Added Mass and Vortical Impulse: Theory and Experiment
Date
2019-01-10
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Abstract
The classical decomposition of aerodynamic force into added-mass and circulatory components is derived under the assumption of inviscid flow. In the present thesis, this decomposition is shown to be valid for viscous flows. The classical added-mass force, derived using (acyclic) potential flow theory, is superimposable onto the circulatory force regardless of the presence of a vortical wake. This generalized added-mass and circulatory (GAMC) force decomposition is derived from impulse theory using a Helmholtz decomposition of the velocity field, and is valid for rigid bodies of any shape in unbounded incompressible fluid domains. Two supporting theoretical contributions were made in the course of the derivation, and these have been referred to as the conservation of image-vorticity impulse and the invariance of total vortical impulse to infinity-preserving conformal transformations. The practical utility of the GAMC formulation was investigated by applying it to a numerical simulation (generated by Wang and Eldredge (2013)) of the flow around a pitching plate in a steady free-stream flow. The calculated forces show fairly good agreement with the reported forces, although minor discrepancies suggest further work to quantify errors due to discretization. The GAMC formulation was then applied to particle image velocimetry (PIV) data to estimate force on a linearly accelerating cylinder in quiescent fluid. The resulting estimates capture the trend of the measured force well, but consistent underestimation of 10% to 20% was observed. It is speculated that the underestimation could be a failure to resolve the viscous skin friction due to spatial resolution limitations, and this possibility merits further study. In both the numerical and experimental validations, the GAMC formulation was validated alongside a common expression referred to as the standard impulse formulation (SIF). The inclusion of an image-vorticity impulse term in the GAMC formulation, contrary to the SIF, causes it to be less sensitive to random errors in the acquired velocity field and more tolerant to the omission of near-body vorticity data. These features of the GAMC formulation make it an attractive option for application to PIV studies in which near-body data acquisition is challenging.
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Keywords
fluid mechanics, vortex dynamics, particle image velocimetry
Citation
Limacher, E. J. (2019). Added Mass and Vortical Impulse: Theory and Experiment (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.