Evaluating fluid forces on bluff bodies using partial velocity data

The forces on a bluff body are evaluated by using only velocity information from flow simulations. The “flux” equation formulated by Noca et al. 1999 in 551 is used to achieve this. This only requires time and space derivatives of the velocity field on a surface encompassing the bluff body. This study aims to quantify the accuracy of force predictions when only a subset of the field data is used. Accurate simulations of the two-dimensional (2-D) and three-dimensional (3-D) flow past a circular cylinder provide the time-dependent velocity fields. For purely 2-D flow, the velocity information is limited to a section of the wake and potential flow is assumed on the remaining surface. When the flow is three dimensional, it is assumed that only a 2-D projection of the velocity field on a single plane is known (as is often the case with experimental PIV measurements). Statistical quantities of the lift and drag forces from these predictions are compared to the forces obtained by directly integrating the pressure and shear stress over the body surface. The relative phasing between the two signals is also presented in the 2-D flow case. In the 3-D flow case, predictions from numerous planes are averaged in an attempt to improve the overall force estimate. The results show that some quantities can be accurately predicted, such as the phasing of the lift and drag forces in the 2-D simulations, and the mean drag force and the fluctuating lift force for the 3-D flows. Predictions are generally better when the integration boundary is closer to the cylinder. Importantly, this study provides an indication of the maximum accuracy achievable using restricted experimentally derived velocity fields to compute forces experienced by bluff bodies.