Simulations of incompressible convection-dominated flows, such as vortical flows or wake flows, require accurate and efficient numerical methods. Among the various approaches, the vortex particle-mesh (VPM) method stands out for its ability to combine the strengths of mesh-based methods, such as efficient elliptic solvers and finite difference stencils, with the advantages of particle methods, which minimize numerical dispersion and dissipation errors. However, most VPM implementations consider a uniform grid. This can lead to a prohibitive computational cost, especially in three dimensions. This challenge can be addressed effectively through adaptive mesh refinement (AMR), which significantly reduces simulation costs by dynamically adjusting the local grid resolution to meet the requirements of the underlying physics. In this work, we present a novel VPM method that leverages the benefits of AMR. Building upon murphy, a wavelet-based block-structured AMR framework, we propose a new approach to represent the particles that allows for their refinement or coarsening. We show that our method achieves high-order accuracy, grid adaptation, and CFL relaxation at the same time. We then demonstrate the scalability of our method from 128 to 16,384 cores, and compare its performance with a uniform resolution framework for the simulation of aircraft wake vortices. We show that despite the increased complexity due to the overhead of the AMR operations, the resulting gains in computational efficiency and reductions in memory footprint are substantial.

The development of safe and efficient air traffic separation policies relies on the accurate quantification of the wake turbulence generated by aircraft and rotorcraft, and on the accurate understanding of the upset experienced by a follower aircraft or rotorcraft if encountering such wakes. To date, most research on wake turbulence has focused exclusively on fixed-wing aircraft. To address the existing gap in rotorcraft-specific studies, this paper first presents Large Eddy Simulations of the wake produced by a helicopter rotor in forward flight, performed using the Vortex Particle-Mesh method coupled with a multi-body solver. The effect of the airspeed is investigated, from a high value of 100 kt to a low value of 12.5 kt. For each case, the wake is characterized at equivalent dimensionless ages, and the wake-induced hazard produced on a follower fixed-wing reference aircraft is quantified using the rolling moment coefficient (RMC) metric. At low airspeeds, the wake departs from the rolled-up wake configuration typical of fixed-wing aircraft and rotorcraft flying at high airspeed, exhibiting increased vortex spacing and higher turbulence levels. The inverse proportionality between flight speed and vortex circulation is also shown to break down; the RMC value saturates, and it also rapidly decreases downstream. In a second scenario, the rotorcraft is considered as a follower flying through a wake. For three airspeeds of the follower rotorcraft (100 kt, 50 kt, and 25 kt), simulations of the rotor flying quasi-steadily through rolled-up wake vortices are performed, and the resulting aerodynamic loads are quantified. The wake-induced pitching moment, which is the dominant perturbation, is found to scale with the airspeed of the follower rotorcraft. A pitching moment severity metric is evaluated against the numerical simulation: while it provides a useful first-order estimate, it fails to capture the observed speed dependence.

Multigrid solvers are among the most efficient methods for solving the Poisson equation, which is ubiquitous in computational physics. For example, in the context of incompressible flows, it is typically the costliest operation. The present document expounds upon the implementation of a flexible multigrid solver that is capable of handling any type of boundary conditions within murphy, a multiresolution framework for solving partial differential equations (PDEs) on collocated adaptive grids. The utilization of a Fourier-based direct solver facilitates the attainment of flexibility and enhanced performance by accommodating any combination of unbounded and semi-unbounded boundary conditions. The employment of high-order compact stencils contributes to the reduction of communication demands while concurrently enhancing the accuracy of the system. The resulting solver is validated against analytical solutions for periodic and unbounded domains. In conclusion, the solver has been demonstrated to demonstrate scalability to 16,384 cores within the context of leading European high-performance computing infrastructures.

