Scaling of slow-drift motion with platform size and its importance for floating wind turbines

Slow drift is a large, low-frequency motion of a floating platform caused by nonlinear hydrodynamic forces. Although slow drift is a well-known phenomenon for ships and other floating structures, new platforms for floating wind turbines are significantly smaller in scale, and it is yet to be established how important slow drift is for them. In this paper we derive an approximate expression for the scaling of the slow drift motion with platform size, mooring characteristics and wave conditions. This suggests that slow drift may be less important for floating wind turbines than other, larger, floating structures. The accuracy of the approximations is discussed; in the one case where detailed data is available, the approximate result is found to be conservative by a factor of up to 40.Engineering and Physical Sciences Research Council (doctoral training award ID: 1089390), GL Garrad Hassa

Complex but negligible: non-linearity of the inertial coupling between the platform and blades of floating wind turbines

Approximate linearised models can be important for preliminary design of floating wind turbines, but their value depends on how well they approximate the real-world non-linear behaviour. This paper focuses on the non-linear inertial coupling between motion of the floating platform and the blade dynamics, using a simplified model to demonstrate how the inertial coupling works, and systematically studying the linearity of the dynamic blade response to different directions, amplitudes and frequencies of motion. Simplified equations of motion are derived and approximately solved analytically, showing that the blade response contains harmonics at a range of frequencies, some linear and some non-linear in the amplitude of the platform motion. Comparison to numerical simulations shows that the analytical results were qualitatively useful but inaccurate for large platform motions. Because of the multiple harmonics in the response, there are more combinations of rotor speeds and platform motions leading to large resonant blade responses and non-linear behaviour than might be expected. Overall, for realistically low rotor speeds and platform frequencies (below 20 rpm and 0.2 Hz), non-linear inertial loading due to platform motion should be negligible. The implications of this work for the use of linearised structural models and the relevance of scale model testing are discussed.This work was funded by an EPSRC doctoral training award (ref. 1089390) and supported by GL Garrad Hassan

Complex but negligible: Non-linearity of the inertial coupling between the platform and blades of floating wind turbines

Approximate linearised models can be important for preliminary design of floating wind turbines, but their value depends on how well they approximate the real-world non-linear behaviour. This paper focuses on the non-linear inertial coupling between motion of the floating platform and the blade dynamics, using a simplified model to demonstrate how the inertial coupling works, and systematically studying the linearity of the dynamic blade response to different directions, amplitudes and frequencies of motion. Simplified equations of motion are derived and approximately solved analytically, showing that the blade response contains harmonics at a range of frequencies, some linear and some non-linear in the amplitude of the platform motion. Comparison to numerical simulations shows that the analytical results were qualitatively useful but inaccurate for large platform motions. Because of the multiple harmonics in the response, there are more combinations of rotor speeds and platform motions leading to large resonant blade responses and non-linear behaviour than might be expected. Overall, for realistically low rotor speeds and platform frequencies (below 20 rpm and 0.2 Hz), non-linear inertial loading due to platform motion should be negligible. The implications of this work for the use of linearised structural models and the relevance of scale model testing are discussed

Frequency-domain modelling of floating wind turbines

The development of new types of offshore wind turbine on floating platforms requires the development of new approaches to modelling the combined platform-turbine system. In this thesis a linearised frequency-domain approach is developed which gives fast but approximate results: linearised models of the structural dynamics, hydrodynamics, aerodynamics and control system dynamics are brought together to find the overall response of the floating wind turbine to harmonic wind and wave loading. Initially, a nonlinear flexible multibody dynamics code is developed and verified, which is then used to provide reference nonlinear simulation results. The structural dynamics of a wind turbine on a moving platform are shown to be nonlinear, but for realistic conditions the effects are small. An approximate analysis of the second-order response of floating cylinders to hydrodynamic loads suggests slow drift motion may be relatively small for floating wind turbines, compared to other floating offshore structures. The aerodynamic loads are linearised using both harmonic and tangent linearisation approaches; the harmonic linearisation gives improved results when stall occurs. The wake dynamics can also be included. The control system behaviour is linearised using the same method, which works well when the wind speed is far from the rated wind speed; close to the rated wind speed the nonlinearity is stronger, but further improvement should be possible. These sub-models are combined to give a simple but complete model of a floating wind turbine, with flexible blades and a flexible tower, but neglecting the control system behaviour, wake dynamics and nonlinear hydrodynamic loads. For the OC3-Hywind turbine, the accuracy of the results is assessed by comparison to nonlinear time-domain simulations using the commercial code Bladed. Peak-peak errors of less than 5 % are achievable for many harmonic wind and wave inputs, but certain conditions lead to larger errors. The effect of including linearised control system behaviour is demonstrated for a subset of conditions. Overall, the results are promising but more work is needed for practical application.This work was supported by GL Garrad Hassan

