# On the calculation of force from PIV data using the generalized added-mass and circulatory force decomposition

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## Abstract

To understand the forces generated on an accelerating body in a fluid flow, it is useful to have the same framework for theory and experiment. A candidate for this purpose is the decomposition of fluid-dynamic force into added-mass and circulatory components. In its generalized form applicable to viscous incompressible flows, this formulation, referred to as the GAMC formulation, is applied to planar particle image velocimetry data to calculate instantaneous forces in the present study. These estimates are compared to direct force measurements and to an alternative force formulation from impulse theory, referred to as the standard impulse formulation (SIF). The chosen test case is a nominally two-dimensional circular cylinder towed through quiescent water under three acceleration profiles with peak Reynolds numbers between 5100 and 5150. For all three motion profiles, the measured and filtered drag force is consistently greater than the calculated forces with a bias of 10–20%, but the trends are in close agreement. Inspection of the presented equations reveals that the GAMC is less sensitive to near-body vorticity data than the SIF, which has the following consequences. First, forces calculated using the GAMC formulation are less sensitive to random error in the velocity than the SIF. This benefit comes at the cost of increased sensitivity to errors in cylinder position, but the associated uncertainty is negligible in the present study. Second, the GAMC is much more tolerant to the omission of near-body vorticity data, which is an attractive feature for PIV investigations. Finally, when no data are omitted, the SIF is more sensitive to the force components induced by uncharacterized high-frequency vibrations.

## Notes

### Acknowledgements

The authors thank the Natural Sciences and Engineering Research Council (NSERC) for funding this research.

## Supplementary material

## References

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