Wind farm flow control (WFFC) is the discipline of manipulating the flow between wind turbines to achieve a farm-wide goal, like power maximization, power tracking or load mitigation. Specifically, steady-state control approaches have shown promising results in both theory and practice for power maximization. But how are they expected to perform in a dynamically changing environment? This paper presents an open-source wake modeling framework called OFF (abbreviated from the models OnWARDS, FLORIDyn and FLORIS). It allows the approximation of the performance of WFFC strategies in response to environmental changes at a low computational cost. It is rooted in previously published dynamic parametric engineering models and offers a flexible and adaptable platform to explore these models further. The presented study tests the modeling framework by investigating the performance of different wake steering controllers in a 10-turbine wind farm case study based on a subset of the Dutch wind farm Hollandse Kust Noord (HKN). The case study uses a 24 h wind direction time series based on field data and verifies subsets of the time series in a large-eddy simulation (LES). The results highlight how dependent yaw travel is on the controller settings and suggest where users can strike a balance between power gains and actuator usage. They also show the structural differences and similarities between steady-state and dynamic engineering models. The comparison to LES shows what timescales the surrogate models cover and how accurately. While steady-state models capture turbine power signal dynamics up to ≈1/570 Hz, the dynamic wake description can predict dynamics up to ≈1/360 Hz with a better correlation and normalized root-mean-square error. Further results show that the dynamic wake description is mainly advantageous over steady-state wake models for shorter periods (< 20 min). The paper also opens up discussion about the effectiveness of wind farm flow control in a time-marching manner as opposed to a steady-state viewpoint.

This paper investigates the impact of rotor size on the structural displacements and loads of large wind turbines during power production. The actuator line method is used in Large Eddy Simulations and is coupled to a structural solver for the blades. The latter consists either of a linear solver based on the Euler-Bernoulli beam theory, or uses BeamDyn to account for the non-linearities. The effects of upscaling are investigated for three reference wind turbines of various sizes: the NREL-5 MW, the DTU-10 MW and the IEA-15 MW. The study reveals that the larger turbines exhibit higher bending relative to the radius and a significant torsion angle. The torsion angle is primarily linked to the structural non-linearities and substantially affects the mean blade loads of the largest turbines. Consequently, the power and thrust coefficients predicted using the linear structural model differ from those obtained using BeamDyn. However, the variations of the root bending moments are predicted similarly using both structural solvers; also suggesting that a linear structural solver is still sufficient for the fatigue analysis. Finally, the fatigue analysis is extended to the shaft loads due to the entire rotor, and empirical scaling trends are derived.

This paper presents the design and the experimental characterization of a Cyber-Physical System tailored for research in fundamental and applied fluid mechanics (fluid-structure interaction problems), biomechanics (biolocomotion), and civil engineering (wind- or flow-structure interactions). The design is aimed at ideally controlling the six degrees of freedom of the manipulated object, being versatile to different experimental scenarios, and usable in real-time and closed-loop if manipulating an active object. Mechanical design robustness is examined through an experiment emphasizing the crucial constraint of robot rigidity. Subsequently, the robotic Cyber-Physical System kinematic and dynamic capabilities are validated, demonstrating compliance to specifications, along with considerations regarding acceleration saturation. A third experiment analyzes the robot end-effector natural frequencies, yielding frequency ranges that should not be excited in future experiments. Findings contribute to providing directions for refining the mechanical design, synthesizing control strategies, and enhancing the device robustness and performance in various flow-device interaction scenarios.

This work aims at verifying the predictions of OnWaRDS, an open-source wake modelling framework that captures the main features of the wake dynamics, including its meandering, in ancillary services scenarios. OnWaRDS brings together Lagrangian flow modeling and flow sensing and runs in parallel with a wind farm environment (here Large-Eddy simulations coupled to an Actuator Disk model (LES-AD)) in order to use the available rotor states to predict the flow field. The performances of OnWaRDS are first assessed when it runs synchronously with the LES-AD of a down-regulated wind farm and tends to mimic the LES-AD behavior. This synchronous mode implies a continuous feeding of the wake model with LES-AD rotor data. Then, OnWaRDS is used in a predictive mode, in order to predict an alternate reality for the wind farm. In this study, OnWaRDS aims at evaluating, in real-time, what the potential power production would be when the LES-AD is down-regulated to provide operating reserve capacity to the electricity network. Switching to a predictive mode implies that certain measurements at the wind turbine level can no longer be used, because the flow and the rotor behavior change between LES-AD and OnWaRDS. The second part of this study thus aims at verifying the predictions of OnWaRDS, and highlighting the impact of switching from a synchronous to a predictive mode in OnWaRDS.

The Method of Manufactured Solution (MMS) is a powerful technique for code verification. It provides a systematic procedure for generating analytical solutions to be discretized by a numerical solver. Usually, an arbitrary continuous solution is selected before being inserted into the governing equations. Although sufficient in many situations, this procedure may be inappropriate if the problem at hand imposes some constraints on the shape of the manufactured solutions. In such cases, some unknown parameters should be included in the continuous solution and computed to satisfy the imposed constraints. This limitation of the standard MMS has already been recognized in previous work. However, the way to handle it is most of the time case-dependent and based on ad-hoc strategies. In this work, we develop a generic framework based on the Sympy library to produce manufactured solutions complying with arbitrary complex Dirichlet and Neumann-type conditions. It is made available through an open-source Python software. As a challenging illustrative application, analytical solutions obeying the interface jumps conditions of a two-phase compressible Navier–Stokes system are built.

