Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Miles Owen,Abdelkader Frendi

doi:10.3390/fluids5040212

Miles Owen, Abdelkader Frendi

Open Access

https://doi.org/10.3390/fluids5040212

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Abstract

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

Highlights

IntroductionThe aerodynamic, hydrodynamic, and acoustic performance of an airfoil with a wavy leading edge (LE) has been a subject of research for the past 30 years
The aerodynamic, hydrodynamic, and acoustic performance of an airfoil with a wavy leading edge (LE) has been a subject of research for the past 30 years. This airfoil geometry was inspired by the pectoral fin of a humpback whale (Megaptera novaeangliae), which features large LE protuberances that are presumed to aid in maneuverability
For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow

Summary

Introduction

The aerodynamic, hydrodynamic, and acoustic performance of an airfoil with a wavy leading edge (LE) has been a subject of research for the past 30 years. This airfoil geometry was inspired by the pectoral fin of a humpback whale (Megaptera novaeangliae), which features large LE protuberances that are presumed to aid in maneuverability. One feeding behavior of a humpback whale involves swimming in circles of relatively tight radii to create a bubble net, corralling prey for efficient consumption This banking maneuver is efficiently performed if the pectoral fin has a large stall angle combined with increased lift and decreased drag to reduce energy expenditure. Parametric experiments by Johari et al [4] and aerodynamic modeling by van Nierop et al [5] were performed for several sinusoidal LE amplitudes from 2.5% to 12% chord and two wavelengths of 25% and 50% chord

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