On the efficient modeling of generic source directivity in Gaussian beam tracing.

For large-distance sound propagation with complex obstacles, the Gaussian beam tracing (GBT) method is often applied. An omnidirectional source model is commonly implemented in GBT, which, however, neglects the influence of generic directivity patterns of practical acoustic problems. There have been efforts to synthesize or reproduce the target directivity pattern over an observation surface by using multiple distributed point sources. However, the efficiency and applicability of general applications still call for improvement. More specifically, rays from each of the point sources and their traces in the space should be computed and superposed to estimate the sound field, making the computational cost largely dependent on the complexity of the source directivity pattern. In this work, a complex-valued radiation function model is developed to realize the generic source directivity for GBT computation. One advantage of the method is that only one source is required such that computation cost can be greatly reduced. Rays are emitted from the source with direction-dependent amplitude and phase to realize the target directivity pattern. The development of the radiation function is associated with the GBT method. The verification cases show that this method can give good agreement with analytical or wave-based numerical solutions. Capabilities of modeling a complex source model of the spinning sound field to mimic the propeller noise are studied, and the result matches well with analytical solutions. Finally, a demonstration case of a four-propeller-powered drone in an urban region is conducted.

An efficient rectilinear Gaussian beam tracing method for sound propagation modelling in a non-turbulent medium.

Large-distance sound propagation with high-frequency noise sources, multiple obstacles/geometry with varying acoustic impedance is common in real-life applications. To resolve the acoustic governing equations directly is often computationally costly, especially in three-dimensional space. Methods based on geometric acoustics can be more rapid. However, efforts are still being made to improve the efficiency, robustness, and the capability for complex configurations of such methods. In this paper, an efficient implementation of the rectilinear Gaussian beam tracing method is conducted, which combines rectilinear ray tracing with a proposed efficiency-matched dynamic ray tracing algorithm. A continuous medium stratification method is employed to improve the robustness. Also, a ray compression algorithm is proposed to save computation time. Numerical tests show that computation acceleration up to tenfold is achieved, benefiting rapid estimation of large-distance sound propagation. A standard octree data structure is employed in the code, which accelerates ray tracing in the testing cases with complex geometries. The efficiency and capability of the solver are demonstrated by studying several benchmark problems with varying complexity.

A revisit of the tonal noise of small rotors.

In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise increment with thrust (or rotational speed) is determined by orders of blade passing frequency harmonics and the unsteady motion. The axial mean flow influence can be approximated by quadratic functions. At given thrust, the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive. The higher tonal harmonics are significantly increased if unsteady motions, although of small-amplitude, are existed, as indicated by the defined sensitivity function, emphasizing that the unsteady motions should be avoided for quiet rotor designs. The scaling laws are examined by comparing with the full computations of the rotor noise using the frequency-domain method, the implementation of which has been validated by comparing with experiments. Good data collapse is obtained when the proposed scaling laws, which highlights the dominant influence of the design parameters, are incorporated.

An experimental study of trailing edge noise from a pitching airfoil.

In this study, the far-field noise from a pitching NACA 0012 airfoil was measured at a Reynolds number of 6.6 × 104. The pitching motion was in sinusoidal functions with a mean incident angle of 0°. Cases with the pitching amplitude varying from 7.5° to 15° and frequency from 3 to 8 Hz were tested, corresponding to the reduced frequency from 0.094 to 0.25. A microphone was placed in the far-field and the particle image velocimetry technique was utilized to study the flow structures near the trailing edge. The short-time Fourier transformation results of the noise signals revealed that a high-level narrow-band noise hump occurred at a specific angle of attack in a pitching cycle. At the corresponding moment, a coherent vortex street convecting on the airfoil surface was observed, and the vortex shedding frequency was in good agreement with the central frequency of the noise hump. The occurrence of the noise humps was attributed to the laminar boundary layer separation. In one pitching period, the moment when the narrow-band noise hump occurs is independent from the pitching amplitude and it is delayed as the pitching frequency increases. Larger pitching frequency or amplitude results in lower peak level of the noise humps.