Unsteady force estimation using a Lagrangian drift-volume approach

Abstract

A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure the unsteady force on an accelerating body. A methodology using multiple drift volumes is described and evaluated on an experimental test case containing highly-separated, vortical flow. The inherent advantage of the force estimation technique presented is that, unlike many modern Eulerian techniques, gradient operations and near-body measurements are not required to be calculated. These noise amplifying processes are avoided since the drift volume is calculated only from particle displacements in the flow field, reducing the importance of having high quality acceleration and spatial gradient data near walls and in regions of high shear. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force during high accelerations, a region in which comparable methods suffer. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian force estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means. i Above all else, I would like to thank my supervisor, Dr. David Rival, for his knowledge and teaching, for affording me the opportunities to learn and collaborate with the world's best, for his patience and understanding, and for making me learn the hard way that nothing is ever perfect. I would like to thank all my research group colleagues, specifically Drs. John Fernando, Giuseppe Rosi and Amirreza Rouhi, for their guidance and constructive conversations over the past years. Special thanks goes out to Dr. Jaime Wong for his assistance and dedication of time toward my research. I must also acknowledge the financial support from the Ontario Graduate Scholarship and the Natural Sciences and Engineering Research Council of Canada, which made this work possible. I would like extend a sincere thank you to the entire First Capital Cycling community for taking me in as one of their own. In particular, I owe a large debt of gratitude to Ka-Yu, Matt, Andy, Jim and Sue for being quality role models, pushing my limits, and challenging me to always become a better version of myself. To my family: Thank you for your unwavering support in all aspects of my life over the course of the last few years. Without you all, I would not have made it to where I am today.

The influence of edge undulation on vortex formation for low-aspect-ratio propulsors

“…The additional fluid, which subsequently travels with the propulsor, also requires momentum. Similar to the findings of McPhaden & Rival (2018), equation (43) suggests that the change of vortex volume influences the propulsion forces. To approximate the instantaneous vortex volume V, the topology of the flow is analysed.…”