# Evaluation of Noise-Reduction Techniques for Gas-Turbine Test Stands: A Preliminary Analysis
## 2 Noise-Attenuation Assessment Embleton's Analytical Method  
To identify a calculation model for the acoustic attenuation of a lamellar attenuator, both the analytical method developed by Embleton [16] and the finite-element method using MSC Actran software version 19 were employed. The finite-element method with Actran involves calculating acoustic propagation at each point in the grid, accounting for air impedance, reflections from solid and absorbent objects, propagation through porous materials, and free-field acoustic wave propagation. In the [PERSON] method, a parallel baffle silencer operates as a type of lined duct, wherein each passage between the baffles acts as an individually lined duct. The transmission losses in such systems arise from the sound absorption within the porous lining as the sound waves travel through the duct. When the cross-sectional area of the lining approaches the size of the open area through which the sound travels, additional losses occur due to wave reflections at the lining's end, enhancing the silencer's effectiveness as a reactive silencer. [PERSON]'s method simplifies by assuming a plane-wave propagation, which eases calculations but does not perfectly reflect the physical reality, hence the necessity of going deeper into the phenomenon. This approach allows for the estimation of sound attenuation, significantly accounting for lower modes that persist longer in the lining. The simplicity of [PERSON]'s graph-based method consists of facilitating the prediction of total attenuation by requiring only a few parameters: baffle width, spacing, length, and sound wavelength. Also, the method presented by [PERSON] does not approach the staggered configuration, which would be a proper solution to use on a turbojet test stand. By studying this configuration of staggered baffles, a modification of the prediction formula is compulsory, and it will be further applied for evaluation in this article. Figure 1a presents schematically the geometric parameters of the attenuator and the noise-attenuation curves used by [PERSON]. The parameters necessary for calculating the attenuation include the width of the lamella \(t\), the distance between the baffles \(ly\) (which is the width of the air channel), and the baffle length \(L\). These parameters are used to calculate the percentage of the open area (_POA_ [%]) of the attenuator, the ratio \(ly/\lambda\) (where \(\lambda\) is the wavelength), and the speed of sound in air \(c\). Based on these data, applied to  
Equation (1), the attenuation curves \(A_{ly}\) from Figure 1b are consulted to complete the [PERSON] method [16]. Original works like [PERSON]'s \"Noise and Vibration Control\" (1971) mostly used [PERSON]'s method, and the recent ones are referenced to the Galaitis and Ver methods, which are applied for dissipative noise silencers for parallel baffles [16] [PERSON] developed a software-based prediction method for the calculation of noise attenuation, transmission loss, and insertion loss, but only for lined ducts [17], without taking into consideration a staggered arrangement of the baffles. Based on the open area, the corresponding \(A_{ly}\) curve is selected and then multiplied by the ratio \(L/l_{y}\), yielding the acoustic attenuation of the attenuator, as described by Equation (1). \[Attenuation=A_{ly}*\frac{L}{l_{y}}\left[\text{dB}\right] \tag{1}\]  
The open area is computed using the relation POA = \(l_{y}/(l_{y}+t)\times 100\). For intermediate porosities, values from the graph can be interpolated. The frequency can be determined using Figure 1b, where \(f=(l_{y}/\lambda)\times(c/l_{y})\). The relationships for acoustic attenuation, as presented by [PERSON] [16] in the form of Equation (2), can be adjusted according to the airflow velocity between the baffles according to Equation (2).