(a) Sketch of the experimental setup, showing schematically the scanning of the laser volume. (b) Photograph showing the arrangement of the high-speed video cameras and the calibration plate inside the tank. For sharp images the calibration plate is illuminated with four fiber-optic lights. The laser volume illumination shines from the left towards the cameras.
Comparison of a particle image density from a single illuminated volume (left) and the sum of all 9 volumes (right) acquired using the double-pulse protocol. The horizontal extent of each image is approximately 20 mm along the centerline of the jet.
A simple example of ghost particle population growth with increasing light sheet thickness for a simple 2 camera system with homogeneous seeding density. Black filled circles represent the hypothetical locations of real particles while red hollow circles correspond to locations where ghost particles may be generated due to reconstruction ambiguity.
The four different mirror scanning profiles used in the experiments, sampled using a Tektronix DPO 7254 Digital Oscilloscope, (a) 9 plane double-pulse, (b) 5 plane triple-pulse, (c) 5 plane fast-scan and (d) 5 plane double-pulse. The vertical axes correspond to the amplitudes of scanning signals inputted to the galvano-mirror. The 5V trigger signals of the pulsed-laser (seen here as impulse trains) are rescaled to fit the axes and superimposed to highlight the coordination between the mirror location and the image acquisition during scanning.
Average reconstructed particle intensity across a scanning volume. The intensity of reconstructed particles outside the light sheet is about 50% of the level inside the sheet (the average level inside is shown with a red line), indicating a signal-to-noise ratio of about 2.
Contours of the joint PDFs of select components of ∇ · V for cube sizes (left to right) of W, 2W, and 4W. (a) Data correspond to the Re = 10 700 case with 20 contour levels ranging from (left to right) 0.01–0.07, 0.01–0.2, and 0.01–0.6, respectively. (b) Data correspond to the Re = 2, 640 case with 20 contour levels ranging from (left to right) 0.01–1, 0.01–2, and 0.01–7, respectively. Divergence free data lie along the 45° line. The distributions are highly peaked at the origin. ΔX, ΔY, and ΔZ represent the dimensions of the cubes used to generate each ensemble, while V x , V y , and V z are the velocities averaged on the cube surfaces.
(a) PDF of divergence error, ξ, as proposed by Zhang et al. 6 (data curves are highly overlapping) (b) PDF of ∇ · V normalized by the 2-norm of the velocity gradient tensor. Blue and red lines correspond to the Re = 10 700 and Re = 2640 cases, respectively.
Contours of the joint PDF of the 2-norm of the velocity gradient tensor and the normalized divergence residual for cube sizes (left to right) of W, 2W, and 4W. (a) Data correspond to the Re = 10 700 case with 20 contour levels ranging from (left to right) 0.01–0.2, 0.01–0.6, and 0.01-1.2, respectively, and (b) data correspond to the Re = 2640 case with 20 contour levels ranging from (left to right) 0.01–1, 0.01–1.7, and 0.01–5, respectively.
Vorticity magnitude PDFs scaled by the RMS vorticity, ω′, for Re = 10700 experiments using different optical magnifications. The statistical ensembles for both PDFs were extracted from the same subsections of the jet, between 1 and 1.5 half-widths (r half ).
(a) Axial mean contours for Re = 10 700 where 9 scanning volumes were employed. (b) Axial mean contours for Re = 2640 where 5 scanning volumes were employed. Green lines represent the interfaces between the assembled reconstructed particle images and red lines represent the extents of the reconstructed domains for both cases.
(a) (Left to right) axial, radial and azimuthal RMS profiles for Re = 10 700, (b) (left to right) axial, radial, and azimuthal RMS profiles for Re = 2640. One component of the Reynolds stress tensor for (c) Re = 10 700 and (d) Re = 2640. Black data points are scanning-TPIV results while red and green data points correspond to hot-wire 23 and stereo-PIV 25 data, respectively.
