Ultra-High-Speed 3D Astigmatic PTV in Supersonic Underexpanded Impinging Jets

Transcription

1 17th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, July 7-1, 214 Ultra-High-Speed 3D Astigmatic PTV in Supersonic Underexpanded Impinging Jets Christian Cierpka 1, Nicolas A. Buchmann 1,2, Julio Soria 2 and Christian J. Kähler 1 1 Institute of Fluid Mechanics and Aerodynamics, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, Neubiberg, Germany, nicolas.buchmann@unibw.de 2 Laboratory of Turbulence Research in Aerospace and Combustion, Monash University, Melbourne, 38 Victoria, Australia Abstract Ultra-high-speed three-component, three-dimensional (3C3D) velocity measurements of micronsized particles suspended in a supersonic impinging jet flow are presented. Understanding the dynamics of individual particles in such flows is important for the design of particles impactors for drug delivery or cold gas dynamic spray processing. The underexpanded jet flow is produced via a converging nozzle and micron-sized particles (d p = 11 µm) are introduced into the gas flow. The supersonic jet impinges onto a flat surface and the particle impact velocity and particle impact angle are studied for a range of flow conditions and impingement distances. The imaging system consist of an ultra-high-speed digital camera (Shimadzu HPV-1) capable of recording rates of up to 1 Mfps. Astigmatism particle tracking velocimetry (APTV) is used to measure the 3D particle position [6] by coding the particle depth location in the 2D images by adding a cylindrical lens to the high-speed imaging system. Based on the reconstructed 3D particle positions the particle trajectories are obtained via a higher-order tracking scheme that takes advantage of the high temporal resolution to increase robustness and accuracy of the measurement. It is shown how the particle velocity and impingement angle depend on the nozzle pressure ratio and stand-off distance and that higher pressure ratios and stand-off distances lead to higher impact velocities and larger impact angles. 1. Introduction High-speed particle laden flows can be found in a number of applications such as particle impactors [7], needle free drug delivery systems [12] or cold gas dynamic spray processes [9 11]. Common to all these processes is the acceleration of micron-sized particles (1 1 µm) to very high particle velocities (3 12 m/s) via a high-speed gas flow such that the particles attain sufficient kinetic energy to penetrate or deposit onto a solid substrate upon impaction. The optimal application of these processes is characterised by a critical particle impact velocity and particle impact angle, both of which are a complex function of the fluid dynamics of the impinging supersonic jet flow. Understanding how the particle motion is affected by the highly unsteady, turbulent and three-dimensional nature of the supersonic gas flow and its complex shock structure requires experimental data to resolve the individual three-component, three-dimensional (3C3D) particle velocity over time and length scales comparable to their velocity and size. However, this is exceedingly difficult to achieve at supersonic speeds due to the large dimensional difference between the very small particles ((O(1 6 ) m) and their very large velocities (O(1 3 ) m/s). In order to resolve the 3D motion of these particles ultrahigh-speed imaging methods are required. The present paper presents measurements of the 3C3D particle velocities in a particle-laden supersonic jet flow by means of astigmatism particle tracking velocimetry (APTV) [5, 6]. By using a single ultra-high-speed CCD camera capable of recording one million frame per second combined with a long distance microscope and pulsed LED light illumination the 3C3D particle motions is determined

