Simultaneous digital image correlation/particle image velocimetry to unfold fluid–structure interaction during air-backed impact
Introduction
Warships and submarines should be designed to survive extreme loading conditions, such as shock waves caused by underwater explosive blasts (Porfiri and Gupta, 2009, Mouritz, 2017). Germane to these problems is the loading configuration of many structural elements, which are in contact with both water and air. Understanding the dynamic response of air-backed structures to hydrodynamic loading is an open area of research, which is critical to the design of material solutions for resilient, high-performance marine vessels.
The response of air-backed structures to impulsive loading has been investigated extensively in laboratory settings (Hung et al., 2005, LeBlanc and Shukla, 2010, Kwon and Owens, 2011, LeBlanc and Shukla, 2011, LeBlanc and Shukla, 2014, Ren and Zhang, 2014, Avachat and Zhou, 2015, Avachat and Zhou, 2016, Kwon et al., 2016, Huang et al., 2016, Ren et al., 2019). Several loading mechanisms have been employed in the literature in an effort to experimentally reproduce the impulsive loading conditions that might be experienced by naval vessels. For example, some authors have studied the impact of a rigid impactor on an air-backed structure, which could be reminiscent of blast debris impacting a vessel after the initial shock wave (Kwon and Owens, 2011, Kwon et al., 2016). On the other hand, shock waves have been generated by detonating small amounts of explosives (Hung et al., 2005, LeBlanc and Shukla, 2010, LeBlanc and Shukla, 2011, LeBlanc and Shukla, 2014, Ren et al., 2019), or by firing projectiles on sliding pistons that are in contact with water (Huang et al., 2016). Through the quantification of the structural deformation and the characterization of the pressure wave, the response of a variety of air-backed composites (Avachat and Zhou, 2015, Huang et al., 2016, Avachat and Zhou, 2016, Ren et al., 2019) and monolithic panels (Hung et al., 2005, Ren and Zhang, 2014) has been examined. Notably, some studies have even been carried out at a larger scale, beyond laboratory setting, shedding light on the effectiveness of different material solutions and geometries on mitigating underwater blasts (Arora et al., 2012).
Despite remarkable experimental (Hung et al., 2005, LeBlanc and Shukla, 2010, LeBlanc and Shukla, 2011, Kwon and Owens, 2011, LeBlanc and Shukla, 2014, Ren and Zhang, 2014, Avachat and Zhou, 2015, Avachat and Zhou, 2016, Huang et al., 2016, Kwon et al., 2016, Ren et al., 2019), theoretical (Rajendran and Lee, 2008), and numerical efforts (LeBlanc and Shukla, 2010, Ren and Zhang, 2014, Avachat and Zhou, 2016, Ren et al., 2019, Meng et al., 2019), our understanding of the fluid–structure interaction associated with hydrodynamic loading of air-backed structures remains elusive. Full-field measurements of structural deformation have been achieved through three-dimensional digital image correlation (DIC) (LeBlanc and Shukla, 2014, Huang et al., 2016), but, to the best of our knowledge, information about the flow physics is limited to point measurement via pressure transducers (Hung et al., 2005, Ren and Zhang, 2014, Avachat and Zhou, 2015, Avachat and Zhou, 2016). To date, the investigation of fluid–structure interaction is largely based on numerical simulations, which rely on critical assumptions about the form of the hydrodynamic loading used as input for the fluid–structure interaction solvers (LeBlanc and Shukla, 2014, Ren and Zhang, 2014, Meng et al., 2019). Although numerical studies have demonstrated reasonable agreement with point-wise experimental measurements, the lack of simultaneous, full-field measurement of flow physics and structural dynamics hinders our understanding of the mechanisms underlying fluid–structure interaction in air-backed impact.
In this study, we propose a combined experimental framework based on DIC and particle image velocimetry (PIV) for the study of fluid–structure interactions due to impulsive hydrodynamic loading of air-backed structures. Toward this aim, we designed an experimental setup, consisting of a flexible panel clamped at the bottom of a water tank. The impulsive hydrodynamic loading was elicited through a solid end-effector penetrating the water surface, actuated by a pneumatic system. The structural response of the plate and the flow field in its vicinity were simultaneously quantified using the combined DIC/PIV approach, yielding spatially- and temporally-refined measurements of the fluid–structure interaction.
DIC is a full-field experimental technique for the quantification of surface deformation of structures (Chu et al., 1985). DIC requires the creation of a random speckle pattern on the surface of the structure, which is then recorded during the experiment through a high-speed camera. The surface displacement field is computed through cross-correlation of the recorded speckles images. In the literature, important insight has been gathered about the response of structures to air-back impact through the use of three-dimensional DIC. For example, DIC has helped elucidate blast-resistance of sandwich structures to impulsive pressure loading (LeBlanc and Shukla, 2011, Huang et al., 2016) and quantify the effect of surface coating on composite plates subject to shock (LeBlanc and Shukla, 2014). Different from standard practice (Chu et al., 1985, Pan et al., 2009), where the deflection of the test plate could be recorded by a side-view camera, in our experiment, the side-view of the plate was obstructed by the clamp, thereby hindering direct quantification of the deflection. To mitigate this issue, we adopted an indirect approach, in which we obtained the out-of-plane deflection from a bottom-view camera, whose axis was perpendicular to the plate surface. First, the apparent in-plane deformation was quantified through DIC. The out-of-plane deflection was then reconstructed from the apparent in-plane deformation using a pin-hole camera model (Tay et al., 2005, Quan et al., 2008, Réthoré et al., 2014). Although the deflection could also be fully recorded by three-dimensional DIC similar to LeBlanc and Shukla, 2011, LeBlanc and Shukla, 2014 and Huang et al. (2016), the use of a single camera constitutes a significant methodological advancement toward the simultaneous acquisition of flow physics.
