Examination of propeller sound production using large eddy simulation

The flow field of a five-bladed marine propeller operating at design condition, obtained using large eddy simulation, is used to calculate the resulting far-field sound. The results of three acoustic formulations are compared, and the effects of the underlying assumptions are quantified. The integral form of the Ffowcs-Williams and Hawkings (FW-H) equation is solved on the propeller surface, which is discretized into a collection of $N$ radial strips. Further assumptions are made to reduce FW-H to a Curle acoustic analogy and a point-force dipole model. Results show that although the individual blades are strongly tonal in the rotor plane, the propeller is acoustically compact at low frequency and the tonal sound interferes destructively in the far field. The propeller is found to be acoustically compact for frequencies up to 100 times the rotation rate. The overall far-field acoustic signature is broadband. Locations of maximum sound of the propeller occur along the axis of rotation both up and downstream. The propeller hub is found to be a source of significant sound to observers in the rotor plane, due to flow separation and interaction with the blade-root wakes. The majority of the propeller sound is generated by localized unsteadiness at the blade tip, which is caused by shedding of the tip vortex. Tonal blade sound is found to be caused by the periodic motion of the loaded blades. Turbulence created in the blade boundary layer is convected past the blade trailing edge leading to generation of broadband noise along the blade. Acoustic energy is distributed among higher frequencies as local Reynolds number increases radially along the blades. Sound source correlation and spectra are examined in the context of noise modeling.

Figure 1

The setup of the acoustic problem, computational domain, and boundary conditions. The propeller rotates about the $x$ axis with the origin located at the center of the rotor disk. All acoustic results were calculated at an observer radius of $100D$ at 360 locations in the $xy$ plane; one such observer location is shown.

Figure 2

A schematic showing how the propeller is broken down into strips for the case of five strips per blade resulting in 25 strips in total. The strips are equal in thickness along the radial direction.

Figure 3

(a) Pressure and viscous contribution to thrust $\left(K_{T_P},K_{T_V}\right)$ generated by the propeller and (b) radial distribution of thrust coefficient: pressure side, –$△$–; suction side, –$\square$–.

Figure 4

Directivity of total sound pressure level $\left(\text{SPL}\right)$ at $r=100D$, perpendicular to the rotor plane comparing each of the models for a blade discretization of ten strips. Every fifth data point has been plotted for clarity. The origin is set to 40 dB.

Figure 5

Comparison of the additional FW-H loading $\left(-\blacksquare -\right)$ and thickness $\left(-•-\right)$ sources with CSA (–). Every fifth point has been plotted for clarity. The origin is 0 dB.

Figure 6

Comparison of the energy spectra of the point-force dipole to: (a) the point-force dipole with the contribution of the hub, (b) the Curle strip acoustic analogy, and (c) the Ffowcs-Williams and Hawkings strip acoustic analogy. Spectra are calculated at an observer position of $\theta ={90}^{\circ }$.

Figure 7

The instantaneous total propeller sound field $\left(p^{\prime }\right)$ at an arbitrary time step from $r=100D$ to $150D$ in the $xy$ plane. Note the axes in $\left(-100D,100D\right)$ are not plotted to scale. The most intense oscillations occur in the positive and negative $x$ directions, which agrees with the directivity in Fig. 4.

Figure 8

Logarithmic contour levels of $p_{{}_{\text{RMS}}}$ on the propeller surface highlight the interaction between the blade roots and hub. The propeller rotates clockwise.

Figure 9

Isocontour of ${\lambda }_2$ colored with axial velocity to show the hub, blade root, and tip vortices.

Figure 10

Directivity of the hub's contribution to SPL, perpendicular to the rotor plane. The origin is 0 dB. The maximum value is 46.4 dB in the rotor plane and 44.3 dB along the rotation axis.

Figure 11

Energy spectrum of the hub's contribution to overall sound calculated at an observer position of $\theta ={90}^{\circ }$. The spectrum shows the broadband nature of the hub sound, which is characteristic of turbulence.

Figure 12

Time histories of $\partial K_F/\partial \tau$ at five equally spaced radial location on the propeller, starting at (a) $r=0.24R$ to (e) $r=0.88R$. Time derivatives of the coefficients of thrust and the $y$ component of the side force are plotted for all five blades at each radial location. Blade 1: ${\dot{K}}_T(—)$, ${\dot{K}}_{F_y}(–\cdot )$, blade 2: ${\dot{K}}_T(—)$, ${\dot{K}}_{F_y}(–\cdot )$, blade 3: ${\dot{K}}_T(—)$, ${\dot{K}}_{F_y}(–\cdot )$, blade 4: ${\dot{K}}_T(—)$, ${\dot{K}}_{F_y}(–\cdot )$, blade 5: ${\dot{K}}_T(—)$, ${\dot{K}}_{F_y}(–\cdot )$.

Figure 13

Phase-averaged time histories of the nondimensional coefficients of blade radial force (a) and blade azimuthal force (b).

Figure 14

Mean-blade spectra of azimuthal force on each of ten blade strip locations. The dashed vertical line represents the propeller rotation rate.

Figure 15

Comparison of strip generated sound pressure level for the Curle strip analogy and Ffowcs-Williams and Hawkings strip analogy with ten strips per blade. The origin is set to 20 dB in all figures.

Figure 16

Logarithmic contour levels of $p_{{}_{\text{RMS}}}$ on the propeller surface indicate the strength of the acoustic source. Propeller rotation is clockwise. The strongest sources are concentrated near the blade trailing edge.

Figure 17

Comparison of the mean energy spectra of strip generated sound from FW-H, with five strips per blade. Three strips are plotted to decrease clutter.

Figure 18

Contour plots of turbulent kinetic energy (TKE) at three radial stations, just above the hub, $0.27R$ (a), near maximum blade loading, $0.72R$ (b), and near the blade tip, $0.96R$ (c). Note the contour levels of in the inset of (b) are decreased an order of magnitude.

Figure 19

Comparison of the blade generated sound pressure level from the Curle strip analogy and Ffowcs-Williams and Hawkings strip analogy. The origin is set to 40 dB to minimize empty plotting space.

Figure 20

Comparison of the energy spectra of blade generated sound between the Curle strip analogy and Ffowcs-Williams and Hawkings strip analogy.

Figure 21

The radial variation of the source correlation length, $\mathcal{L}$.