Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of 2-D flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we derive reduced-order models valid in the neighborhood of this unstable steady state. The actuation is modeled as a localized body force near the leading edge of the flat plate, and the sensors are two velocity measurements in the near-wake of the plate. A reduced-order Kalman filter is developed based on these models and is shown to accurately reconstruct the flow field from the sensor measurements, and the resulting estimator-based control is shown to stabilize the unstable steady state. For small perturbations of the steady state, the model accurately predicts the response of the full simulation. Furthermore, the resulting controller is even able to suppress the stable periodic vortex shedding, where the nonlinear effects are strong, thus implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure

Manifestations of Drag Reduction by Polymer Additives in Decaying, Homogeneous, Isotropic Turbulence

The existence of drag reduction by polymer additives, well established for wall-bounded turbulent flows, is controversial in homogeneous, isotropic turbulence. To settle this controversy we carry out a high-resolution direct numerical simulation (DNS) of decaying, homogeneous, isotropic turbulence with polymer additives. Our study reveals clear manifestations of drag-reduction-type phenomena: On the addition of polymers to the turbulent fluid we obtain a reduction in the energy dissipation rate, a significant modification of the fluid energy spectrum especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments.Comment: 4 pages, 3 figure

Single polymer dynamics: coil-stretch transition in a random flow

By quantitative studies of statistics of polymer stretching in a random flow and of a flow field we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition at the value of the criterion close to theoretically predicted.Comment: 4 pages, 5 figure

Hydrogen solubility in zirconium intermetallic second phase particles

The enthalpies of solution of H in Zr binary intermetallic compounds formed with Cu, Cr, Fe, Mo, Ni, Nb, Sn and V were calculated by means of density functional theory simulations and compared to that of H in {\alpha}-Zr. It is predicted that all Zr-rich phases (formed with Cu, Fe, Ni and Sn), and those phases formed with Nb and V, offer lower energy, more stable sites for H than {\alpha}-Zr. Conversely, Mo and Cr containing phases do not provide preferential solution sites for H. In all cases the most stable site for H are those that offer the highest coordination fraction of Zr atoms. Often these are four Zr tetrahedra but not always. Implications with respect to H-trapping properties of commonly observed ternary phases such as Zr(Cr,Fe)2, Zr2(Fe,Ni) and Zr(Nb,Fe)2 are also discussed.Comment: manuscript accepted for publication in Journal of Nuclear Materials (2013

Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives

We carry out a direct numerical simulation (DNS) study that reveals the effects of polymers on statistically steady, forced, homogeneous, isotropic fluid turbulence. We find clear manifestations of dissipation-reduction phenomena: On the addition of polymers to the turbulent fluid, we obtain a reduction in the energy dissipation rate, a significant modification of the fluid energy spectrum, especially in the deep-dissipation range, a suppression of small-scale intermittency, and a decrease in small-scale vorticity filaments. We also compare our results with recent experiments and earlier DNS studies of decaying fluid turbulence with polymer additives.Comment: consistent with the published versio

Second-order closures for compressible turbulence

This viewgraph presentation discusses project description, turbulence models, and computational engine and results for second-order closures for compressible turbulence

Post-copulatory opportunities for sperm competition and cryptic female choice provide no offspring fitness benefits in externally fertilizing salmon

There is increasing evidence that females can somehow improve their offspring fitness by mating with multiple males, but we understand little about the exact stage(s) at which such benefits are gained. Here, we measure whether offspring fitness is influenced by mechanisms operating solely between sperm and egg. Using externally-fertilising and polyandrous Atlantic salmon (Salmo salar), we employed split-clutch and split-ejaculate in vitro fertilisation experiments to generate offspring using designs that either denied or applied opportunities for sperm competition and cryptic female choice. Following fertilisations, we measured 140 days of offspring fitness after hatch, through growth and survival in hatchery and near-natural conditions. Despite an average composite mortality of 61%, offspring fitness at every life stage was near-identical between groups fertilised under the absence versus presence of opportunities for sperm competition and cryptic female choice. Of the 21,551 and 21,771 eggs from 24 females fertilised under monandrous versus polyandrous conditions, 68% versus 67.8% survived to the 100-day juvenile stage; sub-samples showed similar hatching success (73.1% versus 74.3%), had similar survival over 40 days in near-natural streams (57.3% versus 56.2%), and grew at similar rates throughout. We therefore found no evidence that gamete-specific interactions allow offspring fitness benefits when polyandrous fertilisation conditions provide opportunities for sperm competition and cryptic female choice

The clock is ticking : temporally prioritizing eradications on islands

Funding Funding was awarded to Z.T.C. by the New Zealand Government through a New Zealand International Doctoral Research Scholarship. Funding was awarded to T.W.B. by the European Union's Horizon 2020 research and innovation programme Marie Skłodowska Curie Fellowship (Grant No. 747120). Funding was awarded to J.C.R. by the Royal Society of New Zealand Rutherford Discovery Fellowship (Grant No. RDF-UOA1404) and the BioHeritage National Science Challenge (Grant No. 1617-44-003). Additional supporting information may be found in the supplementary material of this article. The associated code and dataset are archived and are publicly available at the University of Auckland figshare database (https://doi.org/10.17608/k6.auckland.13542203.v1) and at GitHub (https://github.com/carterz2/temporal‐island‐prioritization).Peer reviewedPostprin