Turbulence enhances bird tail aerodynamic performance

TL;DR

A wake instability that arises in laminar flow is suppressed in turbulent flow, which enhances tail efficiency, benefiting flight control, and these insights may inspire engineers to design aerial vehicle tails with improved flight control in turbulence.

Abstract

Turbulence is omnipresent in the atmosphere and a long-standing scientific conundrum that makes flight complex. This complexity is little understood; surprisingly, when turbulence arises, air vehicles struggle while birds seem to thrive. Birds often encounter intense turbulence during takeoff and landing, because of turbulent boundary layer effects. During landing, birds respond by fanning their tail over a wide range of spreads and angles of attack. How their tail functions aerodynamically under these conditions is little understood. Here, we use a bio-hybrid feathered robot model of a pigeon tail in a wind tunnel to compare its aerodynamics in laminar versus turbulent flow. We measured the lift and drag forces generated by the tail as a function of angle of attack, tail spread, and flow condition. We found tail spread scarcely changes tail aerodynamic lift and drag force coefficients, despite large aspect ratio variations. Consequently, tail spread primarily changes force via tail area modulation, simplifying flight control. The effect of laminar versus turbulent flow is pronounced; at the same tail spread and angle of attack, turbulence increases lift and drag by approximately a factor two. Quantitative flow measurement analysis with proper orthogonal decomposition shows force enhancement is linked to modifications in the spatial and temporal structure of the wake. The results suggest a wake instability that arises in laminar flow is suppressed in turbulent flow, which enhances tail efficiency, benefiting flight control. These insights may inspire engineers to design aerial vehicle tails with improved flight control in turbulence.

Figures (4)

• Figure 1: (A) A pigeon in cruising flight (left) with folded tail ($\alpha\simeq 10°$) and a pigeon during slow flight (right) with a wide spread tail typical for takeoff and landing ($\alpha\simeq 150°$). (B) The bio-hybrid pigeon tail with real tail feathers encased in a 3D-printed compliant strip that spreads the tail feathers (rectrices) like a fan. A NACA 0025 cylinder replaces the tail-end of the bird's body. (C) Measured biohybrid tail aspect ratio $AR$ as a function of tail spread angle $\Delta$ ($S$, surface area of the tail; $2b$, tail span; $c$, tail chord). Recordings for 1 set of racing pigeon feathers, tested under laminar versus turbulent conditions (see methods).
• Figure 2: Pigeon tail spread has little effect on aerodynamic force coefficients, which makes tail force proportional to area. (A) Polar curves of the speed specific lift $C_L S$ as a function of the speed specific drag $C_D S$ for different spread angles show force depends on tail area (semi-transparent white areas in A, B, C indicate sensor resolution limits). (B) Polar curves for the different spread angles of the lift coefficient $C_L$ as a function of the drag coefficient $C_D$ shows the coefficients depend primarily on angle of attack. (C) Lift $C_L$ coefficients as a function of the angle of attack $\alpha$ for different spread angles. Shaded areas represent $95\%$ CI values. (D) Streamwise vorticity $\omega_x$ fields in the transverse plane behind the tail. Rows present different angles of attack $\alpha$ and columns present different spread angles $\Delta$. The projection of the tail is represented by its contour. All measurements in this figure were obtained in laminar conditions (tail avatar color codes spread angle).
• Figure 3: Turbulence shifts the location of the wake while conserving circulation. (A) Streamwise vorticity $\omega_x$ fields in the transverse plane behind the tail at different angles of attack $\alpha$ (rows) and spread angles $\Delta$ (columns) in laminar (left) and turbulent (right) conditions. Tail projection is represented by its contour. Inflow turbulence causes vortices to become rounder and secondary structures to subside. (B) Proper Orthogonal Decomposition (POD) of the streamwise vorticity $\omega_x$ fields for the configuration ($\alpha=33°$, $\Delta=36°$). (left) Distribution of the enstrophy across the first 5 modes for laminar (circles) versus turbulent (squares) inflow. Enstrophy is more equally distributed across POD modes in turbulence. (right) Associated POD modes 1 to 3. Comparing laminar (L) versus turbulent (T) conditions, the first mode shows a similar vortex structure and enstrophy. The secondary modes reveal a quadrupole vortex instability (at intermediate angles of attack) for laminar inflow that is absent for turbulent inflow. (C) Location of the vortex core ($y/b$, $z/c\sin \alpha$) and radius $r_{\rm vortex}/b$ as a function of tail spread angle $\Delta$ (color) and angle of attack $\alpha$ (transparency) for laminar (left) versus turbulent (right) inflow. In turbulence, the vortices are on average bigger and located closer to the tail tip. (D) Vortex radius $r_{\rm vortex}/b$ as a function of peak vorticity $\Omega_{\rm max}b/U_\infty$ in laminar (circles) versus turbulent (squares) conditions (marker size encodes angle of attack; 5, 40 and 90 degrees are example sizes across the full range). Both in laminar and turbulent conditions, the trend of vortex size versus intensity follows a $-1/2$ scaling relation, associated with the conservation of circulation. The offset between low versus high angle of attack separates two regimes below and above the $-1/2$ scaling trendline.
• Figure 4: Tail lift and drag coefficients approximately double in turbulence. (A) Heatmap of the highest performance in average downwash velocity $w_{\rm min}$ (upper rectangle) and lift production $C_L$ (lower rectangle). The ratio of turbulent (salmon) over laminar (teal) values are plotted for each ($\Delta,\alpha$) combination. Two regimes can be identified, one at low angles of attack where the highest performance is found in laminar conditions and one at high angles of attack where turbulence enhances lift production. The lowest angle of attack force data is at the resolution limit of the force sensor, at $\alpha=21°$ force data observations are supported with downwash velocity $w_{\rm min}$ measurements. (B) Distribution of the instantaneous lift ($L(t)$) and dynamic pressure ($\Delta P(t)$) measurements in laminar (teal, darkened for more contrast) and turbulent (salmon) conditions for the spread angle $\Delta=90°$ at $\alpha=21°$ (top) versus $\alpha=55°$ (bottom). Time-averaged values are represented by circles (laminar) and squares (turbulence). Lift coefficients are correlated from the slope of the dashed (laminar) and dotted (turbulent) lines. (C) Tail lift $C_L$ and drag $C_D$ coefficients as function of the angle of attack $\alpha$ for different spread angles in turbulence (orange to purple). The envelopes of $C_L$ and drag $C_D$ generated in laminar conditions (teal area) are shown for reference. Shaded areas represent $95\%$ CI values. As in Fig. \ref{['fig:spread']}.A, tail spread angle has no clear effect on coefficient value, but turbulence doubles the lift and drag coefficients in the intermediate to high angles of attack. (Semi-transparent white areas in A, C indicate sensor resolution limit; $C_L$, $C_D$ values beyond 3 are cut-off in C).