Three-dimensional particle tracking velocimetry in a Tesla...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Three-dimensional particle tracking velocimetry in a Tesla turbine rotor using a non-intrusive calibration method

Constantin Schosser1,*, Thomas Fuchs2, Rainer Hain2, Stefan Lecheler1, Christian J. Kähler2 1: Department of Technical Thermodynamics, Faculty of Mechanical Engineering, Bundeswehr University Munich, Germany

2: Institute of Fluid Mechanics and Aerodynamics, Faculty of Aviation and Aerospace Engineering, Bundeswehr University Munich, Germany * Correspondent author: [email protected]

Keywords: Tesla turbine, non-intrusive calibration, 3D measurement techniques, PTV processing

ABSTRACT

This paper introduces the measurement results of the velocity distribution in the gap between the co-rotating disks of a Tesla-radial turbine, using three-dimensional optical flow velocimetry techniques and a non-intrusive calibration approach. Usually, a calibration target has to be imaged within the measurement volume at different positions in depth, when three-dimensional measurement techniques, such as 3D-PTV and tomographic PIV are applied. However, for flow domains with limited spatial access and small dimensions it can be extremely difficult and inaccurate or even impossible to place and move the calibration target. The non-intrusive calibration approach overcomes these disadvantages by using a projected calibration target, which enables 3D-PTV measurements. As both disks of the Tesla turbine’s rotor are equipped with bull’s eyes, the surface reflections of a traversable continuous wave laser can be used to generate a set of calibration points, if their physical coordinates are known. The number of calibration points and the distances in-between are adjustable. Therefore, the spatial resolution of the calibration target can be chosen individually. The calibration technique allows for the measurement of the velocity distribution across the inter-disk spacing in radial and tangential direction in Tesla turbines. Highly-resolved laminar and turbulent velocity profiles across the gap between the disks of only 0.5 mm are obtained for different operating conditions of the Tesla rotor. The error propagation of the 3D-PTV measurement results is carried out. Furthermore, the velocity profiles, which are obtained by means of 3D-PTV, agree well with the laminar and turbulent CFD results. In case of laminar flow conditions, the axial distribution of the radial velocity component can be described by a parabolic polynomial, as expected from theoretical investigations. However, the distribution of the tangential velocity component across the gap, which is crucial for the performance of Tesla turbines, can best be approximated using a fourth-order polynomial for laminar flows. It differs clearly from the parabolic velocity profile and therefore corrects previous assumptions.

1. Introduction The Tesla or friction-type turbine was invented by the famous scientist Nikola Tesla [21] at the beginning of the 20th century. Worldwide, it is broadly believed that such devices can be utilized for small-scale power generation [2], [5]. Furthermore, these turbines might offer an economical alternative to conventional turbomachinery, if individual and scalable solutions at lowest costs are required. Moreover, Tesla-radial turbines are characterized by their particularly simple and robust


rotor design [2], [16]. It consists of several circular, parallel, flat, equally spaced, and co-rotating disks with narrow gaps. The central outlet passage is located at the centre of rotation. In general, the flow is delivered by guide vanes or nozzles and feeds the rotor gap. Driven by a pressure difference across the rotor, the flow takes a spiral path towards the axis of rotation, where it leaves the turbine via a hollow shaft. The momentum exchange between the rotor and the fluid creates

Fig. 1 Working principle of a Tesla turbine [17].

torque and power [16]. Romanin et al. [14], Sengupta et al. [19], and Guha et al. [6] solved governing equations of the laminar rotor bulk flow by numerical means. Furthermore, Romanin [14] partially validated a laminar flow model by performance map measurements. Schosser et al. [16, 17] presented and validated the fully analytical solution of the incompressible, laminar rotor flow in Tesla turbines. Most of the experimental investigations focus on black box measurements of the performance and the efficiency maps, like Lemma et al. [10]. Recent CFD studies of Sengupta et al. [20] and Guha et al. [6] are impressive, but lacking the experimental validation of the inter-disk velocity distribution. Ladino [9] assumed that the measurement of the inter-disk velocity distribution is impossible, because of the small gap widths below 1 mm. However, the measurement of the velocity profiles would significantly improve the accuracy of the flow models and would validate turbulent CFD results. Nevertheless, during the last decades, digital particle imaging measurement techniques have become powerful tools for flow analyses. They are one of the most widespread methods for the instantaneous measurement of flow fields without disturbing the flow. Especially, three-dimensional particle imaging offers the possibility to detect volumetric flow features. Nowadays, tomographic particle image velocimetry (tomo-PIV) and three-dimensional particle tracking velocimetry (3D-PTV) are the most versatile approaches for three-dimensional flow field measurements [11], [15]. For example measurements of turbulent boundary layers, vortices, periodic flow phenomena, separated, and reattached flows are some of the widespread applications of the above-mentioned 3D techniques. In turbomachinery however, particle imaging is not usually applied, because of the nature of those measurement domains. These small measurement volumes require 3D measurement approaches, as 2D techniques cannot resolve strong velocity gradients, due to the integration over the light sheet thickness [7], [8]. However,


