Seongkyu Lee

Acoustic Scattering in the Time Domain Using an Equivalent Source Method

A numerical method to solve acoustic scattering in the time domain is presented in the present paper. Equivalent sources are embedded within a scattering surface and their strengths are determined as a function of time by the pressure-gradient boundary condition on a scattering surface. Once the strengths are determined, the equivalent sources are used to predict the scattered pressure. Linear shape functions are used to discretize the strength of the equivalent sources in time, and singular value decomposition is used to find the least-squares solution and to overcome potential numerical instabilities. The predictions are found to be in excellent agreement with the exact solutions for sound from a point monopole source and band-passed broadband sound. The method works well even at the irregular frequencies at which internal resonance modes occur. Finally, the method is used to predict the scattering of sound from a moving source. It is shown that the method has the capability to capture aperiodic characteristics very well.

Assessment of Time-Domain Equivalent Source Method for Acoustic Scattering

Equivalent source methods have been developed in the frequency and time domain to provide a fast and efficient computation for acoustic scattering. Although the advantages and capabilities of the method have been demonstrated, the limitations and drawbacks of the method have not yet been explored in detail. A detailed understanding of the equivalent source method is needed to use the method in a wide range of applications with more confidence. This paper presents an assessment of the time-domain equivalent source method for the prediction of acoustic scattering. The sensitivity of the method to numerical parameters, including the number of the surface collocation points, the number and position of the equivalent sources, the time step, and the cut-off singular value, is investigated and suggestions for these parameters are given for accurate predictions. A numerical instability issue is shown and a way to stabilize the solution with a time-averaging scheme is introduced. The sound power is calculated using the equivalent source strength to demonstrate the redistribution of the sound intensity by a scattering body and the conservation of the total power. Finally, scattering of sound from a source in a short duct is tested to demonstrate the utility of the tool for a more complicated shape of the scattering surface.

Potential Panel and Time-Marching Free-Wake-Coupling Analysis for Helicopter Rotor

A potential-based panel method coupled with advanced time-marching free-wake techniques is developed to achieve fast and accurate prediction for unsteady aerodynamics and wake dynamics of helicopter rotating blades. This coupling analysis is enabled by using the equivalence of the doublet-wake panels and the vortex filaments. The coupled panel method allows the inclusion of the self-induced velocity of curved vortex filaments and high-order time integration for the computation of wake convection. A parallel computation is applied to the wake convection for fast numerical calculation. The computation of the induced velocity from each vortex filament is parallelized and computed separately. The velocity-field integration technique is used to avoid numerical singularity during the interaction between the wake and blades. It is found that blade-pressure predictions and the wake roll-up agree well with the measured data for helicopter rotors, both in hover and forward flight. Tip-vortex pairing phenomena are also predicted and compared with the measured data.

Review: The Use of Equivalent Source Method in Computational Acoustics

This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequency-domain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

Prediction of far-field wind turbine noise propagation with parabolic equation

Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics.

Improved Algorithm for Nonlinear Sound Propagation with Aircraft and Helicopter Noise Applications

An efficient numerical method to solve nonlinear sound propagation is presented. The frequency-domain Burgers equation, which includes nonlinear steepening and atmospheric absorption, is formulated in the form of the real and imaginary parts of the pressure. The new formulation effectively eliminates possible numerical issues associated with zero amplitude at higher frequencies occurring in a previous frequency-domain algorithm. In addition, to circumvent a high-frequency error that can occur in the truncated higher frequencies, a split algorithm is developed, in which the Burgers equation is solved below a cutoff frequency and a recursive analytic expression is used beyond the cutoff frequency. Finally, the Lanczos smoothing filter is incorporated to remove the Gibbs phenomenon. The new method is found to successfully eliminate high-frequency numerical oscillations and to provide excellent agreement with the exact solution for an initially sinusoidal signal with only a few harmonics. The new method is applied to a broad range of applications with a comparison to other methods to assess the robustness and numerical efficiency of the method. These include sonic boom, broadband supersonic jet engine noise, and helicopter high-speed impulsive noise. It is shown that the new method provides the fastest and most accurate predictions compared to the other methods for all the application problems.

Comment on "Acoustic Velocity Formulation for Sources in Arbitrary Motion"

Comments on “Acoustic Velocity Formulation for Sources in Arbitrary Motion” Seongkyu Lee 1 Department of Mechanical and Aerospace Engineering University of California, Davis Kenneth S. Brentner 2 Department of Aerospace Engineering The Pennsylvania State University October 28, 2015 1 Assistant 2 Professor; Professor; skulee@ucdavis.edu, AIAA Senior Member ksb16@engr.psu.edu, AIAA Associate Fellow

Nonlinear Acoustic Propagation Predictions with Applications to Aircraft and Helicopter Noise

A new and efficient numerical method to solve nonlinear sound propagation is presented. The frequency-domain Burgers equation, which includes nonlinear steepening and atmospheric absorption, is formulated in the form of the real and imaginary parts of the pressure. The new formulation effectively eliminates possible numerical issues associated with zero amplitude at higher frequencies occurring in a previous frequency-domain algorithm. In addition, to circumvent a high frequency error that can occur in the truncated higher frequencies, a split algorithm, in which the Burgers equation is solved below a cut-off frequency and a recursive analytic expression is used beyond the cut-off frequency, is developed. Finally, the Lanzcos smoothing filter is incorporated to remove the Gibbs phenomenon. The new method is found to successfully eliminate high frequency numerical oscillations and to provide excellent agreement with the exact solution for an initially sinusoidal signal with only a few harmonics. The new method is applied to a broad range of applications with a comparison to other methods to assess the robustness and numerical efficiency of the method. These include sonic boom, broadband supersonic jet engine noise, and helicopter high-speed impulsive noise. It is shown that the new method provides the most accurate and fast predictions compared to the other methods for all the application problems.

Prediction of Acoustic Scattering in the Time Domain Using a Moving Equivalent Source Method

A new and ecient numerical method to solve acoustic scattering in the time domain is presented in the present paper. Equivalent sources are embedded within a scattering surface and their strengths are determined as a function of time by the pressure-gradient boundary condition on a scattering surface. Once the strengths are determined, the equivalent sources are used to predict the scattered pressure. Linear shape functions are used to discretize the strength of the equivalent sources in time and singular value decomposition is used to find the least-squares solution and to overcome potential numerical instabilities. The predictions are found to be in excellent agreement with the exact solutions for sound from a point monopole source and band-passed broadband sound. The method works well even at the irregular frequencies at which internal resonance modes occur. Finally, the method is used to predict the scattering of sound from a moving source. It is shown that the method has the capability to capture aperiodic characteristics very well.

Validation and numerical parameter study of a semi-empirical trailing edge noise model

This paper presents the validation and numerical parameter study of a semi-empirical trailing edge noise model. Turbulent boundary layer trailing edge noise is the main contributor of wind turbine noise and aircraft airframe noise. To predict this self-noise generated due to the interaction between a turbulent boundary layer flow and an airfoil trailing edge, a semi-empirical model was developed in NASA. The model has been widely used in academia and industry to predict the trailing edge noise. The capabilities and limitations of this semi-empirical model is further studied in this paper by comparing the predictions of the model with experimental data that were presented in a recent Benchmark Problems for Airframe Noise Computations (BANC) workshop. In order to better understand the behavior of trailing edge noise with operating conditions, numerical parameter study is investigated by varying variables such as chord length, Reynolds number, and Mach number.