Experimental study on the effect of adaptive flaps on the aerodynamics of an Ahmed body

We perform an experimental study on the turbulent flow around a square-back Ahmed body of height, $h$, at varying $Re=u_{\infty }h/\nu \in [0.5,1]\times {10}^5$, where $u_{\infty }$ is the free-stream velocity and $\nu$ is the incoming flow kinematic viscosity, under different yaw angles $\beta =(0^{\circ },-5^{\circ },-{10}^{\circ })$, to analyze the use of rear flexibly hinged parallel plates as a control strategy to reduce the drag in a self-adaptive manner under changing flow conditions. The model implements rear parallel rigid flaps of depth $d=0.5h$, which are mounted with torsional joints through embedded flexible foils of calibrated thickness. This holding system restricts the motion of the plates to a rotary displacement, $\theta$. The fluid-structure dynamics is characterized by the reduced velocity, defined as $U^{*}=u_{\infty }/f_{n}h$, where $f_n$ is the natural frequency of rotary oscillations of the hinged plates, measured in free-decay tests of flaps. In fact, we have explored the range of reduced velocity, $U^{*}=[0,65]$, varying $u_{\infty }$ and consequently Re. We perform force and pressure measurements to quantify the variations of the drag and the base pressure coefficients while laser displacement sensors are used to obtain the angular flaps motion. Results show that the hinged plates decrease the drag coefficient of the original body by nearly $4.4\%$ for flow conditions aligned with the body axis. Under cross-flow conditions, their efficiency is even larger, attaining relative reductions drag of nearly 9.1% at $\beta =-{10}^{\circ }$ (13.5% in comparison with a body with fixed rigid plates of the same depth). Such variations are shown to be associated with a passive reconfiguration process of rear flaps. Additionally, hinged flaps are shown to interact with the reflectional-symmetry-breaking (RSB) modes, typically present in the wake of three-dimensional bodies. At aligned conditions, the interaction with the RSB modes is characterized by two regimes, in such a way that the hinged flaps manage to partially stabilize the RSB modes, and consequently to inhibit the bistable behavior at low values of $U^{*}$ (in a similar manner to rigid flaps), while at high values of $U^{*}$, they respond dynamically to switches between the opposite wake deflections of the RSB modes, deviating themselves accordingly.

Figure 1

Sketch of the experimental setup.

Figure 2

(a) Detail of the flexibly-hinged flap system. (b) Instantaneous angular displacement $\theta {(}^{\circ })$ of the flap from a free-decay test.

Figure 3

Evolution of the (a) averaged drag $C_x$, (b) base drag $C_B$, and (c) remaining drag $C_R$ coefficients with the Reynolds number for the baseline case (B, squares) at different yaw angles ($\beta =0^{\circ }$ in blue, $\beta =-5^{\circ }$ in red and $\beta =-{10}^{\circ }$ in green).

Figure 4

Evolution of (a) averaged drag, (b) base drag, and (c) remaining drag coefficients relative change with respect to case B ($\mathrm{\Delta }{C}_x, \mathrm{\Delta }{C}_B$, and $\mathrm{\Delta }{C}_R$, respectively) against Reynolds number for RF (rigid flaps, diamonds) and HF (hinged flaps, circles) cases at different yaw angles ($\beta =0^{\circ }$ in blue, $\beta =-5^{\circ }$ in red, and $\beta =-{10}^{\circ }$ in green).

Figure 5

(a) Evolution of the time-averaged flaps deflection at yaw $\beta =0^{\circ },-5^{\circ },-{10}^{\circ }, {\mathrm{\Theta }}_1$ (leeward flap) and ${\mathrm{\Theta }}_2$ (windward flap) with the reduced velocity $U^{*}$. (b) Evolution of the time-averaged horizontal pressure gradient $G_y$ with the Reynolds number $Re$ for the three configurations and $\beta =-5^{\circ }$ and $-{10}^{\circ }$. (c), (d) Corresponding correlation of the trailing bluffness $H_r$ with the relative variations of drag (c) and base drag (d) coefficients, $\mathrm{\Delta }{C}_x$ and $\mathrm{\Delta }{C}_B$, with respect to reference values of B configuration, as a function of the yaw angle. Solid lines depicting the associated linear fit are included.

Figure 6

Evolution of lateral force coefficient with $Re$ at different yaw angles: (a) $\beta =0^{\circ }$, (b) $\beta =-5^{\circ }$, and (c) $\beta =-{10}^{\circ }$ for the tested configurations (B, RF, HF). In the case of aligned conditions, ${\widehat{C}}_y$ instead of $C_y$ is depicted.

Figure 7

(a) Temporal evolution of horizontal base pressure gradient, $g_y$, for the tested configurations (B, RF, HF) at $Re\simeq {10}^5$. (b) Corresponding probability density (PDF) of $g_y$. Contours of pressure gradients PDFs from (c)–(e) $g_y$ and (h)–(j) $g_z$ at the tested Reynolds number Re (and $U^{*}$), for the three configurations B, RF, and HF. Joint horizontal and vertical base pressure gradients PDF for selected values of $Re$ for the (f), (g) B and the (k), (l) HF configurations. All PDFs are normalized with their corresponding maxima.

Figure 8

RSB dynamics at $\beta =0^{\circ }$. (a), (b) Temporal evolution of horizontal, vertical base pressure gradients and flap deflection fluctuating angles, ${\widehat{\theta }}_1$ and ${\widehat{\theta }}_2$, for B and HF configurations at $\text{Re}\sim {10}^5$. (c) PDF of the observed averaged deflected angle, ${\widehat{\theta }}_1$ and ${\widehat{\theta }}_2$, position for HF configuration. The PDF is normalized with its maximum value. (d) Nondimensional switching events, $N_s^{*}$, evolution with $Re$ for B and HF configurations. Error bars are included for the different tests performed.

Figure 9

Sketch of the interaction between flaps and the RSB mode: (a) N state observed with negative flaps deflection and (b) P state observed with positive flaps deflection. Flaps are represented using thick solid lines, while thin solid lines indicates mean deflected positions. Dashed lines are the flaps deflection of the opposite state that is not observed.