Application of the energized-mass concept to describe gust-body interactions

Abstract

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.