Experimental study of the turbulence ingestion noise of rotor blades

The ingestion of turbulence can cause additional noise sources of rotor blades, which should be considered for multirotor powered urban air mobility vehicles encountering atmospheric turbulence. In this work, a turbulence grid was installed in the exit of an open-jet anechoic wind tunnel to generate turbulent flows. The grid turbulence was characterized using hot-wire anemometry, showing that turbulence intensity decays with the streamwise locations downstream of the grid, following a power law of $-5/7$. The power spectral properties of the grid turbulence were also assessed, and it agrees well with the von Kármán turbulence spectrum in the inertial subrange. Then, the aerodynamic force and noise of a rotor with a diameter of 217.2 mm were measured under both clean and turbulent flows. Force measurements show that the thrust and torque coefficients decrease with the advance ratio $J$. Noise measurements show that the tonal noise at the blade pass frequency (BPF) is more significant at the upstream locations under high advance ratios, and high-order BPF harmonics can also be amplified. Moreover, the turbulence ingestion noise mainly dominates the broadband contents from 10 to 50 BPF harmonics. The broadband noise can be scaled by the Mach number scaling of $M_{\infty }^2{M}_c^4$, where $M_{\infty }$ is the freestream Mach number and $M_c$ is the corresponding Mach number of the rotating speed at the blade tip.

Figure 1

Schematic of the turbulence measurement: (a) the jet nozzle with turbulence grid installed; (b) measured points on each measurement plane.

Figure 2

The dimensions of turbulence grid: rod diameter $d$ and mesh size $M$.

Figure 3

The hot-wire anemometry: (a) a photo of the hot-wire measurement setup and (b) sketches of the cross-wire probe and the single-wire probe.

Figure 4

Schematic of the noise measurement: (a) a photo of the rotor interacting with grid turbulence; (b) top view (not to scale).

Figure 5

Flow homogeneity at $U_{\infty }=10$ m/s: (a) mean velocity $U$ (symbols with solid lines) and $V$ (inset, symbols with dashed lines); (b) velocity fluctuations $u^{\prime }$ (symbols with solid lines) and $v^{\prime }$ (inset, symbols with dashed lines). All the data were acquired at $X/d=97.8$, and they were normalized by $U_{\infty }$.

Figure 6

Flow homogeneity at $U_{\infty }=15$ m/s. Others are the same as those in Fig. 5.

Figure 7

Streamwise turbulence intensity profiles measured at the wind tunnel center vs $X/d$. The results show a decay power law of $-5/7$ for nearly isotropic grid turbulence [42].

Figure 8

Comparison of the power spectra of grid turbulence and von Kármán model for isotropic turbulence at (a) $U_{\infty }=5$ m/s, (b) $U_{\infty }=10$ m/s, and (c) $U_{\infty }=15$ m/s.

Figure 9

Isotropy ratios, $u^{\prime }/v^{\prime }$, in the streamwise direction of the grid turbulence. The data were acquired by the cross-wire probe at the center of the jet exit.

Figure 10

Streamwise integral length scale profiles of both $L_{uu}$ and $L_{vv}$: (a) $U_{\infty }=10$ m/s and (b) $U_{\infty }=15$ m/s. The data were acquired by the cross-wire probe at the center of the jet exit.

Figure 11

Probability density function of the streamwise velocity fluctuations $u^{\prime }$ at (a) $U_{\infty }=10$ m/s and (b) $U_{\infty }=15$ m/s. The data were acquired by the single-wire probe at the center of the measured plane at $X/d=77.8$.

Figure 12

Probability density function of the time derivatives of streamwise velocity fluctuations, $\partial u^{\prime }/\partial t$, at (a) $U_{\infty }=10$ m/s and (b) $U_{\infty }=15$ m/s. The data were acquired by the single-wire probe at the center of the measured plane at $X/d=77.8$. The values of $\partial u^{\prime }/\partial t$ are normalized by their rms values.

Figure 13

Force measurement results of (a) thrust and (b) torque. Measurement points are indicated by black and gray scatters for clean flow and grid turbulence, respectively.

Figure 14

Nondimensionalized force measurement results of (a) $C_T$ and (b) $C_Q$.

Figure 15

SPL spectra comparison of rotor noise under various thrusting conditions at two observer angles: (a) $J=0.2,\theta ={60}^{\circ }$; (b) $J=0.2,\theta ={90}^{\circ }$; (c) $J=0.6,\theta ={60}^{\circ }$; (d) $J=0.6,\theta ={90}^{\circ }$; (e) $J=0.84,\theta ={60}^{\circ }$; (d) $J=0.84,\theta ={90}^{\circ }$. The rotation rate of the rotor is 120 RPS.

Figure 16

SPL contours (at $\theta ={90}^{\circ }$) of the first 10 BPF harmonics for (a) 90 RPS, (b) 100 RPS, (c) 110 RPS, and (d) 120 RPS. Left column: clean flow; right column: grid turbulence. The background noise was removed from the contours.

Figure 17

SPL contours (at $\theta ={90}^{\circ }$) of rotor broadband noise. Other setups are the same as those in Fig. 16.

Figure 18

Directivities comparison for tonal noise under various thrusting conditions. The rotor was rotating at 120 RPS.

Figure 19

Directivities comparison for the OASPL of broadband noise (from 1000 to 20 000 Hz) under various thrusting conditions. The rotor was rotating at 120 RPS.

Figure 20

1/3 octave band spectra comparison: unscaled results at (a) $\theta ={90}^{\circ }$ and (b) $\theta ={60}^{\circ }$; scaled results with the $M_{\infty }^2{M}_c^4$ vs $U_{\infty }/R$ scaling at (c) $\theta ={90}^{\circ }$ and (d) $\theta ={60}^{\circ }$.

Figure 21

Problem statement: (a) the rotor streamtube contraction in the presence of an open-jet wind tunnel; (b) schematic top view of the open-jet shear layer expansion downstream of the jet nozzle.

Figure 22

Estimated results of potential core radius $R_o$ at various working conditions under (a) clean flow and (b) grid turbulence.