Performance of an ideal turbine in an inviscid shear flow

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines

Scenario selection method for system scenario analysis

Scenario analysis is a frequently-used method to explore what a proposed system is required to do in the early phases of system development leading towards finding system requirements. A system which is intended to perform a variety of roles under a range of conditions is likely to result in the need for a quantity of scenarios that becomes intractably pluriform. The consequence of too many scenarios is that either the number of scenarios to be analysed must be reduced to a manageable number or the analysis is likely to be perfunctory, diminishing the value of the analysis. We present a method for reducing the number of scenarios to be analysed through study of the organization of the factors which distinguish scenarios from each other, and for selecting which scenarios need analysis through identifying their points of commonality and identifying where differences may impact system capability. Our method organises the types and potential values of factors related to a particular system development in order to reduce the number of scenarios to be investigate

Scenario selection method for system scenario analysis

Scenario analysis is a frequently-used method to explore what a proposed system is required to do in the early phases of system development leading towards finding system requirements. A system which is intended to perform a variety of roles under a range of conditions is likely to result in the need for a quantity of scenarios that becomes intractably pluriform. The consequence of too many scenarios is that either the number of scenarios to be analysed must be reduced to a manageable number or the analysis is likely to be perfunctory, diminishing the value of the analysis. We present a method for reducing the number of scenarios to be analysed through study of the organization of the factors which distinguish scenarios from each other, and for selecting which scenarios need analysis through identifying their points of commonality and identifying where differences may impact system capability. Our method organises the types and potential values of factors related to a particular system development in order to reduce the number of scenarios to be investigate

Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors

On testing global optimization algorithms for space trajectory design

In this paper we discuss the procedures to test a global search algorithm applied to a space trajectory design problem. Then, we present some performance indexes that can be used to evaluate the effectiveness of global optimization algorithms. The performance indexes are then compared highlighting the actual significance of each one of them. A number of global optimization algorithms are tested on four typical space trajectory design problems. From the results of the proposed testing procedure we infer for each pair algorithm-problem the relation between the heuristics implemented in the solution algorithm and the main characteristics of the problem under investigation. From this analysis we derive a novel interpretation of some evolutionary heuristics, based on dynamical system theory and we significantly improve the performance of one of the tested algorithms

Decision and function problems based on boson sampling

Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and the possible usefulness of boson-sampling devices is mainly limited to the proof of quantum supremacy. The purpose of this work is to investigate whether boson sampling can be used as a resource of decision and function problems that are computationally hard, and may thus have cryptographic applications. After the definition of a rather general theoretical framework for the design of such problems, we discuss their solution by means of a brute-force numerical approach, as well as by means of non-boson samplers. Moreover, we estimate the sample sizes required for their solution by passive linear interferometers, and it is shown that they are independent of the size of the Hilbert space.Comment: Close to the version published in PR

Optimisation of air cooled, open-cathode fuel cells: Current of lowest resistance and electro-thermal performance mapping

Selecting the ideal operating point for a fuel cell depends on the application and consequent trade-off between efficiency, power density and various operating considerations. A systematic methodology for determining the optimal operating point for fuel cells is lacking; there is also the need for a single-value metric to describe and compare fuel cell performance. This work shows how the ‘current of lowest resistance’ can be accurately measured using electrochemical impedance spectroscopy and used as a useful metric of fuel cell performance. This, along with other measures, is then used to generate an ‘electro-thermal performance map’ of fuel cell operation. A commercial air-cooled open-cathode fuel cell is used to demonstrate how the approach can be used; in this case leading to the identification of the optimum operating temperature of ∼45 °C

The set-down and set-up of directionally spread and crossing surface gravity wave groups

For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above (for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of and above, which are known to occur in the ocean