Figure 1 presents the schematic of the experimental rig and the PIV system employed in this study. The test tube was manufactured with an acrylic pipe (d = 54 mm, L = 770 mm) 3.0 mm thick. Two baffles (3 mm thick) were installed in the test tube with 13% of the cutoff ratio (approximately 7.02mm). The detailed diagram of the test tube is shown in Figure 2, which has flow direction, such as parallel and counter flows. A swirl generator with tangential slots was employed to produce swirling flow. For the without-swirling flow generation, the swirl generator was taken out and replaced with honeycombs to produce uniform flow.

Figure 1: 
Schematic of the apparatus and PIV system

Figure 2: 
Schematic of the test tube

The flow rate was measured by employing a flow meter installed at the outlet of the main pipe. The Reynolds number (Re) with the diameter of the main pipe was 7,200 to 14,000. The measurement region X is the horizontal direction of the vertical pipe, Y the vertical direction, and Z the out-of-plane direction. Given that the test tube was circular, the images captured by the two cameras were strongly distorted. Thus, a square box was installed outside the circular tube and water was filled in the empty space between the circular tube and the square box to reduce such effect.

Two digital high-speed cameras (Basler 2.3 k × 1.7 k, 250 fps) with lenses (60 mm, MICRO NKKOP) were used for stereoscopic measurements and arranged as shown in Figure 1.

The flow field was visualized with a continuous laser light sheet (thickness = 2 mm to 3 mm) (Ar–ion laser, 2 W). The two cameras were horizontally installed, maintaining 30° angles toward the measurement area. The seeding particles (nylon, d = 100 μm) were suspended in the working fluid (water) for PIV measurements and added at the entrance of the main pipe (d = 54 mm, L = 770 mm). The particle supply was made through a small hole (d = 5 mm) at the main pipe, whereas the working fluid was not circulated by the pump.

Camera calibration should be performed before the main experiments to enable 3D measurements with the two-camera system. The calibrator is a flat plate (50 mm × 50 mm) on which grid lines are formed with regular intervals of 10 mm lines. This plate was traversed back and forth to the direction of the camera lens so that the grid images at six locations can be obtained. This plate was traversed inside of the test tube to consider the refractive indexes of the working fluid (water) and the acrylic walls. To perform this process, a cover on the circular cylinder tube was installed. During the main experiments, the cover was completely closed to prevent any leakage of water.

The calibration method and 3D measurement algorithms developed by Doh et al. [13] were used for camera calibration and stereoscopic PIV measurements. Equation (1), the collinear equation, was used for 3D calculations, where cx and cy are the focal distances for the x and y components of the coordinate; Δx and Δy are the lens distortions; l refers to the distance between the origin O (0, 0, 0) and the principal point (X0, Y0, Z0 ) of the camera; (x, y) represents the photographical coordinate of the image centroid of the calibration targets; (Xm, Ym, Zm) represents the point P position of the calibrator when the the photographical (camera coordinate) and physical coordinates are set in a collinear line after rotation with tilting angles mx and my, which correspond to the point at which the normal vector from the origin O (X0, Y0, Z0 ) of the camera coordinate meets with the X–Y plane. Equation (1) has 10 unknown parameters, specifically 6 exterior parameters (l, mx, my) and 4 interior parameters (cx, cy, k1, k2). The regression method by Doh et al. [13] was adopted to calculate these 10 unknown parameters.

After all unknown camera parameters were calculated, the relations between the photographic (camera coordinate) and absolute coordinates (physical coordinate) of the target or particle image can be expressed through Equation (2), where (X, Y, Z) represents the absolute coordinate of the target position P in the photographic coordinate. The matrix MM used for rotational transformation contains the 10 unknown parameters.

