This work aims at the development of a numerical method for the analysis of acoustic scattering in the time domain and its applications to rotorcraft noise. This purpose is achieved by developing two independent methods: (1) an analytical formulation of the pressure gradient for an arbitrary moving source and (2) a time-domain moving equivalent source method.
First, the analytical formulation for the pressure gradient is developed to fulfill the boundary condition on a scattering surface to account for arbitrary moving incident sources. A semi-analytical formulation was derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation needs to calculate the observer time differentiation outside the integrals numerically. A numerical algorithm is developed to implement this formulation in an aeroacoustic prediction code. A new analytical formulation is presented in the thesis. In this formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these two formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. One of the advantages of this analytic formulation is that it efficiently provides the boundary condition for the acoustic scattering of sound generated from an arbitrary moving source, such as rotating blades, which undergoes rotation, flapping and lead-lag motions. The formulation is applied to the rotor noise problems for two model rotors (UH-1H and HART-I). For HART-I rotor, CFD/CSD coupling was used to provide unsteady aerodynamics and trim solutions of the blade motion. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.
The formulation for the pressure gradient is first used to predict acoustic scattering in the frequency domain. The prediction is validated with the exact solution for acoustic scattering generated by a monopole source by a stationary sphere. A Bo105 helicopter and a notional heavy lift quad tilt rotor are considered to demonstrate a potential significance of acoustic scattering of rotorcraft noise. NASA’s Fast Scattering Code is used for the frequency-domain scattering solver.
Secondly, a new and efficient time domain acoustic scattering method using a moving equivalent source is developed to predict acoustic scattering in the time domain efficiently. The time-domain method provides entire frequency solutions in a single computation and is able to predict acoustic scattering of aperiodic signals. The method assumes an acoustically rigid surface for a scattering body and neglects the refraction effect by non-uniform flow around the scattering body. The pressure-gradient boundary condition is determined on a scattering surface and then the scattered field is calculated by using equivalent sources located within the scattering surface. Linear shape functions are used to discretize the strength of the equivalent sources in time and singular value decomposition is used to overcome potential numerical instability. The detailed numerical algorithm is addressed in the thesis. The method is more efficient numerically and easier to implement than other time-domain methods using a finite difference scheme or boundary integral equations because it is not necessary to find the solution in the entire domain, it uses a fewer number of equivalent sources than the surface mesh points, and it does not involve surface integrals. The method is validated against exact solutions for various cases including a single frequency monopole source, a dipole source, multiple sources, beat, and broadband noise sources. The predictions are found to be in excellent agreement with the exact solutions. The effect of the computational parameters including the number of surface mesh points, the number of equivalent sources, and the position of equivalent sources, etc, on the prediction is investigated and optimum parameters are presented. Acoustic scattering of sound from a moving source by a stationary body is studied to demonstrate scattering of an aperiodic signal. Acoustic scattering of sound produced by a moving source by a moving body is analyzed and the effect of the moving body on the scattered field is shown.
The numerical method is used to predict acoustic scattering of Bo105 helicopter rotor noise in the time domain. The time-domain code results of SPL are validated against the results obtained by the FSC. The effect of the geometry of the scattering body on the scattering of rotor noise is presented. Acoustic scattering of an impulsive noise is investigated to simulate main rotor BVI noise and its significance is addressed. From the computation of a range of frequencies in a single computation, computational time saving was achieved by a factor of about 200 compared to the frequency-domain approach.