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.@en

A kinetic-energy-based, semi-empirical model for unsteady force estimation has been de-veloped, inspired by the concept of the Darwinian drift volume. The limitations of potential flow added mass and vortex impulse approaches were explored, and compared to experimental results. An optical towing tank facility was used to measure the forces and flow around a circular flat plate normal to the free-stream for an acceleration moduli of 4. Lagrangian particle tracks were produced using Eulerian vector-fields and synthetic particle tracking velocimetry. Forces predicted by potential flow added mass theory and vortex impulse modelling exhibited poor agreement compared to measured forces. The kinetic-energy-based approach showed strong agreement with measured forces, and allowed for the direct calculation of an “energized mass”, analogous to added mass derived from potential flow. Contrary to classical theory, the energized mass was not constant in time, which contributed to additional work done by the body. Forces on the body predicted using the semi-empirical model captured the major trends present in the measured forces. The component of the force due to the rate of change of energized mass is shown to be a significant contribution to the total force.@en

The Energized-Mass approach [1] offers a simple and robust framework for modeling forces in separated flow, requiring only kinematics, Reynolds-number, and geometry-based inputs. To this end, an energized-mass-based force model has been developed to describe the force response of a generic gust-body interaction, and is tested against numerical simulations of an accelerating sphere at moderate-to-high sub-critical Reynolds numbers. An analytic expression for the instantaneous force due to energized-mass growth is derived based on shear-layer mass flux arguments. The forming vortex ring is controlled by the Reynolds-number-dependent boundary layer thickness, which in turn, governs the energized-mass accumulated by the body. Entrainment effects are increasingly significant at greater Reynolds number as vortex formation transitions from laminar to turbulent, promoting mass flux beyond the predictions of shear-layer feeding arguments. Model predictions of instantaneous energized mass and resultant forces exhibit strong agreement with simulated results, suggesting energized-mass growth in sub-critical regimes is well-described by laminar-boundary-layer feeding. Thus, the current study provides a framework for future low-order force models, using the kinematics, Reynolds number and geometry to describe energized-mass time evolution.@en