Comparison of momentum and impulse formulations for PIV-based force estimation

The estimation of fluid-induced loads using particle image velocimetry (PIV) data is investigated using momentum- and impulse-based control volume methods, which require additional calculations of pressure and vorticity surrounding the immersed body, respectively. A new, comprehensive comparison of the two methods is presented based on two-dimensional velocity data. The effects of random error, finite spatio-temporal resolution, and spatial filtering of the velocity fields are considered using numerical (CFD) data of flow around a stationary circular cylinder in a steady freestream at a Reynolds number of . In general, the momentum method is found to be more robust, exhibiting lower random-error sensitivity and lower errors due to discretization, except at coarse spatial resolutions, for which a significant underestimation of drag arises using the momentum method. The impulse method is best suited to cases where vorticity does not leave the control volume, or in cases where a deforming control volume can be defined to minimize the presence vorticity on the outer control surface. For example, the impulse method performed as well as the momentum method when applied to particle image velocimetry (PIV) data obtained around a cylinder accelerating from rest in quiescent fluid (with a peak Reynolds number of 5100). For the broad class of flows involving a steady freestream and an established wake, the momentum method can be applied with greater confidence than the impulse method.