In this work, we introduce a novel application of the adaptive mesh refinement (AMR) technique for the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial since an inadequate resolution might introduce numerical noise that triggers premature transition to turbulence. With AMR, we enable the design of three different and independent meshes for the non-linear base flow and the linear direct and adjoint solutions. Each of these is designed to reduce the truncation and quadrature errors for its respective solution, based on the spectral error indicator. We provide details about the workflow and the refining procedure. The numerical framework is validated for the two-dimensional flow past a circular cylinder, computing a portion of the spectrum for the linearised direct and adjoint Navier–Stokes operators.

Rotors play a major role in various applications including ventilation and propulsion systems such as in helicopters, drones, gas turbines and wind turbines. This visualization of instantaneous vortical structures (identified by the k₂ criterion) shows complex flow structures emanating from a twisted drone rotor that is impulsively starting to rotate at 1600 rpm. Initially, a starting vortex is formed as a result of lift generation and shed as a connected vortex tube from the entire surface of the blade, which has a strong connection to the blade tip via the so-called tip vortex. Leading edge separation occurs at span positions of high twist, followed by wave-induced breakdown to turbulence along the whole wing span. This turbulence then sheds as small-scale vortices into the wake and dissipates. Understanding the behaviour of these vortices from such complex blades and how they interact with the other blade is critical to design more efficient and potentially more silent propellers.

The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. Most techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that is, they require access to all available samples of a time series at once. In addition to the impossibility of online monitoring of uncertainties during the course of simulations, such an offline approach can lead to input/output (I/O) deficiencies and large storage/memory requirements, which can be problematic for large-scale simulations of turbulent flows. Here, we designed, implemented and tested a framework for estimating time-averaging uncertainties in turbulence statistics in an in-situ (online/streaming/updating) manner. The proposed algorithm relies on a novel low-memory update formula for computing the sample-estimated autocorrelation functions (ACFs). Based on this, smooth modeled ACFs of turbulence quantities can be generated to accurately estimate the time-averaging uncertainties in the corresponding sample mean estimators. The resulting uncertainty estimates are highly robust, accurate, and quantitatively the same as those obtained by standard offline estimators. Moreover, the computational overhead added by the in-situ algorithm is found to be negligible allowing for online estimation of uncertainties for multiple points and quantities. The framework is general and can be used with any flow solver and also integrated into the simulations over conformal and complex meshes created by adopting adaptive mesh refinement techniques. The results of the study are encouraging for the further development of the in-situ framework for other uncertainty quantification and data-driven analyses relevant not only to large-scale turbulent flow simulations, but also to the simulation of other dynamical systems leading to time-varying quantities with autocorrelated samples.

Swirl switching refers to the temporal rotation of the plane of symmetry of the crosssectional vortices about the equatorial plane of the curved pipe and may induce significant vibrations in piping systems. The origin of this phenomenon is not yet understood, and its relationship with turbulent fluctuations in the upstream straight section is still debated in the literature. To assess the effect of upstream turbulence, direct numerical simulations are performed for spatially developing bent pipe flows under both laminar and turbulent inflow conditions. Additionally, the influence of the bending angle on swirl switching and time-averaged flow characteristics is investigated. Proper orthogonal decomposition (POD) is applied to three-dimensional velocity fields to extract spatially coherent structures responsible for swirl switching. The phenomenon is observed for both inlet velocity profiles and bending angles, although it does not correspond to the dominant mode in the case of laminar inflow conditions. A reduced-order reconstruction using the most energetically relevant antisymmetric POD modes indicates a link between swirl switching and the shear layer within the bend. We therefore infer that swirl switching could arise because of a symmetry-breaking shear layer instability, representing a stage in the bifurcation cascade that leads to turbulence.

