italian Ministry of University and Research (MiUR). References Andreini, A., Bianchini, C., Armellini, A., Casarsa, L., 2011a. Flow field analysis of a trailing edge cooling channel. ASME paper GT2011-45724, ASME Turbo Expo 2011, June 6–10, 2011, Vancouver, Canada. Andreini, A., Bianchini, C., Facchini, B., 2011b. Numerical analysis of the heat transfer in a trailing edge cooling duct in stationary and rotating conditions. In: 9th European Turbomachinery Conference, 21–25 June, Istanbul, Turkey. Armellini, A., Casarsa, L., Giannattasio, P., 2009. Separated flow structures around a cylindrical obstacle in a narrow channel. Experimental Thermal and Fluid Science 33, 604–619. Armellini, A., Coletti, F., Arts, T., Scholtes, C., 2010. Aero-thermal investigation of a rib-roughened trailing edge channel with crossing-jets Part I: Flow field analysis. Journal of Turbomachinery 132 (1), 011009-1–011009-9. Astarita, T., Cardone, G., 2005. Analysis of interpolation schemes for image deformation methods in PIV. Experiments in Fluids 38, 233–243. Ballio, F., Bettoni, C., Franzetti, S., 1998. A survey of time-averaged characteristics of laminar and turbulent horseshoe vortices. Journal of Fluids Engineering 120, 233–242. Bons, J.P., Kerrebrock, J.L., 1999. Complementary velocity and heat transfer measurements in a rotating turbine cooling passage. Journal of Turbomachinery 121, 651–662.

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