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.

**SÃ¶ren Wellenberg**RWTH-Aachen University, Germany

Co-authors:

Benedikt Roidl (1)

^{F}

^{P}Wolfgang SchrÃ¶der (1)

(1) RWTH-Aachen University, Aachen, Germany

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## Abstract

**Synthetic turbulence generation method for numerical investigations of turbulent wind fields****Introduction**

The dynamics of power extraction and the structural loads of a wind energy system are defined by the spatial and temporal behavior of a turbulent atmospheric boundary layer. In the development process of wind turbines computational fluid dynamics (CFD) methods and stand-alone turbulence models are applied to predict those dynamic processes. A synthetic turbulence model is presented which includes the significant impact of organized patterns of coherent turbulent structures to further analyze the turbulent mechanisms in atmospheric boundary layers and their impact on the structure and power extraction of future wind turbines.

**Approach**

In the IEC64100-1 specification [1] the turbulent wind field is proposed to be computed by the turbulence models, i.e., synthetic turbulence generation (STG) methods, provided by Mann [2] and Kaimal et al. [3]. Among other authors WÃ¤chter et al. [4] pointed out that the knowledge of the organized patterns of coherent structures in the turbulent flow field is of significant importance to reliably predict the temporal behavior of the power output and structural loads of wind turbines. This is not explicitly included in contemporary simulations of synthetic turbulent wind fields. Furthermore, turbulent flow fields generated with an STG method may in general not represent a physical solution of the instantaneous Navier-Stokes equations [5].

The presented ansatz based on the reformulated synthetic eddy generation (RSTG) method [5] is extended to mimic arbitrary energy spectra, length scales, and structural patterns to meet the requirements of variable wind fields. The application of the method is two folded. First, the synthetic turbulence generation method can be used as an inflow condition for a large-eddy simulation (LES) which provides a very short transition to physical turbulence. Second, the method shall also be used in the future as a stand-alone turbulence model similar to those of [2] and [3].

The coherent structures are generated by superimposing eddy cores which are defined in a volume that has the size of the computational domain. Each eddy core has individual spectral properties that are associated with turbulent length and time scales which depend on the location of the core in the boundary layer. Correlations of the Reynolds-stress tensor are used to scale the velocity fluctuations. The organized patterns of coherent structures are prescribed on the basis of the analysis of pure LES solutions via dynamic-mode decompositions [6]. If the STG method is applied as an LES-inflow approach the eddy cores and the volume of the computational domain are virtually defined and the integrated influence, which results in turbulent velocity fluctuations, is mapped on to the inflow boundary. In the following the method is called RSTGN.

**Main body of abstract**

A self similar zero-pressure gradient boundary layer is used as validation case of the RSTGN method. The Reynolds number based on the momentum thickness is about 7000. Roughness effects, changes in the wind direction, low-level jets, temperature variations, etc., are neglected for the validation case. It goes without saying that these effects, however, are of great importance to reliably predict the turbulent behavior of atmospheric boundary layers [7]. However, this study focuses on the transition from synthetic to physical turbulence starting with a generic flow problem.

The RSTGN method is applied at the inlet of an LES simulation which is called RSTGN-LES in the following. The size of the computational domain is 8 boundary-layer thicknesses in the streamwise, 5 in the wall-normal, and 2 in the spanwise direction. To resolve the turbulent length scales that mainly contribute to the energy spectrum, a grid resolution of less than 20 wall units in the streamwise and less than 12 wall units in the spanwise direction were chosen. The boundary layer contains about 100 grid points resulting in 23 million grid points for the entire computational domain. Similar to the work in [5] the resulting velocity fluctuations of the RSTGN method are superposed on a velocity profile of a pure Reynolds-averaged Navier-Stokes (RANS) simulation which also serves as a reference solution.

An in-house CFD solver, details of which are given in [8], is applied to perform the LES computations and. A sponge layer formulation damps spurious pressure fluctuations, which would deteriorate the resulting flow field in the computational domain. The performance of the RSTGN method is evaluated by the development of the skin-friction coefficient and the vorticity field determined by the Q-criterion.

Figure 1 presents the results of the Q-criterion with mapped-on local velocity for the RSTGN-LES computation. A compact transition from the injected synthetic turbulent to physical turbulent structures within 2 boundary layer thicknesses is observed. If the wrong length scales were chosen or a random pattern were introduced at the inflow boundary, the transition to physical turbulence would develop over about 10 boundary layer thicknesses. Due to the high Reynolds number the coherent structures satisfying the chosen iso-surface value of the Q-criterion are rather small compared to the integral length scale in the spanwise direction. At these conditions and at this wall-normal distance it is approximately 10% of the boundary-layer thickness. Furthermore, organized packages of structures cannot be identified by the Q-criterion.

