A technique for separating sound fields using two closely spaced parallel measurement surfaces and based on equivalent source method is proposed. The method can separate wave components crossing two measurement surfaces in opposite directions, which makes nearfield acoustic holography (NAH) applications in a field where there exist sources on the two sides of the hologram surface, in a reverberant field or in a scattered field, possible. The method is flexible in applications, simple in computation, and very easy to implement. The measurement surfaces can be arbitrarily shaped, and they are not restricted to be regular as in the traditional field separation technique. And, because the method performs field separation calculations directly in the spatial domain—not in the wave number domain—it avoids the errors and limitations (the window effects, etc.) associated with the traditional field separation technique based on the spatial Fourier transform method. In the paper, a theoretical description is first given, and the performance of the proposed field separation technique and its application in NAH are then evaluated through experiments.

The accuracy, resolution, and economic cost of near-field acoustic holography (NAH) are highly dependent on the number of spatial sampling points. Generally, higher accuracy and resolution require more spatial sampling points, which may increase the workload of measurement or the hardware cost. Compressive sensing (CS) is able to solve the underdetermined problems by utilizing the sparsity of signals, and thus it can be applied to NAH to reduce the number of spatial sampling points but at the same time provide a high-resolution reconstruction image. Based on the CS theory, this paper proposes a compressed modal equivalent point source method (CMESM). In the method, a sparse basis that is obtained from the eigen-decomposition of the power resistance matrix is introduced to compress the equivalent point source strengths, and the ${\ell }_1–\text{norm}$ minimization is used to promote sparse solutions. Both numerical simulation and experimental results demonstrate the validity of the proposed CMESM and show its advantage over the existing methods when the number of spatial sampling points is reduced.

In previous studies, a sound field separation technique based on the equivalent source method (ESM) was successfully applied to separate the incoming and outgoing fields composing a non-free field. However, if the incoming wave is scattered by the source surface, the outgoing field is not the field that would be generated by the source in a free field. The object of the present work was to provide an equivalent source technique that allows the recovery of that free field in a noisy environment. In this approach, the incoming and outgoing fields, including the scattered and directly radiated fields on the measurement surface, are separated to obtain the free-field pressure that would be radiated by the source in an anechoic environment. The recovered free-field pressure is then used to reconstruct the whole free field of the source by using near-field acoustical holography based on the ESM, which makes the results equivalent to those that could be obtained from a free-field measurement. A theoretical description of the technique is given first, and then three numerical cases are investigated to demonstrate the ability of the proposed method.

Nearfield acoustic holography based on the compressed sensing theory can realize the accurate reconstruction of sound fields with fewer measurement points on the premise that an appropriate sparse basis is obtained. However, for different types of sound sources, the appropriate sparse bases are diverse and should be constructed elaborately. In this paper, a block sparse Bayesian learning (SBL) equivalent source method is proposed for realizing the reconstruction of the sound fields radiated by different types of sources, including the spatially sparse sources, the spatially extended sources, and the mixed ones of the above two, without the elaborate construction of the sparse basis. The proposed method constructs a block sparse equivalent source model and promotes a block sparse solution by imposing a structured prior on the equivalent source model and estimating the posterior of the model by using the SBL, which can achieve the accurate reconstruction of the radiated sound fields of different types of sources simply by adjusting the block size. Numerical simulation and experimental results demonstrate the validity and superiority of the proposed method, and the effects of two key parameters, the block size, and sparsity pruning threshold value are investigated through simulations.

In a noisy environment, the sound field of a source is composed of three parts, which are: The field that would be radiated by the target source into free space, the incoming field from disturbing sources or reflections, and the scattered field that is created by the incoming wave falling on the target source. To accurately identify the sound source with nearfield acoustic holography in that situation, the last two parts must be removed from the mixed field. In a previous study, a method for recovering the free sound field in a noisy environment was proposed based on the equivalent source method and measurements of pressure [J. Acoust. Soc. Am. 131(2), 1260-1270 (2012)]. In the present paper, that method was modified by allowing the input data to be measurements of particle velocity instead of pressure. An experiment was carried out to examine both the pressure- and velocity-based methods, and the performance of the two methods was compared. It was found that both methods are capable of reconstructing the free-field pressure radiated by the target source based on measurements made in a noisy environment, but the velocity-based method shows a large benefit in the reconstruction of the free-field particle velocity.

Large Eddy Simulation (LES) and Ffowcs Williams-Hawkings acoustic analogy are performed to study the effect of trailing-edge blowing on airfoil self-noise. Simulations were conducted using a National Advisory Committee for Aeronautics 0012 airfoil at zero angle of attack and a chord-based Reynolds number of $4\times {10}^5$ . The aerodynamic and aeroacoustic characteristics of the baseline airfoil were thoroughly verified by comparison with previous numerical and experimental data. The noise reduction effects of continuous and local blowing with different blowing ratios and blowing momentum coefficients were compared. A maximum noise reduction of 20 dB was achieved via trailing-edge blowing and the noise reduction mechanisms of the two blowing methods were discussed. The LES results show a pair of recirculation bubbles in the airfoil wake which are suppressed by trailing-edge blowing. As the blowing vortices convect into the wake, they stretch and stabilize the shear flows from airfoil surfaces. Instantaneous vorticity and root mean square velocity fluctuations are also weakened. There is a decrease in the spanwise coherence and an increase in the phase difference, which contribute to noise reduction. It is concluded that the suppression of turbulence fluctuations in the near wake is the main mechanism of noise reduction for airfoil trailing-edge blowing.