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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 summaryMigratory 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.

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.

In a fuel-efficient extended formation flight of commercial airplanes, the aerodynamic benefits depend on one’s ability to surf wake vortices. This paper presents a wake vortex detection scheme bas...

This paper provides the analytical solution to a one-parameter Šesták–Berggren kinetic model for the thermoanalytical study of pyrolysis reactions involving multiple independent parallel reactions. Such multiple independent parallel reactions are widely used, for instance, in the modeling of the pyrolysis of thermal protection materials used in heatshields for spacecraft during the atmospheric entry phase. Solving inverse problems to infer parameters of the kinetic model through optimization techniques or Bayesian inference methods for uncertainty quantification may require a large number of evaluations of the response and its sensitivities (derivatives with respect to parameters). Moreover, in the case of kinetic equations, the Arrhenius parameters can exhibit strong dependence that can require further model evaluations for an accurate parameter calibration. The interest of this analytical solution is to reduce computation cost while having high accuracy to perform parameter calibration from experiments and sensitivity analysis. We propose to use exponential–integral functions to express the solution of the temperature integral, and we derive the analytical solution and its sensitivities for the parallel reaction model both for constant temperature (isothermal) and for constant heating rate conditions. The solution is validated on a six-equation model using parameters inferred in a previous work from the experimental data of the pyrolysis of a phenolic-impregnated carbon ablator material, and we compare the computational cost and accuracy of the implemented analytical solution with a numerical solution. Our results show that the use of such analytical solution with an accurate computation of the exponential–integral function significantly reduces the computational cost compared to the numerical solution.

A Fourier-based Library of Unbounded Poisson Solvers (FLUPS) for 2D and 3D homogeneous distributed grids is presented. It is designed to handle every possible combination of periodic, symmetric, semi-unbounded and fully unbounded boundary conditions for the Poisson equation on rectangular domains with uniform resolution. FLUPS leverages a dedicated implementation of 3D Fourier transforms to solve the Poisson equation using Green's functions, in a fast and memory-efficient way. Several Green's functions are available, optionally with explicit regularization, spectral truncation, or using lattice Green's functions, and provide verified convergence orders from 2 to spectral-like. The algorithm depends on the FFTW library to perform 1D transforms, while Message Passing Interface (MPI) communications enable the required remapping of data in memory. For the latter operation, a first available implementation resorts to the standard all-to-all routines. A second implementation, featuring non-blocking and persistent point-to-point communications, is however shown to be more efficient in a majority of cases and especially while taking advantage of the shared memory parallelism with OpenMP. The scalability of the algorithm, aimed at massively parallel architectures, is demonstrated up to 73 720 cores. The results obtained with three different supercomputers show that the weak efficiency remains above 40\% and the strong efficiency above 30% when the number of cores is multiplied by 16, for typical problems. These figures are slightly better than those expected from a third party 3D Fast Fourier Transform (FFT) tool, with which a 20% longer execution time was also measured on average., Comment: SIAM Journal on Scientific Computing (SISC): submitted on December 5th 2019, accepted on November 17th 2020

The current trend of wind turbine upscaling has led to the use of long and slender blades prone to large structural deformations. In the present study, the impact of the aeroelastic effects is assessed for the NREL-5MW wind turbine in a turbulent wind. To this end, an actuator curve method coupled to a one-dimensional finite-element structural solver is implemented in a fourth-order finite difference code that can perform large eddy simulation (LES) of realistic winds. The approach is computationally affordable compared to blade-resolved simulations and hence long time series can be computed. This, combined to the ability of the LES to capture the relevant scales of the unsteadiness wind, leads to a better estimation of the fluctuating loads and power of the turbine. The results are here shown for one and two wind turbines operating in a neutrally stable atmospheric boundary layer. It appears that the blade mostly deforms according to its first bending mode. The rotation of the blade in the sheared atmospheric flow is responsible for large amplitude deformations, but the turbulence also plays a role in causing deformations at higher frequencies with a smaller amplitude. The azimuthal distributions of loads and of power are significantly affected when the aeroelasticity is considered.

