# Evaluation of Noise-Reduction Techniques for Gas-Turbine Test Stands: A Preliminary Analysis
## 3 Noise-Attenuation Assessment--Finite-Element Method  
The validation of the Embleton model and the finite-element method was conducted by comparing the results with the experimentally obtained values. For this purpose, an experimental stand was set up to test lamellar attenuators. The finite-element method involves creating a geometric model of the test bench, as presented in Section 3, meshing it, applying boundary conditions, and then conducting the acoustic analysis. The numerical scheme considers phenomena such as acoustic propagation in gaseous and porous media, acoustic reflections and absorptions, and the propagation of acoustic waves in a free  
Figure 2: Noise attenuation of a single-level attenuator as a function of the Mach number. field. Figure 3 presents the internal geometry of the test bench. To reduce computational time, a 2D simulation was performed. The applied boundary conditions are as follows: the blue line represents the boundary condition of acoustic pressure, with a pressure of 100 Pa applied along it, representing the acoustic source; the black lines represent the walls of the test bench, modeled as perfectly reflective surfaces; the red line represents the free-field boundary condition, allowing the propagation of acoustic waves from inside the domain to the exterior, without returning to the computational domain; the green lines represent the perforated panel with a porosity of \(POA=30\%\), hole diameter \(\varphi=4\) mm, panel thickness \(b=0.5\) mm, corresponding to the tested structure. The blue-colored surface inside the test bench represents the fluid domain with a sound speed \(c=340\) m/s and density \(\rho_{0}=1.225\) kg/m\({}^{3}\), while the yellow domain represents the mineral wool for which was introduced a flow resistivity \(\sigma=30\),000 Rays/m, simulating a mineral wool density of approximately 80-100 kg/m\({}^{3}\). In the acoustic analysis for the calculation of acoustic absorption and interior propagation through the porous material, the Delany-Bazley calculation model was used [20,21]. The Delany-Bazley method is used to predict the acoustic properties of porous materials in terms of sound absorption and attenuation characteristics. The method estimates complex wave numbers and the characteristic impedance of porous materials based on flow resistivity. The following equations describe the acoustic characteristics:  
\[Z_{c}=\rho_{0}c\left(1+0.0571\left(\frac{\rho_{0}f}{\sigma}\right)^{-0.754}-j0.087\left(\frac{\rho_{0}f}{\sigma}\right)^{-0.732}\right) \tag{4}\]  
\[K_{c}=\frac{\omega}{c}\left[1+0.0571\left(\frac{\rho_{0}f}{\sigma}\right)^{-0. 7}-j0.189\left(\frac{\rho_{0}f}{\sigma}\right)^{-0.595}\right] \tag{5}\]  
where \(\sigma\) is the flow resistivity of the fluid, \(f\) is the propagation frequency, \(\rho_{0}\) the density of the fluid, and \(\omega\) is the angular frequency. A Delany-Bazley method was applied by [PERSON] and [PERSON] [22] to analyze the transmission loss of a partitioned rectangular duct in numerical simulations and experimental validation, although without considering the flow condition. The red dots indicate the positions of the microphones used in the tests to evaluate the attenuation capacity of the silencers. The mesh, shown on the right side of Figure 3, is composed of rectangular elements with a maximum dimension of 8 mm, corresponding to  
Figure 3: Test-bench geometry and computational grid: (**a**) top view of geometry with a boundary condition—baffle (yellow), acoustic domain (light blue), free domain (red); (**b**) 2D mesh (element size of 7 mm)—baffle (yellow), free domain (red); (**c**) 3D mesh (element size of 7 mm)—baffle (grey), acoustic domain (green), free domain (blue). a maximum analysis frequency of approximately 10 kHz. A mesh with quadratic elements was utilized with a rule of a minimum of four elements per wavelength, which must be followed to accurately capture the propagation of the acoustic wave.