# Combined CFD-Stochastic Analysis of an Active Fluid Injection System for Jet Noise Reduction
## 1 Introduction  
The problem of noise generation by compressible turbulent jets has been the subject of studies since the early 1950s, with the introduction of the turbojet also in commercial aircraft. It has continued, even later since the 1980s, with the introduction of turbofan with high bypass ratios, inherently less noisy than previously, due to the reduced exhaust velocity. In recent decades, the problem of jet noise prediction has been numerically addressed through a broad range of methods. Despite the application of Direct Numerical Simulation (DNS) to jet-noise prediction [1; 2; 3; 4], becoming more feasible with the growing advancement in computational resources, due to the large disparities of length and energy scales between fluid and acoustic fields, the use of fully solved Navier Stokes equations without turbulence modeling (DNS) is still restricted to low Reynolds number flows. Instead, the numerical simulation of aeroacoustics through the solution of filtered Navier Stokes equations, either using fully Large Eddy Simulation (LES) or hybrid Reynolds Averaged NavierStokes-LES approaches, such as the detached eddy simulation (DES), is a major area of research [5; 6; 7]. However, despite the increase in computational power, even these types of simulations are not yet feasible for industrial purposes. Indeed, industry interest is mainly devoted to reliable numerical tools to be applied to realistic configurations for redesign of old configurations and for the development of new technologies. Furthermore, the growing interest on multi-disciplinary and multi-objective optimization necessarily lead to approaches that require low computational time. Therefore, Reynolds Averaged Navier Stokes (RANS) simulations still remains the more feasible approach for Computational Fluid Dynamics (CFD) applications of industrial interest. However, RANS computations are not able to model, solely, the aeroacoustic phenomena. In this context, the stochastic approach for the prediction of noise from turbulence has received a great deal of interest in recent years. It was introduced by [PERSON] [8] and [PERSON] [9], and it is based on the idea that Fourier components of solenoidal velocity fluctuations can be sampled in the wave-number space from a prescribed mono-dimensional energy spectrum. The revision and improvement of these methods for aeroacoustic applications have produced the stochastic noise generation and radiation (SNGR) methods [10; 11; 12; 13; 14; 15]. Concerning the jet-noise reduction devices, in recent decades, chevron nozzles attracted much attention to their noise reduction benefits and are currently one of the most popular jet-noise reduction devices. Chevrons typically reduce low frequency noise, while increasing high frequency noise [16] with a limited thrust loss of only about 0.25%. Downstream vortex, generated by chevron, improves mixing in the shear layer, which leads to a decrease or increase in noise at certain frequency ranges. Several RANS computational studies were conducted about chevron nozzles [17; 18; 19]. The first LES calculations for the chevron nozzle jets appeared to be performed by [PERSON] et al. [20; 21]. A promising technology seems to be the fluidic chevron, as alternative solution to the mechanical chevron. This device consists of small injectors that inject high pressure air or other fluids, such as water, near the nozzle exit edge in order to emulate the mixing and the noise reduction features of the mechanical chevron. Numerous studies and experiments have been carried out to develop fluid chevron technology, especially at NASA Langley Jet Noise lab [22; 23; 24]. Fluidic chevrons, tested at NASA, were the first of their kind, designed with small slots near the nozzle exit edge to allow air injection into the stream and promote mixing between the core flow and the flow from the fan. Despite the simplicity of the mechanical chevron, the fluidic injection technique allows a greater flexibility.