Optimal pressure reconstruction based on planar particle image velocimetry and sparse sensor measurements
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RESEARCH ARTICLE
Optimal pressure reconstruction based on planar particle image velocimetry and sparse sensor measurements Roshan Shanmughan1 · Pierre‑Yves Passaggia1 · Nicolas Mazellier1 · Azeddine Kourta1 Received: 16 April 2020 / Revised: 15 July 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract An adjoint-based approach for the accurate estimation of pressure of steady turbulent flows is developed and validated using both numerical and experimental data. The approach considers a simple algorithm to correct for the pressure in the domain solely based on sensor measurements at the wall. Adjoint looping is shown to provide both an accurate and fast algorithm where only minor modifications are required to implement the present procedure in an existing pressure solver. The algorithm is first validated using a set of time-averaged unsteady Reynolds-averaged Navier–Stokes equation in the wake of a D-shaped bluff body. The effect of noise is also investigated and shows that combining both a Helmholtz decomposition to recover a divergence-free velocity field and the adjoint-based correction provides consistent results for the pressure field. The approach is then applied to a wind-tunnel experiment for the same geometry. An independent comparison of drag, estimated between pressure measurements at the wall and the corrected pressure field shows good agreement. Finally, the role of domain size for the adjoint-based approach is addressed. The present algorithm naturally extends to time-dependent measurements without additional modifications. Graphic abstract
1 Introduction
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00348-020-03059-6) contains supplementary material, which is available to authorized users. * Pierre‑Yves Passaggia pierre‑yves.passaggia@univ‑orleans.fr 1
University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France
Pressure plays an important role in the dynamics of fluid flows. It is linked to various physical flow phenomena such as the formation of coherent structures (Elsinga and Marusic 2010; Naka et al. 2015), vorticity fluctuations (Brachet 1991; Pumir 1994), wake topology of separated flows (Roshko 1955, 1993; Spedding and Hedenström 2010; Felli et al. 2011), inception of cavitation (Ran and Katz 1994; Liu and Katz 2008), aero-acoustics (Koschatzky et al. 2011) to only name a few. Pressure is also a key component to
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obtain aerodynamic force estimated from near-field wake data for immersed bodies (Unal et al. 1997; Van Oudheusden et al. 2006; David et al. 2009; Ragni et al. 2009). Alternative approaches have been proposed to circumvent the requirement for pressure. An earlier example can be found in the works of Antonia and Rajagopalan (1990) where the transverse momentum equation is used to approximate the pressure in the wake and estimate drag. But it fails in the near wake because of strongly non-parallel-shear component of
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