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  1. Article ; Online: The background method: theory and computations.

    Fantuzzi, Giovanni / Arslan, Ali / Wynn, Andrew

    Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

    2022  Volume 380, Issue 2225, Page(s) 20210038

    Abstract: The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background ... ...

    Abstract The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background method can be formulated systematically within a broader 'auxiliary function' framework for bounding mean quantities, and explain how symmetries of the flow and constraints such as maximum principles can be exploited. All ideas are presented in a general setting and are illustrated on Rayleigh-Bénard convection between stress-free isothermal plates. Second, we review a semidefinite programming approach and a timestepping approach to optimizing bounds computationally, revealing that they are related to each other through convex duality and low-rank matrix factorization. Open questions and promising directions for further numerical analysis of the background method are also outlined. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
    Language English
    Publishing date 2022-04-25
    Publishing country England
    Document type Journal Article ; Review
    ZDB-ID 208381-4
    ISSN 1471-2962 ; 0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
    ISSN (online) 1471-2962
    ISSN 0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
    DOI 10.1098/rsta.2021.0038
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Book ; Online: Sensitivity analysis of wake steering optimisation for wind farm power maximisation

    Gori, Filippo / Laizet, Sylvain / Wynn, Andrew

    eISSN: 2366-7451

    2023  

    Abstract: Modern large–scale wind farms consist of multiple turbines clustered together, usually in well–structured formations. Clustering has a number of drawbacks during a wind farm’s operation, as some of the downstream turbines will inevitably operate in the ... ...

    Abstract Modern large–scale wind farms consist of multiple turbines clustered together, usually in well–structured formations. Clustering has a number of drawbacks during a wind farm’s operation, as some of the downstream turbines will inevitably operate in the wake of those upstream, with a significant reduction in power output and an increase in fatigue loads. Wake steering, a control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, is a promising strategy to mitigate power losses. The purpose of this work is to investigate the sensitivity of open-loop wake steering optimisation in which an internal predictive wake model is used to determine the farm power output as a function of the turbine yaw angles. Three different layouts are investigated with increasing levels of complexity. A simple 2×1 farm layout in aligned conditions is first considered, allowing for a careful investigation of sensitivity to wake models and operational set-points. A medium-complexity case of a generic 5×5 farm layout in aligned conditions is examined, to enable the study of a more complex design space. The final layout investigated is the Horns Rev wind farm (80 turbines), for which there has been very little study of the performance or sensitivity of wake steering optimisation. Overall, the results indicate a strong sensitivity of wake steering strategies to both analytical wake model choice, and to the particular implementation of algorithms used for optimisation. Significant variability can be observed in both farm power improvement and optimal yaw settings, depending on the optimisation set-up. Through a statistical analysis of the impact of optimiser initialisation and a study of the multi-modal and discontinuous nature of the underlying farm power objective functions, this study shows that the uncovered sensitivities represent a fundamental challenge to robustly identifying globally optimal solutions for the high-dimensional optimisation problems arising from ...
    Subject code 621
    Language English
    Publishing date 2023-03-15
    Publishing country de
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Sensitivity analysis of wake steering optimisation for wind farm power maximisation

    Gori, Filippo / Laizet, Sylvain / Wynn, Andrew

    eISSN: 2366-7451

    2023  

    Abstract: Modern large-scale wind farms consist of multiple turbines clustered together, usually in well-structured formations. Clustering has a number of drawbacks during a wind farm's operation, as some of the downstream turbines will inevitably operate in the ... ...

    Abstract Modern large-scale wind farms consist of multiple turbines clustered together, usually in well-structured formations. Clustering has a number of drawbacks during a wind farm's operation, as some of the downstream turbines will inevitably operate in the wake of those upstream, with a significant reduction in power output and an increase in fatigue loads. Wake steering, a control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, is a promising strategy to mitigate power losses. The purpose of this work is to investigate the sensitivity of open-loop wake steering optimisation in which an internal predictive wake model is used to determine the farm power output as a function of the turbine yaw angles. Three different layouts are investigated with increasing levels of complexity. A simple 2×1 farm layout under aligned conditions is first considered, allowing for a careful investigation of the sensitivity to wake models and operating conditions. A medium-complexity case of a generic 5×5 farm layout under aligned conditions is examined to enable the study of a more complex design space. The final layout investigated is the Horns Rev wind farm (80 turbines), for which there have been very few studies of the performance or sensitivity of wake steering optimisation. Overall, the results indicate a strong sensitivity of wake steering strategies to both the analytical wake model choice and the particular implementation of algorithms used for optimisation. Significant variability can be observed in both farm power improvement and optimal yaw settings, depending on the optimisation setup. Through a statistical analysis of the impact of optimiser initialisation and a study of the multi-modal and discontinuous nature of the underlying farm power objective functions, this study shows that the uncovered sensitivities represent a fundamental challenge to robustly identifying globally optimal solutions for the high-dimensional optimisation problems arising ...
    Subject code 621
    Language English
    Publishing date 2023-09-15
    Publishing country de
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Data-driven optimisation of wind farm layout and wake steering with large-eddy simulations

    Bempedelis, Nikolaos / Gori, Filippo / Wynn, Andrew / Laizet, Sylvain / Magri, Luca

    eISSN: 2366-7451

    2023  

    Abstract: Maximising the power production of large wind farms is key to the transition towards net zero. The overarching goal of this paper is to propose a computational method to maximise the power production of wind farms with two practical design strategies. ... ...

