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

Recovering piecewise smooth functions from nonuniform Fourier measurements

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree

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

Determining Formative Winds Through Geomorphology: Herschel Crater, Mars

The purpose of this study was to characterize the surface winds for a region of Mars by applying known relationships between wind and landforms observed on Earth to Mars. Eolian landforms apparent in Mars Orbital Camera imagery of the Herschel Crater region of Mars were investigated. A "wind map" of the area was produced using geomorphic analogy of terrestrial eolian landforms to infer the direction(s) of formative Martian surface winds. Movement of dunes over time at Herschel Crater was also investigated. The compiled wind direction results were then compared to an existing computer generated general circulation model of Martian surface winds. The results indicate that dune movement on a scale large enough to observe is not present. The comparison to a general circulation model indicates correlation only for the strongest winds of Martian southern hemisphere summer.Boone Pickens School of Geolog

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

Transformed-FNV:Wave forces on a vertical cylinder — A free-surface formulation

Existing force models for a vertical surface-piercing cylinder require water depth integration from the seabed to the free surface to determine the total inline force. However, acquiring the full wave kinematics profiles beneath the water surface presents a significant computational task. We revisit the finite water depth version of the well-known FNV theory (Kristiansen and Faltinsen, 2017) and propose a transformed version that expresses the total force solely in terms of the fully nonlinear wave properties at the free surface. This novel Transformed-FNV (T-FNV) formulation treats the Morison inertia term exactly and approximates the remaining two convective-derivative type terms with an assumption of slowly varying kinetic energy type terms. We evaluate the accuracy of this transformation against the original formulation, using wave kinematics obtained from fully nonlinear numerical simulations. Two T-FNV formulations are proposed with different input properties required. The first formulation uses the fully nonlinear wave kinematic properties at the free surface, whereas a fully approximated T-FNV formulation requires only the nonlinear free-surface elevation time history measured or calculated at the position of the column but in its absence. Both T-FNV formulations demonstrate good accuracy for wave forces for both deep and shallow-water cases against the original FNV model. The new T-FNV formulations also show the increased role of higher harmonics in the predicted force time histories when compared to those in the free-surface displacement, and the importance of using accurate higher order harmonic wave profiles in nonlinear force calculations

Transformed-FNV:Wave forces on a vertical cylinder — A free-surface formulation

Existing force models for a vertical surface-piercing cylinder require water depth integration from the seabed to the free surface to determine the total inline force. However, acquiring the full wave kinematics profiles beneath the water surface presents a significant computational task. We revisit the finite water depth version of the well-known FNV theory (Kristiansen and Faltinsen, 2017) and propose a transformed version that expresses the total force solely in terms of the fully nonlinear wave properties at the free surface. This novel Transformed-FNV (T-FNV) formulation treats the Morison inertia term exactly and approximates the remaining two convective-derivative type terms with an assumption of slowly varying kinetic energy type terms. We evaluate the accuracy of this transformation against the original formulation, using wave kinematics obtained from fully nonlinear numerical simulations. Two T-FNV formulations are proposed with different input properties required. The first formulation uses the fully nonlinear wave kinematic properties at the free surface, whereas a fully approximated T-FNV formulation requires only the nonlinear free-surface elevation time history measured or calculated at the position of the column but in its absence. Both T-FNV formulations demonstrate good accuracy for wave forces for both deep and shallow-water cases against the original FNV model. The new T-FNV formulations also show the increased role of higher harmonics in the predicted force time histories when compared to those in the free-surface displacement, and the importance of using accurate higher order harmonic wave profiles in nonlinear force calculations

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