When the camera center is set to a vector (X0,Y0,Z0), the collinear equation for one object(or particle) can be expressed as P(X, Y, Z)=(a_Jq+X₀,a₂q+Z₀), where q is an arbitrary vector and a₁, a₂, and a₃ represents the corresponding terms that can be reconstructed from Equation (3). The cross-section position constructed from the following two collinear equations for the two cameras were defined as the 3D positions in the absolute coordinate.

t and s were obtained by the least square method. The coefficients (a₁₁, a₁₂, a₁₃) and (b₁₁, b₁₂, b₁₃) represent the corresponding terms that can be reconstructed from Equation (2) for camera 1, whereas (a₂₁, a₂₂, a₂₃) and (b₂₁, b₂₂, b₂₃) for camera 2. The cross-sectional points do not always intersect at one point because of measurement uncertainties. Therefore, the center of the shortest distance between the two collinear equations was used as the final 3D position of the object defined as Equation (4).

where XA, YA, and ZA represent the absolute coordinates for Camera A defined by Equation (3), and XB, YB, and ZB represent the absolute coordinates for Camera B. After obtaining the positions of the vector grid points (vector start points), the 3D vector terminals were obtained by vector addition with the two sets of two-dimensional vector terminals obtained by the same method used by Cho et al. [14], who adopted the gray-level cross-correlation method (Kimura et al., 1986). The Gaussian fitting method (Huang et al., 1997) was also adopted to attain the sub-pixel resolution. The interrogation size for the correlation calculation was set to 32 × 32 and the calculation grid to 42 × 21.

The measured velocity components U, V, and W were defined as the horizontal, vertical, and azimuthal components, respectively. The measured velocities were normalized with time mean velocity calculated from the flow rate.

Figure 3 shows the raw image of particles at the entry of the front baffle without swirling flow. The calculated velocity vectors of the particles are shown in Figure 4 for the parallel flow at Re = 7,200. The movement of particles is slightly slow along the tube wall and near the baffle, but faster at the upper opening of the front baffle. The baffle is considered a barrier to the flow of the particles. Figure 4 demonstrates the velocity vectors of particles between the test tube and the front baffle. The vector profiles are concentrated on the upper opening of the front baffle and then rapidly passed through the gap.

Figure 3: 
Raw image of particles at the entry of the front baffle without swirl for parallel flow at Re = 7,200.

Figure 4: 
Velocity vectors of the entry of the front baffle without swirl for parallel flow at Re = 7,200

Figure 5 shows the raw image of the particles between two baffles without swirl for the parallel flow at Re = 7,200. The particles are slightly faster at the outlet of the upper opening of the front baffle, and then moved down near the rear baffle to pass through its lower opening. However, some particles moved to the opposite side of the rear baffle, making weekly bigger circles between the two baffles.

Figure 5: 
Raw image of particles between two baffles without swirl for parallel flow at Re = 7,200.

The movement of the particle flow from the opening of the front baffle is considered fast.

Figure 6 shows the local velocities of the particles between the two baffles without swirl. As expected, the axial velocity is bigger than the tangential and radial velocities near the opening. In this velocity, the particles move fast from the outlet of the upper opening of the front baffle. However, the axial velocity decreases along the X and the velocity indicates negative and then increases when the particles move to the lower opening of the rear baffle or circulate between two baffles. Further more, the tangential and radial velocities between two baffles do not significantly change, except for the surrounding of the opening of the rear baffle.

Figure 6: 
Velocity profiles between two baffles without swirl for parallel flow at Re = 7,200

Figure 7 is demonstrated axial velocities along with y varying for without swirl flow at Re=7,200. The axial velocity profile near upper wall(y=-796) is showing positive values, but they are slowly decreased along with the distance of x. But, the velocities are very fluctuated at y=0.232(near the center line), it is considered the recirculating flow between two baffles. However, this values are increased near the opening of the rear baffle for exhausting through it.

Figure 7: 
Comparisons of axial velocity with varying y without swirl at Re=7,200

Figure 8 shows the local velocity profiles for the counter flow without swirl. The axial velocities showed higher values at the outlet of the lower opening, and then steeply decreased between two baffles. However, the values increased near the rear baffle. The tangential and radial velocities gradually increased along the distance of the two baffles. In comparisons with two Figs, the whole contour of velocities profiles are not much changed except tangential velocity.

Figure 8: 
Velocity profiles between two baffles without swirl at y = −0.388 for the counter flow Re = 7,200