Reconstruction of Unsteady Lift Force Measurements Using Non-Dimensional Scaling Optimization

Measuring dynamic forces acting on a structure over an extended bandwidth is difficult because of the influence of system dynamics. Such is the case for the measurement of the unsteady lift exerted on a flat-plate airfoil, the forces on which scale according to fluid dynamics scaling laws. To correct unsteady lift measurements for a flat-plate airfoil over a wider bandwidth, we present a force reconstruction technique using non-dimensional scaling laws as optimization criteria. In this non-dimensional scaling law, the amplitude and frequency of the power spectral densities (PSDs) of the total force measured over a range of flow speed conditions scale such that they collapse to a single curve. Two sets of optimization criteria, namely, minimizing the variance between the collapsed forces and curve-fitting a functional form for the force, are established to estimate modal participation factors for a specified number of resonance modes. Modal parameters, including natural frequencies and loss factors, are estimated by operational modal analysis. Simulation cases are provided as initial validation. Experimental validation was performed using an experiment in which distributed forces are applied to a flexible structure via a series of electromagnets mounted on individual force gages to measure the applied forces.