Abstract
The computational cost of the design optimisation of wind turbines, as well as the optimisation of the operation and maintenance of offshore wind farms represents a limitation to the application of conventional simulation methods. New techniques such as reduced order modelling (ROM) and technologies such as hybrid-analysis methods and digital twins have increased in popularity due to their ability to deliver numerical results at a significant speed-up with reasonable accuracy. This work presents a hybrid projection-based proper orthogonal decomposition (POD) strategy applied to transient turbulent flow problems. Key feature of this work is the applicability of the methodology to high Reynolds number cases and the stabilisation of pressure in the online phase via the assembly of the so-called pressure Poisson equation. Another significant part of this work is the implementation of an interpolation scheme for the eddy viscosity field in the classical POD-Galerkin strategy. The sampling procedure and the calculation of the reduced operators in the offline phase is carried out using the finite volume method (FVM), OpenFOAM’s libraries specifically, while the construction of the reduced basis and the solution of the online phase is carried out in Python. The capability of the resulting ROM is tested using the two-dimensional flow around a NACA0015 airfoil at 17° angle of attack with Reynolds number of approximately 300 000.
Highlights
The complexity of offshore wind aerodynamics, with varying external flow fields, platform movement effects and upstream wakes requires the study of a large number of cases, making the use of conventional methods prohibitive
The sampling procedure and the calculation of the reduced operators in the offline phase is carried out using the finite volume method (FVM), OpenFOAM’s libraries while the construction of the reduced basis and the solution of the online phase is carried out in Python
The option that is presented in this work is the use of a data-driven reduced order modelling (ROM), in this case proper orthogonal decomposition (POD)-I, for the eddy viscosity as proposed in [8], giving rise to a combined projection and data-driven POD, a hybrid, which allows for application to turbulent problems, while being independent of the turbulence model used in the offline stage
Summary
The complexity of offshore wind aerodynamics, with varying external flow fields, platform movement effects and upstream wakes requires the study of a large number of cases, making the use of conventional (high-fidelity) methods prohibitive. The work in [7] offers an excellent introduction and contains a useful comparison of such strategies applied in POD-Galerkin ROMs. the option that is presented in this work is the use of a data-driven ROM, in this case POD-I, for the eddy viscosity as proposed in [8], giving rise to a combined projection and data-driven POD, a hybrid, which allows for application to turbulent problems, while being independent of the turbulence model used in the offline stage. In order to expand this work to turbulent flows, we use the FVM framework for both ROM phases. In this work, striving for consistency with the Full-Order Model (FOM), we adapt the pressure Poisson equation to include turbulent effects. In accordance with the fact that the proposed methodology is independent of the closure model, no turbulence model is specified in (1)
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