# Prediction of the Absorption Characteristics of Non-Uniform Acoustic Absorbers with Grazing Flow
## 1 Introduction
They found that the mixed arrangement of perforated plates with different parameters could broaden the noise absorption bandwidth. [PERSON] et al. [21] designed a new type of non-uniform acoustic absorber which includes a slanted porous septum concept with varying open areas and a MultiFOCA (Multiple FOlded Cavity Absorber) concept. The results demonstrated that the new structure can improve broadband absorption performance. [PERSON] et al. [22] proposed a non-uniform axially segmented liner to attenuate fan noise at high supersonic fan speeds. They found that the acoustic energy was scattered into high radial mode orders, which was better absorbed by the liner. [PERSON] et al. [23] presented a low drag, axially variable depth acoustic absorption structure containing pairs of resonators coupled together by shared inlet volumes just below the facesheet. This type of absorption structure has the potential to achieve the targeted impedance with fewer openings in the facesheet, and therefore less drag than previous designs. The theoretical analysis methods of the duct with axial [24; 25; 26] and circumferential non-uniform [27; 28; 29; 30] absorbers have adopted many assumptions and ignored the effects of turbulence and air viscosity, resulting in unreliable predictions in some cases. In view of this, most of the studies on non-uniform acoustic absorbers in ducts were carried out by numerical computation techniques. [PERSON] et al. [31] compared COMSOL finite element (FE) results of transmission loss of acoustic absorption structure with experimental measurements, and showed that the FE results were highly reliable. [PERSON] et al. [32] performed an overview of engine liner modeling and a description of the key physical mechanisms. They pointed out that the mid-fidelity tools, such as COMSOL and ACTRAN, are critical enablers for the evaluation and construction of future complex acoustic liners. [PERSON] et al. [33] used ACTRAN FE code to compute the insertion loss of an acoustic liner for the given duct flow conditions, and identified the need for highly accurate insertion loss modeling. [PERSON] et al. [34] investigated the response of slit acoustic liners and their impedance properties under incident waves with different intensities and frequencies, as well as with different grazing flow Mach numbers. They developed a fully predictive impedance reduction technique by solving the compressible Navier-Stokes equations with accurate boundary conditions. The use of mid-fidelity tools allows researchers to explore in more detail the physics of the more sophisticated absorber designs. In particular, a high-fidelity method that is based on large eddy simulation (LES) can also be used to capture the local unsteady flow effects inside the perforation holes under acoustic excitation [35; 36; 37]. Since mid-fidelity as well as high-fidelity approaches are based on a direct resolution of the absorption structure perforations and geometry details in the numerical grid, the computational cost is particularly expensive. A variable-depth absorber contains chambers with different depths tuned for different frequencies. However, this design will result in a higher structure thickness and lower space utilization [21]. In view of this, this paper first develops a kind of broadband non-uniform acoustic absorber with a thin thickness. The basic building block of the developed absorption structures consists of an MPP and detuned cavities with different volumes. Since the desired cavity volumes in the BAU are mainly realized along the MPP surface, the broadband absorption of the BAU structure can be implemented by a smaller thickness compared with the variable-depth design, and there is no surplus space. The IBNSE method that is based on the semi-empirical Goodrich model, was developed to predict the acoustic absorption characteristics of the duct lined by a non-uniform acoustic absorber at grazing flow condition. The accuracy and the computational efficiency of the developed method were verified by FNSE simulations.