The flow physics associated with air-backed impact was, in turn, simultaneously studied through PIV. PIV is a non-intrusive technique, which constitutes the gold standard for flow measurement in experimental fluid mechanics (Raffel et al., 2007). Similar to the speckle pattern of DIC, the fluid flow is seeded with micro-sized particles. Within planar PIV measurements, a laser sheet is used to illuminate the fluid flow on a desired measurement plane, and a high-speed camera is employed to record the motion of the particles therein. Analogously to DIC, the velocity field is obtained through cross-correlation of consecutive particle images. Based on the velocity field, the hydrodynamic pressure can be reconstructed integrating Navier–Stokes equations (van Oudheusden, 2013).
A combined DIC/PIV approach has been demonstrated in our recent work (Zhang and Porfiri, 2019), in which we investigated low speed impact response of a flexible panel resting on a water surface. Therein, the accuracy of a combined approach was validated through comparison with sensor readings. Distributed measurements of the flow field and the plate deflection revealed a complex interaction between the fluid flow and structural response.
The present work is different from Zhang and Porfiri (2019) in both the problem it addresses and the methodological advances it brings forward. The problem considered in Zhang and Porfiri (2019) entailed two-dimensional deformation of a flexible plate, in contrast with three-dimensional deformation considered herein. Addressing this issue required the formulation of an experimental approach that could leverage symmetries in the problem to tease out out-of-plane deflection from in-plane membrane stretching. The presence of three-dimensional deformation patterns also required the development of a dedicated approach for warping and dewarping particle images to perform PIV. While a steady free surface close to the structure was available to perform the integration of Navier–Stokes equations in Zhang and Porfiri (2019), a tailored approach was required for the study of air-backed impact. Not only was the free surface in our experiments far from the structure, but also it experienced violent sloshing during the motion of the end-effector. Specifically, the pressure reconstruction process was combined with direct pressure measurement using a pressure sensor installed at the bottom of the end-effector. Using sensor measurements as a reference helped us mitigate the lack of a pressure reference point on the water surface, while offering a robust estimation of the hydrodynamic loading that reduced spatial accumulation of errors in the pressure integration process.
The rest of the paper is organized as follows. The experimental setup is described in Section 2. Details about our approach to data analysis across structural dynamics and flow physics are presented in Section 3. The main findings of our study are illustrated in Section 4, including spatially- and temporally-resolved measurements of structural dynamics and flow physics. The major conclusions of the work are summarized in Section 5.
Section snippets
Experimental design
We designed an experimental setup to investigate fluid–structure interaction associated with impulsive loading of air-backed panels, see Fig. 1(a). A water tank of dimensions 22.018.0 cm (length width height) was fabricated using clear acrylic panels (McMaster-Carr; 8560K355). A circular opening of radius was carved from its bottom to place a flexible panel of thickness . The panel was fabricated using a highly flexible material, Polydimethylsiloxane (PDMS), which has
DIC analysis
The structural response of the plate was quantified through DIC analysis of the speckle pattern. First, the apparent in-plane displacement was computed from the speckle pattern. A linearized pin-hole camera model was then implemented to infer the out-of-plane deflection from the in-plane displacement. The feasibility of this indirect approach was demonstrated in Tay et al., 2005, Quan et al., 2008 and Réthoré et al. (2014).
The in-plane displacement encoded in the speckle pattern was analyzed
Results and discussion
The unsteady fluid–structure interaction was quantified simultaneously through PIV and DIC. First, we studied the motion of the end-effector, from which we inferred a few characteristic physical quantities. Then, we measured several spatially-distributed variables, including the plate deflection, velocity and pressure field distributions, and hydrodynamic loading on the plate, toward the ultimate goal of investigating structural dynamics and flow physics.
Conclusions
In this study, we demonstrated a combined DIC/PIV experimental approach to investigate fluid–structure interaction associated with impulsive hydrodynamic loading on air-backed plates. Structural dynamics and flow physics were simultaneously quantified through DIC and PIV, respectively, leading to spatially- and temporally-resolved measurements, which have never been documented in the literature. Experiments were carried out in a custom-made setup, where an air-backed, highly-compliant circular
CRediT authorship contribution statement
Peng Zhang: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing - original draf. Alessia Carretto: Formal analysis, Investigation. Maurizio Porfiri: Conceptualization, Methodology, Formal analysis, Investigation, Writing review & editing, Supervision, Project administration, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the Office of Naval Research, USA through grant number N00014-18-1-2218 with Dr. Yapa D. S. Rajapakse as program manager. The authors would like to thank Ms. Amrutha Ajjarapu for her help with assembling the experimental setup.
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