Surrogate-based optimization of tidal turbine arrays: a case study for the Faro-Olhão inlet

This paper presents a study for estimating the size of a tidal turbine array for the Faro-Olhão Inlet (Potugal) using a surrogate optimization approach. The method compromises problem formulation, hydro-morphodynamic modelling, surrogate construction and validation, and constraint optimization. A total of 26 surrogates were built using linear RBFs as a function of two design variables: number of rows in the array and Tidal Energy Converters (TECs) per row. Surrogates describe array performance and environmental effects associated with hydrodynamic and morphological aspects of the multi inlet lagoon. After validation, surrogate models were used to formulate a constraint optimization model. Results evidence that the largest array size that satisfies performance and environmental constraints is made of 3 rows and 10 TECs per row.Eduardo González-Gorbeña has received funding for the OpTiCA project (http://msca-optica.eu/) from the Marie Skłodowska-Curie Actions of the European Union's H2020-MSCA-IF-EF-RI-2016 / GA#: 748747. The paper is a contribution to the SCORE pro-ject, funded by the Portuguese Foundation for Science and Technology (FCT–PTDC/AAG-TEC/1710/2014). André Pacheco was supported by the Portuguese Foun-dation for Science and Technology under the Portuguese Researchers’ Programme 2014 entitled “Exploring new concepts for extracting energy from tides” (IF/00286/2014/CP1234).info:eu-repo/semantics/publishedVersio

Adjoint-based optimization methods for flow problems

Over the last decade, adjoint sensitivity analysis has become an established technique for the task of shape optimisation when many degrees of freedom are present. The success stems from the fact that the adjoint approach only needs one flow simulation for both the primal and the adjoint system, no matter how many design parameters are present. The derivation of the continuous adjoint approach is based on an augmented cost function which inheres the primal governing equations (here the RANS-equations) as constraints which have to be satisfied in the computational domain. Accordingly, the primal RANS equations are augmented with Lagrange multipliers and added to the thermal-fluid dynamic cost function. For shape optimisation, the variational formulation of the augmented cost function indicates the behaviour of the cost function with the variation of the shape, i.e. the variation of the surface mesh in normal direction. We present the derivation and application of the continuous adjoint approach for the incom- pressible Reynolds-averaged Navier-Stokes (RANS) equations augmented with heat transfer. The derived approach is implemented into the framework of the C++ CFD toolbox OpenFOAM in order to derive a complete design cycle for shape optimisation. The derived optimisation process is applied to dimpled surface geometries in order to optimise cooling devices

Aplikasi Algoritma Simulated Annealing untuk Menentukan Formasi Tata Letak Turbin pada Marine Current Turbine Farm di Selat Riau

Artikel ini mempresentasikan permasalahan penentuan tata letak turbin pada sebuah Marine Current Turbine Farm (MCTF) dengan pendekatan model matematis. Fungsi tujuannya adalah minimisi biaya per produksi energi yang dihasilkan pada MCTF. Model matematis yang digunakan mempertimbangkan interaksi yang terjadi antar turbin yang dipengaruhi oleh wake effects, dimana wake effect menyebabkan penurunan kecepatan arus yang melewati turbin yang diletakkan di hilir. Algoritma Simulated Annealing diaplikasikan untuk menyelesaikan permasalahan tersebut. Hasil studi kasus di Selat Riau menunjukkan bahwa algoritma Simulated Annealing memiliki performa yang lebih baik dibandingkan algoritma Tabu Search. Hal ini ditandai dengan formasi tata letak yang dihasilkan algoritma Simulated Annealing memiliki biaya per produksi energi yang lebih rendah dibandingkan algoritma Tabu Search.&nbsp

Discrete adjoint-based simultaneous analysis and design approach for conceptual aerodynamic optimization

In this paper, a simultaneous analysis and design method is derived and applied for a non-linear constrained aerodynamic optimization problem. The method is based on the approach of defining a Lagrange functional based on the objective function and the aerodynamic model’s equations, using two sets of multipliers. A fully-coupled, non-linear system of equations is derived by requiring that the Gateaux variation of the Lagrange functional vanishes for arbitrary variations of the aerodynamic model’s dependent variables and design parameters. The optimization problem is approached using a one-shot technique, by solving the non-linear system in which all sensitivities and problem constraints are included. The computational efficiency of the method is compared against a gradient-based optimization algorithm using adjoint-provided gradient. A conceptual-stage aerodynamic optimization problem is solved, based on a non-linear numerical lifting-line method with viscous corrections

