Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV

The unsteady aerodynamic forces acting on a square cross-sectional cylinder are investigated by means of time-resolved particle image velocimetry (TR-PIV) at Reynolds number 4,900. The objective of the investigation is to prove the feasibility of non-intrusive force measurements around two-dimensional bodies. The PIV measurements performed at a rate of 1 kHz enable a time resolved (TR) description of the vortex shedding phenomenon occurring at 10 Hz and to follow the time evolution of vortex dominated wake. The instantaneous aerodynamic force coefficients are obtained from the integration of the force equations within a control volume enclosing the object. The required instantaneous pressure distribution is inferred making use of two physical models: Bernoulli relation is adopted in the potential slowly-evolving flow region; in the turbulent wake, the Navier–Stokes equations are invoked to determine the pressure gradient spatial distribution, which integrated in space yields the pressure distribution. The spatial acceleration field is directly obtained from the temporal difference of the time-filtered velocity field. For a choice of the control volume approximately one model height away from the surface the contributions to the aerodynamic forces coming from the different terms of the force equation are individually examined. The convective term dominates the unsteady lift forces whereas the pressure term prevails for the drag. The temporal evolution of CL returns a clear periodic pattern in phase with the vortex shedding at a frequency of 10.1 Hz (Strouhal number St = 0.128) with oscillation amplitude of 0.9, whereas CD barely shows periodicity. The measurement uncertainties associated to the evaluation of all the terms in the force equation and especially in relation to TR-PIV measurements are discussed.