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

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

Unstable Attractors: Existence and Robustness in Networks of Oscillators With Delayed Pulse Coupling

We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. 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

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

Peroral intestinal biopsy

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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