134 research outputs found
Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions
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
FluSI: A novel parallel simulation tool for flapping insect flight using a Fourier method with volume penalization
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
Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint
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,
, tends to zero. The eigenvalues and eigenfunctions are determined either
analytically or numerically as functions of , both in the continuous case
and after applying Fourier or finite difference discretization schemes. For
fixed , we find that only the part of the spectrum corresponding to
eigenvalues 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 and . Surprisingly, in the Stokes
case, we show that the eigenfunctions approximately satisfy, with a precision
, Navier slip boundary conditions with slip length equal to
. Moreover, for a given discretization, we show that there exists
a value of , 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
Evolution of the Leading-Edge Vortex over an Accelerating Rotating Wing
AbstractThe flow field over an accelerating rotating wing model at Reynolds numbers Re ranging from 250 to 2000 is investigated using particle image velocimetry, and compared with the flow obtained by three-dimensional time-dependent Navier-Stokes simulations. It is shown that the coherent leading-edge vortex that characterises the flow field at Re~200-300 transforms to a laminar separation bubble as Re is increased. It is further shown that the ratio of the instantaneous circulation of the leading-edge vortex in the accel-eration phase to that over a wing rotating steadily at the same Re decreases monotonically with increasing Re. We conclude that the traditional approach based on steady wing rotation is inadequate for the prediction of the aerodynamic performance of flapping wings at Re above about 1000
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
Bumblebees minimize control challenges by combining active and passive modes in unsteady winds
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
- âŠ