High Speed Particle Image Velocimetry Measurements During Water Entry of Rigid and Deformable Bodies

Transcription

1 High Speed Particle Image Velocimetry Measurements During Water Entry of Rigid and Deformable Bodies A. Nila 1,*, S. Vanlanduit 1, S. Vepa 2, D. Van Nuffel 2, W. Van Paepegem 2, J. Degroote 3, J. Vierendeels 3 1: Department of Mechanical Engineering, Vrije Universiteit Brussels, B-1050 Brussels, Belgium 2: Department of Materials Science and Engineering, Universiteit Gent, 9000 Gent, Belgium 2: Department of, Heat and Combustion Mechanics, Universiteit Gent, 9000 Gent, Belgium * correspondent author: alexandru.nila@avrg.be Abstract This paper presents experimental results regarding the slamming of rigid and deformable bodies on to initially calm water surface with constant entry speeds. Three test cases, corresponding to a rigid wedge, a rigid cylinder and a deformable cylinder are analyzed. High speed Particle Image Velocimetry (PIV) is employed in order to determine features of the flow around slammed bodies, with interest in the velocity field and free surface elevation characterization. The free surface elevation profiles are compared with analytical results, and are found to be in good agreement. Further, numerical simulations using the LS- Dyna software are conducted for the rigid wedge test-case, and the velocity fields obtained from the experiments are compared with calculated velocity fields from the simulations, showing good overall agreement. The limitations of the optical technique are also discussed. For the cylinder slamming test cases, free surface elevation profiles and velocity fields are presented, with a comparison of the flow features between rigid and deformable cylinders test cases. This approach attempts to offer the possibility of validating numerical results with non-intrusive measurements performed by PIV for test cases that are numerically challenging, such as the deformable body impact on the water surface. 1. Introduction Wave impact or slamming is a phenomenon that has drawn attention from researchers in the fields of ocean engineering, ship engineering, or more recently offshore structures for decades. The slamming effect can be identified as having two distinct manifestations in real life applications, namely bottom slamming, which occurs when a structure rises out of the water and then falls back into the water, and breaking wave slamming, which occurs when a wave breaks as it hits the structure from a side. Both types play an important role in the design process of offshore structures, and it is very important to fully understand the loading range and parameters that effect it. First studied as an application to seaplane floats stress analysis by von Karman [1] in 1929, the problem of water impact on two-dimensional bodies was solved analytically by approximating the shape of the object with a flat plate. Later, Wagner [2] continued the research by including the effects of the water uprise on the body in a simplified way.. Mei et al. [3] developed an analytical solution for the wave impact problem of general two-dimensional bodies where exact body boundary conditions are fulfilled. Numerous papers during the past decades have dealt with slamming phenomenon by using numerical simulations - Dobrovol'skaya [4], Zhao and Faltinsen [5]- or experimental investigations - Zhao and Faltinsen [6], Lin and Shieh [7], De Backer et al. [8], Hughes [9]. All this previous work has contributed to a better understanding of the impact phenomenon and occurring loads. However, little work has been carried out regarding flow characterization of the problem (Greenhow and Lin [10]). In the present paper, non-intrusive measurements performed by means of Particle Image Velocimetry, are used to analyse the impact problem of axisymmetric bodies on to the water surface. The results are compared with results of CFD analysis performed with the LS- Dyna software in which the experimental conditions are reproduced and the same field of view is used for comparison

