63,819 research outputs found
Characterization and modeling of aperiodic pressure oscillations in combustion chambers
Classification of the long-term dynamical
behavior of pressure oscillations in a
laboratory combustion chamber has been
performed using methods of modern dynamical
systems theory. The method involves the
construction of a phase-space representation
from a single pressure record or time series using
the time-delay embedding method. The
pointwise correlation dimension of the resulting
attractor in phase-space provides a lower
bound on the number of modes that participate
in the oscillations. The results show that the
oscillations are quasiperiodic with a dimension
near two over an order of magnitude of
amplitudes. Quasiperiodicity is a result of the
incommensurate frequencies of the system
acoustic modes. A model for the dynamics is
constructed by converting the governing
equations to a kicked-oscillator model. When
compared with the experimental data, the
model results have similar pressure and
velocity spectra and the attractor dimension
verifies that quasiperiodic oscillations are
present
Learning stable and predictive structures in kinetic systems: Benefits of a causal approach
Learning kinetic systems from data is one of the core challenges in many
fields. Identifying stable models is essential for the generalization
capabilities of data-driven inference. We introduce a computationally efficient
framework, called CausalKinetiX, that identifies structure from discrete time,
noisy observations, generated from heterogeneous experiments. The algorithm
assumes the existence of an underlying, invariant kinetic model, a key
criterion for reproducible research. Results on both simulated and real-world
examples suggest that learning the structure of kinetic systems benefits from a
causal perspective. The identified variables and models allow for a concise
description of the dynamics across multiple experimental settings and can be
used for prediction in unseen experiments. We observe significant improvements
compared to well established approaches focusing solely on predictive
performance, especially for out-of-sample generalization
Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches
The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module.
The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density
Thermoacoustic instability - a dynamical system and time domain analysis
This study focuses on the Rijke tube problem, which includes features
relevant to the modeling of thermoacoustic coupling in reactive flows: a
compact acoustic source, an empirical model for the heat source, and
nonlinearities. This thermo-acoustic system features a complex dynamical
behavior. In order to synthesize accurate time-series, we tackle this problem
from a numerical point-of-view, and start by proposing a dedicated solver
designed for dealing with the underlying stiffness, in particular, the retarded
time and the discontinuity at the location of the heat source. Stability
analysis is performed on the limit of low-amplitude disturbances by means of
the projection method proposed by Jarlebring (2008), which alleviates the
linearization with respect to the retarded time. The results are then compared
to the analytical solution of the undamped system, and to Galerkin projection
methods commonly used in this setting. This analysis provides insight into the
consequences of the various assumptions and simplifications that justify the
use of Galerkin expansions based on the eigenmodes of the unheated resonator.
We illustrate that due to the presence of a discontinuity in the spatial
domain, the eigenmodes in the heated case, predicted by using Galerkin
expansion, show spurious oscillations resulting from the Gibbs phenomenon. By
comparing the modes of the linear to that of the nonlinear regime, we are able
to illustrate the mean-flow modulation and frequency switching. Finally,
time-series in the fully nonlinear regime, where a limit cycle is established,
are analyzed and dominant modes are extracted. The analysis of the saturated
limit cycles shows the presence of higher frequency modes, which are linearly
stable but become significant through nonlinear growth of the signal. This
bimodal effect is not captured when the coupling between different frequencies
is not accounted for.Comment: Submitted to Journal of Fluid Mechanic
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