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Parcel Eulerian-Lagrangian Hamiltonian formulations have recently been used in structure-preserving numerical schemes, asymptotic calculations and in alternative explanations of fluid parcel (in)stabilities. A parcel formulation describes the dynamics of one fluid parcel with a Lagrangian kinetic energy but an Eulerian potential evaluated at the parcel's position. In this paper, we derive the geometric link between the parcel Eulerian-Lagrangian formulation and well-known variational and Hamiltonian formulations for three models of ideal and geophysical fluid flow: generalized two-dimensional vorticity-stream function dynamics, the rotating two-dimensional shallow-water equations and the rotating three-dimensional compressible Euler equations.

Patient-specific aortic geometry and its influence on the flow in the vicinity of Transcatheter Aortic Valve (TAV) has been highlighted in numerous studies using both in silico and in vitro experiments. However, there has not yet been a detailed Particle Image Velocimetry (PIV) experiment conducted to quantify the relationship between the geometry, flow downstream of TAV, and the flow in the sinus and the neo-sinus. We tested six different patient-specific aorta models with a 26-mm SAPIEN 3 valve (Edwards Lifesciences, Irvine, CA, USA) in a left heart simulator with coronary flow. Velocities in all three cusps and circulation downstream of TAV were computed to evaluate the influence of the ascending aorta curvature on the flow field. The in vitro analysis showed that the patient-specific aortic curvature had positive correlation to the circulation in the ascending aorta (p = 0.036) and circulation had negative correlation to the particle washout time in the cusps (p = 0.011). These results showed that distinct vortical flow patterns in the ascending aorta as the main jet impinges on the aortic wall causes a recirculation region that facilitates the flow back into the sinus and the neo-sinus, thus reducing the risk of flow stagnation and washout time.

The initiation of leading-edge-vortex formation in unsteady airfoil flows is governed by flow criticality at the leading edge. While earlier works demonstrated the promise of criticality of leading-edge suction in governing LEV shedding, this criterion is airfoil and Reynolds number dependent. In this work, by examining results from Navier–Stokes computations for a large set of pitching airfoil cases at laminar flow conditions, we show that the onset of flow reversal at the leading edge always corresponds to the boundary-layer shape factor reaching the same critical value that governs laminar flow separation in steady airfoil flows. Further, we show that low-order prediction of this boundary-layer criticality is possible with an integral-boundary-layer calculation performed using potential-flow velocity distributions from an unsteady panel method. The low-order predictions agree well with the high-order computational results with a single empirical offset that is shown to work for multiple airfoils. This work shows that boundary-layer criticality governs LEV initiation, and that a low-order prediction approach is capable of predicting this boundary-layer criticality and LEV initiation.

Re-entrant jet causes cloud cavitation shedding, and cavitating vortical flow results in flow field instability. In the present work, a method of water injection is proposed to hinder re-entrant jet and suppress vortex in cloud cavitating flow of a NACA66 (MOD) hydrofoil (Re = 5.1 × 105, σ = 0.83). A combination of filter-based density corrected turbulence model (FBDCM) with the Zwart–Gerber–Belamri cavitation model (ZGB) is adopted to obtain the transient flow characteristics while vortex structures are identified by Q criterion & λ2 criterion. Results demonstrate that the injected water flow reduces the range of the low-pressure zone below 1940 Pa on the suction surface by 54.76%. Vortex structures are observed both inside the attached and shedding cavitation, and the water injection shrinks the vortex region. The water injection successfully blocks the re-entrant jet by generating a favorable pressure gradient (FPG) and effectively weakens the re-entrant jet intensity by 46.98%. The water injection shrinks the vortex distribution area near the hydrofoil suction surface, which makes the flow in the boundary layer more stable. From an energy transfer perspective, the water injection supplies energy to the near-wall flow, and hence keeps the steadiness of the flow field.

Performance of simple, fluidic harvesters consisting of a piezoelectric cantilever strongly relies on a time-dependent fluid forcing they experience. To quantify this forcing, an analytical solution of  a pressure Poisson equation (PPE) is presented that uses particle image velocimetry (PIV) data to calculate pressure around the harvester. This analytical solution is based on a modified Green’s function approach and provides a favorable method of calculating the pressure field from PIV data. It eliminates a need to compute higher-order derivatives of velocity that are present in the viscous terms and it eliminates the need to integrate Navier–Stokes equations to find the pressure along the boundaries of interest. An experiment was carried out to validate this solution. Pressure distribution along the piezoelectric cantilever was calculated by solving PPE analytically as a single vortex passed over it. This distribution was then integrated to calculate the net force acting on the beam. Euler–Bernoulli theory was then used to predict the beam’s dynamic response based on the calculated pressure. Using dielectric properties of the piezoelectric harvester, the voltage and total power output were computed from the motion of the beam. These values were compared to the voltage and power directly measured during the experiment.