비정상유동이 조류발전단지 배치최적화에 미치는 영향

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 황진환.Due to the global climate crisis and the air pollution, demand on the renewable energy is consequently increasing as one of the main efforts. Wind and solar energy are taking the lead on the renewable energy industry, and as of the next competitive resource, tidal power is estimated to have a huge potential, thanks to its high energy density and easily predictable characteristics. Tidal power has not reached the practical level yet, due to financial challenges. In terms of reducing the cost and reach the competitive level of LCOE, the power extraction should be maximized within the constraints by conducting layout optimization of the turbines deployed, hence, understanding, and predicting the algorithm for layout optimization is necessary. The layout optimization for the tidal turbine is somewhat sophisticated, due to the unsteady tidal current condition in the nature, hence previous studies have found the problem under the steady condition. However, since the unsteadiness is a critical feature of the tidal current, there needs a study on the distinctive optimization characteristics under the unsteady condition. This study aims to find the tidal turbine farm layout optimization problem under the simplified unsteady tidal current condition in the nature and identify if the tidal turbine farm layout optimization procedure under unsteady condition can converges to find the global optimum. A number of numerical experiments were handled during the study to find the general trend/pattern of convergence to the global optimum under the various unsteady condition, with variation in the amplitude and the direction. The study first demonstrated the difference in the wake profile and the energy production of a single turbine under steady & unsteady flow, to be used as the basic assumption when figuring out the characteristics of layout optimization procedure under unsteady condition. The study also demonstrated the insight of the optimized layout and the minimum velocity threshold that enables the optimization to converge to the globally optimized layout at a given tolerance under steady condition. Finally, generalization of the strategy for the tidal turbine farm layout optimization under the unsteady flow was presented by finding the difference in the optimization procedure between steady & unsteady flow. It has been discovered that optimal layout under unidirectional, unsteady flow condition is similar to the optimal layout under steady condition when it satisfies the minimum velocity threshold condition. However, optimal layout under bidirectional conditions was totally different to the optimal layout under unidirectional conditions, to consider the wake effect from both directions. Under the bidirectional flow condition, the turbines were found to be staggered with respect to each other in order to take advantage of local speedups between upwind turbines. The numerical experiments were performed with OpenTidalFarm, an open-source solver for specific PDE-constrained, gradient-based optimization problems, especially those related to tidal farm design. The simulation domain was described as a rectangular farm, PDE is given as two-dimensional nonlinear shallow water equations, total power output is the target functional to be maximized, and turbine was parameterized as a bump function. Adjoint method was used as to compute the gradient for the optimization problem.