Volumetric measurement of turbulence and flow topology in an asymmetric diffuser

The turbulent flow in a three-dimensional asymmetric diffuser was experimentally investigated using time-resolved, three-dimensional particle tracking velocimetry (3D-PTV). The diffuser geometry chosen for this study was a benchmark geometry devised and studied experimentally by Cherry et al. [Intl. J. Heat Fluid Flow 29, 3 (2008)], with a few subsequent numerical simulations at a Reynolds number of 10 000. In the present paper, we applied a state-of-the-art 3D-PTV to measure the 3D structure of the flow field in the entire diffuser for five Reynolds numbers (Re), ranging from 9200 up to 29 400. We found that the mean velocity fields were qualitatively similar across all Re studied. The volumetric fraction of the backflow region, when quantified using an intermittency factor of $\gamma <$ 0.8, was in the range of 11–14%, with a marginal decrease with increasing Re. The maximum values of normal and shear Reynolds stresses were located in the regions close to the edge of the backflow region, and the peak values for the streamwise normal Reynolds stress increased with Re. The corner vortices, which formed in the channel preceding the diffuser, showed the existence of secondary flow well within the diffuser region. The strength of these vortices reduced with increasing Re. A modal decomposition of the turbulent fluctuations using spectral proper orthogonal decomposition (SPOD) showed large-scale structures in the flow. The SPOD analysis revealed that these large-scale structures were associated with low frequency oscillations in the band of St = [0.003 0.03], with two frequency peaks at St = 0.012 and 0.028. The three-dimensional separation along the two diverging walls of the diffuser was characterized by detecting critical points in the near-wall streamlines. These critical points were investigated in relation to three large-scale vortical structures identified within the diffuser. The flow topology in the diffuser showed that two of these vortical structures originated from the wall with the largest diverging angle and were connected by a separation surface. The third vortical structure originated from the neighboring diverging wall and was bound by another large separation surface.

Figure 1

Schematic showing the diffuser geometry studied in the present paper. The geometry is identical to the one devised by Cherry et al. [9]. The different views shown here are (a) top, (b) isometric, (c) front, and (d) side view.

Figure 2

Schematic showing an outline of the flow conditioning and diffuser sections used in the present paper. The flow loop also consists of a reservoir and a pump that are omitted from the schematic for clarity.

Figure 3

A schematic of the experimental setup used for (a) planar PIV and (b) 3D-PTV measurements. The coordinate axes used are as shown in the figure. In (a), a laser sheet is directed along the $xz$ plane to illuminate the midplane ($y/h$ = 1.65) for both FOV 1 and FOV 2. In (b), the FOV shown is illuminated using volumetric expansion of the laser beam.

Figure 4

Instantaneous particle tracks for the Re = 9200 case. The particle tracks shown here are from five successive time instants, with the time step being 0.66 ms at 1.5 kHz. The particles are color coded using their streamwise velocity magnitudes.

Figure 5

(a) Near-wall log law for different Re cases, with Re = 9200 ($\mathrm{\Delta }$), 14 400 ($\circ$), 19 200 ($\square$), 24 000 ($\diamond$), 29 400 ($\mathbf{\nabla }$). (b) Reynolds stress components for different Re. The normal stresses $〈u^2〉$ and $〈w^2〉$ are denoted by circles and triangles, respectively, whereas the shear stress $〈uw〉$ is denoted by squares. The different Re values shown are 9200 ($black$), 14 400 ($blue$), 19 200 ($red$), 24 000 ($green$), and 29 400 ($magenta$).

Figure 6

Streamwise velocity contours from 3D-PTV measurements. The cross section shown is at approximately $4h$ before the diffuser throat.

Figure 7

Isosurfaces showing streamwise velocity for the Re = 9200 case. The isosurfaces shown here are at $〈U〉/U_b$ = 0.8 (blue) and $-0.03$ (red).

Figure 8

Mean flow contours of streamwise velocity for the Re = 9200 case. (a) shows an $xz$ section at the $y$ center plane of the diffuser section. The zero velocity contour is shown as a thick solid line. The mean streamwise velocity profiles at six different streamwise locations are superimposed on the velocity contour plot, along with the velocity profiles (red dots) at $x/h$ = 8 and 12 from the DNS of Ohlsson et al. [11]. The inset of (a) shows the same plot from planar PIV measurements. The cross-flow ($yz$) slices at three different streamwise locations are shown at $x/h$ = (b) 2, (c) 8, and (d) 12.

