Dmitry Kolomenskiy

A Fourier spectral method for the Navier-Stokes equations with volume penalization for moving solid obstacles

An efficient numerical scheme to compute flows past rigid solid bodies moving through viscous incompressible fluid is presented. Solid obstacles of arbitrary shape are taken into account using the volume penalization method to impose no-slip boundary condition. The 2D Navier-Stokes equations, written in the vorticity-streamfunction formulation, are discretized using a Fourier pseudo-spectral scheme. Four different time discretization schemes of the penalization term are proposed and compared. The originality of the present work lies in the implementation of time-dependent penalization, which makes the above method capable of solving problems where the obstacle follows an arbitrary motion. Fluid-solid coupling for freely falling bodies is also implemented. The numerical method is validated for different test cases: the flow past a cylinder, Couette flow between rotating cylinders, sedimentation of a cylinder and a falling leaf with elliptical shape.

A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles

A volume penalization method for imposing homogeneous Neumann boundary conditions in advection-diffusion equations is presented. Thus complex geometries which even may vary in time can be treated efficiently using discretizations on a Cartesian grid. A mathematical analysis of the method is conducted first for the one-dimensional heat equation which yields estimates of the penalization error. The results are then confirmed numerically in one and two space dimensions. Simulations of two-dimensional incompressible flows with passive scalars using a classical Fourier pseudo-spectral method validate the approach for moving obstacles. The potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no-slip and no-flux boundary conditions are imposed, respectively.

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones—micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 104–105 or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems. This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.

Bumblebee flight in heavy turbulence

High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments, or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.

Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces

SUMMARY Up to now, the take-off stage has remained an elusive phase of insect flight that was relatively poorly explored compared with other maneuvers. An overall assessment of the different mechanisms involved in force production during take-off has never been explored. Focusing on the first downstroke, we have addressed this problem from a force balance perspective in butterflies taking off from the ground. In order to determine whether the sole aerodynamic wing force could explain the observed motion of the insect, we have firstly compared a simple analytical model of the wing force with the acceleration of the insects center of mass estimated from video tracking of the wing and body motions. Secondly, wing kinematics were also used for numerical simulations of the aerodynamic flow field. Similar wing aerodynamic forces were obtained by the two methods. However, neither are sufficient, nor is the inclusion of the ground effect, to predict faithfully the body acceleration. We have to resort to the leg forces to obtain a model that best fits the data. We show that the median and hind legs display an active extension responsible for the initiation of the upward motion of the insects body, occurring before the onset of the wing downstroke. We estimate that legs generate, at various times, an upward force that can be much larger than all other forces applied to the insects body. The relative timing of leg and wing forces explains the large variability of trajectories observed during the maneuvers.

Aerodynamic Ground Effect in Fruitfly Sized Insect Takeoff

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.

Reduced-Order Modelling of Turbulent Jets for Noise Control

A reduced-ordermodelling (ROM) strategy is pursued to achieve a mechanistic understanding of jet flow mechanisms targeting jet noise control. Coherent flow structures of the jet are identified by the proper orthogonal decomposition (POD) and wavelet analysis. These techniques are applied to an LES data ensemble with velocity snapshots of a three-dimensional, incompressible jet at a Reynolds number of Re=3600. A low-dimensionalGalerkin model of a three-dimensional jet is extracted and calibrated to the physical dynamics. To obtain the desired mechanistic understanding of jet noise generation, the loudest flow structures are distilled by a goal-oriented generalisation of the POD approach we term ’most observable decomposition’ (MOD). Thus, a reduction of the number of dynamically most important degrees of freedom by one order of magnitude is achieved. Capability of the presented ROM strategy for jet noise control is demonstrated by suppression of loud flow structures.

Numerical simulation of fluid-structure interaction with the volume penalization method

We present a novel scheme for the numerical simulation of fluid-structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid-solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

We report the results of a study on 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,