Fluidic control of a precessing axisymmetric body by near-wake coupling

The angular motion of a forebody-gimbaled axisymmetric cylindrical bluff body wind tunnel model that is free to pitch, yaw, and roll in a uniform stream in response to flow-induced aerodynamic loads is modified by fluidic actuation of its near wake. The model is anchored at its leading edge by a low-friction gimbal coupling attached to a wire-mounted short streamwise sting where each of the eight support wires is connected to a servo actuator for position and attitude control of the sting. Aerodynamic moments on the model and thereby its angular motions are controlled in a closed loop using fluidic modification of its near wake by azimuthally segmented flow attachment over its aft end. Actuation is effected using fourfold symmetrically distributed and independently activated synthetic jet actuators. Coupled effects of actuation-induced transitory changes in the attitude of the model are measured by an image-tracking system and the evolution of the near wake captured using high-speed stereo particle image velocimetry (SPIV). Dynamic mode decomposition (DMD) of the time-dependent near-wake flow field indicates that suppression or amplification of the natural oscillations of the model are associated with controlled changes in the symmetry and spectral content of the primary dynamic modes. It is shown that these controlled wake interactions can be harnessed to tune the temporal attitude response of the model, with natural oscillation suppression of $>50-65\%$ in pitch and 75–85% in yaw across the entire investigated range of Reynolds numbers of $1.32\times {10}^5$ to $1.92\times {10}^5$. In addition, an example of amplification of the natural oscillations of $>150\%$ is illustrated at a Reynolds number of $1.62\times {10}^5$.

Figure 1

Deconstructed view of (a) the three degrees of freedom (3-DOF) model components, (b) upstream view of the centered wind tunnel model with four synthetic jets marked in green, and (c) a depiction of the counterbalanced model mounted through the inner nose piece.

Figure 2

(a) Top and (b) aft views of a single synthetic jet actuator orifice and (c) a variation of the jet momentum coefficient with the actuation carrier frequency for the power input $P_{\mathrm{A}}^{*}\times {10}^3=2 \left(◊\right)$, 3.3 (□), and 4.6 (○). The selected carrier frequency is marked by the dashed line.

Figure 3

(a) Six degrees of freedom traversing mechanism utilizing eight servo actuators and support wires to an upstream sting and (b) a top view schematic of the sting-mounted model, along with the high-speed stereo particle image velocimetry (SPIV) interrogation region (light green), and motion analysis system (purple).

Figure 4

Realized perturbations of the model in (a) roll, (b) pitch, and (c) yaw, shown in blue, and best fits to a mass-spring-damper model shown in green.

Figure 5

Flow induced dynamics of the model (in blue) and sting (in red) at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$ for instantaneous time traces of (a) roll, (c) and (g) pitch, and (e) and (i) yaw, and (b), (d), (f), (h), and (j) their respective power spectra, along with probability density functions of the respective (k), (l) pitch and yaw over 25 measurements.

Figure 6

Variations of the model (blue) and sting (red) (a)–(c) average root mean square (RMS) amplitude and (d)–(f) characteristic frequency in (a) and (d) roll, (b) and (e) pitch, and (c) and (f) yaw, with Reynolds number.

Figure 7

An instantaneous snapshot of (a)–(d) the wake behind the unactuated model and time traces of (e)–(h) the horizontal centerline and (i)–(l) vertical centerline (a), (e), and (i) streamwise $U_x$ and (b), (f), and (j) cross-stream $U_y$ and (c), (g), and (k) $U_z$ velocity components and (d), (h), and (l) streamwise vorticity ${\zeta }_x$, at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 8

Contour plots of the streamwise velocity proper orthogonal decomposition (POD) modes ${\varphi }_{n,u}$, with mode number (a) $n=1$, (b) $n=2$, (c) $n=3$, (d) $n=4$, (e) $n=5$, (f) $n=6$, and (g) $n=7$, and (h) the energy distribution of the modes for the base flow at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 9

Quiver plots of the proper orthogonal decomposition (POD) modes of the cross-stream velocities ${\varphi }_v$ and ${\varphi }_w$, with mode number (a) $n=1$, (b) $n=2$, (c) $n=3$, (d) $n=4$, (e) $n=5$, (f) $n=6$, and (g) $n=7$, colored by their streamwise vorticity ${\varphi }_{\zeta }$ for the base flow at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 10

Phase plots of 10 instantaneous traces of (a) and (c) the model pitch rate ${\stackrel{.}{\alpha }}_y$, (b) and (d) yaw rate ${\stackrel{.}{\alpha }}_z$, and moment coefficients (e) and (g) $C_{\mathrm{M}}$ and (f) and (h) $C_{\mathrm{Y}}$, for open-loop actuation by (a), (b), (e), and (f) a single jet and (c), (d), (g), and (h) all four jets for $t/{\tau }_{\mathrm{conv}}=-170$ to 0 (black), 0–170 (cyan), and 170–510 (blue) after the onset of actuation at a fixed $C_{\mu }=0.003$ and $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 11