three-dimensional techniques require an accurate calibration to capture velocity fields with high resolution and accuracy. Using 2D techniques, a calibration target is regularly placed into the measurement volume and is imaged. An algorithm determines the calibration points on the sensor planes and derives the calibration function, if the physical coordinates are known. However, for 3D techniques, the target has to be imaged at different locations in depth. Placing a multi-plane or moving a single-plane calibration target within the measurement volume is often not possible in turbomachinery or other fields of application. The spatial access to the measurement volume is often significantly limited or even impossible without major disassembly of the devices. Furthermore, moving optical equipment can originate misalignments, which may lead to spatial errors in mapping. It is even possible that the calibration cannot be derived from the calibration images. In case of the test rig for the investigation of rotor flows in Tesla turbines, which is described in Schosser et al. [16], the dimensions of the measurement volume yield a size of 12 x 4 x 0.5 mm³ are too small for commercial or even printed out calibration targets. The disassembly of the test rig would involve huge misalignments and result in large errors of the allocation between the three-dimensional physical coordinates and the calibration points on the senor planes. The developed calibration method is entirely non-intrusive and suitable for at least some of the above-mentioned critical environments [18].

2. Application of the non-intrusive calibration technique in the Tesla turbine test rig Since the dimensions of the measurement volume are strongly constrained by the rotor geometry and the spatial access is strongly limited, only the non-intrusive calibration can overcome these drawbacks. A detailed illustration of the measurement volume inside the rotor is shown in Fig. 2.

Fig. 2 Experimental rotor of a Tesla turbine, equipped with bull’s eyes. The outer disk diameter is

250 mm, the inner disk diameter is 60 mm, and the inter-disk spacing is 0.5 mm.

bull’s eyes (Ø 75 mm)

double-pulsed laser beam

measurement volumes


Due to the limited optical access and the high velocity gradients across the gap between the co-rotating disks, the flow field is determined, using a stereoscopic 3D-PTV approach, as it allows an useful examination of flows with strong velocity gradients [7], [8]. In order to establish the calibration of a multi-camera optical system, a set of calibration points is required. Furthermore, the physical locations of the calibration points (xi, yj, z0) and (xi, yj, z1) have to be known and the points have to be visible on all camera sensors, regardless of their geometry. In addition to that, the corresponding calibration points on all sensors have to be matched uniquely. This leads to a set of n coordinates (Xi,n; Yi,n) for each sensor for i cameras. The calibration function (mapping) is computed from a set of sensor coordinates and the corresponding physical coordinates in three-dimensional space. Usually, third-order polynomials are used as calibration functions in tomographic PIV applications. In contrast to conventional calibration targets, laser light reflections on the glass surfaces of the rotors’ bull’s eyes (flow boundaries) are used to establish the calibration points. However, the rotor is placed inside the test rig (Fig. 3), which is equipped with the calibration sys-tem. It consists of two cameras, a continuous wave laser (Ø4 mm), which is perpendicularly aligned

Fig. 3 Rotor in test rig with calibration unit.

to the rotors’ glass surfaces, and a two-dimensional traverse. The beam of the traversable constant wave laser is focused to a diameter of approximately 0.1 mm using two spherical lenses with focal lengths of f = -50 mm and f = +50 mm. The laser beam partially illuminates the measurement volume at certain x and y traverse locations with respect to a known reference position, which is marked on the test rig. Thereby, reflections occur on the surfaces of both transparent rotor disks and establish two calibration points (x, y, z0) and (x, y, z1) in two different axial planes, as illustrated


