Dmitry Kolomenskiy, Yossef Elimelech, Kai Schneider
The paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number $Re=250$. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method with volume penalization. The transition from stable attachment of the leading-edge vortex to periodic vortex shedding is explored, as a function of the wing aspect ratio and the angle of attack. It is found that, in a stable configuration, the spanwise flow in the recirculation bubble past the wing is due to the centrifugal force, incompressibility and viscous stresses. For the flow outside of the bubble, an inviscid model of spanwise flow is presented.
Di Chen, Dmitry Kolomenskiy, Hao Liu
Flapping and revolving wings can produce attached leading edge vortices (LEVs) when the angle of attack is large. In this work, a low order model is proposed for the edge vortices that develop on a revolving plate at 90 degrees angle of attack which is the simplest limiting case, yet showing remarkable similarity with the generally known LEVs. The problem is solved analytically, providing short closed-form expressions for the circulation and the position of the vortex. A good agreement with the numerical solution of the Navier-Stokes equations suggests that, for the conditions examined, the vorticity production at the sharp edge and its subsequent three-dimensional transport are the main effects that shape the edge vortex.
Dmitry Kolomenskiy, Ryo Onishi, Hitoshi Uehara
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data. The effectiveness of this method is demonstrated by applying it to example numerical tests, ranging from idealized configurations to realistic global-scale simulations.
Hung Truong, Thomas Engels, Dmitry Kolomenskiy, Kai Schneider
Wing flexibility plays an essential role in the aerodynamic performance of insects due to the considerable deformation of their wings during flight under the impact of inertial and aerodynamic forces. These forces come from the complex wing kinematics of insects. In this study, both wing structural dynamics and flapping wing motion are taken into account to investigate the effect of wing deformation on the aerodynamic efficiency of a bumblebee in tethered flight. A fluid-structure interaction solver, coupling a mass-spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier-Stokes equations, is implemented for this purpose. We first consider a tethered bumblebee flying in laminar flow with flexible wings. Compared to the rigid model, flexible wings generate smaller aerodynamic forces but require much less power. Finally, the bumblebee model is put into a turbulent flow to investigate its influence on the force production of flexible wings.
Peng Yu, Ramiro Godoy-Diana, Benjamin Thiria, Dmitry Kolomenskiy, Thomas Engels
Flapping wings are the primary means by which dragonflies generate forces, but they are susceptible to damage due to their inherent fragility. The damage results in a reduction in wing area and a distortion of the original wing, which in turn leads to a decline in flight ability. Furthermore, the flows of dragonfly fore- and hindwings exhibit an interaction, thus damage to the forewing can also impact the aerodynamic performance of the ipsilateral hindwing. In this study, we examine this problem through CFD (computational fluid dynamics) simulations on a series of damaged dragonfly fore-/hindwing models according to the probability of area loss from the literature. The flow fields and aerodynamic forces for the different damaged wing cases are compared with those for the intact wings. This comparative analysis reveals how the different patterns of wing damage modify the vortex structures around the flapping wings and lead to a drop in aerodynamic force production. The causes behind the diminishing aerodynamic performance are shown to be subtler than the pure area loss and are regulated by the changes in the flow field that result from wing damage. Wing-wing interaction becomes particularly important when forewing damage occurs.
Dmitry Kolomenskiy, Romain Nguyen van yen, Kai Schneider
We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretisation and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.
Dmitry Kolomenskiy, Sridhar Ravi, Taku Takabayashi, Teruaki Ikeda, Kohei Ueyama, Thomas Engels, Alex Fisher, Hiroto Tanaka, Kai Schneider, Jörn Sesterhenn, Hao Liu
The aerial environment in the operating domain of small-scale natural and artificial flapping wing fliers is highly complex, unsteady and generally turbulent. Considering flapping flight in an unsteady wind environment with a periodically varying lateral velocity component, we show that body rotations experienced by flapping wing fliers result in the reorientation of the aerodynamic force vector that can render a substantial cumulative deficit in the vertical force. We derive quantitative estimates of the body roll amplitude and the related energetic requirements to maintain the weight support in free flight under such conditions. We conduct force measurements of a miniature hummingbird-inspired robotic flapper and numerical simulations of a bumblebee. In both cases, we demonstrate the loss of weight support due to body roll rotations. Using semi-restrained flight measurements, we demonstrate the increased power requirements to maintain altitude in unsteady winds, achieved by increasing the flapping frequency. Flapping fliers may increase their flapping frequency as well as the stroke amplitude to produce the required increase in aerodynamic force, both of these two types of compensatory control requiring additional energetic cost. We analyze the existing data from experiments on animals flying in von Kármán streets and find reasonable agreement with the proposed theoretical model.