2 2. Experimental set-up In the present paper three different experimental test cases are presented. The test cases correspond to three different bodies that were used in the slamming experiments, namely a rigid wedge, a rigid cylinder and a deformable cylinder. The slamming set-up illustrated in Fig. 1 was built at the Department of Mechanical Engineering at VUB Brussel, having in mind the deployment of the PIV technique from the start, therefore conferring optimal optical access. It comprises of a Plexiglas water tank of 1000mm x 600mm x 500mm, and a linear motor that controls the vertical movement of the body connected through a rigid aluminium profile assembly. The linear motor used is a Copley Controls XM3804S ServoTube Module with an accuracy of 350 micron, controlled through a Xenus XTL23018S controller that provides the option of programmable digital input functions. Feedback is provided on actual load position, velocity and acceleration. The high speed PIV system used for the measurements is comprised of a Quantronix Darwin Duo Nd:YLF double pulsed laser capable of repetition rates of up to 10kHz, with a total pulse energy of 50mJ, and a 12 bit Photron Fastcam SA1.1 camera, with a CMOS sensor and 1024 x 1024 pixel resolution (at 5 khz). The seeding used is comprised of hollow glass spheres of 10 µm mean diameter. Fig. 1 - Experimental set-up As mentioned before, three test cases are discussed, corresponding to three different impacting bodies. For the first test case, a 90 steel wedge with a width of 240 mm and length of 400 mm was used. The wedge is pushed downward with a controlled, constant speed of 1.5 m/s, with an error margin of about 5% during the analysed time sequence. High speed recordings of the seeded flow are taken at 10kHz for a total recording time of 37 ms. The second test case represents the rigid cylinder slamming, in which a PVC cylinder with a diameter of 86 mm and length of 400 mm is impacted on the water surface, for three different entry speeds, of 1 m/s, 1.5 m/s and 2 m/s. The cylinder is hollow, with a thickness of 5 mm, however due to the reduced impact velocities, it is considered to be acting as a rigid body

3 The third body used in the experiments is a glass fiber composite cylinder, with the same dimensions as the PVC cylinder. The composite cylinder is manufactured by hand layout with two glass fiber mat layers and epoxy resin, having a thickness of 1mm. For the slamming experiments, the same three entry velocities were considered as in the rigid cylinder case. For both the two cylinders, recordings were taken at fps for a total time of 100ms.For all test cases here considered, the flow is assumed to be left-right symmetric at the moment when the tip of the body touches the water surface, therefore only half of the wedge and cylinders respectively are considered for the analysis in both experimental measurements and the numerical model. 3. PIV processing For the post-processing of the recorded images, a commercially available software - PIVview - is used with automated batch processing of the sequence of pictures. The velocity data is recovered on a grid of 102 mm by 102 mm for the wedge case, and 170 mm by 155 mm for the cylinder cases (in vertical and horizontal direction respectively). Cross-correlation on a 32 by 32 pixel interrogation window with 50% overlap, and multi-grid scheme was found to be the appropriate setting for the entire batch of pictures. Sub-pixel image shifting and 3-point Gauss fit was used for peak fitting, resulting in a mean correlation coefficient of 0.8 for the wedge case and 0.87 for the cylinder. However, to further improve the results, the algorithm is adjusted to include automated adaptive masking of the body and of the air region. This procedure lead to a significant improvement in outlier detection and correlation coefficient values, as can be seen in Fig. 2, where valid data percentages are plotted against the entire time series of the experiment. As observed, the error increases slightly at later stages of the experiment for the wedge case, as the effective field of view (water region) decreases and less particle image pairs are available for correlation. However, the masking procedure is found to give a considerable increase of valid velocity data, with around 10% throughout the experiments. Fig. 2 - Evolution in time of valid data detection, with and without masking. Left - wedge slamming sequence; Right - cylinder slamming sequence The masking procedure is done in two steps: first the body is masked off using information on actual position from actuator controller. This approach was preferred due to the flexibility conferred by knowing the position of the body at each time step thanks to the position encoder of the controller. Secondly, using contours of brightness levels, the free surface is identified on the images and masking of the air region is performed. Fig. 3 shows the raw data and the processed - 3 -

