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Evaluation of the pressure field on a rigid body entering a quiescent fluid through particle image velocimetry

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Abstract

The objective of this work is to verify the accuracy of indirect pressure measurement from particle image velocimetry in water entry problems. The pressure is evaluated by solving the incompressible Navier–Stokes equations, whose kinematic components are estimated from particle image velocimetry. We focus on the water entry of a rigid wedge, for which we explore variations of the entry velocity. Experimental results are verified through comparison with well-established analytical formulations based on potential flow theory. Our findings demonstrate the feasibility of accurately reconstructing the hydrodynamic pressure field over the entire duration of the impact. Along with a thorough experimental validation of the method, we also offer insight into experimentally relevant factors, such as the maximum resolved fluid velocity and the required spatial integration area.

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Acknowledgements

This work was supported by the Office of Naval Research through the Grant N00014-10-1-0988 with Dr. Y.D.S. Rajapakse as the program manager. Views expressed herein are those of the authors and not of the funding agency.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, 6 MetroTech Center, Brooklyn, NY, 11201, USA

    Riccardo Panciroli & Maurizio Porfiri

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  1. Riccardo Panciroli
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  2. Maurizio Porfiri
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Correspondence to Maurizio Porfiri.

Appendix

Appendix

1.1 A Influence of the size of the integration area on the accuracy of the pressure estimation

To ascertain the robustness of the present method to the variation of the size of the integration area, we study its influence on the measurement of the hydrodynamic pressure. The analysis is performed by independently varying the horizontal and the vertical dimensions of the region (Fig. 14).

A quantitative comparison between results obtained with the largest integration region, corresponding to the whole field of view, and those stemming from smaller domains is performed by computing the error defined in Eq. (6), with \(\hat{p}_{\rm t}(i)\) and p t(i) being, respectively, the measurement of the pressure obtained by using the full field of view or a smaller domain. The number of data points N on the wet surface of the wedge over which the error is computed remains the same when the integration domain is varied.

Thus, we find that the error is reduced by three orders of magnitude when expanding the horizontal size of the integration region from once to twice the horizontal wet length of the wedge r, shown in Fig. 1, independently from the number of vectors over which the pressure is computed. Instead, results are not affected by the vertical dimension of the domain.

The present method is thus found to be robust to variations of the size of the integration region. The increase in the error when reducing the horizontal dimension is attributed to the loss of information in the bright area shown in Fig. 5. In this case, the reference pressure is not imposed on the free surface, but on an interior point, leading to substantial errors. We expect that such uncertainties could be reduced by minimizing light reflections at the water surface.

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Panciroli, R., Porfiri, M. Evaluation of the pressure field on a rigid body entering a quiescent fluid through particle image velocimetry. Exp Fluids 54, 1630 (2013). https://doi.org/10.1007/s00348-013-1630-3

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