Katherine Vilinski-Mazur, Bogdan Kirillov, Oleg Rogozin, Dmitry Kolomenskiy
A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing. Lack of oxygen within tissue spheroids hinders metabolism of cells and eventually leads to cell death. Prevention of necrosis is crucial to success of tissue engineering methods and such prevention requires estimation of cell viability in the spheroid. We propose a novel approach for numerical modeling of diffusion in tissue spheroids during their fusion. The approach is based on numerical solutions of partial differential equations and the application of Functional Representations (FRep) framework for geometric modeling. We present modeling of oxygen diffusion based on meshes derived from the geometry of fusing spheroids, a method for selecting optimal spheroid size, and several statistics for estimating cellular viability. Our findings provide insights into oxygen diffusion in three-dimensional cell cultures thus improving the robustness of biotechnological methods that employ tissue spheroids.
Hung Truong, Thomas Engels, Henja Wehmann, Dmitry Kolomenskiy, Fritz-Olaf Lehmann, Kai Schneider
Insect wings can undergo significant deformation during flapping motion owing to inertial, elastic and aerodynamic forces. Changes in shape then alter aerodynamic forces, resulting in a fully coupled Fluid-Structure Interaction (FSI) problem. Here, we present detailed three-dimensional FSI simulations of deformable blowfly (Calliphora vomitoria) wings in flapping flight. A wing model is proposed using a multi-parameter mass-spring approach, chosen for its implementation simplicity and computational efficiency. We train the model to reproduce static elasticity measurements by optimizing its parameters using a genetic algorithm with covariance matrix adaptation (CMA-ES). Wing models trained with experimental data are then coupled to a high-performance flow solver run on massively parallel supercomputers. Different features of the modeling approach and the intra-species variability of elastic properties are discussed. We found that individuals with different wing stiffness exhibit similar aerodynamic properties characterized by dimensionless forces and power at the same Reynolds number. We further study the influence of wing flexibility by comparing between the flexible wings and their rigid counterparts. Under equal prescribed kinematic conditions for rigid and flexible wings, wing flexibility improves lift-to-drag ratio as well as lift-to-power ratio and reduces peak force observed during wing rotation.
Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider
A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge-Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.
Dmitry Kolomenskiy, Masateru Maeda, Thomas Engels, Hao Liu, Kai Schneider, Jean-Christophe Nave
Aerodynamic ground effect in flapping-wing insect flight is of importance to comparative morphologies and of interest to the micro-air-vehicle (MAV) community. Recent studies, however, show apparently contradictory results of either some significant extra lift or power savings, or zero ground effect. Here we present a numerical study of fruitfly sized insect takeoff with a specific focus on the significance of leg thrust and wing kinematics. Flapping-wing takeoff is studied using numerical modelling and high performance computing. The aerodynamic forces are calculated using a three-dimensional Navier--Stokes solver based on a pseudo-spectral method with volume penalization. It is coupled with a flight dynamics solver that accounts for the body weight, inertia and the leg thrust, while only having two degrees of freedom: the vertical and the longitudinal horizontal displacement. The natural voluntary takeoff of a fruitfly is considered as reference. The parameters of the model are then varied to explore possible effects of interaction between the flapping-wing model and the ground plane. These modified takeoffs include cases with decreased leg thrust parameter, and/or with periodic wing kinematics, constant body pitch angle. The results show that the ground effect during natural voluntary takeoff is negligible. In the modified takeoffs, when the rate of climb is slow, the difference in the aerodynamic forces due to the interaction with the ground is up to 6%. Surprisingly, depending on the kinematics, the difference is either positive or negative, in contrast to the intuition based on the helicopter theory, which suggests positive excess lift. This effect is attributed to unsteady wing-wake interactions. A similar effect is found during hovering.