Fig. 4 Spatial calibration point coordinates, defined by laser position [18].

in Fig. 4. Only the reflections on the boundaries of the measurement volume (x, y, z0) and (x, y, z1) are needed and imaged with both cameras. An image of two calibration points from one cameras’ point of view is exemplarily shown in Fig. 5. The translation of the laser beam in the xy-plane leads

Fig. 5 Inverted grayscale image of light reflections on the glass surfaces in a single spatial

calibration point, which are seen from one camera [18]. to a set of calibration points in two z-planes with the known physical positions (xi, yj, z0,1) and the particular sensor locations of their reflections X and Y on each camera. The z-coordinate is known from the CAD model of the test rig. The coordinate z0 is set to zero, the coordinate z1 equals the inter-disk spacing of 0.5 mm. However, the light reflections, which are created by the continuous wave laser, are influenced by imperfections of the beam profile, scratches on the glass surfaces, inhomogeneities of the windows, and contamination of the optical access, to name a few. This on the other hand, can lead to discrepancies in the calibration function, because the sensor location of the reflections need to be fitted. These imperfections can be averaged out, by applying a slight rotation of the rotor, using a longer exposure time. This enables the use of a Gaussian fit in both directions of the sensors on each camera. The fits are performed applying sub-pixel accuracy. Figure 6 exemplarily shows the light intensity distribution of a reflection on one sensor.


Fig. 6 Light intensity distribution of a cut through a light reflection.

Rotation cannot be applied in many other applications. If this is the case, a subsequent self-calibration method is suggested to correct the calibration function. A self-calibration, as it is used for standard stereo-PIV is suitable, if the measurement depth is in the range of the light sheet thickness [22]. However, self-calibrations remove random errors, while systematic errors cannot be corrected. 384 calibration points in two axial planes are established in total. The laser approaches 192 positions, yielding 24 rows in y-direction and 8 columns in x-direction with a spacing of Δx = Δy = 0.5 mm. In contrast to typical calibration targets, the non-intrusive, optical calibration method enables a fully variable number of calibration points with variable distances. This ensures a sufficient number of calibration points for differing magnifications and fields of views. The calibration system, which controls traverse movement, timing, and imaging, is entirely automated.

Fig. 7 Focused laser and non-intrusive calibration target [18].


3. Experimental and numerical approach The non-intrusive calibration approach is developed for the challenging task to measure the radial and the tangential velocity distribution between the co-rotating disks of a Tesla turbine, using stereoscopic 3D-PTV. Therefore, two PCO 2000 cameras with f = 60 mm lenses, each equipped with one 2x magnifying teleconverter, and a Scheimpflug adapter, are used (see Fig. 3). In order to alleviate the astigmatic aberrations, which are caused by the angled view through the static and the upper rotating window, a larger depth of focus is established by choosing an aperture of f# = 16. The reproduction scale in the centre of the image is 11 µm/pixel at a magnification of M = 0.67. The measurement volume (12 x 4 x 0.5 mm³) is illuminated by a Nd-YAG laser with two cavities and a maximum intensity of 2 x 30 mJ. Altogether, 4000 double-frame images are recorded in each operational point. Image recording is executed by a hardware trigger, whenever the rotating bull’s eyes pass the static optical access in the housing of the test rig. The corresponding particle images on the sensor of each camera have to be determined, when using the 3D-PTV technique. In a second step, the sensor locations of the particle images are triangulated to estimate the physical particle location within the measurement volume. In order to achieve explicit matching of the particle images, the seeding density needs to be relatively low. Furthermore, only two cameras are used, which makes the unique matching worse, if the seeding density is too high. After the triangulation, the flow velocities are estimated using a probabilistic tracking algorithm, described by Ohmi et al. [12]. As the test facility with rotating parts always involves vibrations, a self-calibration is applied to each measurement. However, it is not applied to correct the calibration function, but the particle image sensor locations are corrected by a single correction value, which is applied for the entire image, because the depth of the measurement volume lies in the range of the light sheet thickness. After the sensor locations of the particle images are corrected, a second triangulation is performed to determine the flow velocities. The maximum value of the triangulation error distribution of all possible triangulations is used as the correction value. The standard deviation of the correction value is σΔXY ≈ ± 0.25 pixel. Thereby, the operational points of the test rig do not show significant influences. Although, the non-intrusive calibration routine is carried out, using a Cartesian coordinate system, the velocity profiles in Tesla turbines are desired to be presented in a cylindrical coordinate system. Therefore, the flow velocities are decomposed into cylindrical coordinates. The measurement results are compared to steady CFD calculations, using ANYSY CFX and ICEM. Turbulent and laminar flow regimes are considered. Mesh independency studies and y+ adaption for the turbulent cases are performed. The standard SST turbulence model is applied, where turbulent flows are expected.


