## 1 Introduction  
Due to the marked environmental impact of increased air transportation that is expected in the future, the long-term scenarios for civil aviation are mostly concerned with reducing carbon dioxide (CO\({}_{2}\)) and nitrous oxide (NO\({}_{x}\)) emissions. The release of these substances from aviation is estimated to be more dangerous than comparable emissions at sea level, making it a significant driver of the climate change. In fact, though recent advancement in airframe and engine technologies leads to increased aircraft efficiency and reduced emissions, the total amount of global aviation emissions could nevertheless increase as a result of the predicted large rise in air transport [1]. To understand how potential next-generation aircraft might look, alternative and environmentally friendly energy sources, as well as modern aircraft designs, need to be considered, because it appears that the set-out goals cannot be achieved using traditional airframes and classical propulsion systems [2]. In the context of future aircraft technologies, computational fluid dynamics (CFD) has been continuously developing as a powerful design and analysis tool, where novel and physics-based numerical methods have gained great attention [3]. Distinguishing features for the aircraft design based on CFD methods include geometric flexibility, accuracy and efficiency, robustness, and scalability. Basically, in the aeronautical industry, the low-cost Reynolds-averaged Navier-Stokes (RANS) simulation remains the most widely followed approach for engineering design, analysis, and optimization of high-Reynolds-number flows [4]. The method, which is generally based on the turbulent eddy-viscosity concept, has been proven to be quite useful in determining the mean flow over airplanes at cruising speeds, being actively employed in the design of the most recent commercial aircrafts by leading companies [5]. In the framework of aerodynamic applications, although the Spalart-Allmaras one-equation model [6] remains often used, owing to its low computational complexity, two-equation eddy-viscosity turbulence models have become very popular. Also, considering the unsuitability of the \(k\)-\(\epsilon\) model for problems involving adverse pressure gradients, large separations, and reattachments, the \(k\)-\(\omega\) model is the one usually employed. In particular, the shear stress transport (SST) version of this model likely represents the most commonly used model in the aerospace industry, given its high accuracy-to-cost ratio [7]. Indeed, the \(k\)-\(\omega\) SST model provides a better prediction of flow separation than most RANS models, owing to its good behavior in adverse pressure gradients. On the negative side, it causes unphysical large turbulence levels in stagnation flow regions, even though this effect is much less pronounced than with the \(k\)-\(\epsilon\) model. However, unfortunately, the RANS-based methods frequently fail to predict highly separated flows, which are dominated by unsteady flow structures with a broad range of scales and, thus, require more complex modeling of the turbulence Reynolds stresses [8]. On the other hand, scale-resolving simulation (SRS) methods, such as large eddy simulation (LES) and hybrid RANS-LES techniques, which are known to be significantly more accurate, are generally deemed to be prohibitively expensive by industrial researchers [9]. In addition, the wide range of flow configurations, depending on either geometry (shape, angle of attack, computational domain) or freestream conditions (Reynolds number, turbulence intensity), makes it difficult to accurately predict practical aeronautical flows using a single turbulence model, amplifying the unavoidable inconsistencies between experiments and numerical simulations [10]. In fact, the development of universal modeling techniques, especially valid for largely separated flows, is critical in achieving the CFD technology needs for modern aircraft design.