From small drones to large Urban Air Mobility vehicles, the market of vertical take-off and landing (VTOL) aircraft is currently booming. Modern VTOL designs feature a variety of configurations involving rotors, lifting surfaces and bluff bodies. The resulting aerodynamics are highly impacted by the interactions between those components and their wakes. This has consequences on the aircraft performance and on the downstream wake. Studying the effects of those interactions through CFD can inform the development of cheaper numerical models. In this work, we focus on the interaction between rotors and bluff bodies based on the example of a generic quadcopter in forward flight. Using the Vortex Particle–Mesh method, a CFD method well-suited for wake studies, we analyze the influence of the rotor-airframe interaction on the loads and on the development of the aircraft near wake. Our results show that the presence of the airframe induces a change in average thrust of maximum 2.4% on the rear rotors. Correspondingly, the contribution of the rotors to the overall aircraft lift and drag changes by less than 2%, suggesting that the airframe can be ignored if one seeks a simple model of the rotor forces. On the other hand, the airframe experiences peak loads due to its proximity with the blades. Thus, the rotor-airframe interaction must be accounted for in the prediction of airframe loads. Finally, comparing simulations with and without the airframe, we find that the trailing wake vortices converge to circulations less than 0.2% different. However, the vortex spacing decreases when the airframe is accounted for.

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the obstacle, reducing its computational and implementation complexity. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, which provides the key to simulations with multiply connected domains and outflow boundaries. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

Building on the well-known Prandtl lifting line, this work proposes an extended framework for mollified lifting lines, which is valid for multidimensional Gaussian smoothings. The smoothing length scale σ can be taken as constant or variable across the span. In this framework, slender lifting device and its wake are represented by a mollified vortex tube and a mollified vortex sheet. Although the resulting formulation is similar to the original one, it is shown that a sectional mean downwash must be used in the integrodifferential equation from which the circulation distribution is obtained. Interestingly, it is also shown that this equation is unaffected by the presence of mollification in the streamwise direction. As an application, the case of the elliptical wing is revisited with several smoothing configurations. The results are consistent with the original singular lifting line, and the peculiarities of the circulation and downwash distributions are investigated. A uniform downwash is also recovered for a specific configuration. Finally, the constant and the variable σ regularizations are found to yield similar results. Overall, the proposed method provides accurate results that can be compared with those from numerical methods, such as the actuator line model, immersed lifting lines, or other similar methods.

Ablative materials are extensively used in aerospace applications to protect the integrity of the spacecraft during atmospheric entry. Both thermal and mechanical stresses have to be withstood in the severe operating conditions typical of space missions. An accurate modeling of the phenomena taking place when these materials are exposed to such a harsh environment is crucial to ensure the success of future, more demanding, missions. This study aims to couple two tools able to handle two different aspects of the ablative material modeling: a stagnation-line flow solver featuring an integrated ablative boundary condition, and a material response code. The coupling algorithm allows for time accurate solutions of the ablative material thermal response accounting for detailed surface chemistry, in-depth material behavior, and surface recession. Two different coupling strategies have been implemented, based either on a direct or an iterative procedure. The developed tool is used to rebuild plasma wind tunnel experiments performed in the von Karman Institute Plasmatron facility. The outcomes of the two strategies are compared, showing a satisfactory agreement with the experimental data. Among the two analyzed coupling procedures, the direct coupling proved to be computationally less expensive, while conserving the same accuracy of the more complex iterative procedure for the analyzed cases. A sensitivity analysis is also conducted to understand the discrepancy with experimental data and show the effects of four uncertain material parameters: thermal conductivity, density, emissivity, and catalytic efficiency.