Navigating efficiently across vortical flow fields presents a significant challenge in various robotic applications. The dynamic and unsteady nature of vortical flows often disturbs the control of underwater robots, complicating their operation in hydrodynamic environments. Conventional control methods, which depend on accurate modeling, fail in these settings due to the complexity of fluid-structure interactions (FSI) caused by unsteady hydrodynamics. This study proposes a deep reinforcement learning (DRL) algorithm, trained in a data-driven manner, to enable efficient navigation of a robotic fish swimming across vortical flows. Our proposed algorithm incorporates the LSTM architecture and uses several recent consecutive observations as the state to address the issue of partial observation, often due to sensor limitations. We present a numerical study of navigation within a Kármán vortex street created by placing a stationary cylinder in a uniform flow, utilizing the immersed boundary-lattice Boltzmann method (IB-LBM). The aim is to train the robotic fish to discover efficient navigation policies, enabling it to reach a designated target point across the Kármán vortex street from various initial positions. After training, the fish demonstrates the ability to rapidly reach the target from different initial positions, showcasing the effectiveness and robustness of our proposed algorithm. Analysis of the results reveals that the robotic fish can leverage velocity gains and pressure differences induced by the vortices to reach the target, underscoring the potential of our proposed algorithm in enhancing navigation in complex hydrodynamic environments.

This paper presents a two-stenosis aorta model mimicking vortical flow in vascular aneurysms. More specifically, we propose to virtually induce two adjacent stenoses in the abdominal aorta to develop various vortical flow zones post stenoses. Computational fluid dynamics (CFD) simulations were conducted for the virtual two-stenosis model based on physiological and anatomical data (i.e., diameters, flow rate waveforms) from adult rabbits. The virtual model includes adult rabbits' infra-renal portion of the aorta and iliac arteries. 3D CFD simulations in five different dual-stenosis configurations were performed using a commercial CFD package (FLUENT). In-house software assessed the evolution of flow vortices. Notably, spatial-temporally averaged wall shear stress (STA-WSS) and oscillatory shear index (OSI), the total volume of vortex flow, the number of vortices, and the phase-to-phase overlap of vortex flow within each region were evaluated. In all models, we found consistent patterns of the vortex flow parameters, indicating that the adjacent stenoses induced three different hemodynamic zones, namely, stable vortical flow (after the first stenosis), transient vortical flow (after the second stenosis), and unstable vortical flow (further distal to the second stenosis). Also, different degrees of flow disturbance can be achieved in these three zones. It is significant to note that, although the 'dual-stenosis' geometry is completely hypothetical, it allows us to create various vortical flows in consecutive vessel segments for the first time. As a result, if implemented as a pre-clinical model, the proposed two-stenosis model offers an attractive, tunable environment to investigate the interplays between subject-specific hemodynamics and vascular remodeling. This aspect remains in our future directions. Graphical Abstract

This paper introduces a generic model for the study of aerodynamic behaviour relevant to fifth-generation high-performance aircraft. The model design is presented, outlining simplifications made to retain the key features of modern high-performance vehicles while ensuring a manufacturable geometry. Subsonic wind tunnel tests were performed with force and moment balance measurements used to develop a database of experimental validation data for the platform at a freestream velocity of 20 m/s. Numerical simulations are also presented and validated by the experiments and further employed to ensure the vortex behaviour is consistent with contemporary high-performance platforms. A sensitivity study of the computational predictions from the turbulence modelling approach is also presented. This geometry is the first in a suite of representative aircraft geometries (the Sydney Standard Aerodynamic Models), in which all geometries, computational models, and experimental data are made openly available to the research community (accessible via this link: https://zenodo.org/communities/ssam_gen5/) to serve as validation test cases and promote best practices in aerodynamic modelling.

In hydro turbines, the draft tube vortex rope is one of the most crucial impact factors causing pressure pulsation and vibration. It is affected by operating conditions due to differences in the flow rate and state and can be symmetric or asymmetric along the rotational direction. It may influence the stability of draft tube flow. To achieve a better understanding, in this work, dynamic mode decomposition is used in a draft tube case study of a simplification of a vortex rope. As the flow rate increases, the shape of the vortex rope becomes clear, and the flow rotation becomes more significant as the inlet flow rate increases. Dynamic mode decomposition was used to determine the relative frequencies, which were 0 (averaged), 0.7 times, and 1.4 times the features of the reference frequency. As the inlet flow rate increases, the order of high-energy modes and their influence on the vortex rope gradually increase, and this characteristic is exhibited further downstream of the draft tube. When the inlet flow rate is low, the impact of mode noise is greater. As the flow velocity increases, the noise weakens and the rotation mode becomes more apparent. Identifying the mode of the vortex flow helps extract characteristics of the vortex rope flow under different operating conditions, providing a richer data-driven basis for an in-depth analysis of the impact of operating conditions on the flow stability of a draft tube.

We study the time-harmonic acoustic radiation in a fluid in flow. To go beyond the convected Helmholtz equation adapted only to potential flows, starting from the Goldstein equations coupling exactly the acoustic waves to the hydrodynamic field, we develop a new model in which the description of the hydrodynamic phenomena is simplified. This model, initially developed for a carrier flow of low Mach number M, is proved theoretically to be accurate, associated to a low error bounded by M². Numerical experiments confirm the M² law and show that the model remains of very good quality for flow of moderate Mach numbers.