An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

Abstract

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, selfpropelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-ofplane effects. Particle image velocimetry measurements of a freely swimming jellyfish medusa and a freely swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data.

Pressure evolution in the shear layer of forming vortex rings

“…In order to examine the pressure evolution in the shear layer of developing vortex rings, pressure fields were derived from the PIV velocity vector fields using a recently developed computational algorithm [12]. This method derives the pressure gradient field using the Navier-Stokes equation and integrates it along several paths throughout the domain.…”

“…In contrast to an earlier method by Liu and Katz [13], median polling, rather than averaging, is then used to select the best estimate for the pressure at every point. Further details concerning this algorithm can be found in Dabiri et al [12], which also presents a validation of the model using several test cases. A review of other pressure calculation techniques derived from PIV data can be found in van Oudheusden [14].…”

“…A particularly relevant validation performed on the present pressure algorithm, detailed in Appendix 1 of Dabiri et al [12], studies the effect of adding Gaussian noise to the velocity field of a computational simulation of 2D flow past a square. The authors found that for signal-to-noise ratios comparable to those in typical PIV data sets, the quantitative pressure estimates are consistent with the pressure values found when noise is omitted.…”

Characterization of zebrafish larvae suction feeding flow using μPIV and optical coherence tomography

“…The pressure gradient can be computed from the velocity field, including two-dimensional effects (Dabiri et al 2014);…”

Load-estimation techniques for unsteady incompressible flows

“…Unal et al (1997), Jardin et al (2009), Rival et al (2010, and Dabiri et al (2013) have used this method to good success, although challenges with error propagation are rampant. Alternatively, if the complete velocity field within the control volume is accessible and boundary conditions that are known, the Poisson equation can be used to extract the pressure distribution instead, as performed by van Oudheusden et al (2007), and then later reviewed in detail by van Oudheusden (2013).…”