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Blade-tip vortices can lead to wakes, cavitation and noise, and their control remains a significant challenge for tidal and wind turbines. In the present work, we propose and investigate controlling tip vortices through local permeability. Blade-resolved Reynolds-averaged Navier-Stokes simulation has been employed on a model-scale horizontal-axis turbine, following a rigorous validation and verification process. The tip-speed ratio of the turbine varies from 4.52 to 7.54. The tip permeability is modelled by including a porous zone over the blade tip section, within which Darcy's law is applied. The results demonstrate that there is an optimal range of permeability, corresponding to a non-dimensional Darcy number, Da, of around 10^{-5}, that can substantially decrease the tip vortex intensity. The revealed flow physics show that the permeable tip treatment can effectively enlarge the vortex viscous core radius with little change to the vortex circulation. As the tip vortex intensity is significantly reduced, the permeable tip treatment can increase the minimal pressure-coefficient at the vortex core by up to 63%, which significantly alleviates the cavitation risk due to tip vortices. This approach has negligible influence on the turbine's energy-harvesting performance because the spanwise extent of the permeable tip treatment is only in the order of 0.1% turbine diameter. Our findings demonstrate this approach's great promise to break the upper tip-speed ratio limit capped by cavitation for tidal turbines. These will contribute to developing more efficient and resilient turbines.

Tip leakage flow in turbomachinery inherently generates intense unsteady features, named self-excited unsteadiness, which has not been well understood. A Zonalised LES (ZLES) is employed around a linear cascade, with wall-modelled Large Eddy Simulation (LES) forced to be active in the tip region. The simulation is well validated and demonstrated the advantages of effectively reducing the computational effort while maintaining an equivalent prediction accuracy in the region of interest. The time-averaged and spatial-spectral characteristics of tip leakage vortex (TLV) structures are systematically discussed. The self-excited unsteady processes of TLV include unsteady vortex separation inside the tip gap, the tip leakage jet-mainstream interaction, the primary tip leakage vortex (PTLV) wandering motion and the induced separation near endwall. The Spectral Proper Orthogonal Decomposition (SPOD) is used to examine the dominant frequencies and their coherent structures. It is found that these unsteady features change from a single high-frequency mode to a multiple lower-frequencies mode due to the PTLV breakdown. The SPOD and correlation analyses reveal that the self-excited unsteadiness is mainly induced by the interactions between unsteady vortex separation, tip leakage jet, and mainstream. The associated unsteady fluctuations are convected along the tip leakage jet trajectory, causing the wandering motion of PTLV core. Based on the cause of the investigated unsteadiness, a micro-offset tip design is proposed and validated for effectively suppressing this unsteadiness, and associated turbulence generation and hence pressure fluctuations. This work improves the understanding of tip-leakage-flow dynamics and informs the control of the associated unsteady fluid oscillation and noise.

A computationally efficient high-order solver is developed to compute the wall distances by solving the relevant partial differential equations, namely: Eikonal, Hamilton-Jacobi (HJ) and Poisson equations. In contrast to the upwind schemes widely used in the literature, we explore the suitability of high-order central difference schemes (explicit/compact) for the wall-distance computation. While solving the Hamilton-Jacobi equation, the high-order central difference schemes performed approximately $1.4-2.8$ times faster than the upwind schemes with a marginal improvement in the solution accuracy. A new pseudo HJ formulation based on the localized artificial diffusivity (LAD) approach has been proposed. It is demonstrated to predict results with an accuracy comparable to that of the Eikonal equation and the simulations are $\approx$ 1.5 times faster than the baseline HJ solver using upwind schemes. A curvature correction is also incorporated in the HJ equation to correct for the near-wall errors due to concave/convex wall curvatures. We demonstrate the efficacy of the proposed methods on both the steady and unsteady test cases and exploit the unsteady wall-distance solver to estimate the instantaneous shape and burning surface area of a dendrite propellant grain in a solid propellant rocket motor.

Earth's magnetosphere is vital for today's technologically dependent society. To date, numerous design studies have been conducted and over a dozen science missions have own to study the magnetosphere. However, a majority of these solutions relied on large monolithic satellites, which limited the spatial resolution of these investigations, as did the technological limitations of the past. To counter these limitations, we propose the use of a satellite swarm carrying numerous and distributed payloads for magnetospheric measurements. Our mission is named APIS (Applications and Potentials of Intelligent Swarms), which aims to characterize fundamental plasma processes in the Earth's magnetosphere and measure the effect of the solar wind on our magnetosphere. We propose a swarm of 40 CubeSats in two highly-elliptical orbits around the Earth, which perform radio tomography in the magnetotail at 8-12 Earth Radii (RE) downstream, and the subsolar magnetosphere at 8-12RE upstream. In addition, in-situ measurements of the magnetic and electric fields, plasma density will be performed by on-board instruments. In this article, we present an outline of previous missions and designs for magnetospheric studies, along with the science drivers and motivation for the APIS mission. Furthermore, preliminary design results are included to show the feasibility of such a mission. The science requirements drive the APIS mission design, the mission operation and the system requirements. In addition to the various science payloads, critical subsystems of the satellites are investigated e.g., navigation, communication, processing and power systems. We summarize our findings, along with the potential next steps to strengthen our design study., Comment: Accepted in Acta Astronautica

Summarizes goals of state education aid, presents a conceptual model of aid's welfare effects, and examines the literature of tax and expenditure effects. Capitalization changes the relative desirability of two goals; equalizing resources across districts becomes less important than equalizing school districts' actual spending levels. (Contains 45 references.) (MLH)