2 with up to 1 Mfps temporal resolution and nano-second exposure times high spatial resolution and high signal-to-noise level no need for complex camera calibration procedures The first part of the paper discusses the experimental setup and 3C3D particle velocity determination. The second part assesses the calibration of the proposed method, which is then applied to measure the 3C3D particle velocity in a supersonic particle-laden gas flow. The paper concludes with a discussion of the measurement results and some remarks. 2. Experimental Methods 2.1 Experimental Setup The particle-laden high-speed gas flow is produced via a converging nozzle of diameter D = 2 mm. The gas velocity is adjusted by changing the nozzle pressure ratio NPR, which is defined as the ratio between the static pressure upstream of the nozzle and the ambient pressure (NPR = p /p ). For NPR 1.9 the flow in the nozzle becomes choked and the nozzle reaches its maximum exit velocity of approximately 313 m/s. For higher NPRs the flow at the nozzle exit is underexpanded and characterised by a series of shock and expansion waves (see [2] for details). The solid particles (Vestosint 131) with a mean diameter of d P = 11 µm and a specific density of ρ = 1.6 g/cm 2 are suspended in the airflow co-axially via a purpose-built seeding system. The particle-laden jet exhausts into an octagonal flow chamber as shown in Figure 1 from which the particles are extracted via a vacuum pump. The optical arrangement consists of an ultra-high-speed CCD camera of type Shimadzu HPV-1 capable of recording 12 successive images at a frame rate of up to 1,, fps and 25 ns exposure time. The digital CCD array has a size of pixel 2, a spatial resolution of 66.3 µm and a 1 bit dynamic intensity range. In order to increase the spatial resolution of the current system, the camera is equipped with a custom-built long-distance microscope consisting of a Micro Nikkor lens with a focal length of 15 mm and an extension tube. The magnification is set to M = 2.1, which yields an effective spatial resolution of 31.5 µm/pixel and a diffraction limit of 44.3 µm (or 1.4 pixel). Illumination of the spray particles is provided by a current-pulsed high-power LED (Luminus CBT- 12, λ = 532 nm) that is mounted inline with the high-speed camera. The light of the LED is highly divergent and therefore collimated by a set of spherical lenses. Overdriving the LED with high current pulses at short durations produces light pulses with sufficient energy to achieve large signal-to-noise levels even at high framing rates [3, 13]. The LED is operated with a drive current of I f,max = 1 15 A with a 1 µs pulse width at 25 khz repetition rates. Higher repetition rates are possible (see [13]), but drastically reduce the lifetime of the LED at high pulse-currents. The advantage of the present high-speed LED illumination is the high degree of spatial and temporal uniformity of the illumination and the ability to reduce the exposure time below the limit of the high-speed camera (e.g. pulse width less than 25 ns are possible) D Astigmatism Particle Reconstruction The depth position of the particles is coded onto the 2D image by placing a standard cylindrical lens with focal length f cyl = 2 mm in front of the high-speed camera sensor as shown in Figure 1. The cylindrical lens is positioned such that its curvature acts in the y z plane of the imaging system. The focal plane F xz in the x z plane is determined by the long-distance microscope whereas in 2

3 particle extraction pulsed highpower LED y lens + bellow assembly high-speed Camera z jet nozzle collimation lens viewing windows cylindrical lens Figure 1: Schematic of the experimental setup. Figure 2: Ray tracing schematic of astigmatism PTV (APTV). The distance to the in-focus plane F xz is shortened by the additional lens in the y z plane producing a new focal plane F yz (after [6]). the y z plane the cylindrical lens causes a shortening of the distance between the camera and F xz to create a second focal plane F yz in the y z plane. This is shown schematically in Figure 2, which shows the optical arrangement from the top and side view and is explained in more detail in [5, 6]. Consequently, the images of the particles located between the two focal planes will be distorted according to their depth position. Particles close to F xz will appear elongated along the x direction, while particles located closer to F yz will be distorted in the y direction. Thus, the particles appear elliptical in the image plane. The depth of the measurement volume is related, but not limited by the distance between the two in-focus planes δ z = F xz F yz and corresponds to approximately 5.1 mm for the current setup. Using appropriate image pre-processing and calibration [5], the particle depth location is obtained with sub-pixel accuracy from the elliptical particle image shape at each time-step. 2.3 Higher-Order 3C3D Particle Tracking The 3C3D particle velocity is determined by tracking the particles between consecutive time steps using a probabilistic approach where the particle velocity is given as u(x,y,z) = x/(t 2 t 1 ). The probabilistic particle tracking takes the motion of neighbouring particles into account and computes the most probable particle trajectory in conjunction with a temporal predictor to decrease the search radius in the second frame using information from the previous frames. This method yields very reliable results even for high seeding concentrations. For the current investigation velocity vectors are only accepted if the trajectory exists for at least four consecutive time steps. A second order curve is fitted to the trajectory at the four time steps and the velocity vector is determined by integration of the particle path [4]. This procedure decreases both random and systematic errors due to vector reallocation in the case of curved trajectories and reliably removes outliers. 3

