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

John O Dabiri,Sanjeeb Bose,Brad J Gemmell,John H Costello,Sean P Colin

doi:10.1242/jeb.092767

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, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-of-plane 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.

Highlights

A long-standing challenge for empirical observations of fluid flow is the inability to directly access the instantaneous pressure field using techniques analogous to those established to measure the velocity field
The first flow is used to characterize a quasi-steady implementation of the algorithm, in which the pressure field is estimated from a single velocity field measurement
Quasi-steady pressure estimation Fig. 1 compares an instantaneous pressure field from the numerical simulation of flow past a stationary bluff body with the pressure field estimated from the corresponding velocity field using the quasi-steady form of the present algorithm

Summary

Introduction

A long-standing challenge for empirical observations of fluid flow is the inability to directly access the instantaneous pressure field using techniques analogous to those established to measure the velocity field. If each integration path is taken as a straight line through the domain, the method requires interpolation of the estimated pressure gradient field in order to evaluate integration path points that do not coincide with the original data grid.

Results

Conclusion