    Abstract Maximising the power production of large wind farms is key to the transition towards net zero. The overarching goal of this paper is to propose a computational method to maximise the power production of wind farms with two practical design strategies. First, we propose a gradient-free method to optimise the wind farm power production with high-fidelity surrogate models based on large-eddy simulations and a Bayesian framework. Second, we apply the proposed method to maximise wind farm power production by both micro-siting (layout optimisation) and wake steering (yaw angle optimisation). Third, we compare the optimisation results with the optimisation achieved with low-fidelity wake models. Finally, we propose a simple multi-fidelity strategy by combining the inexpensive wake models with the high-fidelity framework. The proposed gradient-free method can effectively maximise wind farm power production. Performance improvements relative to wake-model optimisation strategies can be attained, particularly in scenarios of increased flow complexity, such as in the wake steering problem, in which some of the assumptions in the simplified flow models become less accurate. The optimisation with high-fidelity methods takes into account nonlinear and unsteady fluid mechanical phenomena, which are leveraged by the proposed framework to increase the farm output. This paper opens up opportunities for wind farm optimisation with high-fidelity methods and without adjoint solvers.
    Subject code 621
    Language English
    Publishing date 2023-09-05
    Publishing country de
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

  5. Book ; Online: Bounds for internally heated convection with fixed boundary heat flux

    Arslan, Ali / Fantuzzi, Giovanni / Craske, John / Wynn, Andrew

    2021  

    Abstract: We prove a new rigorous bound for the mean convective heat transport $\langle w T \rangle$, where $w$ and $T$ are the nondimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper ... ...

    Abstract We prove a new rigorous bound for the mean convective heat transport $\langle w T \rangle$, where $w$ and $T$ are the nondimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper boundary with a fixed heat flux. The quantity $\langle wT \rangle$ is equal to half the ratio of convective to conductive vertical heat transport, and also to $\frac12$ plus the mean temperature difference between the top and bottom boundaries. An analytical application of the background method based on the construction of a quadratic auxiliary function yields $\langle w T \rangle \leq \tfrac{1}{2}\big(\tfrac{1}{2}+ \tfrac{1}{\sqrt{3}} \big) - 1.6552\, R^{-\frac13}$ uniformly in the Prandtl number, where $R$ is the nondimensional control parameter measuring the strength of the internal heating. Numerical optimisation of the auxiliary function suggests that the asymptotic value of this bound and the $-1/3$ exponent are optimal within our bounding framework. This new result halves the best existing (uniform in $R$) bound (Goluskin 2016, Springer, Table 1.2) and its dependence on $R$ is consistent with previous conjectures and heuristic scaling arguments. Contrary to physical intuition, however, it does not rule out a mean heat transport larger than $\frac12$ at high $R$, which corresponds to the top boundary being hotter than the bottom one on average.

    Comment: 11 pages, 3 figures
    Keywords Physics - Fluid Dynamics
    Subject code 532 ; 551
    Publishing date 2021-03-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book ; Online: Optimisation of Region of Attraction Estimates for the Exponential Stabilisation of the Intrinsic Geometrically Exact Beam Model

    Artola, Marc / Rodriguez, Charlotte / Wynn, Andrew / Palacios, Rafael / Leugering, Günter

    2021  

    Abstract: A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results based on ... ...

    Abstract A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results based on Lyapunov arguments, the main contribution of the presented work is to maximise the analytically found bounds on the initial datum, for which local exponential stability is guaranteed, via search of (optimal) polynomial Lyapunov functionals using an iterative semi-definite programming approach.

    Comment: Accepted in: IEEE Conference on Decision and Control 2021
    Keywords Mathematics - Optimization and Control ; Electrical Engineering and Systems Science - Systems and Control
    Publishing date 2021-10-12
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Book ; Online: Investigating Bayesian optimization for expensive-to-evaluate black box functions

    Diessner, Mike / O'Connor, Joseph / Wynn, Andrew / Laizet, Sylvain / Guan, Yu / Wilson, Kevin / Whalley, Richard D.

    Application in fluid dynamics

    2022  

    Abstract: Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters ... ...

    Abstract Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g. in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of Bayesian optimization to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.
    Keywords Computer Science - Machine Learning
    Subject code 006
    Publishing date 2022-07-19
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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