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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'How does the wind blow behind wind turbines and in wind farms?' taking place on Tuesday, 11 March 2014 at 16:30-18:00. The meet-the-authors will take place in the poster area.

Yngve Heggelund Christian Michelsen Research, Norway
Co-authors:
Yngve Heggelund (1) F P Chad Jarvis (1) Marwan Khalil (2) Chad Jarvis (1)
(1) Christian Michelsen Research, Bergen, Norway (2) GexCon AS, Bergen, Norway

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Abstract

Model reduction based on CFD for fast and accurate computation of wind farm flow fields

Introduction

Wake losses limit the power production of wind farms. The annual wind farm wake losses depend on positioning of turbines in relation to each other, i.e. the wind farm layout. Therefore, there is a need for methods assisting in finding improved wind farm layouts with respect to wake losses. To assess the performance of a layout, these methods must compute the flow field and the wake losses for a range of wind speeds and wind directions.

Approach

The idea in model reduction is to formulate the governing equations in a reduced finite dimensional solution space spanned by a set of orthogonal basis modes.
Model reduction approximates solutions of the governing equations quickly for variations of a specific problem, and has successfully been applied to Computational Fluid Dynamics (CFD) models within other areas of application. This work is an adaptation of the technique for wind farm flow fields.

The reduced space is constructed by the method of snapshots combined with Proper Orthogonal Decomposition (POD). The snapshots are produced by running Reynolds Averaged Navier-Stokes (RANS) CFD simulations for different setups with respect to wind conditions and turbine arrangements.

The method uses a tiling approach where a tile represents a subdomain of the wind farm. Two tile types are used with separate reduced solution spaces for each tile type. One tile type contains a single turbine and the other tile type is without turbines. This approach enables the user to interactively move turbines into new configurations.

By limiting the solutions to linear combinations of the modes in the reduced space, the solution time can be reduced from the order of hours for a CFD simulation using RANS models to the order of seconds. The approach includes the nonlinear terms of the governing equations. The accuracy of the model reduction results depend on the size and the representativeness of the reduced space and the construction of the reduced space is therefore a critical step in model reduction which will be explored in this paper.


Main body of abstract

A theoretical framework for model reduction of the steady state RANS equations for solving wind farm flow problems is presented. The method is developed for an interactive wind farm layout design tool considering offshore or flat terrain conditions. Test cases are used for demonstration, and the results are verified with corresponding flow field solutions from a CFD simulator. The CFD simulator used here is CMR-Wind which is based on the commercial CFD code FLACS. CMR-Wind is a research version of FLACS which is dedicated to wind farm modeling (Khalil et al. 2013).

We have previously presented results from setups of three and six turbines where downstream turbines can be moved in the crosswind direction (Heggelund et al., 2012). The results were verified by comparison to CFD and showed that the flow fields and power production in the six-turbine wind farm was approximated quite well using a basis constructed from the case of three-turbine wind farm. This highlights the ability of the model reduction technique to compute cases with more complex arrangements of turbines from a basis built from cases of lower complexity. We have also showed that a setup of 21 turbines is computed in less than a second.

In this work we study the multiple wake effect. When the wind blows so that multiple turbines are downstream of each other, the production in the downstream turbines will be significantly reduced. How much the production will drop is a difficult modeling problem. We investigate which and how many CFD simulations will have to be performed to create a reduced space which can be used to reproduce verification cases with acceptable accuracy.

The CFD simulations in this work consist of a set of ten regularly-spaced turbines aligned with a neutrally-stratified ambient flow over a surface with roughness length of 3 cm. The turbines applied in the simulations are of type BONUS 2MW with hub height 64 m and rotor diameter 76 m. The hub height wind speed is 7 m s-1. A sketch of the setup is shown in figure 1.


In the first test, we study the ability of the model reduction to reproduce a case of ten turbines with uniform inter-turbine separation distance of 5 rotor diameters. The reduced space is built from CFD simulations with less than ten turbines. The result is shown in figure 2 where it can be seen that the production is reproduced well from a space constructed from a simulation with only three turbines.


In the second test, we study the performance of the basis when uniformly varying the inter-turbine distances. The basis is built using an equal number of snapshots from simulations with turbine distances of 5 and 9 rotor diameters respectively. We study how well this basis can reproduce the flow for cases where the distances are 5, 6, 7, 8, and 9 rotor diameters. The production results of the reduced model for the case with a turbine distance of 7 rotor diameters is shown in figure 3.


In the third test, we introduce empty tiles (tiles without turbines) and explore the behavior of the results when empty tiles are inserted into the turbine row, as illustrated in figure 4.


Conclusion

The method has been verified with CFD solutions and shows the ability to produce multiple wake effect with accuracy comparable to CFD for the analysis of wind farm energy yield in a matter of seconds. In previous presentations we have showed verification with CFD of setups of three and six turbines, and in this work the multiple wake effect has been studied in setups of turbines aligned with the ambient flow. The method is physical in the sense that it solves the non-linear flow equations in a reduced space.

In addition to computing the velocity fields, the technique is also able to compute the fields for turbulent kinetic energy and turbulent viscosity. These fields can be used to estimate the wake induced fatigue loads on turbines which are important to assess operation costs. The load calculation can be realized through coupling our results to an application which computes fatigue loads. A combined prediction of power and fatigue load will enable a more holistic approach to layout assessment. The technique can also be a component in a broader framework of methods and tools for improving the design and operation of wind farms.

The further work includes testing the technique on more general arrangements of turbines in larger wind farms with realistic wind data. In parallel the CFD simulator will undergo further validation, and potential improvements to the CFD modeling will be implemented and tested. Since the model reduction builds on the results of the CFD simulator, improvements to the CFD simulator can easily be transferred to the model reduction technique.



Learning objectives
In this presentation, delegates will learn about:
1. A novel method for simulation of wind fields based on model reduction.
2. Verification methodology of reduced order modeling applied to wind farm flow fields.



References
Heggelund Y., Skaar I.-M., and Jarvis C. Interactive design of wind farm layout using CFD and model reduction of the steady state RANS equations, 11th World Wind Energy Conference, Bonn, Germany. 3-5 July (2012).

Khalil M. and Sælen, L. 2013 . Near and far wake validation study for two turbines in line using two sub-grid turbine models. EWEA conference, Vienna, Austria, 4-7 February 2013.