4 3. Results 3.1 Calibration using Stationary Particles In order to test the APTV method for the current conditions and to derive a calibration an experiment with stationary particles is performed first. For this, 11 µm particles are attached to a microscope slide and traversed in z direction through the measurement volume in steps of 1 mm. The conditions for this test are nearly identical to the experimental conditions with M = 2.1, f cyl = 2 mm, 25 khz acquisition rate and 1 µs exposure time. Figure 3 (left) shows the evolution of the particle image width a x and height a y versus the depth position z. The focal planes are located at z locations where the particle elongation reaches a minimum in the respective direction and correspond to z mm and z 5.1 mm. Further away from the focal planes the particles become more out-of-focus and the SNR decreases drastically resulting in a significant scatter in the calibration curves for large z values. Outside the focal planes the particle elongations a x and a y are ambiguous, but by using an parametric calibration model such as in Figure 3 (right), valid measurements can also be obtained outside the focal plane spacing using for example a lookup table of the form z P = f (a x,a y ) (see [5] for more details). ax,ay ax ay ay z [mm] a x Figure 3: Application of the intrinsic calibration applied to stationary particles: (left) particle width and height a x, a y in pixel; (right) distribution of a y against a x in pixel. (d P = 11 µm, M = 2.1). Dashed lines indicate the position of the focal planes F xz, F yz. 3.2 Supersonic Impinging Particle-laden Jet The ultra-high-speed 3D astigmatic particle tracking technique is applied to measure the particle velocity in two underexpanded impinging jets with nozzle pressure ratios NPR = 3.75 and 6. at stand-off distances Z/D = 3 and 4. The time-averaged flow structure of the flows is illustrated in Figure 4 by means of coherent laser imaging (see [2] for more details). The major differences between the two configurations is the formation of a Mach disk (normal shock) and the larger re-circulation zone (distance of the plate shock from the wall) for NPR=6., Z/D = 4. The strength and spacing of the shocks depend on the operating conditions of the nozzle and both are known to increase with NPR and Z/D. The plate-shock for the NPR = 3.75 and NPR = 6. case is located at z/d 2.5 and z/d 3., respectively. The Mach disk for the latter case is at z/d = 1.5, while no Mach disk is observed at NPR = In order to obtain converged statistics, each experiment is repeated 15 times, resulting in a total of 15, images. On these images, approximately particles are tracked and after processing 4

5 Figure 4: Coherent light visualisations of the gas phase of the underexpanded jet; (left) NPR = 3.75, Z/D = 3; (right) NPR = 6, Z/D = 4. Flow is from top to bottom. approximately individual valid measurements are accepted to compile the statistical results. The time averaged particle distribution and particle velocity for NPR = 6., Z/D = 4 is shown in Figure 5 using laboratory coordinates (x, y, z). The distribution of the reconstructed particle positions is symmetric with respect to the jet centre axis as is expected for an axis-symmetric jet (Fig. 5 right). Two distinct velocity regions are noticeable; the first region corresponds to high-speed particles that exit the nozzle at x/d = and impinge at the substrate at x/d = 4. Under the present conditions ux (m/s) x/d z/d y/d.5 y/d Figure 5: Instantaneous particle distribution and streamwise particle velocity ux. The existence of impinging high-speed and deflected low-speed particles is clearly visible; (left) x y plane; (right) y z plane, only the high-speed particle are shown. Flow is from top to bottom. 5

6 the spray particles do not reach the critical velocity required to adhere or coat the surface and are therefore deflected at the impingement surface to form a second region of low-speed particles. The distribution of streamwise particle velocity u z (z) integrated in the azimuthal direction is illustrated in Figure 6 (left). The polydisperse particle size distribution (11 ± 32 µm) causes a relatively large data scatter since the particles reach different velocities according to their inertia. Furthermore, as will be shown later, the streamwise particle velocity also depends on the radial position of the particles, which further contributes to the data scatter in Figure 6 (left). The uncertainty in the streamwise particle velocity is estimated to 2δ x / t 1.3 m/s and thus is significantly smaller than the observed data scatter. Therefore, the observed variations in particle velocity are attributed to true physical effects of the gas flow and particle dynamics. From the instantaneous data ensemble averaged profiles are determined by binning the data into intervals of.2d with 75% overlap. Figure 6 (right) illustrates the averaged velocity profile for NPR = 3.75 and NPR = 6. where the error bars correspond to one standard deviation above the mean for all cases presented. Depending on NPR, the particles leave the nozzle with an average velocity of approximately 1 12 m/s, which is significantly lower than the local gas velocity of 345 m/s (speed of sound) at the nozzle exit. In principle, the smaller the particles and the longer the nozzle, the higher the particle exit velocity. In the present case the nozzle has a fixed length of L = 12 mm and due to the relatively large particle response time (τ p = 1 3 s), the particles are not sufficiently accelerated within the nozzle to reach the gas velocity at the nozzle exit. As a consequence, the averaged particle Mach number at the nozzle exit Ma p = 1 u/c is as high as meaning that shocks may form at the trailing end of the particles (see [1] and [8] for visualisations of the particle flow interaction). After leaving the nozzle the particles are continuously accelerated in the streamwise direction by the surrounding gas flow and reach average impact velocities of 15 and 18 m/s for NPR = 3.75 and 6.. Note that instantaneous impact velocities can be as high as 225 m/s. Yet, these velocities are insufficient to achieve measurable deposition of the spray particles. In fact, the particles tend to break up upon impact and are deflected in radial direction as discussed before. Both flow cases exhibit a qualitative similar evolution of streamwise particle velocity with the NPR = 6. case reaching higher impact velocities due to the greater pressure ratio and stand-off distance. The particle displacement between two consecutive image frames is u t.25.45d, which con uz(m/s) z/d uz(m/s) NPR=6, Z/D = 4 NPR=3.75, Z/D = z/d Figure 6: Particle velocity u z against streamwise distance z/d: (left) Time averaged velocity for NPR = 6., Z/D = 4; (right) ensemble averaged velocity for NPR = 3.75, Z/D = 3 and NPR = 6., Z/D = 4. Errorbars are one standard deviation from the mean. 6

