Advances in the visualization and analysis of boundary layer flow in swimming fish

Abstract

In biology, the importance of fluid drag, diffusion, and heat transfer both internally and externally, suggest the boundary layer as an important subject of investigation, however, the complexities of biological systems present significant and unique challenges to analysis by experimental fluid dynamics. In this investigation, a system for automatically profiling the boundary layer over free-swimming, deforming bodies was developed and the boundary layer over rigid and live mackerel, bluefish, scup and eel was profiled. The profiling system combined robotics, particle imaging velocimetry, a custom particle tracking code, and an automatic boundary layer analysis code. Over 100,000 image pairs of flow in the boundary layer were acquired in swimming fish alone, making spatial and temporal ensemble averaging possible. A flat plate boundary layer was profiled and compared to known laminar and turbulent boundary layer theory. In general, profiles resembled those of Blasius for sub-critical length Reynolds numbers, Rex. Transition to a turbulent boundary layer was observed near the expected critical Rex and subsequent profiles agreed well with the law of the wall. The flat plate analysis demonstrated that the particle tracking and boundary layer analysis algorithms were highly accurate.

(cont.) In rigid fish, separation of flow was clearly evident and the boundary layer transitioned to turbulent at lower Rex than in swimming fish and the flat plate. Wall shear stress, [tao]o, forward of separation was slightly higher than flat plate values. Friction drag in rigid and swimming fish was determined by integrating [tao]o over the surface of the fish. The analysis was facilitated by the definition of the relative local coefficient of friction. In general, there was no significant difference in friction drag between the rigid-body and swimming cases. In swimming, separation was, on average, delayed. Therefore, pressure drag was estimated on the basis of thickness ratio and used to calculate an upper-bound total drag on a swimming fish. Total drag was used to determine the required muscle power output during swimming and compare that with existing muscle power data. [tau]o and boundary layer thickness oscillated with undulatory phase. The magnitude of oscillation appears to be linked to body wave amplitude.