Assessment of the derivative-moment transformation method for unsteady-load estimation

Abstract

It is often difficult, if not impossible, to measure the aerodynamic or hydrodynamic forces on a moving body. For this reason, a traditional control-volume technique is typically ap plied to extract the unsteady forces. However, measuring the acceleration term within the volume of interest can be limited by optical access, reflections as well as shadows. There fore in this study an alternative approach, termed the Derivative-Moment Transformation (DMT) method, is introduced and tested on a synthetic data set produced using numerical simulations. The test case involves the unsteady loading of a flat plate in a two-dimensional, laminar periodic gust. The results suggest that the DMT method can accurately predict the acceleration term so long as appropriate spatial and temporal resolutions are maintained. It was shown that for large control volumes, and with realistic spatial resolution, the accuracy of the DMT method would also suffer. Therefore, a delicate compromise is required when selecting control-volume size in future experiments. lll l V

Load-estimation techniques for unsteady incompressible flows

“…To date, no robust studies on uncertainty estimation have been performed for instantaneous force estimations with noisy data (be its classical, DMT, or with vorticity formulations). However, the short temporal discrepancies in estimates on the order of 10% observed in the synthetic test case of Mohebbian and Rival (2012) can be attributed to significant error propagation across the wake, as discussed by Kurtulus et al (2007). These idealized results show that the discrepancies are strongest in the direction of drag due to the higher gradients of velocity across the rear control surface, associated with the crossing of wake vortices.…”

“…(4), as shown in Mohebbian and Rival (2012): where is the position vector measured from any fixed frame of reference. This transformation is applied under the conditions that the velocity field is divergence free (incompressible flow) and that the body is thin, e.g., most lifting bodies.…”

“…The Föppl transformation used above has been checked on synthetic cases by Wu et al (2005), Minotti (2011), and Mohebbian and Rival (2012). Limitations regarding the size and proximity of the control surfaces relative to the body of interest, as well as the effect of vortical structures in the wake, have been examined in the latter paper.…”

“…Despite this inherent advantage in the temporal resolution, problems involving fluid-structure interaction do not scale easily from air to water unless great lengths are taken with techniques, such as cyber-physical fluid dynamics, e.g., Mackowski and Williamson (2011) and Onoue and Breuer (2016). Furthermore, particle images in water are generally larger, such that PIV recordings will have a finer spatial resolution in the air, which is critical for capturing, for instance, regions of shear crossing control surfaces; see Mohebbian and Rival (2012). As discussed by Kähler et al (2012a), the spatial resolution of PIV is limited by seeding particle size (and therefore inter-particle spacing), such that the only substantial measure to increase resolution in such unsteady force estimates is in fact to move towards Lagrangian particle tracking, as will now be discussed in the outlook section in the following.…”

Design and analysis of aerodynamic force platforms for free flight studies

“…Aerodynamic force can be calculated by integrating in vivo flow measurements using the control surface formulation of the Navier-Stokes equations (Noca et al 1999, Mohebbian andRival 2012). The flow field is typically measured using particle image velocimetry (PIV), and then integrated to obtain the pressure field and the net force using the momentum equation (van Oudheusden 2013).…”