Secondary flow vortices and flow separation of 2-D turning diffuser via particle image velocimetry

It is often necessary in fluid flow systems to simultaneously decelerate and turn the flow. This can be achieved by employing turning diffusers in the fluid flow systems. The flow through a turning diffuser is complex, apparently due to the expansion and inflexion introduced along the direction of flow. In the present work, the flow characteristics of 2-D turning diffuser by means of varying inflow Reynolds number are investigated. The flow characteristics within the outlet cross-section and longitudinal section were examined respectively by the 3-D stereoscopic PIV and 2-D PIV. The flow uniformity is affected with the increase of inflow Reynolds number due to the dispersion of the core flow throughout the outlet cross-section. It becomes even worse with the presences of secondary flow of 22% to 28%. The secondary flow vortices occur almost the same scale at both left and right sides of the outlet. The flow separation takes place within the inner wall region early on half of the inner wall length and is gradually resolved with the increase of inflow Reynolds number.


Introduction
Turning diffuser is often introduced in fluid flow systems either as an adaptor or ejector to simultaneously decelerate and turn the flow. It is characterised by expansion directions namely two dimensional (2-D) turning diffuser and three dimensional (3-D) turning diffuser [1,2,3]. A geometric layout of a 90 o turning diffuser is shown in Figure 1. A 2-D turning diffuser expands its cross-section in either x-y or y-z axis plane, whereas a 3-D turning diffuser expands its cross-section in both x-y and y-z planes.
Chong et al. [4] designed a 90 o turning diffuser with quadrants of circles at both the inner wall and centerline. The outer wall was shaped using circular arcs with the centers placed along the centerline and the circumferences tangent to the inner wall. It was designed such that equal area distributions were established between the inner and outer wall passages relative to the centerline. The gross geometry of a turning diffuser could be described in terms of four parameters, namely, the inner wall length to the inlet throat width ratio (Lin/W1), the outlet area to the inlet area ratio (AR) , the outletinlet configurations (W2/W1, X2/X1) and the turning angle () [5].
The flow through a 90 o turning diffuser is complex, apparently due to the expansion and sharp inflexion introduced along the direction of flow. The inner wall was subjected to curvature-induced effects where under a strong adverse pressure gradient, the boundary layer on the inner wall was likely to separate, and the core flow tended to deflect toward the outer wall region [2,6]. Flow separation was basically undesirable as it would decrease the core flow area, induce the presence of secondary   [4]. The flow uniformity index (out) is used to measure how much the dispersion of local oulet velocity from the mean outlet velocity exists. The out was strongly dependent on the dispersion of core flow, y and the presence of secondary flow, Sout throughout the outlet cross-section [7].