4. Measurements of the radial and tangential velocity distribution in the gap of a Tesla turbine The radial and tangential velocity profiles in the gap between co-rotating disks is captured by means of 3D-PTV for different radial positions (see Fig. 2). The results are compared to CFD calculations using ANSYS CFX. The velocities obtained from the 3D-PTV and the CFD are normalised with their maximum velocities. The peak values of the radial velocity profile V(Z) and the tangential relative velocity profile C(Z) are calculated, using the median of all velocity vectors, which are located ±2.5% around the centre of the gap between the disks. The inter-gap position Z is normalised by half of the inter-disk spacing of 0.25 mm. Due to relatively strong velocity gradients in the main flow direction, the binning technique is applied. Each velocity profile is composed of the velocity vectors over a small radial slice (bin) of the measurement volume at a certain radial position. Their layer thickness is 0.4 mm, respectively ±0.2 mm. The Figs. 8 and 9 exemplarily show the laminar velocity distribution across the gap between the disks in the relevant direction, using cylindrical coordinates. Figure 8 shows the velocity profiles at an outer radial position of r = 110 mm. However, Fig. 9 shows the profiles at an inner radial position of r =

Fig. 8 Tangential and radial laminar velocity profiles at the outer measurement volume.


Fig. 9 Tangential and radial laminar velocity profiles at the inner measurement volume.

52 mm. All profiles show deviations of the (time) average profile. The velocity fluctuations decay further downstream along the radius. This is a first indication that the oscillations seem to be physically correct. Due to the relatively large radial gap between guide vanes and rotor, one possible explanation might be that the open jet breaks up, hits the outer rim of the disks, and creates pressure fluctuations. Simplified and two-dimensional transient laminar CFD simulations emphasise this statement (see Fig. 10). The velocity oscillates perpendicularly to and in the main flow direction. However, it is impossible to detect the frequency of the fluctuations, as the repeti-

Fig. 10 Two-dimensional, transient, laminar CFD using a simplified rotor-stator geometry

(gap width = 0.5 mm; uin = 20 m/s; pout = 1 bar).

tion rate of the laser, used in this set-up, is too low. The systematic errors are corrected, as far as it was possible. Furthermore, the theoretical stability analysis, carried out by Chesnokov [4] indicates that this hypothesis is useful. Chesnokov [4] demonstrated that smallest pressure oscillations can result in velocity fluctuations, which can reach values comparable to the mean velocity. The laminar CFD results agree reasonably well with the velocity profiles determined by means of 3D-PTV. Nevertheless, there are deviations in the radial profile shapes at a radius of r =


52 mm, which might be originated by the outflow passage of the rotor. In addition to that, the turbulent profiles, shown in Fig. 11 and Fig. 12, provide similar fluctuations, comparable to the laminar profiles. However, they are in superposition with the turbulent fluctuations. Unfortunately, they cannot be separated from each other, as the frequency of the double-pulsed laser is too low to detect the frequency of the fluctuations. They also cannot be estimated from the CFD results, as the standard SST turbulence model simulates Reynolds stresses instead of turbulent fluctuation values. Depending on the operating conditions, the turbulent profiles agree sometimes more and sometimes less with the 3D-PTV profiles. In general, the prediction of the velocity gradients are slightly higher at the outer radius (r = 110 mm). However, the agreement is better at the inner radius (r = 52 mm).

Fig. 11 Tangential and radial turbulent velocity profiles at the outer measurement volume.

Fig. 12 Tangential and radial turbulent velocity profiles at the inner measurement volume.