4 images after identification of the features in the image for the wedge test case. Fig. 3 - PIV data at time t = 20.2 ms. Left - PIV raw image; Middle - Intensity contour image; Right - Simplified image with feature identification Feature identification is performed by selecting the contours of image intensities according to their size, shape and location. The particle images are filtered out and the wedge body image is recognized based on current position in the frame and body shape. Then, the free surface is identified and the region above it is masked off, resulting in complete masking of the wedge body and air. The same procedure is applied to the rigid cylinder test case. 4. Wedge slamming The first step taken in the analysis of the results was to compare the free surface elevation profiles with available data in literature. The free surface contours information is provided for each time step by the masking procedure explained above, and the position of the body is known from the actuator encoder information. Three snapshots of the free surface profiles are identified in Fig. 4, corresponding to three time steps, at 12.8 ms, 20.2 ms and 27.6 ms respectively. The information is made dimensionless by dividing with Vt, which is the instantaneous draft relative to calm water, for purpose of comparison with the analytical solution of Mei et al. [3]. As can be observed in Fig. 5, the comparison with the solution of Mei results in a very good agreement between the two. Fig. 4 - Free surface elevation for wedge impact with constant speed V=1.5 m/s - 4 -

5 Fig. 5 - Comparison of free surface elevation for wedge impact with constant speed between PIV and the analytical solution of Mei et al. [3]. Vt is the instantaneous draft relative to calm water. For validation purposes, a numerical simulation using the commercial software LS-Dyna was performed, with experimental conditions reproduced in a quasi-three dimensional fashion, with only one element in thickness, and constrained degrees of freedom in this direction. The model uses a non-uniform grid that stretches from the symmetry line of the wedge body to the walls of the water tank, with the lagrangian boundary of the wedge body overlapped onto the fluid mesh. The element size is kept constant in the region of interest that is used for comparison with the PIV measurements, and it is increased away from this region. The pressure coefficient resulting from the LS-Dyna simulations - C p - as determined from equation (1) where p is the pressure on the wedge wall, p a the atmospheric pressure, V is the entry velocity and ρ the fluid density, is compared against the results of Mei et al. [3] and Wu et al. [11] with good agreement (Fig. 6) p pa C p = (1) 1 V 2 ρ 2 Fig.6 - Pressure Coefficient (C p ) on wedge wall. Vt - the instantaneous draft relative to calm water - 5 -

6 The velocity field determined from the PIV measurements is compared against results of the simulations for the entire time series. Fig. 7 shows the normalized root mean squared (NRMS) error between the two velocity field results across the entire field of view, over the considered time series. For the first 1 ms of water entry a higher error between measured and numerical velocity fields can be observed, due to the small correlation coefficient caused by the highly localized flow. For the cross-correlation algorithm, on average only one particle image pair is giving true velocity vector information for this first stage of impact. After the initial moment of impact, the error is around 10%, and after 10 ms, it becomes less than 5% error. This is in part due to the fact that small variations in wedge velocity are inevitable in the experimental conditions, as opposed to the constant speed imposed in the CFD model. Fig. 7 NRMS Error levels. Highlighted values are for time steps at 12.8 ms, 20.2 ms, and 27.6 ms. Although results are generally in good agreement, qualitatively, a few differences are to be noticed. The PIV measurements tend to underestimate the velocity magnitude especially in the region close to the spray root, where three dimensional effects also need to be accounted for, and where particle image pairs availability is limited. Also, the differences in fluid velocities close to the wall of the wedge body are mainly due to the presence of surface reflections. Snapshots of the fluid velocity field at 27.6 ms are presented in Fig. 8. In the left column, PIV measured horizontal and vertical components of velocity show a good qualitative agreement with the results of the simulation (right column), with the measured y-component of velocity giving a closer quantitative agreement. The area with larger errors between measurements and simulations is close to the spray root, where PIV data is underestimating the magnitude. This is caused by reflections of the laser light on the wedge wall and free surface, and limitations to particle images pairs for correlation. Although a few particle images are present in this area, the high velocity at the spray root causes the inability to accurately get enough image pairs in between two consecutive frames. Also, the high velocity gradients cannot be captured on such a small area, as PIV interrogation windows are still limited by the presence of enough particle image pairs

