We present, for the first time, the mean deflection evolution of a flexible rotor blade using a coupled model based on Navier–Stokes equations, for the fluid flow, and linear elasticity equations for the blade deformation. Three turbulence models are tested to reach Reynolds numbers as high as 8 104. The absolute tip speed ratios are in the range [0,25]. The numerical results are validated by comparisons with available tip displacements from experiments. For the parameter ranges, above mentioned, the elastic behavior of the flexible rotor is characterized, and the vorticity field is compared with results obtained for a rigid rotor. The effects of the pitch, the tip speed ratio (or frequency), and its sign on the blade deformation are reported. Typically, the blade deforms in the downstream direction, and it is shown that this deformation is a non-monotonic function of the rotation frequency and the pitch angle. Furthermore, it is found that, for particular values of the frequency and pitch angle, the blade is subject to deformations in the upstream direction. It is shown also that the flexible rotor could develop a vortex ring state, but not the rigid one, under the same conditions. It is found that there is a supercritical frequency associated with the apparition of this vortex ring state and this frequency occurs for negative pitches only, for the considered blade. The vorticity field revealed, as well, that the tip vortex changes sign with that of the blade deflection. Finally, we present the effect of the pitch and frequency on the twist angle of the blade and characterize its evolution along the span.

Prior research has recognized that the compound- and dual-technique-based branching redesign measures, used as alternatives to the conventional technique-based one, were effective in upgrading steel pipe-based pressurized hydraulic systems. Principally, the compound technique used two different plastic material types for the short-penstock instead of the single material type utilized in the conventional technique. However, the dual technique is based on splitting the single penstock installed in the conventional technique into a set of dual subpenstocks placed at each connection of the main-piping system to hydraulic parts. This handling aimed at improving the conventional technique efficiency with regard to the tradeoff between the magnitude attenuation and period expansion effects of the transient pressure-wave signal. Accordingly, this study proposed a comprehensive comparison between the compound- and dual-technique-based branching strategy with particular focus on the tradeoff between the two last parameters. The plastic material types demonstrated in this study included the high- or low-density polyethylene. The application addressed a waterhammer maneuver initiated into a reservoir-steel-pipe-valve system. Numerical computations used the method of characteristics for the discretization of the 1D extended pressurized-pipe flow model, embedding the Kelvin–Voigt and Vitkovsky formulations. The finding of this study suggested that the high- or low-density polyethylene (HDPE–LDPE) setup of the compound technique is the most prominent protected system setup, providing an acceptable tradeoff between the attenuation of magnitude and the expansion of the period of pressure-wave oscillation.

H-Darrieus vertical-axis wind turbines (VAWTs) capture wind regardless of its direction and operate effectively even in challenging and turbulent wind conditions. As a result, the blades operate under erratic and intricate aerodynamic loads, which cause them to bend. The performance of the H-Darrieus rotor will therefore be impacted by the blade’s deflection. This study aims at investigating the dynamic aerostructure influence on a novel convex-bladed H-Darrieus geometry. The results are compared to a straight-bladed baseline rotor. To do so, a two-way fluid–structure interaction (FSI)-coupled approach is performed to accurately address this issue. This approach allows for the simultaneous resolution of the fluid flow around the rotor and the mechanical structure responses inside the blades. The turbulent flows are resolved using the k-ω-SST model together with the URANS equations through computational fluid dynamics (CFD), while the structural deflections of the blades are assessed using finite element analysis (FEA). The results show that the performance of both H-Darrieus turbines decreases with increasing deformation. In addition, the study found that the carbon fiber composite (M1) material has the least deformation in the convex and straight blades, with values of 9.1 mm and 20.331 mm, respectively. The glass-fiber-reinforced epoxy composite (M3) material shows the most significant deflection across both types, with displacements of 32.50 mm and 73.78 mm for the straight blade and 19.02 mm and 43.03 mm for the convex blade. This study also reveals that the straight blade has a peak displacement of 73.785 mm when using the M3 material at TSR = 3, while the convex blade has a minimum displacement of 20.331 mm when using the M1 material, highlighting the varying performance characteristics of the materials. The maximum stress observed occurs in the straight blade, registering at 324.1 MPa with TSR = 3, which aligns closely with the peak displacement values, particularly for the aluminum alloy material (M2). In contrast, the convex blade made from the first material (M1) exhibits the lowest stress levels among the tested configurations.

Using numerical solutions of the Langevin equations, to simulate a magnetic separation of colloidal suspensions under an external magnetic-field gradient, we show the existence of a regime of dynamic scaling. We find that the separation time depends strongly on the size (or length) of aggregates taking place in the separation process. In the irreversible aggregation regime, we show that linear chains of particles steadily grow and their average size, S, increases with time as a power low. The chain-size (s) distribution-function ($c_s$ ) approaches (for long times) the following scaling form $c_s(t)\propto s^{-2}f(s/S)$ . The exponent, z, of the mean chain size $S(t)\propto t^z$ is compatible with Smoluchowski's coagulation equation, with a homogeneous kernel, even if the separation is a process with particle migration. We also show that the regime corresponding to the dynamic scaling is limited in time due to the separation. Furthermore, we find a characteristic time, which we identify as a similarity variable, and we relate it to the separation time.

Flexibility plays a crucial role in the design and performance of modern rotors. Its impact on rotor performance and its ability to adapt to external flow disturbances are well-established. In this study, we employ numerical simulations to explore the behavior of a flexible rotor submerged in a turbulent flow, aiming to forecast the influence of its flexibility on performance metrics. The rotational motion of the rotor and the forces imposed by the flow induce deformations in the blades, including bending and twisting. These deformations not only disrupt the flow patterns (vortices) in the turbulent wake but also modify the aerodynamic profiles, thereby affecting essential performance aspects such as thrust, drag, and lift. Our objective is to uncover the relationships between blade deformations, rotation frequencies, and rotor performance in a turbulent flow with a Reynolds number, $Re=O\left(10^4\right)$, and for a tip speed ratio in the range $[0,18]$. We demonstrate that the mean blade bending angle can be effectively expressed using a modified Cauchy number, revealing a scaling law. We also examined how the aerodynamic performance of the rotor blade is affected by variations in the tip speed ratio, either amplifying or reducing it. Through this research, we advance our understanding of the interplay between rotor flexibility, deformation, and performance, contributing to the optimization of rotor design and operational efficiency.