The time traces of (a)–(d) and (i)–(l) the horizontal centerline and (e)–(h) and (m)–(p) vertical centerline (a), (e), (i), and (m) streamwise $U_x$ and (b), (f), (j), and (n) cross-stream $U_y$ and (c), (g), (k), and (o) $U_z$ velocity components and (d), (h), (l), and (p) streamwise vorticity ${\zeta }_x$ for (a)–(h) the open-loop single-jet and (i)–(p) four-jet actuation applied at $t=0$, at a fixed $C_{\mu }=0.003$ and $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 12

Contour plots of the streamwise velocity proper orthogonal decomposition (POD) modes ${\varphi }_{n,u}$, with mode number (a) and (f) $n=1$, (b) and (g) $n=2$, (c) and (h) $n=3$, and (d) and (i) $n=4$, and (e) and (j) the energy distribution of these modes for (a)–(e) open-loop single-jet and (f)–(j) four-jet actuations at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 13

Spatial probability density functions of flow-induced dynamics of the model over 25 instantaneous measurements of $680{\tau }_{\mathrm{conv}}$ for (a) the unactuated flow along with actuation by (b) open-loop single-jet, (c) two adjacent jets in the pitch direction, (d) two opposite jets, (e) two adjacent jets in the yaw direction, and (f) four-jets, at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 14

Phase plots of closed-loop actuations: (a), (b), (e), and (f) hold center and (c), (d), (g), and (h) amplify pitch presented in the same fashion as the data in Fig. 10, using a maximum $C_{\mu }=0.003$.

Figure 15

Time history plots of hold-center closed-loop actuation with measured model (a) roll, (b) pitch, and (c) yaw and output jet momentum coefficients $C_{\mu }$ for (d)–(g) jets 1–4, respectively.

Figure 16

The time development of the wake for the closed-loop control algorithms (a)–(h) hold center and (i)–(p) amplify pitch presented in the same fashion as the data in Fig. 11, using a maximum $C_{\mu }=0.003$.

Figure 17

Contour plots of the streamwise velocity proper orthogonal decomposition (POD) modes ${\varphi }_{n,u}$, with mode number (a), (f), and (k) $n=1$, (b), (g), and (l) $n=2$, (c), (h), and (m) $n=3$, and (d), (i), and (n) $n=4$, and (e), (j), and (o) the energy distribution of the modes for $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$, for (a)–(e) closed-loop oscillation suppression, (f)–(j) pitch amplification, and (k)–(o) yaw amplification.

Figure 18

Spatial probability density functions of flow-induced dynamics of the model for closed-loop actuations: (a) unactuated, (b) amplify pitch, (c) amplify yaw, (d) hold center, (e) hold pitch up, and (f) hold yaw left presented in the same fashion as the data in Fig. 13.

Figure 19

Model (blue) and sting (red) closed-loop control induced maximum deflections with (a)–(c) hold-right or hold-up actuations, (d)–(f) hold-center root mean square (RMS) amplitude, and (g)–(i) hold-center characteristic frequency in the (a) and (d) roll, (b) and (e) pitch, and (c) and (f) yaw directions, with Reynolds number.

Figure 20

Spatial probability density functions of (a)–(c) the model (blue) and (d)–(f) sting (red) dynamics over 25 instantaneous measurements of $680{\tau }_{\mathrm{conv}}$ for (a) and (d) the unactuated flow and closed-loop flow control for the model (b) and (e) to follow the sting motion and (c) and (f) to remain centered independent of the sting motion at $\mathrm{R}{\mathrm{e}}_{\mathrm{D}}=1.62\times {10}^5$.

Figure 21

(a)–(d) Dynamic mode decomposition (DMD) spectral distributions and (e)–(l) color raster plots of the streamwise velocity distributions of dynamic modes ${\mathrm{\Psi }}_{n,u}$ for (a), (e), and (i) the unactuated flow and closed-loop actuation goals: (b), (f), and (j) hold center, (c), (g), and (k) pitch amplify, and (d), (h), and (l) yaw amplify. The mode order (i.e., the $n\mathrm{th}$ peak) and respective frequency are noted.

Figure 22

(a), (c), (e), and (g) Dynamic mode decomposition (DMD) growth rates (40 modes) and (b), (d), (f), and (h) the time development of the growth of the least stable mode within a 2 s (340 ${\tau }_{\mathrm{conv}}$) interval with actuation starting at $t=0$, for (a) and (b) the unactuated flow and the actuated closed-loop control for (c) and (d) hold center, (e) and (f) pitch amplify, and (g) and (h) yaw amplify.

Figure 23

Schematics of the traverse trajectory tracking controller for measuring and effecting the five degrees of freedom (5-DOF) sting mount and the six degrees of freedom (6-DOF) axisymmetric model; the angular three degrees of freedom (3-DOF) of the axisymmetric model are decoupled and effected solely by flow control.

Figure 24

Schematics of the closed-loop flow controller.