We leverage Large Eddy Simulation (LES) of wind farms to study the performances of an open-loop wake steering controller. This global controller is elaborated based on Lookup Table (LUT) generated using FLORIS. Our objectives are to highlight the potential problems that can arise from model errors due to its steady-state formulation and from difficulties to properly define the ambient flow state. We consider two wind farm configurations: a first theoretical layout of six machines, and a second layout representing a commercial wind farm that is currently studied for wake steering strategy, the King Plains wind farm. We represent our wind farm environment using LES within which the turbines are modeled as actuator disks. In addition to the standard local controller, the wind farm utilizes a LUT to compute the optimal yaw offset angles. Before its integration into the controller, this LUT is first populated using the yaw optimizer integrated into FLORIS. The primary input parameters for the LUT are derived from the freestream atmospheric conditions, which are parametrized in terms of TI, hub height wind speed, and wind direction. In this work, we investigate different strategies for estimating the ambient wind direction fed as input to the LUT during the control and their impact on the dynamics of the yaw actuation. While results confirm the potential of this type of controller, they also highlight the importance of a proper sensing to determine the freestream state.

Wind farm flow control aims at mitigating wake effects in order to maximize power production in wind farms. This work mostly focuses on the Helix strategy, which relies on individual pitch control to radially offset the application point of the thrust force from the rotor center and to dynamically change its azimuthal position. Previous studies have shown that power gains for a downstream turbine are higher for a counter-clockwise (CCW) rotation of the application point than for a clockwise (CW) one. In the CCW case, the wake develops as a right-handed helix, while in the CW case, a left-handed helix is observed. Using Large Eddy Simulations, this paper shows that the helix handedness in the wake matters due to its interaction with the wake swirl. Results of the CCW and CW helix first highlight the formation of streamwise vorticity in the near wake, which is transformed into strong coherent vortices in the far wake. Those vortex structures, to some extent similar to the counter-rotating vortex pair in the wake of yawed wind turbines, are responsible for (i) displacing the wake thanks to their induced velocities and (ii) deforming the shape of the wake.

In the context of wind turbine pitch control for load alleviation or active wake mixing, it is relevant to provide the time- and space-varying wind conditions as an input to the controller. Apart from classical wind measurement techniques, blade-load-based estimators can also be used to sense the incoming wind. These consider blades to be sensors of the flow and rely on having access to the operating parameters and measuring the blade loads. In this paper, we wish to verify how robust such estimators are to the control strategy active on the turbine, as it impacts both operating parameters and loads. We use an extended Kalman filter (EKF) to estimate the incoming wind conditions based on the blade bending moments. The internal model in the EKF relies on the blade element momentum (BEM) theory in which we propose accounting for delays between pitch action and blade loads by including dynamic effects. Using large-eddy simulations (LESs) to test the estimator, we show that accounting for the dynamic effects in the BEM formulation is needed to maintain the estimator accuracy when dynamic wake mixing control is active.

This paper investigates the impact of blade flexibility on the aerodynamics and wake of large offshore turbines using a flexible actuator line method (ALM) coupled to the structural solver BeamDyn in large-eddy simulations. The study considers the IEA 15 MW reference wind turbine in close-to-rated operating conditions. The flexible ALM is first compared to OpenFAST simulations and is shown to consistently predict the rotor aerodynamics and the blade structural dynamics. However, the effect of blade flexibility on the loads is more pronounced when predicted using the ALM compared with using the blade element momentum theory. The wind turbine is then simulated in a neutral turbulent atmospheric boundary layer with flexible and rigid blades. The significant flapwise and torsional mean displacements lead to an overall decrease of 14 % in thrust and 10 % in power compared to a rotor with no deformation. These changes influence the wake through a reduced time-averaged velocity deficit and turbulent kinetic energy. The unsteady loads induced by the rotation in the sheared wind and the turbulent velocity fluctuations are also substantially affected by the flexibility and exhibit a noticeably different spectrum. However, the influence of these load variations on the wake is limited, and the assumption of rigid blades in their deformed geometry is shown to be sufficient to capture the wake dynamics. The influence of the resolution of the flow solver is also evaluated, and the results are shown to remain consistent between different spatial resolutions. Overall, the structural deformations have a substantial impact on the turbine performance, loads, and wake, which emphasizes the importance of considering the flexibility of the blades in simulations of large offshore wind turbines.

