# Evaluation of Noise-Reduction Techniques for Gas-Turbine Test Stands: A Preliminary Analysis
## 2 Noise-Attenuation Assessment Embleton's Analytical Method
This relationship takes into account the influences of convective phenomena and the self-noise of the baffles on acoustic attenuation  
\[Attenuation_{flow}=A\left(1-1.5*M+M^{2}\right)\left[\text{dB}\right] \tag{2}\]  
where \(A\) is the noise attenuation without flow, and \(M\) is the Mach number, and it is valid only for \(-0.3<M<0.3\) (with the physical meaning of reverse and direct flow condition relative to the noise location) [18]. The main disadvantage of the Embleton method is that the calculation model does not account for changes in the structural properties of the mineral wool, even though density is a known critical parameter that significantly influences acoustic attenuation by shifting the absorbed frequency. Another disadvantage is that this method neglects the properties of the perforated panel. Additionally, the calculation model is only applicable to simple attenuator geometries with linear and parallel baffles. However, the main advantage of this method is that it does not require complex software or significant computing resources, resulting in a short turnaround time to obtain results. Noise attenuation is an intrinsic acoustic parameter of an attenuator. Another acoustic parameter is self-noise, manifested by noise generated from the flow interaction with the baffles. The noise generated by flow has different characteristics, depending on the direction of the flow, as is the case of the gas-turbine test cell, where sound waves travel  
Figure 1: Embleton method—parameters: (**a**) Schematic duct geometry of the attenuator; (**b**) noise curves used for attenuation prediction (Embleton). in the direction of flow (exhaust domain) and in the opposite direction of flow (intake domain). Figure 2 presents an evaluation of the noise attenuation produced by a single-level attenuator and the influences of airflow through the baffles using [PERSON]'s formulas. It proves that, compared to the static case without flow, a Mach number of 0.3, whether positive or negative, leads to a decrease or increase in attenuation by up to 10 dB. The Embleton method was used to calculate the noise attenuation and the flow correction using Equation (2). The geometrical parameters of the attenuator were \(ly=0.1\,\mathrm{m}\), \(t=0.1\,\mathrm{m}\), and \(L=0.6\,\mathrm{m}\). Flow-induced noise, also known as self-noise, is an inevitable consequence of fluid movement and an underlying factor to consider in any system involving airflow. If self-noise becomes excessive, redesigning the baffle silencer becomes necessary, as other noise-reduction methods might have limited effectiveness. Excessive self-noise is a result of a high level of turbulence, which has an unwanted and possible dramatic consequence in the test-cell environment, leading to subsonic drops or chocking of the engine, for example. In this study, for a more accurate determination of self-noise, which takes into consideration also the temperature and the distribution of perforation areas, an analytical method proposed by [PERSON] [19] is used for the calculation of self-noise for the linear version of attenuators, and the results are compared with results from the finite-element method (FEM). [PERSON]'s method is employed to estimate the acoustic power level generated by flow-induced noise in systems with baffles, such as noise attenuators. Equation (3) is used in this evaluation method:  
\[L_{w,self}=10\mathrm{log}_{10}\left(2.16\times 10^{5}*U^{5.4}.\frac{A_{b}}{ \left(T+273\right)^{2.27}\left(\frac{POA}{100}\right)^{4}}\right)\left[\mathrm{ dB}\right] \tag{3}\]  
where \(U\) is the flow velocity [m/s], \(A_{b}\) is the front area of the baffles [m\({}^{2}\)], \(T\) is the air temperature [\({}^{\circ}\)C], and \(POA\) is the percentage of the open area of the attenuator [%]. Self-noise is highly dependent on flow velocity. An increase in flow velocity will significantly impact the acoustic power level, as the power of flow-induced noise increases exponentially with the flow velocity.