세계적인 기후 위기와 대기 오염으로 인해, 재생 에너지에 대한 수요가 증가하고 있다. 풍력과 태양광 발전이 신재생에너지 산업을 선도하고 있으며, 조류 발전은 높은 에너지 밀도와 예측 가능한 특성으로 인해 앞으로의 잠재력이 클 것으로 추정된다. 조류 발전은 아직 가격 경쟁의 측면에서 실용화 수준에 이르지 못했다. 가격 경쟁력을 확보하기 위한 비용절감의 수단으로는 전력 추출 극대화를 위한 노력이 필요하며, 이에 제약 조건 내에서의 터빈 배치 최적화를 위한 알고리즘에 대한 이해가 선행되어야 한다. 조류발전 단지 배치 최적화에 대한 연구는 기존에 다수 진행되어 왔으나, 비정상 유동에서의 최적화 해를 도출하는 것이 다소 복잡해 정상유동 상태의 가정이 주를 이루었다. 그러나, 조류는 달과 태양의 기조력에 의한 조류에 의해 발생하는 현상임에 따라, 비정상 유동이라는 특성이 크게 작용하는 바, 본 연구에서는 이러한 특성을 반영한 배치 최적화 연구가 진행되었다. 따라서 본 연구는 비정상 유동 하에서의 조류발전단지 배치 최적화에 관한 이해를 기반으로 이 때의 민감도 기반 최적화의 해가 전역 최적해에 수렴하는가를 수치실험을 통해 확인하는 것을 목적으로 하였다. 다양한 진폭과 방향 등의 조건에서 수백개의 수치실험이 이루어졌으며 이를 통해 비정상 유동 하에서의 조류발전단지 배치 최적화에 대한 일반적인 추세와 최적해를 확인하였다. 먼저, 정상 유동과 비정상 유동 각각에 단일 터빈을 두어 각 조건 하에서의 후류 형태와 에너지 생산량 차이를 확인하였다. 또한 정상 유동 하에서의 최적 배치 형태와 최적해에 도달할 수 있는 임계 속도 값을 도출하여 비정상 유동 하에서의 수치실험에 선행 가정으로 사용될 수 있도록 하였다. 이러한 실험 결과들을 바탕으로 비정상 유동 하에서의 조류발전단지 배치 최적화에 대한 일반적인 추세와 최적해를 확인할 수 있었다. 비정상 단방향 유동의 경우에는 임계 속도 조건을 만족하였을 때 정상 유동 하에서의 최적 배치와 비슷한 형태를 보였지만, 비정상 양방향 유동의 경우에는 터빈이 교차 배치된 형태를 최적 배치로 갖는 것을 알 수 있었다. 수치실험에는 파이썬 기반 오픈소스 소프트웨어인 OpenTidal Farm이 사용되었다. 수치실험은 직사각형 조류발전 단지 내에서 이루어졌으며, 편미분 방정식은 2차원 천수방정식을 사용했고, 목적함수는 총에너지 추출량으로 구성되었다. 또한, 터빈은 민감도 기반 최적화에 적합하게끔 범프함수로 매개변수화 되어 실험에 사용되었다.ABSTRACT i TABLE OF CONTENTS iv List of Figures vii List of Symbol xi CHAPTER 1. INTRODUCTION 1 1.1 General introduction 1 1.2 Objective 2 CHAPTER 2. THEORETICAL BACKGROUDS 7 2.1 General evolution of the renewable energy 7 2.2 Tidal turbine farm 10 2.2.1 The physics of tide 10 2.2.2 The physics of tidal currents - unsteadiness 13 2.2.3 Tidal turbine 15 2.2.4 Tidal energy resources in Korea 17 2.3 Shallow water equation (SWE) 19 2.4 Gradient-based optimization using adjoint method 21 2.4.1 Problem formulation 22 2.4.2 The adjoint method 22 CHAPTER 3. METHODOLOGY 25 3.1 Numerical model description 25 3.1.1 The design parameters 25 3.1.2 The PDE constraints 25 3.1.3 The turbine parameterization 26 3.1.4 The functional of interest 27 3.1.5 Box and inequality constraints 27 3.1.6 Optimization algorithm 28 3.2 Experiment overview 29 3.2.1 Experiment procedure 29 3.2.2 Experimental flow chart 31 3.3 Simulation set-up 31 3.3.1 Mesh domain 31 3.3.2 Boundary condition 33 3.3.3 Parameter settings 36 CHAPTER 4. Test cases, Results and Discussions 39 4.1 Pilot Test 1: Steady & Unsteady flow impact on a single turbine 39 4.1.1 Wake behavior 39 4.1.2 comparison criterion between steady and unsteady flow based on the energy production 46 4.1.3 Conclusion of Pilot test 1 48 4.2 Pilot Test 2: Minimum velocity threshold (MVT) to converge to QGO and the concept of the optimized layout 49 4.2.1 Test cases 49 4.2.2 Finding minimum threshold of velocity (MVT) 51 4.2.3 Insights on the optimized layout 55 4.2.4 Conclusion of Pilot test 2 57 4.3 Main test: Effect of unsteadiness in the optimization procedure compared to the steady condition 59 4.3.1 Test cases 59 4.3.2 Optimal layout for each flow conditions 62 4.3.3 Strategy to obtain QGO for bidirectional flow condition 70 4.3.4 Conclusion of Main test 71 CHAPTER 5. Conclusions 73 REFERENCES 76 국문초록 80석