10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY - PIV13 Delft, The Netherlands, July 1-3, 2013
The life of Taylor–Couette flow structures in 3D
Sedat Tokgoz1, Gerrit E. Elsinga1and Jerry Westerweel1
1Lab. for Aero & Hydrodynamics, Faculty of Mechanical, Martime and Materials Engineering, Delft University of Technology, Delft, The Netherlands
s.tokgoz@tudelft.nl
ABSTRACT
Time-resolved tomographic PIV was used to investigate the time evolution of turbulent flow structures in Taylor-Couette flow. Turbulence is created by the shear due to exact counter rotation of the cylinders, where the mean velocity is zero in the bulk flow. This enables to observe the structures longer than many other turbulent flow types, sometimes during their whole life-time. Results showed that the structures are produced around streaks of positive and negative velocities. Larger structures appear in different shapes. Most dominant ones have tube-like shape and aligned in the azimuthal direction of the cylinders. Since the measurements are time-resolved in a 3D volume, it is possible to track individual structures over time and observe evolution of their shapes. The large scale structures are found to be advancing despite the zero mean velocity.
INTRODUCTION
The organisation of the turbulent flow structures received a lot of interest over the years [1, 10]. Recently the introduction of fully volumetric measurement techniques such as tomographic PIV [5], enabled experimentally investigating the 3D flow topology. The addition of the time-resolved measurements allowed to study temporal evolution of 3D structures. Previous studies on the temporal evolution of the turbulent flow structures has been performed on different flow conditions, focusing mostly on boundary layer [3, 4, 11, 12], as well as wake flows [6, 8].
In this manuscript, we aim to study the life time of the flow structures in 3D using Taylor-Couette flow. Taylor-Couette geometry consists of two coaxial cylinders and is often used to study stability of flows as well as fully developed turbulence [2]. Using this setup, it is possible to create turbulence in a shear flow, where the cylinders at exact counter-rotation. The exact counter-rotation is defined as the situation where the cylinders are rotating in the opposite directions with exact same wall velocities. As a result, the flow is turbulent but the mean flow is approximately zero in the bulk. Therefore the turbulent flow structures are expected to stay in the measurement volume for much longer compared to other flow types. Since time-resolved tomographic PIV is utilized for the measurement, we expect to observe the whole life time of some structures.
EXPERIMENTAL SETUP
Experiments were performed in the Taylor-Couette setup at the Laboratory for Aero & Hydrodynamics of the Delft University of Technology [9, 13]. The setup consists of two coaxial cylinders with radii of ri= 110 and ro= 120 mm (Figure 1). The height of the
inner cylinder is L = 220 mm. The gap ratio is η = ri/ro= 0.917 and axial aspect ratio is Γ = L/d = 22. The top and bottom endplates
are attached to the outer cylinder. It is not possible to control the temperature of the working fluid inside the current Taylor-Couette setup. However, we measured the temperature immediately before and after the image acquisition. The temperature of the fluid remained constant within ±0.2◦C for all experiments.
The data acquisition and the image processing were performed by commercial software (Davis by LaVision GmbH). Four highspeed cameras (Imager Pro HS 4M) with a maximum resolution of 2016 × 2016 were used. However, only about 860 × 1400 pixels were utilized in order to achieve higher sampling rate and to increase the number of images per time serie. Dimensions of the reconstructed measurement volume was approximately 46.5 × 25 × 10 mm in the axial, azimuthal and radial directions, respectively. The angles between the cameras were ≈ 23 and 44 degrees in the horizontal (axial) and the vertical (azimuthal) directions. We recorded 10000 images for each set of measurements, which corresponds to 31.65 ms integral time scale.
A 532 nm Nd:YLF laser with a maximum 150 Watt output was used to illuminate the volume. The size of the laser beam was extended to a volume using two cylindrical-planar lenses ( f = −90 and −12.5 mm). The illuminated volume was slightly bigger than the measurement volume. Fluorescent (Fluostar) particles and 570 nm lowpass optical filters were implemented to reduce the effect of the background. Reflections were further reduced by implementing a completely black surface inside the inner cylinder. The density of the particles is 1.1 g/cm3, with a mean diameter of 15µm. The seeding density during the experiments was kept around 0.02 particles per pixel. The low seeding density is required to reduce the number of ghost particles [13].
Calibration was done via a 1-mm thick stainless-steel 2D calibration plate. The short edge (20 mm) of the plate was located tangential to the azimuthal direction, whereas the long edge (150 mm) was parallel to the axial direction. The target has a grid consisting of 256 drilled holes, on it. The diameter of the circular holes is 0.4 mm and they are 2.5 mm apart from each other in both directions. The
Figure 1: The experimental setup without the top plate; the cameras, the laser optics and the cylinders (left), view of the cylinders, including the calibration target, between the cameras (right).
calibration target was attached to a micro-traverse system, which can translate the target through the depth of the measurement volume in the radial direction. The target was traversed between three planes within a 5 mm range (50% of the gap d), where the calibration for the remaining part was extrapolated. Volume self-calibration [15] was applied for further improvement of the calibration and reducing any optical distortions due to curved cylinders.