A framework is presented for the spectral-element code Nek5000, which has been, and still is, widely used in the computational fluid dynamics (CFD) community to perform high-fidelity numerical simulations of transitional and high Reynolds number flows. Despite the widespread usage, there is a deficiency in having a comprehensive set of tools specifically designed for conducting simulations using Nek5000. To address this issue, we have created a unique framework that allows, inter alia, to perform stability analysis and compute statistics of a turbulent flow. The framework encapsulates modules that provide tools, run-time parameters and memory structures, defining interfaces and performing different tasks. First, the framework architecture is described, showing its non-intrusive approach. Then, the modules are presented, explaining the main tools that have been implemented and describing some of the test cases. The code is open-source and available online, with proper documentation, to-run instructions and related examples.

Wall-bounded turbulent flows as those occurring in transportation (e.g. aviation) or industrial applications (e.g turbomachinery), are usually subjected to pressure gradients (PGs). The presence of such PGs affects greatly the development and physics of the turbulent boundary layer (TBL), making it an open research area. An important phenomena associated with the presence of strong adverse PGs (APGs) as appearing in wings, is the separation of the boundary layer, which can lead to stall.

The wing-tip vortices are formed near the tip of finite-span, lift-generating surfaces as a result of the pressure difference between the pressure and suction sides of the wing.

High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of Re-c = 200 000 and at various angles of attack up to 10 degrees. The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spanwise pressure gradient as a result of the variable downwash induced by the wing-tip vortices (an inviscid effect typical of finite-span wings); (ii) differences in the flow history at different wall-normal distances, caused by the variable flow angle in the wall-normal direction (due to constant pressure gradients and variable momentum normal to the wall); (iii) laminar flow entrainment into the turbulent boundary layers near the wing tip (due to a laminar-turbulent interface); and (iv) variations in boundary layer thickness across the span, attributed to the variable wall-normal velocity in that direction (a primarily inviscid effect). These physical effects are then used to explain the differences in the Reynolds stress profiles and other boundary layer quantities, including the reduced near-wall peak of the streamwise Reynolds stress and the elevated Reynolds stress levels near the boundary layer edge, both observed in the finite-span wings. Other aspects of the flow, such as the downstream development of wing-tip vortices and their interactions with the surrounding flow, are reserved for future investigations.

High-fidelity simulations were conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with rounded wing-tip geometry at a chord-based Reynolds number of Re_c = 200000 and various angles of attack up to 10^◦. This study aims at discerning the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. After excluding effects from the reduced effective angle of attack due to the induced velocity by the wing-tip vortex and other more localized three-dimensional effects (such as skewed velocity profiles), it was observed that the finite-span boundary layers exhibit a lower near-wall peak in their streamwise Reynolds stress profiles and a higher turbulence level near the boundary layer edge, particularly in regions closer to the wing tip. These discrepancies are explained by variations in adverse pressure gradient levels across the span, differences in flow history in the wall-normal direction caused by the skewed velocity profiles, and the variable boundary layer thickness caused by vortex formation and other finite-span effects. The primary focus of this study is on the turbulent boundary layers, with other aspects of the flow reserved for future investigations.

The coherent structures arising in the turbulent flow around a three-dimensional stepped (or step) cylinder are studied through direct numerical simulation. This geometry is widespread in many applications and the junction substantially modifies the wake behaviour, generating three main cells. The mechanisms of vortex connections on the junction are difficult to be captured and interpreted. We thus use a high-order spectral -element methodology (SEM), and the adaptive mesh refinement technique (AMR) to adequately resolve each region of the domain, capturing the smallest turbulent scales. In this way, we can analyse the vortical interactions on the junction via the A2-criterion and understand the evolution of the train of hairpins, which appears only when the cylinder shear layer gets unstable. Together with the hairpins, four horseshoe and edge vortices coexist on the flat junction surface. A complete picture of the vortices' evolution in time is provided. To extract the large-scale, and most energetic, structures in the wake we perform a three-dimensional proper orthogonal decomposition (POD) of the flow. The first six POD modes correspond to three travelling modes which identify the large (L), the small (S) and the modulation (N) cells. The ReD trend shows that these cells persist at higher Reynolds numbers with a larger separation between the vortex shedding frequencies fN and fL. At the same time, the downwash POD mode gets less strong with a more intense and localised modulation region which affects a more extended portion of the large cylinder wake.