Modeling and dynamics of a two-line kite

A mathematical model of a kite connected to the ground by two straight tethers of varying lengths is presented and used to study the traction force generated by kites flying in cross-wind conditions. The equations of motion are obtained by using a Lagrangian formulation, which yields a low-order system of ordinary differential equations free of constraint forces. Two parameters are chosen for the analysis. The first parameter is the wind velocity. The second parameter is one of the stability derivatives of the aerodynamic model: the roll response to the sideslip angle, known also as effective dihedral. This parameter affects significantly the lateral dynamics of the kite. It has been found that when the effective dihedral is below a certain threshold, the kite follows stable periodic trajectories, and naturally flies in cross-wind conditions while generating a high tension along both tethers. This result indicates that kite-based propulsion systems could operate without controlling tether lengths if kite design, including the dihedral and sweep angles, is done appropriately. If both tether lengths are varied out-of-phase and periodically, then kite dynamics can be very complex. The trajectories are chaotic and intermittent for values of the effective dihedral below a certain negative threshold. It is found that tether tensions can be very similar with and without tether length modulation if the parameters of the model are well-chosen. The use of the model for pure traction applications of kites is discussedThis work was supported by the Ministerio de Economía y Competitividad of Spain and the European Regional Development Fund under the project ENE2015-69937-R (MINECO/FEDER, UE). GSA work is supported by the Ministerio de Economía y Competitividad of Spain under the Grant RYC-2014-15357. MGV was partially supported by grant TRA2013-41103-P (MINECO/FEDER, UE). RS was partially supported by the projects AWESCO (H2020-ITN-642682) and REACH (H2020-FTIPilot-691173)

Flow interaction of three-dimensional self-propelled flexible plates in tandem

Tandem configurations of two self-propelled flexible flappers of finite span are explored by means of numerical simulations. The same sinusoidal vertical motion is imposed on the leading edge of both flappers, but with a phase shift (φ). In addition, a vertical offset, H, is prescribed between the flappers. The configurations that emerge are characterized in terms of their hydrodynamic performance and topology. The flappers reach a stable configuration with a constant mean propulsive speed and a mean equilibrium horizontal distance. Depending on H and φ, two different tandem configurations are observed, namely compact and regular configurations. The performance of the upstream flapper (i.e. the leader) is virtually equal to the performance of an isolated flapper, except in the compact configuration, where the close interaction with the downstream flapper (i.e. the follower) results in higher power requirements and propulsive speed than an isolated flapper. Conversely, the follower’s performance is significantly affected by the wake of the leader in both regular and compact configurations. The analysis of the flow shows that the follower’s performance is influenced by the interaction with the vertical jet induced by the vortex rings shed by the leader. This interaction can be beneficial or detrimental for the follower’s performance, depending on the alignment of the jet velocity with the follower’s vertical motion. Finally, a qualitative prediction of the performance of a hypothetical follower is presented. The model is semi-empirical, and it uses the flow field of an isolated flapper.This work was supported by the State Research Agency of Spain (AEI) under grant DPI2016-76151-C2-2-R including funding from the European Regional Development Fund (ERDF). The computations were partially performed at the supercomputer Caesaraugusta from the Red Española de Supercomputación in activity IM-2020-2-000

Three-dimensional effects on the aerodynamic performance of flapping wings in tandem configuration

Direct numerical simulations have been performed to analyze how three-dimensional effects influence the performance of wings in tandem configuration undergoing a two-dimensional optimal kinematics. This optimal motion is a combination of heaving and pitching of the airfoils in a uniform free-stream at a Reynolds number and Strouhal number . Wings of two different aspect ratios, 2 and 4, undergoing the 2D motion have been considered. It has been found that the interactions between the vortical structures of the fore- and the hind-wings are qualitatively similar to the two-dimensional case for both . However, the ratio between the mean thrust of the hind-wing and the fore-wing decreases from 80% in 2D to 70% in 3D, implying that the 3D effects are detrimental for the vortical interactions between the wings in terms of thrust production. Nonetheless, the propulsive efficiency remains constant both in 2D and 3D, for both . A more realistic flapping motion has also been analyzed and compared to the heaving motion. It has been found that the aerodynamic forces decrease when the wings are in flapping motion. This detrimental behavior has been linked to a sub-optimal motion of the inboard region of the wings. This sub-optimal region of the wings entails a decrease of the mean thrust and of the propulsive efficiency compared to the heaving case, which are more pronounced for the 4 wings.This work was supported by grant DPI2016-76151-C2-2-R (AEI/FEDER, UE). The computations were partially performed at the supercomputer Tirant from the Red Española de Supercomputación in activity FI-2018-2-0025.Publicad

