Pressure–Rate-of-Strain, Pressure Diffusion, and Velocity–Pressure-Gradient Tensor Measurements in a Cavity Flow

Hydrodynamic stress maps on the surface of a flexible fin-like foil

“…Omni-directional schemes can provide higher accuracy [69,75,84,105] but for 3D implementation, the use of GPU-based calculation was demonstrated to achieve accelerated computational times [106]. The terms containing out-of-plane derivatives of the velocity (grouped separately in Eq 6) are not included directly in the computation.…”

“…An alternative approach to calculate the total hydrodynamic force relies on a momentum balance inside a control volume and was also employed in the context of flapping fin-like structures [26,27,35,[54][55][56][57][58][59][60][61][62][63][64][65][66]. A non-invasive method to determine the three-dimensional pressure field inside an unsteady flow domain consists in solving the Navier-Stokes equation, in either one of the two following forms: (1) the pressure gradient is expressed in terms of spatial and temporal derivatives of the velocity field and engaged in a direct spatial integration to compute the pressure values everywhere in the domain [17,[66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84], or (2) the Laplacian of the pressure is obtained by taking the divergence of the latter pressure gradient formulation, and this so-called Poisson equation is solved numerically [70,73,74,81,[85][86]…”

“…Recently, a detailed analysis of error propagation in the omni-directional method for the integration of the pressure gradient field was presented in [104]. Omni-directional approaches offer high levels of accuracy in the resulting pressure field [69,75,84,105,106]. Alternatively, reducing experimental errors in raw fluid velocity fields prior to integrating the pressure gradient can result in a significant improvement of the pressure field accuracy even when using a low number of integration paths such as in the case of the eight-paths integration scheme of [77], as demonstrated in [107] with an irrotation correction method.…”

Reynolds stress tensor and pressure-related turbulence transport terms measured by time-resolved tomographic-PIV

“…A 75% overlap between the interrogation windows gives a vector spacing of 0.21 mm. In this paper, based on 140,000 instantaneous 3D realizations of the cavity flow, we will present converged turbulence statistics on all terms in the Reynolds stress transport equation, with an emphasis on the characterization of the magnitude of the intercomponent turbulence energy fluctuations represented by the pressure-rate-of strain terms, so as to verify the conjecture raised in Liu and Katz (2018) about the magnitude of the third component of the intercomponent energy transfer.…”

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Turbulence is inherently a three-dimensional and time dependent flow phenomenon (Pope, 2001). Because of the ubiquitous existence of turbulent flows in nature, accurate characterization of turbulent flows, either through experimental measurements or through direct numerical simulations, is of paramount importance for modeling turbulence (Liu and Katz, 2018). Since its inception in 1984 (Adrian, 1984), Particle Image Velocimetry (PIV), among several other conventional techniques used for turbulence measurements, has been a valuable tool for providing reliable experimental data for turbulence research.

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