Elsevier

Journal of Theoretical Biology

Volume 320, 7 March 2013, Pages 76-85
Journal of Theoretical Biology

A modeling approach to energy savings of flying Canada geese using computational fluid dynamics

https://doi.org/10.1016/j.jtbi.2012.11.032Get rights and content

Abstract

A flapping flight mechanism of the Canada goose (Branta canadensis) was estimated using a two-jointed arm model in unsteady aerodynamic performance to examine how much energy can be saved in migration. Computational fluid dynamics (CFD) was used to evaluate airflow fields around the wing and in the wake. From the distributions of velocity and pressure on the wing, it was found that about 15% of goose flight energy could be saved by drag reduction from changing the morphology of the wing. From the airflow field in the wake, it was found that a pair of three-dimensional spiral flapping advantage vortices (FAV) was alternately generated. We quantitatively deduced that the optimal depth (the distance along the flight path between birds) was around 4 m from the wing tip of a goose ahead, and optimal wing tip spacing (WTS, the distance between wing tips of adjacent birds perpendicular to the flight path) ranged between 0 and –0.40 m in the spanwise section. It was found that a goose behind can save about 16% of its energy by induced power from FAV in V-formation. The phase difference of flapping between the goose ahead and behind was estimated at around 90.7° to take full aerodynamic benefit caused by FAV.

Highlights

► A flapping goose wing was reconstructed using a two-jointed arm model. ► A goose can save about 15% of its energy by changing the morphology of its wing. ► A goose behind can save about 16% of its energy from flapping advantage vortices. ► Phase difference of flapping between goose ahead and behind was estimated at 90.7°.

Introduction

Many studies have been conducted on the aerodynamics and kinematics of insects (Ellington et al., 1996, Srygley and Thomas, 2002) and various vertebrates such as bats (Michael, 2008, Muijres et al., 2008) and small birds flying at very low speeds (Videler et al., 2004, Warrick et al., 2005). They discovered that these animals use the leading edge vortex (LEV) as a principal mechanism of the lift force generation. However, for migrating birds such as Canada geese (Branta canadensis), great white pelicans (Pelecanus onocrotalus), and Arctic terns (Sterna paradisaea), lift force and drag reduction are obtained by continuously changing the morphology of the wings (Poore et al., 1997). The wings' downstroke generates primary lift and propulsion with outstretched wings, and their upstroke involves rapid withdrawal of the wing toward the body to reduce drag force.

Flight kinematics of large and heavy birds in previous work has largely been limited to flight modes over forward flight speeds (Park et al., 2001, Parslew and Crowther, 2010, Rosén et al., 2007, Tobalske et al., 2003). They did not study kinematics of avian wings in terms of flapping mechanism and morphology, but use several models; Parslew and Crowther (2010) employed multi-segment bird model whereas Rosén et al. (2007) used a simple two-frequency model derived from Fourier analysis. The relative ease with which flight conditions have changed the flight modes has resulted in comparatively little study on understanding fundamental aspects of flight kinematics itself. This study explores avian kinematics, specifically Canada geese, in more detail with the goal of identifying the role of each part of a bird wing that produces lift and drag reduction.

Swans, geese, cranes, cormorants, pelicans, flamingos, and other large birds migrate in flocks using a specific V-formation. The explanation for this flight formation in birds is still controversial. However, the two hypotheses currently being considered are energy saving and communication (Andersson and Wallander, 2004).

Many studies concerning energy saving have been done empirically (Badgerow, 1988, Cutts and Speakman, 1994, Hainsworth, 1987, Hainsworth, 1988, Hainsworth, 1989, Speakman and Banks, 1998, Weimerskirch et al., 2001, Williams et al., 1976), and theoretically (Andersson and Wallander, 2004, Hummel, 1983, Lissaman and Shollenberger, 1970, May, 1979). These studies reported that migrating birds reduce flight power demand by adopting a specific V-formation during flight. According to Weimerskirch et al. (2001), great white pelicans save 11.4∼14% of total energy by flying in a vortex wake from the flight formation while having lower wing beat frequency, slower heart rate, and longer glide time. Communication hypothesis is also favored by some researchers (Cutts and Speakman, 1994, Gould and Heppner, 1974, Heppner et al., 1985). Although evidence of this hypothesis is weaker than energy saving, both mechanisms might complement each other (Andersson and Wallander, 2004).