Midway between a vortex method and a grid-based CFD, the Vortex Particle-Mesh method with Immersed Lifting Lines is intended to provide medium-fidelity results on rotor loadings, together with a realistic representation of the 3-D vortical wakes and their dynamics over long distances. We assess the potential of this hybrid approach for the Large-Eddy Simulation of helicopter rotors in hover. A novel Poisson solver with mixed unbounded-outflow boundary conditions here further enables the computation of turbulent hovering scenarios in tight domains. Considering the Knight and Hefner experiment and the S-76 test case as references, we present and compare blade integrated and distributed loads, induction velocities, and wake characteristics. While the quality of the performance predictions highly depends on external polar data, the obtained wakes exhibit similar characteristics to those recently identified in other CFD analyses, here at a moderate computational cost. Based on these results, we further investigate the secondary vortex structures forming between the main tip vortices, and we bring additional clues on their relation to the phenomenon of wake breakdown. We finally discuss the strengths and difficulties of hybrid vortex methods for the challenging analysis of hovering rotors.

Groups of aircraft have the potential to save significant amounts of energy by flying in formations; all but the leading aircraft can benefit from the upwash of the wakes of preceding aircraft. A potential obstacle as the number of aircraft in such a formation increases is that disturbances at one aircraft, for example caused by turbulence or wake meandering, can propagate and grow as each following aircraft tries to track the optimal energy-saving position relative to the one in front. This phenomenon, known as string instability, has not yet been adequately examined in the context of aircraft formations. We discuss some trade-offs involved in designing string stable controllers whose objective is to minimize energy, and present a control design method to achieve both string stability and energy efficiency of an aircraft formation. In simulations of a 10-aircraft linear formation in the presence of 2% turbulence intensity, our controller achieves string stability while reduced energy consumption by an average of 13% with respect to solo flight., Comment: 27 pages, 14 figures, 17 figure files

This paper investigates stability analysis of flapping flight. Due to time-varying aerodynamic forces, such systems do not display fixed points of equilibrium. The problem is therefore approached via a limit cycle analysis based on Floquet theory. Stability is assessed from the eigenvalues of the Jacobian matrix associated with the limit cycle, also known as the Floquet multipliers. We developed this framework to analyze the flapping flight equations of motion of a bird in the longitudinal plane. Such a system is known to be not only nonlinear and time dependent, but also driven by state-dependent forcing aerodynamic forces. A model accounting for wing morphing under prescribed kinematics is developed for generating realistic state-dependent aerodynamic forces. The morphing wing geometry results from the envelope of continuously articulated rigid bodies, modeling bones and feather rachises, and capturing biologically relevant degrees of freedom. A sensitivity analysis is carried out which allows studying several flight configurations in trimmed state. Our numerical results show that in such a system one instability mode is ubiquitous, thus suggesting the importance of sensory feedback to achieve steady-state flapping flight in birds. The effect of wingbeat amplitude, governed by the shoulder joint, is found to be crucial in tuning the gait toward level flight, but marginally affects stability. In contrast, the relative position between the wing and the center of mass is found to significantly affect the values of Floquet multipliers, suggesting that the distribution of pitching moment plays a very important role in flapping flight stability.

In this paper, we formulate a physics-based surrogate wake model in the framework of online wind farm control. A flow sensing module is coupled with a wake model in order to predict the behavior of the wake downstream of a wind turbine based on its loads, wind probe data and operating settings. Information about the incoming flow is recovered using flow sensing techniques and then fed to the wake model, which reconstructs the wake based on this limited set of information. Special focus is laid on limiting the number of input parameters while keeping the computational cost low in order to facilitate the tuning procedure. Once calibrated, comparison with high-fidelity numerical results retrieved from Large Eddy Simulation (LES) of a wind farm confirms the good potential of the approach for online wake prediction within farms. The two approaches are further compared in terms of their wake center and time-averaged speed deficit predictions demonstrating good agreement in the process.