Figure 9

The streamwise location of the separation point ($x_s$) in the $y/h$ = 1.65 plane as a function of Re. The dotted line is a linear fit to the data.

Figure 10

Contours of the intermittency factor $\gamma$ for the Re = 9 200 case. (a) shows an $xz$ section at the $y$ center plane of the diffuser section, and the inset shows the same measurements from planar PIV. The cross-flow sections at three different streamwise locations are shown at $x/h$ = (b) 2, (c) 8, and (d) 12.

Figure 11

Contours of intermittency factor ($\gamma$) for Re = 19 300 and 29 400 cases at different cross-flow sections. (a)–(c) are for Re = 19 300 at $x/h$ = 2, 8, and 10, respectively. (d), (e) are for Re = 29 400 at $x/h$ = 2, 8, and 10, respectively.

Figure 12

The volume fraction of the diffuser section with $\gamma <$ 0.8 as a function of Re. The dotted line is a linear fit to the data.

Figure 13

(a) Isosurfaces showing streamwise vorticity $〈{\omega }_x〉$ = $\pm$ 0.1 ${\mathrm{s}}^{-1}$ contours. The colors red and blue signify negative and positive signs, respectively. (b) Cross-flow section at $x/h$ = 12 showing in-plane streamlines superimposed on streamwise vorticity contours to highlight the secondary flow patterns.

Figure 14

The variation of the averaged peak streamwise vorticity of the secondary flow as a function of Re. The vorticity $〈{\omega }_x〉$ is normalized by the bulk flow velocity ($U_b$) for each Re and the diffuser inlet width ($h$). The dotted line is a linear fit to the data.

Figure 15

Reynolds stress contours of $〈u^2〉/U_b^2$ for Re = 9200. (a) The $xz$ plane at the center plane of $y/h$ = 1.65. Also shown in the inset below are the $〈u^2〉/U_b^2$ contours obtained from planar PIV measurements. The cross-flow slices at three different streamwise locations at $x/h$ = (b) 2, (c) 8, and (d) 12 are also shown.

Figure 16

The peak value of $u_{\text{rms}}/U_b$ as a function of Re. The peak value is detected at a streamwise cross section of $x/h$ = 12 for all Re. The dotted line is a linear fit to the data.

Figure 17

The contours of $〈uw〉$ and $〈uv〉$ of the Reynolds stress tensor. (a)–(c) $〈uw〉/U_b^2$ contours at $x/h$ = 2, 8, and 12, respectively. (d)–(f) $〈uv〉/U_b^2$ at $x/h$ = 2, 8, and 12, respectively. The Re is 9200 in each case.

Figure 18

(a) Averaged PSD plot of 15 probes located at several points in the region bounding the separation bubble. Each streamwise location at $x/h$ = 8, 9, 10, 11, and 12 has three probes at $y/h$ = 1, 1.5, and 2. The $z$ location of all the probes is at $2h$. (b) Averaged PSD plot of six probes located at $x/h$ = 7, 8, 9, 10, 11, and 12, at $y/h$ = 2.1 and $z/h$ = 1.1. These probe locations are approximately located near the peak forward flow region at each streamwise location.

Figure 19

Mode energy spectrum of different modes normalized with the total energy. The fractional mode energy of each mode is shown in the legend.

Figure 20

Spatial organization of mode 1 at Strouhal numbers of (a) 0.003, (b) 0.012. The isosurfaces represent normalized mode magnitude at ${\phi }_i$ = 0.0075 (blue) and ${\phi }_i$ = $-0.0075$ (red).

Figure 21

The streamlines of the mean flow near wall 1 and wall 2 at Re = 9200. Also shown here are the normalized mean streamwise velocity contours.

Figure 22

The in-plane streamlines of the mean velocity at Re = 9200 for planes parallel to wall 2 and wall 1, shown here in the top and bottom sections in each subfigure, respectively. The different planes shown here are at a wall-normal distance of (a) 0.2 $h$, (b) 0.3 $h$, (c) 0.4 $h$, and (d) 0.65 $h$ from their corresponding diverging walls.

Figure 23

A 3D schematic of the structures observed in the near-wall regions of the two diverging walls.

Figure 24

Statistical convergence of all three components of velocity, and three Reynolds stress components are shown for the Re 9200 case. Each variable is normalized with the bulk flow velocity. The bin size is 5 mm in the streamwise ($x$) direction and 1.5 mm along the cross-flow ($y$ and $z$) directions. The center of the bin is located at $x/h$ = 10 and $y/h, z/h$ = 1.6. The $x$ axis is normalized with the total number of particles ($N$) in the bin.