In order to increase the image quality, we subtracted a sliding minimum intensity over 25 × 25 pixels, before applying a 3 × 3 pixel Gaussian smoothing. Multipass cross-correlation was used to compute the vector fields. A 40 × 40 × 40 voxel interrogation volume was chosen for the final three passes. A 75% overlap was used to improve spatial resolution and to capture the finer details of the structures [13]. Outlier vectors were removed by universal outlier detection method [14] and gaps were filled by simple linear interpolation. Final volume contains 145 × 78 × 34 vectors in the axial, azimuthal and radial directions, respectively.
The shear Reynolds number (ReS= (2 |ηReo− Rei|)/(1 + η)) for the presented results is 3500, where Rei(= riΩid/ν) and Reo(=
roΩod/ν) represent the Reynolds numbers of inner and outer cylinders, respectively. All measurements were performed at rotation
number (RΩ= (1 − η)(Rei+ Reo)/(ηReo− Rei)) of 0.0, corresponding to exact counter rotation of the cylinders. Although the flow is
fully turbulent in this range, the mean flow is zero at exact counter-rotation. The velocities of the cylinder walls were V = ±0.158 m/s, where the recording rate was 437 Hz. The recording rate was adjusted to yield maximum particle displacement of 10 pixels, which is appropriate for 40 × 40 × 40 voxel final interrogation volume. Further details of the experimental setup and implementation of tomographic PIV to Taylor-Couette geometry can be found in Tokgoz et al. [13].
RESULTS
The measured volumes clearly show the streaks of positive and negative azimuthal velocities (Figure 2). The streaks appear in different shapes, mostly in meandering pattern. They arranged themselves in an alternating pattern in the axial direction. The width of the streaks at the central plane in the radial direction is approximately 0.2 − 0.3d. The streaks penetrate in to the gap between the cylinders in the radial direction, sometimes even reaching to the opposite cylinder wall. We observed the appearance of new structures (Figure 2; solid-black circle). The breakup (Figure 2; dashed-black circle) and merging (Figure 2; dashed-white circle) of the streaks were also observed.
The vortical structures are visualised by means of the Q-criterion isosurfaces [7]. Initial investigation of the instantaneous data showed that the vortical structures are found predominantly in the shear layer between the streaks (Figure 3). Relatively larger structures are mostly located at the center of the cylinder gap. They appear in different shapes and orientations. Hairpin and blob-like structures are observed. However, tube-like coherent structures appear more frequently than others. They are mostly aligned in the azimuthal direction, parallel to the cylinders. Additionally, structures which are relatively smaller in size are also observed. They are mostly appear closer to the cylinders. Similar to larger structures, smaller structures are also clustered around the shear layers.
Despite the zero mean flow, the structures are found to be slowly advancing in the azimuthal direction whereas their axial position remains approximately the same. An example is given in Figure 4, where the structures move in the direction of inner cylinder rotation. On the other hand, the structures are found to be evolving and changing shape during the advancing process. In some cases, the axes of the vortical structures rotate in a such way that they align themselves in the direction of other another axis.
CONCLUSION
In this manuscript we used time-resolved tomographic-PIV to investigate the flow structures in turbulent Taylor-Couette flow. Production and time evolution of the structures can thus be investigated in 3D. We observed accumulation of the large scale structures around positive and negative azimuthal velocity streaks. These structures appear in different shapes and orientations. In some cases, these structures slowly advance in the azimuthal direction. We also observed the evolution and change of orientation of the structures. The dependence of the results on the Reynolds number should be further investigated. More detailed results will be presented in the conference.
Figure 2: Azimuthal velocity streaks at the mid gap of the cylinders. Time difference between each image is ∆t = 22.9ms. Axes of x, y, z corresponds to axial, azimuthal and radial directions, respectively. The axes are non-dimensionalised with the gap width d.
Figure 3: An instantaneous example of streaks of azimuthal velocity at the mid-gap position. The azimuthal velocities are color coded. Isosurfaces for Q-criterion (Q = 7 × 10−4 s−2) are also shown. Axes of x, y, z corresponds to axial, azimuthal and radial directions, respectively. The axes are non-dimensionalised with the gap width d.
Figure 4: Advancing and evolving vortical structures (isosurfaces for Q-criterion Q = 0.001 s−2. Time difference between two images is ∆t = 45.7 ms. Axes of x, y, z corresponds to axial, azimuthal and radial directions, respectively. The axes are non-dimensionalised with the gap width d.
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