Force estimates in turbulent vortex wakes of accelerating propulsors: The effects of edge undulation on vortex formation

The effects of edge undulation on separated flows and vortex formation are investigated with various geometries of accelerated, low aspect-ratio propulsors. In addition to force measurements, multi-camera planar particle image velocimetry (PIV) is applied for a large field of view of approximately 1.9 m × 0.3 m. Edge undulations with a wavelength λ, that is significantly larger than the thickness δ of the separated shear layer are identified to enhance the propulsion force during the stable vortex growth and before the vortex detaches. Edge undulation leads to a more turbulent vortex core and a faster vortex growth. The application of different approaches to recover the acting forces from PIV data lead to the conclusion, that the three-dimensionality of the turbulent vortex wake leads to both: a loss of out-of-plane vorticity and an underestimation of the kinetic energy in the vortex

On the concept of energized mass: a robust framework for low-order force modeling in flow past accelerating bodies

The concept of added (virtual) mass is applied to a vast array of unsteady fluid-flow problems; however, its origins in potential-flow theory may limit its usefulness in separated flows. A robust framework for modeling instantaneous fluid forces is proposed, named Energized Mass. The energized-mass approach is tested experimentally by acquiring the fluid kinetic-energy history around an accelerating sphere at both subcritical and supercritical terminal velocities. By tracking the energized-mass volume, the force response is shown to be related to changes in shear-layer growth as a function of acceleration moduli and Reynolds number. The energized-mass framework is then used to develop a low-order force model, requiring only body geometry and kinematics as input. An analytical expression for the instantaneous force on a sphere due to energized-mass growth is derived based on shear-layer mass flux arguments. Instantaneous forces determined experimentally, and modeled using the energized-mass approach, show strong agreement with direct force measurements. The results of this investigation thus demonstrate that the energized-mass framework provides a viable low-order modeling approach, and in tandem, can provide new insights into the origin of forces on accelerating bodies.</p