Harmonic linearisation of aerodynamic loads in a frequency-domain model of a floating wind turbine

Abstract: While detailed aero‐servo‐hydro‐elastic simulation codes for modelling floating wind turbines (FWTs) are available, they achieve high accuracy at the expense of calculation speed. For conceptual design and optimisation, fast solutions are needed, and equivalent linearisation techniques combined with frequency‐domain analysis offers to capture the complex behaviour of FWTs in fast, approximate models. The main aim of this paper is to apply a harmonic linearisation approach to model the aerodynamic loading within a complete coupled model of a FWT, quantifying its performance, and where accuracy is unsatisfactory, to give insight into the causes. Two linearised models are derived from a coupled nonlinear aero‐hydro‐servo‐elastic model, using the OC3‐Hywind FWT as a test case: the typical tangent linearisation derived by numerical perturbation of the nonlinear model and the harmonic linearisation yielding improved representation of the aerodynamic loads. Comparisons against nonlinear time‐domain simulations from Bladed show that it is possible to create a frequency‐domain model of a FWT, including a flexible structure, aeroelastic rotor loads and the effect of the control system, with reasonable accuracy. The biggest source of errors is the presence of additional harmonics caused by nonlinear interactions between loads at different frequencies, rather than inaccurate linearisation of the magnitudes of forces. The computational cost of the harmonic linearisation implemented varies, but in most cases is ∼10× slower than the tangent linearisation and ∼100× faster than the time domain solution

Hybrid Sankey diagrams: Visual analysis of multidimensional data for understanding resource use

Sankey diagrams are used to visualise flows of materials and energy in many applications, to aid understanding of losses and inefficiencies, to map out production processes, and to give a sense of scale across a system. As available data and models become increasingly complex and detailed, new types of visualisation may be needed. For example, when looking for opportunities to reduce steel scrap through supply chain integration, it is not enough to consider simply flows of “steel” — the alloy, thickness, coating and forming history of the metal can be critical. This paper combines data-visualisation techniques with the traditional Sankey diagram to propose a new type of “hybrid” Sankey diagram, which is better able to visualise these different aspects of flows. There is more than one way to visualise a dataset as a Sankey diagram, and different ways are appropriate in different situations. To facilitate this, a systematic method is presented for generating different hybrid Sankey diagrams from a dataset, with an accompanying open-source Python implementation. A common data structure for flow data is defined, through which this method can be used to generate Sankey diagrams from different data sources such as material flow analysis, life-cycle inventories, or directly measured data. The approach is introduced with a series of visual examples, and applied to a real database of global steel flows.This work was supported by EPSRC [EP/N02351x/1]

Improved linearised models of wind turbine aerodynamics and control system dynamics using harmonic linearisation

Where non-linearities are not too strong, linearised frequency-domain approaches offer fast calculations, which can be valuable for preliminary design of wind turbine blades, foundations and floating platforms. But the aerodynamic and control system behaviour of a wind turbine is noticeably non-linear. Here we show for the first time that the technique of harmonic linearisation can reduce error in the approximation of aerodynamic and control system non-linearities, compared to the more common tangent linearisation. After deriving the linearised models, comparing linearised results to non-linear simulations for the NREL 5MW turbine shows that: (1) harmonic linearisation captures aero-elastic effects and non-linearity in aerodynamic forces, giving a 2–4x reduction in error compared to the tangent linearisation; (2) harmonic linearisation can capture non-linear wake dynamics; and (3) the torque and pitch controller behaviour can be approximated with good results away from the rated wind speed but with some challenges when the two controllers interact. Further improvements in the linearised model of the control system have been identified. By improving the accuracy of linearised models, harmonic linearisation is a promising means to extend the applicability of frequency-domain approaches for initial design and optimisation of wind turbines.This work was funded by an EPSRC doctoral training award (ref. 1089390) and supported by GL Garrad Hassan