Line formation of migrating birds is well-accepted to be caused by birds exploiting wake benefits to save energy expenditure. A flying bird generates wingtip trailing vortices that stir the surrounding air upward and downward, and the following bird can get a free supportive lift when positioned at the upward airflow region. However, little to no attention has been paid to clarifying birds’ interests in energy saving, namely, do birds intend to reduce their individual energy consumption or the total energy of the flock? Here, by explicitly considering birds’ interests, we employ a modified fixed-wing wake model that includes the wake dissipation to numerically reexamine the energy saving mechanism in line formation. Surprisingly, our computations show that line formation cannot be explained simply by energy optimization. This remains true whether birds are selfish or cooperative. However, line formations may be explained by strategies optimizing energy cost and either avoiding collision or maintaining vision comfort. We also find that the total wake benefit of the formation attained by selfish birds does not differ much from that got by cooperative birds, the maximum that birds can attain. This implies that selfish birds are still able to fly in formation with very high efficiency of energy saving. In addition, we explore the hypothesis that birds are empathetic and would like to optimize their own energy cost and the neighbors’. Our analysis shows that if birds are more empathetic, the resulting line formation shape deviates more from a straight line, and the flock enjoys higher total wake benefit. Author summary Migratory birds can achieve remarkable performance and efficiency in energy exploitation during annual round-trip migration flight. Theoretical and experimental results have shown that this might be achieved because birds fly together in formation with specific shapes, e.g. the noticeable V formation, to utilize the aerodynamic benefits generated by their flock mates. However, it is still unclear whether energy-guided behavior indeed can lead to these formations. We show that the special formation adopted by migratory birds cannot be explained purely by the energy exploitation mechanism, and that birds’ vision performance and collision avoidance very likely also play important roles in the formation emergence. Our results imply that birds fly together in formation because of energy saving, but the specific shape of the formation depends on non-aerodynamic reasons. The research provides further understandings of the emergence of migratory formation and the energy saving mechanism of animal groups. It may also indicate that wing flapping, currently not considered, has an important effect on the way birds exploit aerodynamic benefits from others during the formation flight.

Abstract We propose a reduced-order model for the inviscid flow past self-propelled flexi- ble bodies whose geometry features a wedged trailing-edge. The model leverages an unsteady panel method and its compact representation of vorticity in the free flow allows for computationally tractable simulations. It is strongly coupled to a multi-body system solver which computes the internal bending moments in a swimming system of deforming bodies. The model is assessed against commer- cial computational fluid dynamics and vortex-method predictions on the specific case of anguilliform locomotion. The verified tool is subsequently leveraged in a campaign of numerical experiments to shed light on the collective benefits drawn from swimming in formation. We find that fish initially at rest and engaged in collective swimming demonstrate superior cost efficiency during the initial phases of their motion. However, beyond a certain temporal threshold, these piscine cohorts begin to expend more energy per unit of distance traversed in comparison to their solitary counterparts.

We introduce and validate a weak coupling approach between a body-fitted velocity-pressure solver and a Vortex Particle-Mesh (VPM) method in 2D for the simulation of incompressible external aerodynamics. The approach does not involve inner iterations, conserves circulation up to interpolation accuracy without resorting to a panel method, and accommodates different time steps across the solvers. It also utilizes a mixed boundary condition for the body-fitted solver that ensures the continuity of the vorticity field across the solvers. The second order convergence of the methodology is first demonstrated. We then assess it on the flow past a cylinder at various Reynolds numbers (from Re=550 to 9500), and we finally apply it to the flow past an airfoil at Re=5000.