In fig. 2 the streamwise development of the skin-friction coefficient distribution is presented. The skin-friction distributions of the RSTGN-LES case converge to the pure RANS solution at about two boundary-layer thicknesses downstream of the inlet which corresponds to the findings of fig. 1. Note that the skin-friction value drops slightly downstream of the LES inflow which is due to the transition from synthetic to physical turbulence. To emphasize the importance of the application of organized patterns in the synthetic turbulence formulation the skin-friction distribution of the RSTGN2-LES configuration is also shown in fig. 2. Unlike in the RSTGN-LES formulation random structural patterns instead of physically organized coherent structures are applied in the RSTGN2-LES. It is evident that the corresponding solution does not converge to the pure RANS solution. Note that the streamwise skin-friction distribution conveniently represents the transition process from synthetic to physical turbulence [5].

**Conclusion**

An STG method has been presented which is an extension of the approach of Roidl et al. [5]. Among other features, organized patterns of the coherent turbulent structures have been introduced to generalize the synthetic formulation. These organized patterns were extracted from the analysis of a pure LES solution of self-similar boundary layers via dynamic mode decomposition. Note that the formulation of an STG model has to meet several requirements such as properly prescribed Reynolds stresses or averaged velocity profiles, in order to ensure a rapid transition to physical turbulence. However, the proper physical determination of organized patterns of coherent turbulent structures as well as turbulent length- and time scales is most important to the accuracy of the method.

It was shown that the transition length significantly depends on a proper organization of the coherent turbulent structures. The skin-friction distribution of the solution with the organized pattern converged within 2 boundary-layer thicknesses to the reference solution, whereas the configuration without the organized patterns of turbulent coherent structures did not converge to the pure RANS solution within the length of the computational domain. That is, the presented RSTGN approach leads to a significant reduction of computational resources due to shorter computational domains.

Due to the flexibility of the RSTGN approach it can be applied to generate LES solutions of atmospheric boundary layers with more complex characteristics, i.e., low level jets, variable wind direction and/or wind shear. Furthermore, the RSTGN method shall also be applicable as a prospective stand-alone turbulence model for rapid evaluation of arbitrary wind fields. In future development processes of wind turbines the method can help to reliably predict the dynamics of the velocity field in a turbulent atmospheric boundary layer which in turn does have a major impact on the power extraction and the structural loads. It goes without saying that minimizing these impacts may contribute to a significant increase in plant availability and system efficiency of each wind turbine.

**Learning objectives**

The promising RSTGN approach reduces computational resources in case of pure LES simulation due to rapid transition from synthetic to physical turbulence. The proper description of organized patterns of coherent turbulent structures can improve existing turbulence models to enhance the development process of future wind turbines.

**References**

[1] IEC, International Standard 61400: Wind Turbines, International Standard 61400-12-

1, International Electrotechnical Commission, 2005

[2] J. Mann: Wind field simulation. Prob. Engng. Mech., Vol. 13, No. 4, pp. 269-282, 1998

[3] J.C. Kaimal, J.C. Wyngaard, Y. Izumi, O.R. Cote: Spectral Characteristics of Surface-

Layer Turbulence. Q.J.R. Meteorol. Soc., Vol. 98, pp. 563-598, 1972

[4] M. WÃ¤chter, H. HeiÃŸelmann, M. HÃ¶lling, A. Morales, P. Milan, T. MÃ¼cke, J. Peinke, N.

Reinke, P. Rinn: The turbulent nature of the atmospheric boundary layer and its

impact on the wind energy conversion. J. Turb., Vol 13, pp. 1-13, 2012

[5] B. Roidl, M. Meinke, S. SchrÃ¶der: A reformulated synthetic turbulence generation method for a zonal

RANS-LES method and its application to zero-pressure gradient boundary layers. Int. J. Heat Fluid Flow,

http://dx.doi.org/10.1016/j.ijheatfluidflow.2013.03.017, 2013

[6] Schmid, P. J.: Dynamic mode decomposition of numerical and experimental data. J.

Fluid Mech., Vol. 656, pp. 5-28, 2010

[7] J. Park, S. Basu, L. Manuel: Large-eddy simulation of stable boundary layer turbulence

and estimation of associated wind loads. Wind Energy, DOI:10.1002/we.1580, 2013

[8] M. Meinke, W. SchrÃ¶der, E. Krause, T. Rister: A comparision of second- and sixth-

order methods for large-eddy simulations. Comput. Fluids, Vol. 31, pp. 695-718,2002

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