Re-framing the threat of global warming: an empirical causal loop diagram of climate change, food insecurity and societal collapse

Funder: The General Sir John Monash FoundationFunder: The Cambridge TrustAbstractThere is increasing concern that climate change poses an existential risk to humanity. Understanding these worst-case scenarios is essential for good risk management. However, our knowledge of the causal pathways through which climate change could cause societal collapse is underdeveloped. This paper aims to identify and structure an empirical evidence base of the climate change, food insecurity and societal collapse pathway. We first review the societal collapse and existential risk literature and define a set of determinants of societal collapse. We develop an original methodology, using these determinants as societal collapse proxies, to identify an empirical evidence base of climate change, food insecurity and societal collapse in contemporary society and then structure it using a novel-format causal loop diagram (CLD) defined at global scale and national granularity. The resulting evidence base varies in temporal and spatial distribution of study and in the type of data-driven methods used. The resulting CLD documents the spread of the evidence base, using line thickness and colour to depict density and type of data-driven method respectively. It enables exploration of how the effects of climate change may undermine agricultural systems and disrupt food supply, which can lead to economic shocks, socio-political instability as well as starvation, migration and conflict. Suggestions are made for future work that could build on this paper to further develop our qualitative understanding of, and quantitative complex systems modelling capabilities for analysing, the causal pathways between climate change and societal collapse.</jats:p

Control data, Sankey diagrams, and exergy: Assessing the resource efficiency of industrial plants

Studies analysing the resource use of industrial production are often performed at highly aggregated levels, e.g. yearly across industry sectors. Conversely, the remit of work performed at the operational level is limited to the management of energy or concerned with aspects such as safety or reliability, both of which fail to consider material efficiency options at that scale. This gap is filled by applying the concept of exergy to the disaggregated time-scales and scopes typical of real-time operations. Our tool measures the resource efficiency of processes and visually traces the use of both energy and materials from available control data. This is exemplified through the case study of a Tata Steel basic oxygen steelmaking plant, where resource flows are visualised using Sankey diagrams. An analysis of the resource efficiency variations across batches and days for a period of 30 days - over 900 batches - show the plant's inefficiencies primarily arise from the converter process, the resource efficiency of which varies from 87.4% to 93.7%. By recovering material and energy by-products, and reducing fuel inputs we estimate that 7% of the total exergy input can be saved or further utilised. About 60% of these improvements arise from energy-related measures. The remaining 40% emanates from reductions in material use, a contribution which would be missed if using conventional energy metrics. This approach makes three contributions. First, it gives industry a single metric of resource efficiency that can jointly measure the system-level performance of material and energy transformations. Second, it provides a new picture of the plant's operational resource use. Third, it allows managers to have more detailed information on resource flows and thus helps place material-efficiency improvements on an equal footing to energy efficiency. This, therefore, provides a clearer picture of where interventions can deliver the greatest efficiency gains.This research is funded by Emerson Electric co. This study was supported by Tata Steel UK

How much cement can we do without? Lessons from cement material flows in the UK

Cement manufacture is responsible for 5-7% of world CO2emissions. Cement is primarily used in concrete, the most used material on the planet and a critical part of any analysis of emissions reduction strategy. To estimate the potential for reducing demand, this work analyses material flow in the cement industry, using the UK in 2014 as a case study. Combining published data, analytic assumptions, and interviews we estimated the material flow of cement from the production to a breakdown of its use in applications. Having broken down the demand for cement into 25 applications, multiple material efficiency techniques were considered: substituting cement for calcined clay and limestone, reducing the cement content of concrete, post-tensioning floor slabs, using more precast building elements, reducing construction waste, and reducing the overdesign in construction. We produce a final estimate of the total reduction in emissions achievable from material efficiency: 51.3%. Due to overlap and interactions between the methods, the attribution of the carbon abatement depends on the sequence of application. In this analysis, we have applied the reduction of overdesign last, because it is independent of the others, and would require a cultural change. We show then that cement demand from floors, repairs and maintenance, concrete beams, and applications within the transport sector should be targeted. The substitution of cement with calcined clay and limestone has the biggest potential to reduce cement demand (27%) and carbon emissions in the UK. Reducing the amount of cement in concrete has the next highest potential (10%), followed by post-tensioning floor slabs (3%).NMZL/112 RG82144 EPSRC ref EP/N02351X/