Three-Dimensional Effects on Plunging Airfoils at Low Reynolds Numbers

We present two-dimensional and three-dimensional (3-D) direct numerical simulations of large-amplitude plunging maneuvers at Reynolds numbers of Re=1000 and 5000, with velocity ratios of G=0.5, 1, and 2. For all cases, the evolution of the force coefficients is qualitatively similar. The lift coefficient presents a pronounced peak toward the end of the acceleration phase of the maneuver, a local minimum in the deceleration phase, and a second peak at the end of the maneuver. The amplitude of the main peak increases linearly with G, with limited effect of the Reynolds number and a negligible effect of the three-dimensionality of the flow. On the other hand, both the Reynolds number and three-dimensionality have a stronger effect on the amplitude of the maximum value of the lift coefficient at the end of the maneuver, as well as on the subsequent transient decay toward the static values. The comparison of the evolution of the flow structures near the airfoil shows that these differences in the force coefficients are due to subtle interactions between the various vortices generated during the maneuver, as well as to the development of a 3-D boundary layer on the suction side of the airfoil triggered by the instability of the trailing-edge vortices.This work was supported by the State Research Agency of Spain (AEI) under grant DPI2016-76151-C2-2-R including funding from the European Regional Development Fund (ERDF). The computations were partially performed at the supercomputer Picasso from the Red Española de Supercomputación in activity FI-2018-2-0051. We thank A. Jones and G. Perrotta for providing their experimental data.Publicad

Fluid-structure resonance in spanwise-flexible flapping wings

We report direct numerical simulations of the flow around a spanwise-flexible wing in forward flight. The simulations were performed at Re = 1000 for wings of aspect ratio 2 and 4 undergoing a heaving and pitching motion at Strouhal number Stc ≈ 0.5. We have varied the effective stiffness of the wing Π1 while keeping the effective inertia constant, Π0 = 0.1. It has been found that there is an optimal aerodynamic performance of the wing linked to a damped resonance phenomenon, that occurs when the imposed frequency of oscillation approaches the first natural frequency of the structure in the fluid, ωn,f /ω ≈ 1. In that situation, the time-averaged thrust is maximum, increasing by factor 2 with respect to the rigid case with an increase in propulsive efficiency of approximately 15 %. This enhanced aerodynamic performance results from the combination of larger effective angles of attack of the outboard wing sections and a delayed development of the leading-edge vortex. With increasing flexibility beyond the resonant frequency, the aerodynamic performance drops significantly, in terms of both thrust production and propulsive efficiency. The cause of this drop lies in the increasing phase lag between the deflection of the wing and the heaving/pitching motion, which results in weaker leading-edge vortices, negative effective angles of attack in the outboard sections of the wing, and drag generation in the first half of the stroke. Our results also show that flexible wings with the same ωn,f /ω but different aspect ratio have the same aerodynamic performance, emphasizing the importance of the structural properties of the wing for its aerodynamic performance.Funding. This work was partially supported by grant DPI2016-76151-C2-2-R (AEI/FEDER, UE).Publicad

Characterization of Aerodynamic Forces on Wings in Plunge Maneuvers

We present experiments and simulations of plunging maneuvers of large amplitude, for velocity ratios of G=1 and 2, defined as the ratio between the peak plunge velocity and the freestream velocity. We explore the effect of the airfoil shape by considering a NACA 0012 wing and a flat plate. The experiments are performed with wings with aspect ratios of 4 and 4.86, whereas the simulations are performed using a model of an infinite-aspect-ratio wing. We report the time evolution of the force coefficients and flow visualizations. A good qualitative agreement is found between experiments and simulations, with small discrepancies in the maximum and minimum lift coefficients observed during the maneuvers and somewhat larger discrepancies during the postmaneuver phase. It is found that the airfoil shape has a small effect on the lift coefficient but a somewhat larger effect on the drag coefficient. We also perform a force decomposition analysis to relate vortical structures to the force on the wings, providing a quantitative measurement of the effect of the leading-edge vortex and trailing-edge vortex on the peak aerodynamic forces.This work was partially supported by the State Research Agency of Spain (AEI) under grant DPI2016-76151-C2-2-R, including funding from the European Regional Development Fund and the U.S. Air Force Office of Scientific Research under grant FA9550-16-1-0508. The computations were partially performed at the supercomputer Picasso from the Red Española de Supercomputación in activity FI-2019-1-0030.Publicad

Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary condition

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.O.F. and M.G.-V. were partially supported by Grant TRA2013-41103-P of the Spanish Ministry of Economy and Competitiveness. This grant includes FEDER funding

Numerical simulation of flow over flapping wings in tandem: Wingspan effects

We report direct numerical simulations of a pair of wings in horizontal tandem configuration to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free stream at the Reynolds number Re=1000, and they undergo heaving and pitching oscillation with the Strouhal number St=0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading-edge vortex formed on the hindwing. The aerodynamic performance of the forewing is similar to that of an isolated wing irrespective of the aspect ratio of the hindwing, with a small modulating effect produced by the forewing-hindwing interactions. On the other hand, the aerodynamic performance of the hindwing is clearly affected by the interaction with the forewing's TEV. Tandem configurations with a larger aspect ratio on the forewing than on the hindwing result in a quasi-two-dimensional flow structure on the latter. This yields an 8% increase in the time-averaged thrust coefficient of the hindwing, with no change in its propulsive efficiency.This work was partially supported by the State Research Agency of Spain (AEI) under grant DPI2016-76151-C2-2-R including funding from the European Regional Development Fund (ERDF).The computations were performed at the supercomputer Tirant from the Red Espa˜nola de Supercomputaci´on in activity IM-2019-3-0011

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species’ transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, , and provide the governing PDEs for . This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.MGH, MGV and OF have been partially supported by the Spanish Research Agency and the European Regional Development Fund, under grant number PID2019-107279RB-I00. MGH, MGV, PML, JB and OF have been partially supported by the Comunidad de Madrid and the European Regional Development Fund, under grant number Y2018/BIO-4858 PREFI-CM, and by the Instituto de Salud Carlos III and the European Regional Development Fund, under grant numbers PI15/02211-ISBITAMI and DTS/1900063-ISBIFLOW. AG, EMcV, AK and JCdA have been partially supported by the US National Institutes of Health, under grant 1R01HL160024. JCdA has been partially supported by the US National Insitutes of Health, under grant number 1R01HL158667

Pulmonary vein flow split effects in patient-specific simulations of left atrial flow

Disruptions to left atrial (LA) blood flow, such as those caused by atrial fibrillation (AF), can lead to thrombosis in the left atrial appendage (LAA) and an increased risk of systemic embolism. LA hemodynamics are influenced by various factors, including LA anatomy and function, and pulmonary vein (PV) inflow conditions. In particular, the PV flow split can vary significantly among and within patients depending on multiple factors. In this study, we investigated how changes in PV flow split affect LA flow transport, focusing for the first time on blood stasis in the LAA, using a high-fidelity patient-specific computational fluid dynamics (CFD) model. We use an Immersed Boundary Method, simulating the flow in a fixed, uniform Cartesian mesh and imposing the movement of the LA walls with a moving Lagrangian mesh generated from 4D Computerized Tomography images. We analyzed LA anatomies from eight patients with varying atrial function, including three with AF and either a LAA thrombus or a history of Transient Ischemic Attacks (TIAs). Using four different flow splits (60/40% and 55/45% through right and left PVs, even flow rate, and same velocity through each PV), we found that flow patterns are sensitive to PV flow split variations, particularly in planes parallel to the mitral valve. Changes in PV flow split also had a significant impact on blood stasis and could contribute to increased risk for thrombosis inside the LAA, particularly in patients with AF and previous LAA thrombus or a history of TIAs. Our study highlights the importance of considering patient-specific PV flow split variations when assessing LA hemodynamics and identifying patients at increased risk for thrombosis and stroke. This knowledge is relevant to planning clinical procedures such as AF ablation or the implementation of LAA occluders.This work was partially supported by Comunidad de Madrid (Synergy Grant Y2018/BIO-4858 PREFI-CM), Spanish Research Agency (AEI, grant number PID2019-107279RB-I00), Instituto de Salud Carlos III (grant numbers PI15/02211-ISBITAMI and DTS/1900063-ISBIFLOW), and by the EU-European Regional Development Fund . Funding for open access charge: Universidad de Málaga / CBUA