Hung Truong, Thomas Engels, Dmitry Kolomenskiy, Kai Schneider
The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo significant deformation. In the present work, we present detailed numerical simulations of such deformable wings. Our results are obtained with a fluid-structure interaction solver, coupling a mass-spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier-Stokes equations. We impose the no-slip boundary condition through the volume penalization method; the time-dependent complex geometry is then completely described by a mask function. This allows solving the governing equations of the fluid on a regular Cartesian grid. Our implementation for massively parallel computers allows us to perform high resolution computations with up to 500 million grid points. The mass-spring model uses a functional approach, thus modeling the different mechanical behaviors of the veins and the membranes of the wing. We perform a series of numerical simulations of a flexible revolving bumblebee wing at a Reynolds number Re = 1800. In order to assess the influence of wing flexibility on the aerodynamics, we vary the elasticity parameters and study rigid, flexible and highly flexible wing models. Code validation is carried out by computing classical benchmarks.
Dmitry Zharikov, Maxim Piskunov, Dmitry Kolomenskiy
Many numerical studies validate droplet wall impact using only maximum spreading diameter, yet this metric alone cannot ensure correct droplet dynamics. We present a combined dynamic contact angle (DCA) model that merges the geometric accuracy of the generalized Hoffman-Voinov-Tanner law with the kinematic consistency of a Hoffman function-based approach, improving predictions of droplet spreading and receding. We simulate water-glycerol droplet impact on sapphire glass at Weber numbers 20 -- 250 and assess both contact angle formulations. Simulated radial velocity fields are processed in Python using SciPy and compared with Particle Image Velocimetry measurements in the longitudinal section of the spreading droplet. The Hoffman function-based model captures the main droplet kinematic trends and provides more consistent receding dynamics. The generalized Hoffman-Voinov-Tanner law matches the maximum spreading diameter within 7%. However, during receding, it shows a median absolute error in radial velocity up to three times higher than that of the Hoffman function-based solution. Average radial velocity and spreading velocity can differ from experimental trends even when maximum spreading is reproduced. These findings support validation combining geometric and kinematic metrics and motivate the combined model for predicting spreading and receding. Using the maximum spreading factor $β_{max}$ as the ratio of the maximum spreading diameter over the initial droplet diameter and the characteristic capillary number $Ca_{char}$ defined from the mean internal horizontal velocity at 300 micrometer above the substrate, we introduce a $(β_{max},\,Ca_{char})$ diagram to relate spreading characteristics to internal flow dynamics. We hypothesize that, given sufficient data, the contact-line geometry may be used to estimate internal kinematics.
Yuki Yasuda, Ryo Onishi, Yuichi Hirokawa, Dmitry Kolomenskiy, Daisuke Sugiyama
The present paper proposes a super-resolution (SR) model based on a convolutional neural network and applies it to the near-surface temperature in urban areas. The SR model incorporates a skip connection, a channel attention mechanism, and separated feature extractors for the inputs of temperature, building height, downward shortwave radiation, and horizontal velocity. We train the SR model with sets of low-resolution (LR) and high-resolution (HR) images from building-resolving large-eddy simulations (LESs) in a city, where the horizontal resolutions of LR and HR are 20 and 5 m, respectively. The generalization capability of the SR model is confirmed with LESs in another city. The estimated HR temperature fields are more accurate than those of the bicubic interpolation and image SR model that takes only the temperature as its input. Except for the temperature input, the building height is the most important to reconstruct the HR temperature and enables the SR model to reduce errors in temperature near building boundaries. The SR model considers the appropriate boundary for each building from its height information. The analysis of attention weights indicates that the importance of the building height increases as the downward shortwave radiation becomes larger. The contrast between sun and shade is strengthened with the increase in solar radiation, which may affect the temperature distribution. The short inference time suggests the potential of the proposed SR model to facilitate a real-time HR prediction in metropolitan areas by combining it with an LR building-resolving LES model.
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Marie Farge, Fritz-Olaf Lehmann, Jörn Sesterhenn
Flapping insects are remarkably agile fliers, adapted to a highly turbulent environment. We present a series of high resolution numerical simulations of a bumblebee interacting with turbulent inflow. We consider both tethered and free flight, the latter with all six degrees of freedom coupled to the Navier--Stokes equations. To this end we vary the characteristics of the turbulent inflow, either changing the turbulence intensity or the spectral distribution of turbulent kinetic energy. Active control is excluded in order to quantify the passive response real animals exhibit during their reaction time delay, before the wing beat can be adapted. Modifying the turbulence intensity shows no significant impact on the cycle-averaged aerodynamical forces, moments and power, compared to laminar inflow conditions. The fluctuations of aerodynamic observables, however, significantly grow with increasing turbulence intensity. Changing the integral scale of turbulent perturbations, while keeping the turbulence intensity fixed, shows that the fluctuation level of forces and moments is significantly reduced if the integral scale is smaller than the wing length. Our study shows that the scale-dependent energy distribution in the surrounding turbulent flow is a relevant factor conditioning how flying insects control their body orientation.