5. Error propagation Obviously, the manufacturing tolerances determine the accuracy of the non-intrusive calibration scheme, because the z coordinates of the physical location of all calibration points are denoted by


the boundaries of the flow domain. However, the quality of experiments in such confined geometries is usually very high. A well-known geometrical measure in an experimental set-up is very well suited to replace conventional calibration targets. In order to quantify the fit error of the calibration, the spatial coordinates (xi, yi, z0,1) of the calibration points are mapped to sensor coordinates (X0,1, Y0,1) using the calibration function. However, the new sensor coordinates are compared to those, which are obtained from the non-intrusive calibration points from the calibration images. The average absolute residual for sensor #1 yields 0.36 pixel. Sensor #2 yields 0.30 pixel and therefore shows a slightly better performance. Vice versa, the sensor coordinates derived from the calibration images, using the calibration function, can be triangulated to physical locations in three-dimensional space. The well-known physical coordinates (xi, yi, z0,1) of the calibration points are then compared to the triangulated location, yielding an average spatial residual of 3.3 µm. With a reproduction scale of 11 µm/pixel and an average residual of the sensor locations of approximately 0.3 pixels, a deviation of about 3.3 µm in physical coordinates is obtained. This is in very good agreement with the average spatial residual. Systematic errors of the entire field of displacement vectors certainly arise in the measurement data. This type of error is comprised of rotor deformation, vibrations of the test rig, and the fit error from the determination of the calibration function. The positions of the rotor walls are known from the PTV measurements. The outer rim of the both disks have the tendency to move upwards, while the gap remains almost entirely constant. The displacement of the rotor is systematically corrected in the measurement data. Nevertheless, the systematic errors, which are hidden in the calibration function cannot be systematically corrected. Usually, the axial average velocity component in a Tesla rotor should be zero. Therefore, the average displacement of all particle images dz should also be zero. However, the average displacement of all particle images dz systematically rises with the revolution speed of the rotor and is obviously not physically correct. Measurement positions, which are at the outer radius systematically show higher values of dz, compared to positions at lower radii. The maximum average displacement is reached for the highest revolution speed at the outer radial measurement position of r = 110 mm and yields dz = 0.13 µm. The systematic deviation from the expected average displacement is a strong indicator for a systematic error, which is probably originated from rotor deformation. However, the systematic error for the field of displacement vectors cannot be determined in this test rig. Nevertheless, it can be estimated by dividing the maximum average displacement dz = 0.13 µm by the reproduction scale of 11 µm/pixel and the average particle image displacement of 10 pixel in the main flow direction at the centre of the image. This leads to a systematic error estimation of about 0.1% and is therefore negligible.


Of course, residual errors of single displacement vectors appear in the measurement data. However, with an increasing number of double-frame images, the measurement uncertainty of the field of particle images is almost entirely averaged out.

6. Concluding remarks For the first time in history of Tesla Turbine development, the complex flow field inside a Tesla turbine is captured with a high spatial resolution, using the modern flow measurement technique named stereoscopic 3D-PTV. According to Cierpka et al. [3], Particle tracking velocimetry allows a useful examination of flows with strong velocity gradients and is therefore ideally suited for this measurement task. However, relatively low seeding densities are required, if only two cameras are applicable. Despite certain challenges of the measurement task, the development of a non-intrusive calibration scheme, which utilizes the reflections of a traversable constant wave laser, offered the possibility to determine spatially and highly resolved velocity profiles in an extraordinary environment with considerable limited spatial access to the measurement volume. The calibration approach is tested and thereby further developed. It is of major significance that the non-intrusive calibration approach offers new opportunities concerning the use of optical flow velocimetry. It is conceivable to use this method or similar non-intrusive calibration approaches in turbomachinery, combustion, cavity flows, and other new application. Several operational points of the Tesla turbine are investigated. Furthermore, the measurement results agree well with those obtained from laminar and turbulent CFD. The laminar velocity profiles, determined from 3D-PTV, slightly differs from the initial assumption of a parabolic velocity distribution in radial and tangential direction, made by Rice [13], Beans [1], Carey [2], and other previous Tesla turbine investigators. However, the tangential velocity profile is best approximated by a fourth-order polynomial. This is in good agreement with the CFD investigations of the laminar rotor flow carried out by Schosser et al. [17]. The measurement results seem to be physically valid, indicating that the calibration scheme is working properly. Nevertheless, transient CFD simulations of the stator outlet and rotor inlet region are desirable for future investigations of the velocity fluctuations, which are observed during the measurements.