Instrumentation and measurement setup
The test rig shown in Figure 2(a) was developed. A centrifugal blower controlled using a 3-phase inverter and calibrated previously by [8] was installed at the upstream end. The rig incorporated with several wind tunnel features to produce a fully developed flow at the diffuser entrance [9]. The test section, with inlet cross-section of 13 cm x 5 cm and hydrodynamic entrance length of 28Dh featured no fittings.
The outlet flow uniformity was examined using a 3-D stereoscopic PIV shown in Figure 2(b). The measurement procedures are as follows: i. Two CCD cameras were mounted on top of the target plane while their distance and angle (30 o ) were adjusted until both cameras could capture the target plane entirely. ii. The laser was calibrated to provide a perfect illumination and aligned to the target plane for marking. iii. Calibration for 3-D stereoscopic PIV was performed as follows: a. The standard calibration target board of 200 mm x 200 mm was aligned to be parallel to the marked target plane, i.e. the first position. b. The cameras were traversed to the calibration target. The zoom and aperture of each camera were adjusted optimally. c. The CCD plane of each camera was tilted to satisfy the Scheimpflug condition, to provide best possible focus over the entire image. d. The cameras were run in single frame mode and satisfactory calibration images were acquired and saved for calibration. e. The target board was re-positioned by inclining 10 o each its side at a time, i.e. the other four positions. f. Steps 3 (d) and (e) were repeated until all the positions completed. g. The recorded calibration images were selected and Image model fit (IMF)-Pinhole was adopted. h. A successful calibration was verified by superimposing the calibration IMF plots to the corresponding calibration images. The accurate calibrations should provide the average reprojection error of less than 1. i. The calibrated cameras were traversed back to the target plane. iv. The blower was turned on with the speed regulated to 9 RPM. Seeding particles were injected into the system. Measurements were made after 5 minutes to allow complete mixing between the air and the seeding particles. v. The laser sheet was illuminated at the target plane with the thickness of 20 mm and the intensity of 10. The target plane was placed exactly at the center of the laser sheet. vi. The cameras were run in double frame mode. The time between pulses was set at 20µs. 100 images per camera were acquired and saved. vii. The images were divided into interrogation areas of 128 x 128 pixels. The 2-D velocity vectors, i.e. Vx and Vz velocity components were calculated using cross-correlation. viii. The 2-D velocity vectors were filtered and subsequently masked to remove the unreasonable vectors. ix. The IMF calibration plots and the best 40 treated 2-D vector plots from both cameras were selected. The 3-D velocity vectors, i.e. Vx, Vy and Vz were computed using stereo PIV processing. The 3-D vector plots were selected and the local outlet velocity, Vi and mean oulet velocity, Vout were then calculated using vector statistics. x. The results were numerically and graphically extracted. xi. For verification, the third velocity component, Vy obtained by PIV was picked randomly at one point and compared with the Pitot static probe result. xii. Procedure vi-xi was repeated by varying the time between pulses at 30µs, 50µs, 70µs, 90µs and 110 µs. The most optimum time between pulses should provide the least deviation between the PIV and Pitot static probe results. The confidence interval of the measured data to the repeatability of the experiments is within ±3.9% [10]. xiii. Procedure iv-xiii was repeated by varying the blower speeds from 10, 15, 20 to 25 RPM. xiv. The blower was turned off.
A 2-D PIV setup as shown in Figure 2(c) was used to examine the flow characteristic at the center plane within the longitudinal section. The measurement procedures are as follow: i. The camera was arranged to be perpendicular to the target plane and its distance from the target plane was so adjusted that the target plane could be entirely captured. ii. The laser was calibrated to provide a perfect illumination and aligned to the target plane for marking. iii. Calibration for 2-D PIV was performed as follows: a. The standard calibration target board 200 mm x 200 mm was aligned to be parallel to the marked target plane, i.e. the centre target plane. b. The camera was traversed to the calibration target. The zoom and aperture of the camera were adjusted optimally. c. The camera was run in single frame mode and a satisfactory calibration image was acquired and saved for calibration. d. The recorded calibration image was selected and Image model fit (IMF)-DLT was adopted. e. A successful calibration was verified by superimposing the calibration IMF plot to the corresponding calibration image. The accurate calibration should provide the average reprojection error of less than 1. f. The calibrated camera was traversed back to the target plane. iv.
The blower was turned on with the speed regulated to 9 RPM. Seeding particles were injected into the system. Measurements were made after 5 minutes to allow complete mixing between the air and the seeding particles. v.
The laser sheet was illuminated exactly at the target plane with the thickness of 2 mm and the intensity of 10. vi.
The camera was run in double frame mode. 100 images were acquired and saved. vii.
The images were divided into interrogation areas of 64 x 64 pixels. The velocity vectors within the turning diffuser were calculated using cross-correlation. viii.
The velocity vectors were filtered and subsequently masked to remove the unreasonable vectors. The best 40 treated velocity vector plots were selected. ix.
The results were numerically and graphically extracted. x.
Steps iv-ix were repeated by varying the blower speeds of 10, 15, 20 and 25 RPM. xi.
The blower was turned off. The flow uniformity index (out) was evaluated by calculating the mean standard deviation of outlet velocity. The least absolute deviation corresponds to the greatest uniformity of flow [11]:  where, Vy = velocity in y-direction (m/s) Vy avg = average velocity in y-direction (m/s) Secondary flow index (Sout) represents the percentage of secondary flow at the outlet. The outlet velocity is considered uniform only if secondary flow magnitude at the outlet is less than 10% of the mean outlet velocity [7]:

Results analysis and discussion
Contours as depicted in Figure 3 exhibit the characteristic of the outlet flow. The core flow that is in ydirection is represented by colour-coded. Whereas, the secondary flow that is in x-and z-direction is represented by vector-arrows. In general, each contour shares almost the same characteristic with the rapid flow mostly occurring within the outer wall region and the flow deficit is seen to happen within the inner wall region. There are presences of swirling secondary flow vortices throughout the outlet cross-section and reverse core flows close to the inner wall region in each case. Velocity profiles are extracted across the center of turning diffuser outlet at two (2) different planes. As depicted in Figure 4, the profiles are obtained to be asymmetric in each case. In Plane A, the flows deflect much toward the outer wall due to the existence of reverse core flows within the inner wall region. In Plane B, the flows distort at both left and right sides of the outlet relative to the center. This implies the existences of almost the same scale of secondary flow vortices at both left and right sides of the 2-D turning diffuser outlet relative to the center.
The out is affected with the increase of Rein as indicated in Table 1  inner wall region may occur under a very strong pressure gradient and these not only incur unfavorable flow performance but also considerable losses associated with form drag [13,14].
Vector plots, as in Figure 5, demonstrate the flow structures within the longitudinal section of turning diffuser taken at the center plane. Since the flow structures of each case are almost the same, in order to avoid repetition, only the flow structures of minimum and maximum Rein are included in the paper. The 2-D turning diffuser is subjected to extensive flow separation at minimum Rein where the separation takes place early on half of the inner wall length, S = 0.5Lin/W1. The scale of flow separation however reduces at maximum Rein where the separation takes place later at S = 0.7Lin/W1.

Conclusion
In conclusion, the current work manages to investigate the flow characteristics of 2-D turning diffusers by means of varying Rein = 5.786 x 10 4 -1.775 x 10 5 . The flow uniformity is affected with the increase of Rein mainly because of the dispersion of the core flow throughout the outlet cross-section. It becomes even worse with the presences of secondary flow, 22% to 28% of the mean outlet velocity. The secondary flow vortices occur almost the same scale at both left and right sides of the outlet relative to the center. The flow separation takes place within the inner wall region early on half of the inner wall length and is remedied with the increase of inflow Reynolds number.