Wake topology and hydrodynamic performance of low-aspect-ratio ...

Low-aspect-ratio flapping foils 3391.530°1.020°C L0.510°00°–0.5 0 0.5Figure 24. Polar plot of mean lift versus mean thrust for various pitch-bias angles. For allthree cases in this plot, AR =2.55, St =0.6 andRe = 200.C Tincreases by a factor of about 3.4 as the aspect ratio increases from 1.27 to 2.55and the corresponding increase in efficiency is by a factor of 2.75. In contrast, thecorresponding factors are 1.6 and 1.3, respectively, for thrust and efficiency whenaspect ratio is increased from 2.55 to 5.09. This has some implications for pectoralfins found in nature. Clearly, hydrodynamic considerations alone would tend to leadto pectoral fins with larger and larger aspect-ratios. Conflicting with this tendencyare penalties incurred by the animal for bearing large-aspect-ratio fins. These include,but are not limited to, the need for stronger and therefore heavier body structures towithstand the bending moments produced on large-aspect-ratio fins, a larger visualsignature associated with longer fins and problems associated with operating longslender fins in tight spaces. The current simulations indicate that significant gainsin hydrodynamic performance can be achieved as the fin aspect-ratio is increasedto about 2.5. Further increase in aspect-ratio brings only modest gains which couldeasily be offset by the penalties associated with large-aspect-ratio fins. The abovewould seem to be equally true for insects and bird wings, but the penalty associatedwith large bending moments is probably higher for fishes than for insects or birds.This is so because pectoral fins of most fish are designed to be highly flexible,much more so than insect or bird wings. This property of the fins allows for highlycomplex flapping gaits which the animal uses to manoeuvre and move about inextremely energetic and unsteady environments. Fin flexibility in fish pectoral fins isusually achieved through the use of slender and delicate structural members (suchas rays and membranes) which present very little resistance to bending moments.Furthermore, fishes, especially those that employ labriform (pectoral fin) propulsion,usually swim in complex environments such as rocky coasts and coral reefs where thedisadvantages of operating long slender fins would be significant. Thus, the pressureagainst larger-aspect-ratios is probably highest for fish pectoral fins and this, alongwith the discussion in the previous paragraph provides some explanation for theobservation that most fish pectoral fins are found to have an aspect-ratio somewherebetween 2 and 3.For the pitch-bias angle cases, it is useful to examine the effect of this parameter onthe thrust and lift production. Figure 24 presents a polar plot of mean lift versus mean