However, studies based on both hypotheses revealed that the relationships between depth (the distance along the flight path between birds) and wing tip spacing (WTS, the distance between wing tips of adjacent birds perpendicular to the flight path) are important criteria for the formation. A specific position defined by depth and WTS, where the birds can take full advantage of the energy saving, may be thought. A bird ahead as well as a bird behind can obtain the maximum lift augmentation (or drag reduction) relative to solo flight and reduce energy cost at the position. The depth and WTS corresponding to this position are considered as the optimum. Thus, if we find the optimal depth and WTS that maximize the lift generation (or drag reduction), we inherently demonstrate the advantage of the energy saving hypothesis (Badgerow, 1988).

Although most of previous works on aerodynamic performance attempted to prove the relationship between depth and WTS, they all ignored the complications of flapping wings (May, 1979, Thien et al., 2008). Furthermore, no other quantitative studies have been published on large and heavy birds flying at high speed, seemingly because it is impossible to measure airflow around a bird's wing being held rigidly in a wind tunnel (Michael, 2008) using digital particle image velocimetry (DPIV), correlation image velocimetry (CIV), and a laser sheet. Also, we cannot study the wake behind live birds as the techniques are too dangerous for the animal, therefore making computational fluid dynamics (CFD) a valid approach. Another advantage of using CFD is that the parameter space can be explored in a way that is not possible when using experiments with live animals. Therefore, numerical analysis would be a strong tool to quantify airflow around a flapping wing.

There have been several attempts to understand refinement and evolution of flapping flyers in nature. Some investigators (Sachs, 2005, Sachs and Moelyadi, 2006) provided valuable information about the sweep angle; they concluded that the sweep of the wing contributes to static stability in yaw. Other researchers (Aono et al., 2009, Hu et al., 2011, Persson et al., 2012, Willis et al., 2007) numerically calculated the outstretched flapping wings; however, they neglected the kinematics of wing retraction during upstroke.

Recently, a flapping goose wing in three-dimensional physical space was reconstructed from extracted wing geometry and kinematics, as well as the skeletal structure of the wing using a two-jointed arm model (Liu et al., 2004). This paper shows the numerical results of unsteady aerodynamics and kinematics based on the two-jointed arm model in flapping flight for the Canada goose. Using the obtained numerical results, we investigated the mechanisms of energy savings by changing the morphology of the wing and a pair of three-dimensional spiral flapping advantage vortices (FAV) alternately generated in V-formation flight. Based on the naturally outstretched flapping, we then evaluated the ratios of energy savings from both changing the morphology of the wing and a pair of three-dimensional spiral FAV in V-formation. Furthermore, we quantitatively estimated optimal depth and WTS, and flapping phase difference between a goose ahead and behind in the V-formation to take full aerodynamic benefit created by FAV.

Section snippets

Numerical analysis

The airflow field around a wing model of a Canada goose in unsteady aerodynamic performance was estimated by computational fluid dynamics (CFD) using the Reynolds-averaged Navier–Stokes (RANS) equation with the realizable kε model. These equations have been extensively validated for a wide range of flows (Kim et al., 1999, Shih et al., 1995). We used the commercial CFD package Fluent 6.3 (Fluent Inc., Lebanon, NH) to investigate the mechanisms of energy savings from the airflow fields around a

Energy savings from the change of morphology of the wing

In order to examine the effect of a typical flapping (standard migration flapping) mechanism in migration compared to that of a naturally outstretched flapping mechanism (Case 3), the airflow fields around the wing surface and airfoil (where z=0.6 m at t=0.68 s as a representative in both cases) were compared, as shown in Fig. 4. There are large differences in iso-velocity and vorticity distributions along the hand wing, although distributions were similar along the arm wing. The maximum

Conclusions

We estimated a flapping flight mechanism of the Canada goose using a two-jointed arm model in unsteady aerodynamic performance to examine how much energy can be saved during migration. From the airflow field around the wing and in the wake, the following conclusions were obtained.

  • (1)

    From the distributions of velocity and pressure on the wing, we determined that a goose can save about 15% of its energy by drag reduction from changing the morphology of the wing.

  • (2)

    From the airflow field in the wake, we

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