7 Fig. 8 - Velocity magnitude in m/s at t = 27.6 ms. Left column - PIV Data. Right column - Numerical results. 5. Cylinder slamming In the case of the cylinder slamming, as mentioned earlier, two types of cylinders were used. On one hand, a PVC cylinder with a wall thickness of 5 mm was deployed and considered to be a rigid cylinder slamming case. The second cylinder as can be seen in Fig 9., had the same dimensions and was fabricated from chopped glass fiber mats and epoxy resin, in two layers, with a wall thickness of 1 mm. In both cases, the cylinders were fixed in a line contact fashion using two steel thin plates on the upper side of the cylinder. The plates were attached to the aluminum profiles connected to the actuator. Then, the cylinders were impacted using three constant entry speeds, namely 1 m/s, 1.5 m/s and 2 m/s

8 Fig. 9 - Composite cylinder The masking procedure as well as the PIV post-processing algorithm used are the same as those used for the wedge slamming measurements. However, if for the rigid cylinder the same procedure could be applied without modifications, in the deformable cylinder case, due to the shape evolution of the body, identification of the body shape and masking was performed optically from the highspeed recording, thus eliminating the first step using actuator encoder information. It was found that the deformable cylinder had a maximum displacement of 6.5 mm, reaching an elliptical crosssection, 64.8 ms after impact. In Fig. 10, the free surface profiles of the rigid body slamming for three time instances at 6 ms, 36 ms and 72 ms, are presented. Free surface elevation profiles agree well with available literature results from Greenhow and Lin [10]. Fig Free surface elevation for rigid cylinder impact with constant speed V=1 m/s In Fig. 11 the free surface evolution (right) and body shape evolution (left) for the deformable body are presented for several time instances

9 Fig Free surface elevation for rigid cylinder impact with constant speed V=1 m/s (left) for t = 4.8ms, 14.8ms, 24.8ms, 34.8ms, 44.8ms, 54.8ms and 64.8ms; and deformable cylinder shape (right) for t = 0ms, 34.8ms and 64.8ms The measured velocity fields for the time sequence of the cylinder water entry show important differences between the rigid cylinder case and the deformable one, because of the low stiffness of the composite cylinder that caused it to deform considerably. In Fig. 12, results of the horizontal and vertical components of the velocity are compared between the rigid and the deformable cylinders for two time steps, at 36ms and 72ms after impact. The results are made dimensionless by division with the value of the entry velocity. It was observed that the velocity magnitudes are a factor of 2 smaller for the composite cylinder in both x and y-directions for the initial stages of water entry. However, after 64 ms, as the cylinder reaches its maximum displacement and continues into the water without deforming, the flow features present the same characteristics as for the rigid cylinder case, and the orders of magnitude are comparable. The flow features are indicating the same trends in both cases, with a high velocity magnitude at the spray root of the jet, which for these measurements has been cut-off for reasons of improving the signal-to-noise ratio of the PIV data, due to the reasons discussed in the wedge slamming test case. 6. CONCLUSIONS The present paper elaborates on the use of high-speed PIV measurements on the slamming phenomenon. Rigid and deformable bodies are considered, namely a rigid wedge, a rigid and a deformable cylinder. The comparison of flow features between the experimentally determined data and analytical and simulations results offer an understanding to the limitations and benefits of this optical technique. The experimental velocity field showed overall good agreement, with higher errors in the spray root region, where 3D effects, seeding particle scarcity and surface reflections prove to be a challenge for the optical technique. However, the possibility of having full-field velocity measurements that can be used for validation of numerical codes when more difficult boundary conditions and/or fluid-structure interaction complexity is obvious. Also, PIV data could be useful in calculating pressure fields and loads on the slamming bodies by solving the pressure Poisson equation with a omni-directional integration scheme in order to localize the effects of the errors in the region of the spray root and to prevent these errors from contaminating the entire flow field

10 Fig Velocity magnitudes (dimensionless) at t = 36 ms and t = 72ms. Rigid cylinder (left) and deformable cylinder (right)

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