(a) 2D projection of a 483 vox region of the reconstructed particle image for the full illuminated domain (see Fig. 2(b) ), (b) 2D projection of the same 483 vox region using a scanning protocol, (c) comparison of mean axial velocity profiles across the jet for the fully illuminated (red) and scanning (black) cases highlighting the failure of full volume illumination.
Instantaneous iso-surfaces of coherent structures, identified using four different methods, of (a) vorticity magnitude, ω = 11 s−1, (b) Δ = 20 s−3/2, (c) λ2 = −28 s−2, and (d) Q = 800 s−2. Data correspond to Re = 2640.
(a) Three snapshots of Re = 2640 time-series data over a 0.35 s interval with vorticity magnitude iso-surfaces ω = 11 s−1. Each snapshot is separated by three time steps (0.17 s) to highlight the evolution of the loops. A collection of loops are highlighted with red dashed lines. (b) Vorticity magnitude iso-surfaces for Re = 5280 (left) and Re = 10 700 (right) with values of ω = 21 s−1 and 35 s−1, respectively. A large intense hairpin loop is highlighted for the Re = 10 700 case (red rectangle). (c) Vorticity magnitude iso-surfaces for (left to right) Re = 2640, Re = 5280 and Re = 10 700 with iso-surface values of ω = 11, 21, and 35 s−1, respectively. The views are orthogonal to the scanning direction for each case. The red lines in each image indicate the extent of the reconstructed domains, while the green lines indicate the intersection between adjacent reconstructed scanning volumes (enhanced online). [URL: http://dx.doi.org/10.1063/1.4790640.1] [URL: http://dx.doi.org/10.1063/1.4790640.2]doi: 10.1063/1.4790640.1.
(a)-(h) Evolution of a single “C-shaped” structure for the Re = 10700 case over a 0.15 s interval, with 0.022 s between subsequent snapshots.
Comparison of data quality for velocity calculation using different final correlation window sizes (left to right), 483, 363, and 323 voxels with 75% overlap in each case. These correlation window sizes deliver 1 × 106, 2.2 × 106, and 3 × 106 vectors, respectively. A few equivalent coherent structures are highlighted in red in each image.
Evolution of vortical loops (green vorticity isosurfaces with ω = 11 s−1) and instantaneous Reynolds stress v axial v radial for Re = 2640. Each snapshot of the sequence is separated by 5 time steps (0.29 s) for a total interval of 0.58 s. A positive isosurface value of Reynolds stress is shown in red (v axial v radial = 4 × 10−5 m2/s2) while the blue isosurfaces correspond to a negative value (v axial v radial = −1.5 × 10−5 m2/s2). The yellow arrows in the final frame highlight the approximate direction of fluid flow resulting from intense vortex induction caused by the concentrated vorticity in the loops highlighted with dashed-lines (enhanced online). [URL: http://dx.doi.org/10.1063/1.4790640.3]doi: 10.1063/1.4790640.3.
Instantaneous production, P inst , and dissipation, ε inst , of turbulence kinetic energy in the vicinity of the vortical loops for Re = 2640. The loops are visualized with ω = 11s−1 (shown in green). Intense production, presented here with iso-surfaces of P inst = 5 × 10−5 m2/s3 (shown in blue) is seen to occur in the center of the vortical loops (see loops numbered 1,2,3,4) in regions of strong vortex induction. Intense dissipation (iso-surfaces of ε inst = 1.4 × 10−5 m2/s3 shown in red) is also large in between the legs of the loops (loops numbered 2,3,4). The high levels of production and dissipation in general occur quite close to the loops and appear to embrace the intense vorticity iso-surfaces.
Distribution of 15 extracted vortex cores (numbered) from Re = 5280 data. The cores are followed over a 40 time step interval. The mean flow axis is displayed with a black arrow. The panels show two perpendicular views and one perspective view of the same collection of cores. The interfaces between each reconstructed scanning volume are shown with broken red rectangles while the solid rectangles lines represent the extent of the domain.
