Unsteady lift on a high-amplitude pitching aerofoil

Shūji Ōtomo,Ignazio Maria Viola,Karen Mulleners,Sabrina Henne,Kiran Ramesh

doi:10.1007/s00348-020-03095-2

Shūji Ōtomo, Ignazio Maria Viola + Show 3 more

Open Access

https://doi.org/10.1007/s00348-020-03095-2

Copy DOI

Abstract

The ability to accurately predict the forces on an aerofoil in real-time when large flow variations occur is important for a wide range of applications such as, for example, for improving the manoeuvrability and control of small aerial and underwater vehicles. Closed-form analytical formulations are only available for small flow fluctuations, which limits their applicability to gentle manoeuvres. Here we investigate large-amplitude, asymmetric pitching motions of a NACA 0018 aerofoil at a Reynolds number of 3.2 times 10^4 using time-resolved force and velocity field measurements. We adapt the linear theory of Theodorsen and unsteady thin-aerofoil theory to accurately predict the lift on the aerofoil even when the flow is massively separated and the kinematics is non-sinusoidal. The accuracy of the models is remarkably good, including when large leading-edge vortices are present, but decreases when the leading and trailing edge vortices have a strong interaction. In such scenarios, however, discrepancies between the theoretically predicted and the measured lift are shown to be due to vortex lift that is calculated using the impulse theory. Based on these results, we propose a new limiting criterion for Theodorsen’s theory for a pitching aerofoil: when a coherent trailing-edge vortex is formed and it advects at a significantly slower streamwise velocity than the freestream velocity. This result is important because it extends significantly the conditions where the forces can be confidently predicted with Theodorsen’s formulation, and paves the way to the development of low-order models for high-amplitude manoeuvres characterised by massive separation.Graphic abstract

Highlights

IntroductionResearch on unsteady aerodynamics has significantly grown in recent years due to its relevance to bio-inspired flight (Ellington et al 1996; Birch and Dickinson 2001; Wang 2005; Muijres et al 2008; Lentink et al 2009; Rival et al 2009; Videler et al 2004; Pitt-Ford and Babinsky 2013; Wu 2011; Harbig et al 2013; Krishna et al 2018, 2019), underwater vehicles (Triantafyllou et al 2000; Taylor et al 2003; Beal et al 2006; Fish and Lauder 2006; Borazjani and Daghooghi 2013; Mackowski and Williamson 2015, 2017), flapping-foil energy harvesters (Dabiri 2007; Kinsey and Dumas 2008; Zhu 2011; Kinsey and Dumas 2012; Xiao et al 2012; Liu et al 2013; Young et al 2014; Xiao and Zhu 2014; Ramesh et al 2015; Wu et al 2015; Kim et al 2017; Rostami and Armandei 2017; Su and Breuer 2019), and tidal turbine blades (Sequeira and Miller 2014; Tully and Viola 2016; Smyth and Young 2019; Dai et al 2019; Scarlett et al 2019; Scarlett and Viola 2020)
From the unsteady thin-aerofoil theory (UTAT), we find the normal force for a flat-plate undergoing arbitrary kinematics up to high angles of attack
This study reports the unsteady lift force generation and flow development on a pitching aerofoil at Re = 32, 000 through time-resolved force and velocity field measurements

Summary

Introduction

Research on unsteady aerodynamics has significantly grown in recent years due to its relevance to bio-inspired flight (Ellington et al 1996; Birch and Dickinson 2001; Wang 2005; Muijres et al 2008; Lentink et al 2009; Rival et al 2009; Videler et al 2004; Pitt-Ford and Babinsky 2013; Wu 2011; Harbig et al 2013; Krishna et al 2018, 2019), underwater vehicles (Triantafyllou et al 2000; Taylor et al 2003; Beal et al 2006; Fish and Lauder 2006; Borazjani and Daghooghi 2013; Mackowski and Williamson 2015, 2017), flapping-foil energy harvesters (Dabiri 2007; Kinsey and Dumas 2008; Zhu 2011; Kinsey and Dumas 2012; Xiao et al 2012; Liu et al 2013; Young et al 2014; Xiao and Zhu 2014; Ramesh et al 2015; Wu et al 2015; Kim et al 2017; Rostami and Armandei 2017; Su and Breuer 2019), and tidal turbine blades (Sequeira and Miller 2014; Tully and Viola 2016; Smyth and Young 2019; Dai et al 2019; Scarlett et al 2019; Scarlett and Viola 2020). The LEV plays a crucial role in augmenting lift in both insect/bird flight and bio-inspired flight as well as in enhancing the efficiency of flapping-foil energy harvesters. It becomes more challenging to predict the unsteady forces at play. The classical linear theory of Theodorsen (1935), based on unsteady potential flow theory is widely used to predict forces for sinusoidal aerofoil kinematics. Unsteady thin-aerofoil theory (UTAT) is another potential flow model that is based on the timestepping approach. It assumes attached flow and is applicable to arbitrary small-amplitude kinematics (Katz and Plotkin 2001; Ramesh et al 2013). Researchers proposed extensions to UTAT for solving three-dimensional problems (Boutet and Dimitriadis 2018; Bird et al 2019)

Objectives

Methods

Results

Conclusion