The present work introduces a new strategy for performing an exact tuning of the parameters governing the Von Karman - Pao isotropic energy spectrum for generating a stochastic turbulent velocity field. The tuning is carried out by numerically solving a single-variable equation defined through the confluent hypergeometric function of second kind. This procedure effectively captures the entire turbulent energy content for each point of the domain, yielding distinct and optimized outcomes based on the local turbulence Reynolds number. This stands in contrast to the approach commonly adopted in the same applications, where the spectrum parameters are calculated under the assumption of infinite Reynolds number at each point, assumption not always valid and therefore potentially leading to significant errors, in particular close to physical walls. Additionally, the strategy used to select the parameters defining the numerical integration of the spectrum is innovative as well, enabling an optimal balance between error committed and computational cost.The synthesis of the turbulent velocity field represents the most peculiar step of the Stochastic Noise Generation and Radiation (SNGR) method, in which, starting from the results provided by a RANS or URANS simulation, the aeroacoustic sources are reconstructed and then the radiated acoustic field is computed to estimate the farfield broadband noise. Stochastic Noise Generation (SNG) represents a lower-fidelity but much more computationally efficient strategy compared to directly obtaining the acoustic sources through a LES simulation or a hybrid RANS-LES simulation such as DES/DDES.The first part of the present work illustrates the significant benefits brought by the overall tuning procedure for the cases of a round jet or a 2-D NACA0012 airfoil at AOA = 8°. Subsequently, a direct comparison between the temporal history of the velocity field generated through SNG post-processing (applied both to a RANS and a URANS) and that obtained via a DDES is presented for a 3-D NACA0021 airfoil at AOA = 17°. Despite having a good correspondence of the signals from a statistical point of view, the frequency behavior of those obtained with SNG remains the most limiting aspect of this method in its current version.The simulations have been performed with the open-source software SU2.