In this paper, we develop a high-order method for the steady two-phase compressible Navier–Stokes equations closed by generic equations of state, adapted to gas–liquid flows. Our framework relies on the extended discontinuous Galerkin method that is tailored here to a general viscous compressible two-phase configuration. While the imposition of interface jumps conditions is commonly recognized as one of the main difficulties to overcome in the context of geometrically unfitted methods, the setting considered in this work makes this aspect even more challenging. To enforce the non-linear coupling conditions at the interface in a sharp manner, we devise a novel strategy combining multiphase Riemann solvers to handle the convective fluxes across the interface and a weighted stabilized Nitsche’s method for the viscous jumps. The weak enforcement of the jumps conditions along with implicit steady-state iterations and cell-agglomeration procedure make the approach robust to treat arbitrary large contrast phase interface problems governed by stiff models, irrespective of the interface location on the mesh. The study is here restricted to static interfaces. Based on the method of manufactured solution, reference solutions are designed. This allows to conduct a detailed numerical study investigating the influence of several numerical parameters. It is shown that to reach optimal error convergence, the use of pressure-velocity-temperature variables set, appropriate all-speed bulk Riemann solver and Symmetric Interior Penalty method combined with tensorial penalty is necessary.

For space missions involving atmospheric entry, a thermal protection system is essential to shield the spacecraft and its payload from the severe aerothermal loads. Carbon/phenolic composite materials have gained renewed interest to serve as ablative thermal protection materials (TPMs). New experimental data relevant to the pyrolytic decomposition of the phenolic resin used in such carbon/phenolic composite TPMs have recently been published in the literature. In this paper, we infer from these new experimental data an uncertainty-quantified pyrolysis model. We adopt a Bayesian probabilistic approach to account for uncertainties in the model identification. We use an approximate likelihood function involving a weighted distance between the model predictions and the time-dependent experimental data. To sample from the posterior, we use a gradient-informed Markov chain Monte Carlo method, namely, a method based on an Ito stochastic differential equation, with an adaptive selection of the numerical parameters. To select the decomposition mechanisms to be represented in the pyrolysis model, we proceed by progressively increasing the complexity of the pyrolysis model until a satisfactory fit to the data is ultimately obtained. The pyrolysis model thus obtained involves six reactions and has 48 parameters. We demonstrate the use of the identified pyrolysis model in a numerical simulation of heat-shield surface recession in a Martian entry.

Abstract We propose a reduced-order model for the inviscid flow past self-propelled flexi- ble bodies whose geometry features a wedged trailing-edge. The model leverages an unsteady panel method and its compact representation of vorticity in the free flow allows for computationally tractable simulations. It is strongly coupled to a multi-body system solver which computes the internal bending moments in a swimming system of deforming bodies. The model is assessed against commer- cial computational fluid dynamics and vortex-method predictions on the specific case of anguilliform locomotion. The verified tool is subsequently leveraged in a campaign of numerical experiments to shed light on the collective benefits drawn from swimming in formation. We find that fish initially at rest and engaged in collective swimming demonstrate superior cost efficiency during the initial phases of their motion. However, beyond a certain temporal threshold, these piscine cohorts begin to expend more energy per unit of distance traversed in comparison to their solitary counterparts.

This work presents an investigation of the aeroelastic effects occurring on the IEA 15-MW reference wind turbine in a turbulent atmospheric boundary layer. Large Eddy simulation is carried out using an actuator line method coupled to the finite element beam solver BeamDyn. The results show that the blades experience significant displacements, leading to an important variation of the loads along the blade span. The turbulence also interacts with the blades natural frequencies, resulting in a variation of the spectra of the various loads. The impact of the flexibility is also evaluated on the wake by comparing the undeformed configuration with a statically and dynamically deformed rotor. It appears that the mean deformation plays an important role in the wake development due to changes in the load distribution, but that the dynamic effects have minimal impact on the wake behavior.

Massively parallel Fourier transforms are widely used in computational sciences, and specifically in computational fluid dynamics which involves unbounded Poisson problems. In practice the latter is usually the most time-consuming operation due to its inescapable all-to-all communication pattern. The original flups library tackles that issue with an implementation of the distributed Fourier transform tailor-made for successive resolutions of unbounded Poisson problems. However the proposed implementation lacks of flexibility as it only supports cell-centered data layout and features a plain communication strategy. This work extends the library along two directions. First, flups’ implementation is generalized to support a node-centered data layout. Second, three distinct approaches are provided to handle the communications: one all-to-all, and two non-blocking implementations relying on manual packing and MPI_Datatype to communicate over the network. The proposed software is validated against analytical solutions for unbounded, semi-unbounded, and periodic domains. The performance of the approaches is then compared against accFFT, another distributed FFT implementation, using a periodic case. Finally the performance metrics of each implementation are analyzed and detailed on various top-tier European facilities up to 49,152 cores. This work brings flups up to a fully production-ready and performant distributed FFT library, featuring all the possible types of FFTs and with flexibility in the data-layout.