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn
FluSI, a fully parallel open source software for pseudo-spectral simulations of three-dimensional flapping flight in viscous flows, is presented. It is freely available for non-commercial use under [https://github.com/pseudospectators/FLUSI]. The computational framework runs on high performance computers with distributed memory architectures. The discretization of the three-dimensional incompressible Navier--Stokes equations is based on a Fourier pseudo-spectral method with adaptive time stepping. The complex time varying geometry of insects with rigid flapping wings is handled with the volume penalization method. The modules characterizing the insect geometry, the flight mechanics and the wing kinematics are described. Validation tests for different benchmarks illustrate the efficiency and precision of the approach. Finally, computations of a model insect in the turbulent regime demonstrate the versatility of the software.
Romain Nguyen van yen, Dmitry Kolomenskiy, Kai Schneider
We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $η$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $η$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $η$, we find that only the part of the spectrum corresponding to eigenvalues $λ\lesssim η^{-1}$ approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of $η$ and $λ$. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision $O(η)$, Navier slip boundary conditions with slip length equal to $\sqrtη$. Moreover, for a given discretization, we show that there exists a value of $η$, corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier-Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.
Sridhar Ravi, Dmitry Kolomenskiy, Thomas Engels, Kai Schneider, Chun Wang, Joern Sesterhenn, Hao Liu
The natural wind environment that volant insects encounter is unsteady and highly complex, posing significant flight control and stability challenges. Unsteady airflows can range from structured chains of discrete vortices shed in the wake of an object to fully developed chaotic turbulence. It is critical to understand the flight control strategies insects employ to safely navigate in natural environments. We combined experiments on free flying bumblebees with high fidelity numerical simulations and lower order modeling to identify the salient mechanics that mediate insect flight in unsteady winds. We trained bumblebees to fly upwind towards an artificial flower in a wind tunnel under steady wind and in a von Karman street (23Hz) formed in the wake of a cylinder. The bees displayed significantly higher movement in the unsteady vortex street compared to steady winds. Correlation analysis revealed that at lower frequencies, less than 10 Hz, in both steady and unsteady winds the bees mediated lateral movement with body roll, typical casting motion. At higher frequencies in unsteady winds there was a negative correlation between body roll and lateral accelerations. Numerical simulations of a bumblebee in similar conditions permitted the separation of the passive and active components of the flight trajectories. Comparison between the free-flying and numerical bees revealed a novel mechanism that enables bees to passively ride out high frequency perturbations while performing active maneuvers and corrections at lower frequencies. The capacity of maintaining stability by combining passive and active modes at different timescales provides a viable means for volant animals and machines to tackle the control challenges posed by complex airflows.
Timothy Jakobi, Dmitry Kolomenskiy, Teruaki Ikeda, Simon Watkins, Alex Fisher, Hao Liu, Sridhar Ravi
Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping organisms are linked with their resultant flight trajectories and performance, yet little is understood about how discrete unsteady aerodynamic phenomena affect the interlaced dynamics of such systems. In this study, we examined freely flying bumblebees subject to a single discrete gust to emulate aerodynamic disturbances encountered in nature. Bumblebees are expert commanders of the aerial domain as they persistently forage within complex terrain elements. Physical obstacles such as flowers produce local effects representative of a typified gust which threatens the precise control of intricate maneuvers. By tracking the 3D dynamics of bees flying through gusts, we determined the sequences of motion that permit flight in three disturbance conditions. Bees repetitively executed a series of passive impulsive maneuvers followed by active recovery maneuvers. Impulsive motion was unique in each gust direction, maintaining control purely by passive manipulation of the body. Bees pitched up and slowed-down at the beginning of recovery in every disturbance, followed by corrective maneuvers which brought attitudes back to their original state. Bees were displaced the most by the sideward gust, displaying large lateral translations and roll deviations. Upward gusts were easier for bees to fly through, causing only minor flight changes and minimal recovery times. Downward gusts severely impaired the control response of bees, inflicting strong adverse forces which sharply upset trajectories. Bees used interesting control strategies when flying in each disturbance, offering new insights into insect-scale flapping flight and bio-inspired robotic systems.