609 research outputs found
Efficient aerodynamic derivative calculation in three-dimensional transonic flow
ABSTRACTOne key task in computational aeroelasticity is to calculate frequency response functions of aerodynamic coefficients due to structural excitation or external disturbance. Computational fluid dynamics methods are applied for this task at edge-of-envelope flow conditions. Assuming a dynamically linear response around a non-linear steady state, two computationally efficient approaches in time and frequency domain are discussed. A non-periodic, time-domain function can be used, on the one hand, to excite a broad frequency range simultaneously giving the frequency response function in a single non-linear, time-marching simulation. The frequency-domain approach, on the other hand, solves a large but sparse linear system of equations, resulting from the linearisation about the non-linear steady state for each frequency of interest successively. Results are presented for a NACA 0010 aerofoil and a generic civil aircraft configuration in very challenging transonic flow conditions with strong shock-wave/boundary-layer interaction in the pre-buffet regime. Computational cost savings of up to 1 order of magnitude are observed in the time domain for the all-frequencies-at-once approach compared with single-frequency simulations, while an additional order of magnitude is obtained for the frequency-domain method. The paper demonstrates the readiness of computational aeroelasticity tools at edge-of-envelope flow conditions.</jats:p
Does dynamics reflect topology in directed networks?
We present and analyze a topologically induced transition from ordered,
synchronized to disordered dynamics in directed networks of oscillators. The
analysis reveals where in the space of networks this transition occurs and its
underlying mechanisms. If disordered, the dynamics of the units is precisely
determined by the topology of the network and thus characteristic for it. We
develop a method to predict the disordered dynamics from topology. The results
suggest a new route towards understanding how the precise dynamics of the units
of a directed network may encode information about its topology.Comment: 7 pages, 4 figures, Europhysics Letters, accepte
Unstable Attractors: Existence and Robustness in Networks of Oscillators With Delayed Pulse Coupling
We consider unstable attractors; Milnor attractors such that, for some
neighbourhood of , almost all initial conditions leave . Previous
research strongly suggests that unstable attractors exist and even occur
robustly (i.e. for open sets of parameter values) in a system modelling
biological phenomena, namely in globally coupled oscillators with delayed pulse
interactions.
In the first part of this paper we give a rigorous definition of unstable
attractors for general dynamical systems. We classify unstable attractors into
two types, depending on whether or not there is a neighbourhood of the
attractor that intersects the basin in a set of positive measure. We give
examples of both types of unstable attractor; these examples have
non-invertible dynamics that collapse certain open sets onto stable manifolds
of saddle orbits.
In the second part we give the first rigorous demonstration of existence and
robust occurrence of unstable attractors in a network of oscillators with
delayed pulse coupling. Although such systems are technically hybrid systems of
delay differential equations with discontinuous `firing' events, we show that
their dynamics reduces to a finite dimensional hybrid system system after a
finite time and hence we can discuss Milnor attractors for this reduced finite
dimensional system. We prove that for an open set of phase resetting functions
there are saddle periodic orbits that are unstable attractors.Comment: 29 pages, 8 figures,submitted to Nonlinearit
Influence of gust modelling on free-flight aerofoils
Gust analysis is one key task during design and certification of new aircraft. In the industrial standard, the gust is modelled as a disturbance in velocity and is superposed with the general velocity field surrounding the aircraft. The shape, typically sinusoidal or 1-cos, is uniform in vertical direction and is not changing while travelling through the computational domain. These assumptions known as the field or disturbance velocity method facilitate an efficient way of simulating gust encounter within computational fluid dynamics methods. However, how this frozen gust model effects the accuracy of loads predictions compared to more-realistic models remains an open question. A novel approach to simulate a so-called resolved gust is presented herein. An initial perturbation of the x-velocity is prescribed using a 1-cos shape in two spatial directions. Disturbances in vertical velocity as well as density and pressure are developing after some simulated time. Results are compared to the field-velocity method using the CRANK aerofoil covering subsonic and transonic flow conditions. Lift and moment responses are analysed as well as time histories of velocities at different grid locations. Furthermore, a second aerofoil is added as a horizontal tail-plane to represent a large civil aircraft. This configuration is used to include the effects of flight dynamics while analysing the responses due to the two gust models
Rapid gust response simulation of large civil aircraft using computational fluid dynamics
ABSTRACTSeveral critical load cases during the aircraft design process result from atmospheric turbulence. Thus, rapidly performable and highly accurate dynamic response simulations are required to analyse a wide range of parameters. A method is proposed to predict dynamic loads on an elastically trimmed, large civil aircraft using computational fluid dynamics in conjunction with model reduction. A small-sized modal basis is computed by sampling the aerodynamic response at discrete frequencies and applying proper orthogonal decomposition. The linear operator of the Reynolds-averaged Navier-Stokes equations plus turbulence model is then projected onto the subspace spanned by this basis. The resulting reduced system is solved at an arbitrary number of frequencies to analyse responses to 1-cos gusts very efficiently. Lift coefficient and surface pressure distribution are compared with full-order, non-linear, unsteady time-marching simulations to verify the method. Overall, the reduced-order model predicts highly accurate global coefficients and surface loads at a fraction of the computational cost, which is an important step towards the aircraft loads process relying on computational fluid dynamics.</jats:p
Revealing Network Connectivity From Dynamics
We present a method to infer network connectivity from collective dynamics in
networks of synchronizing phase oscillators. We study the long-term stationary
response to temporally constant driving. For a given driving condition,
measuring the phase differences and the collective frequency reveals
information about how the oscillators are interconnected. Sufficiently many
repetitions for different driving conditions yield the entire network
connectivity from measuring the dynamics only. For sparsely connected networks
we obtain good predictions of the actual connectivity even for formally
under-determined problems.Comment: 10 pages, 4 figure
Model reduction for gust load analysis of free-flying aircraft
The coupling of computational fluid dynamics and rigid body dynamics promises enhanced multidisciplinary simulation capability for aircraft design and certification. Industrial application of such coupled simulations is limited however by computational cost. In this context, model reduction can retain the fidelity of the underlying model while decreasing the computational effort. A model reduction technique is presented herein based on modal decomposition and projection of the non-linear residual function. Flight dynamics eigenmodes are obtained with an operator-based identification procedure which is capable of calculating these global modes of the coupled Jacobian matrix also for an industrial use case with nearly 50 million degrees-of-freedom. Additional modes based on proper orthogonal decomposition to describe the aerodynamic response due to gust encounter are combined with the eigenmode basis. Results are presented for initial disturbance analysis using flight dynamics modes only and for gust encounter simulations using the combined modal basis. Overall, the reduced model is capable of predicting the full order results accurately
Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions
Counting problems, determining the number of possible states of a large
system under certain constraints, play an important role in many areas of
science. They naturally arise for complex disordered systems in physics and
chemistry, in mathematical graph theory, and in computer science. Counting
problems, however, are among the hardest problems to access computationally.
Here, we suggest a novel method to access a benchmark counting problem, finding
chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern
matching algorithm that exploits the equivalence between the chromatic
polynomial and the zero-temperature partition function of the Potts
antiferromagnet on the same graph. Implementing this bottom-up algorithm using
appropriate computer algebra, the new method outperforms standard top-down
methods by several orders of magnitude, already for moderately sized graphs. As
a first application, we compute chromatic polynomials of samples of the simple
cubic lattice, for the first time computationally accessing three-dimensional
lattices of physical relevance. The method offers straightforward
generalizations to several other counting problems.Comment: 7 pages, 4 figure
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