7 stitutes the effective spatial resolution of the velocity measurement close to the impingement surface. As a result, velocity measurements close to the substrate are less frequent and the statistical uncertainty in this region is higher. Increasing the camera frame rate would improve the spatial velocity resolution, but also increase thermal stresses on the high-speed LED illumination and an acquisition rate of f = 25 khz presents an acceptable comprise between hardware limitations and required temporal resolution. 4. Concluding Remarks This paper demonstrates three-dimensional ultra-high-speed measurements of micron-sized particles in a supersonic underexpanded gas flow using astigmatism particle tracking velocimetry (APTV). In the present case a highly magnified high-speed imaging system employed in order to mitigate the limited spatial resolution modern ultra-high-speed digital recording arrays. By introducing controlled image distortions to the imaging system it is possible to code the 3D particle position onto a 2D image requiring only a single camera to measure the 3C3D particle velocity field. This is achieved by including a cylindrical lens in front of the high-speed recording array that causes an elliptical distortion of the particle images according to their depth position in the measurement volume. Using a high power LED the illumination is sufficient to record particle images with a SNR that allows reliable determination of the particle image position and shape. From the reconstructed 3D particle position the 3C3D particle trajectories are obtained using a higher-order particle tracking scheme that takes into account the high temporal resolution of the measurement to improve the robustness and accuracy of the tracking. The paper demonstrates the applicability of high-speed imaging and APTV to measure the particle velocity in a supersonic underexpanded impinging jet. The particles leave the nozzle at subsonic speed and are continuously accelerated by the surrounding gas flow in a manner depending on the local flow structure (i.e. NPR, Z/D). It is also shown, that the flow structure influences the impingement angle of the particles and that a recirculation region forms above the flat plate. References [1] N. A. Buchmann, C. Atkinson, D. Honnery, and J. Soria. High-speed 3d particle tracking using tomographic holographic reconstruction. In 1th International Symposium on Particle Image Velocimetry, Delft, Netherlands, 213. [2] N. A. Buchmann, C. Atkinson, and J. Soria. Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows. Measurement Science & Technology, 24:245(14pp), 213. [3] N. A. Buchmann, C. E. Willert, and J. Soria. Pulsed, high-power led illumination for tomographic particle image velocimetry. Experiments in Fluids, 53: , 212. [4] C. Cierpka, B. Lütke, and C. J. Kähler. Higher order multi-frame particle tracking velocimetry. Experiments in Fluids, 54:1533, 213. [5] C. Cierpka, M. Rossi, R. Segura, and C. J. Kähler. On the calibration of astigmatism particle tracking velocimetry for microflows. Measurement Science & Technology, 22:154, 211. [6] C. Cierpka, R. Segura, R. Hain, and C. J. Kähler. A simple single camera 3C3D velocity measurement technique without errors due to depth of correlation and spatial averaging for microfluidics. Measurement Science & Technology, 21:4541, 21. [7] L. J. Forney. Particle impaction in axially symmetric supersonic flow. Aerosol Science and Technology, 15:49 59,

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