A comparison of methods for evaluating time-dependent fluid dynamic forceson bodies, using only velocity fields and their derivatives

We continue with the 1997 work of Noca er al. and offer some additional clo sed-form expressions (and their derivations) for the evaluation of time-dep endent forces on a body in an incompressible, viscous, and rotational flow, which require only the knowledge of the velocity field (and its derivative s) in a finite and arbitrarily chosen region enclosing the body. In particu lar, we offer an expression for the force which only depends on the velocit y field (and its derivatives) on the surface of an arbitrary control volume . These expressions are particularly useful for experimental techniques lik e Digital Particle Image Velocimetry (DPIV) which provide time sequences of 2-D velocity fields but not pressure fields. For some common flow situatio ns (freely moving objects, flexible bodies, flying and swimming animals, lo w Reynolds number flows, soap him tunnels), these techniques may be more vi able than traditional methods (strain gages). The formulations can also be of some interest to the Computational Fluid Dynamics (CFB) community, espec ially when pressure is not evaluated explicitly, such as in vorticity-based algorithms. From a theoretical point of view, they provide an explicit rel ation between loading and flow structure. In the present work, the formulat ions are tested on a numerical flow simulation using a high-resolution vort ex method and experimentally with DPIV on a circular cylinder flow. (C) 199 9 Academic Press.