5,406 research outputs found
Topology and shape optimization of induced-charge electro-osmotic micropumps
For a dielectric solid surrounded by an electrolyte and positioned inside an
externally biased parallel-plate capacitor, we study numerically how the
resulting induced-charge electro-osmotic (ICEO) flow depends on the topology
and shape of the dielectric solid. In particular, we extend existing
conventional electrokinetic models with an artificial design field to describe
the transition from the liquid electrolyte to the solid dielectric. Using this
design field, we have succeeded in applying the method of topology optimization
to find system geometries with non-trivial topologies that maximize the net
induced electro-osmotic flow rate through the electrolytic capacitor in the
direction parallel to the capacitor plates. Once found, the performance of the
topology optimized geometries has been validated by transferring them to
conventional electrokinetic models not relying on the artificial design field.
Our results show the importance of the topology and shape of the dielectric
solid in ICEO systems and point to new designs of ICEO micropumps with
significantly improved performance.Comment: 18 pages, latex IOP-style, 7 eps figure
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Schnelle Löser für Partielle Differentialgleichungen
This workshop was well attended by 52 participants with broad geographic representation from 11 countries and 3 continents. It was a nice blend of researchers with various backgrounds
A mathematical theory of microscale hydrodynamic cloaking and shielding by electro-osmosis
In this paper, we develop a general mathematical framework for perfect and
approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which
is governed by a coupled PDE system via the field-effect electro-osmosis. We
first establish the representation formula of the solution of the coupled
system using the layer potential techniques. Based on Fourier series, the
perfect hydrodynamic cloaking and shielding conditions are derived for the
control region with the cross-sectional shape being annulus or confocal
ellipses. Then we further propose an optimization scheme for the design of
approximate cloaks and shields within general geometries. The well-posedness of
the optimization problem is proved. In particular, the condition that can
ensure the occurrence of approximate cloaks and shields for general geometries
are also established. Our theoretical findings are validated and supplemented
by a variety of numerical results. The results in this paper also provide a
mathematical foundation for more complex hydrodynamic cloaking and shielding
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Adjoint Methods as Design Tools in Thermoacoustics
In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.</jats:p
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