(a) Visualization of the evolving shape of a tube-like structure for 12 consecutive time steps for Re = 2640 data. The structure is advecting from left to right with the green structure indicating the first in the sequence followed by alternating red and blue for clarity. (b) Streamlines of the fluctuating component of the velocity field for the evolving structure. The dashed lines indicate the interface separating two scanning volumes while the solid black arrow indicates the direction of the axial mean flow.
(a) The fluctuating component of velocity projected onto the structure axis. The red and green vectors are in exactly opposite directions. (b) Vorticity vectors within the structure with a single vortex line displayed for each snapshot (red curves).
Vorticity iso-surfaces, ω = 13.5 s−1, colored by the invariants of the velocity gradient tensor. (a) Second invariant, Q [s−2], and (b) third invariant, R [s−3].
Structure evolutions for the fast-scan case with a high degree of temporal sampling. (a),(b) A structure oriented roughly streamwise over a 74 snapshot interval (0.29 s) visualized using iso-vorticity and vortex lines, respectively. (c),(d) An approximately azimuthally oriented structure over a 125 snapshot interval (0.49 s) again visualized using iso-vorticity and vortex lines, respectively. The volume visualizations (a),(c) are restricted to every 10th time step for clarity.
Time evolution of flow quantities for an axially oriented structure tracked over 74 snapshots of the flow (a 0.29 s interval), where the time axis is replaced with the non-dimensional time, τ. The curves represent a five-point moving-average applied to the point data. (a) The radial distance of the structure centroid to the flow axis. The approximate jet half-width at the centroid of the advecting structure is shown as a dashed line. (b) The orientation of the structure axis relative to the mean flow axis. The dashed line indicates the approximately constant inclination of 37° relative to the mean flow axis. (c) Mean components of vorticity relative to the flow axes; radial, azimuthal, and axial (red, blue, and black, respectively). (d) Mean components of vorticity relative to the structure axis; radial, azimuthal, and axial (red, blue, and black, respectively). The green curves in (c) and (d) show the evolving mean vorticity magnitude within the structure over the interval. (e) Mean value of Q within the structure. (f) Mean value of R within the structure. (g) Time evolution of the instantaneous production (blue) and dissipation (red). (h) Time evolution of stretching (blue) and tilting (red).
Time evolution of flow quantities for an axially oriented structure tracked over 125 snapshots of the flow (a 0.49 s interval), where the time axis is replaced with the non-dimensional time, τ. The curves represent a five-point moving-average applied to the point data. (a) The radial distance of the structure centroid to the flow axis. The approximate jet half-width at the centroid of the advecting structure is shown as a dashed line. (b) The orientation of the structure axis relative to the mean flow axis. The structure relaxes to an orientation approximately orthogonal to the mean flow axis (see dashed line). (c) Mean components of vorticity relative to the flow axes; radial, azimuthal, and axial (red, blue, and black, respectively). (d) Mean components of vorticity relative to the structure axis; radial, azimuthal, and axial (red, blue, black, and respectively). The green curves in (c) and (d) show the evolving mean vorticity magnitude within the structure over the interval. (e) Mean value of Q within the structure. (f) Mean value of R within the structure. (g) Time evolution of the instantaneous production (blue) and dissipation (red). (h) Time evolution of stretching (blue) and tilting (red).
(a) Velocity gradient tensor invariant maps calculated using the entire domain ensemble over a 125 snapshot interval of the evolving flow. 14 contour levels of the joint PDF are displayed, ranging logarithmically with exponents equally spaced from (left to right) −5 to 1, −6 to −1, and −6 to −1, respectively. (b) Velocity gradient tensor invariant maps calculated for a single coherent structure over a 125 snapshot interval of the evolving flow. 10 contour levels of the joint PDF are displayed, ranging logarithmically with exponents equally spaced from (left to right) −2 to 2, −3 to 2, and −1 to 4, respectively.
Turbulent properties of the water jet at the three Reynolds numbers are presented including different scanning protocols and image acquisition rates. The “Image Δt” represents the time interval between image pairs used in the cross correlation step, while “Flow Δt” is the time step of the advancing velocity field.
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