References [1] Beans, E. W., Investigations into the performance characteristics of a friction turbine, Journal of Spacecraft and Rockets, Vol. 3, 131-134 (1966). [2] Carey, V. P., Assessment of Tesla turbine performance for small scale Rankine combined heat and power systems, Journal of Engineering for Gas Turbines and Power, Vol. 132, 122301 (2010).


[3] Cierpka, C., Lütke, B., and Kähler, C. J., Higher order multi-frame particle tracking velocimetry, Experiments in Fluids, Vol. 54, 1533 (2013). [4] Chesnokov, V. M., Oscillations of a viscous fluid in a thin layer between two coaxial disks rotating together, Fluid Dynamics, Vol. 19, 146-149 (1984). [5] Deng, Q., Qi, W., and Feng, Z., Improvement of a theoretical analysis method for Tesla turbines, Proceedings of ASME Turbo Expo 2013, San Antonio, Texas, USA (2013). [6] Guha, A. and Sengupta, S., The fluid dynamics of work transfer in the non-uniform viscous rotating flow within a Tesla disc turbomachine, Physics of Fluids, Vol. 26, 033601 (2014). [7] Kähler, C. J., Scharnowski, S., and Cierpka, C., On the resolution limit of particle image velocimetry, Experiments in Fluids, Vol. 52, 1629-1639 (2012). [8] Kähler, C. J., Scharnowski, S., and Cierpka, C., On the uncertainty of digital PIV and PTV near walls, Experiments in Fluids, Vol. 52, 1641-1656 (2012). [9] Ladino, A. F. R., Numerical Simulation of the Flow Field in a Friction-type Turbine (Tesla Turbine), Institute of Thermal Powerplants, Vienna University of Technology (2004). [10] Lemma, E., Deam, R. T., Toncich, D., and Collins, R., Characterisation of a small viscous flow turbine, Experimental Thermal and Fluid Science, Vol. 130, 052301 (2008). [11] Maas, H. G., Gruen, A., and Papantoniou, D., Particle tracking velocimetry in three-dimensional flows, Experiments in Fluids, Vol. 15, 133-147 (1993). [12] Ohmi, K., Li, H.-Y., Particle-tracking velocimetry with new algorithms, Measurement and Science Technology, Vol. 11, 603-616 (2000). [13] Rice, W., An Analytical and Experimental Investigation of Multiple-Disk Turbines, Journal for Engineering and Power, Vol. 87, 29-36 (1965). [14] Romanin, V. and Carey, V. P., An integral perturbation model of flow and momentum transport in rotating microchannels with smooth or microstructured wall surfaces, Physics of Fluids, Vol. 23, 082003 (2011). [15] Scarano, F., Tomographic PIV: Principles and Practice, Measurement and Science Technology, Vol. 21, 012001 (2013). [16] Schosser, C., Lecheler, S., and Pfitzner, M., A Test rig for the investigation of the performance and flow field of Tesla friction turbines, Proceedings of ASME Turbo Expo 2014, Düsseldorf, Germany (2014). [17] Schosser, C. and Pfitzner, M., A numerical study of the three-dimensional incompressible rotor airflow within a Tesla turbine, Proceedings of CMFF’15 Budapest, Hungary (2015). [18] Schosser, C., Fuchs, T., Hain, R., and Kähler, C. J., Non-intrusive calibration for three-dimensional particle imaging, Experiments in Fluids, Vol. 57, 1-5 (2016). [19] Sengupta, S. and Guha, A., A theory of Tesla disc turbines, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 226, 650–663 (2012). [20] Sengupta, S., and Guha, A., Analytical and computational solutions for three-dimensional flow-field and relative pathlines for the rotating flow in a Tesla disc turbine, Journal of Computers and Fluids, Vol. 88, 344-353 (2013).


[21] Tesla, N., Tesla turbine, US Patent 1,061,206 (1913). [22] Wieneke, B., Stereo-PIV using self-calibration on particle images, Experiments in Fluids, Vol. 39, 267-280 (2005).

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