Wind turbine boundary layer arrays for Cartesian and staggered configurations:Part II, low-dimensional representations via the proper orthogonal decomposition

Wind Energy ◽  
2014 ◽  
Vol 18 (2) ◽  
pp. 297-315 ◽  
Author(s):  
Nicholas Hamilton ◽  
Murat Tutkun ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Low Dimensional ◽  
Proper Orthogonal

Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

2005 ◽  
Vol 127 (4) ◽  
pp. 553-562 ◽  
Author(s):  
Korn Saranyasoontorn ◽  
Lance Manuel
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Low Frequency ◽  
Orthogonal Decomposition ◽  
Response Variance ◽  
Spectral Models ◽  
Inflow Turbulence ◽  
Using Data ◽  
Low Dimensional ◽  
Proper Orthogonal

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition

2017 ◽  
Vol 828 ◽  
pp. 175-195 ◽  
Author(s):  
N. Ali ◽  
G. Cortina ◽  
N. Hamilton ◽  
M. Calaf ◽  
R. B. Cal
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Atmospheric Boundary Layer ◽  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Commercial Application ◽  
Surface Boundary ◽  
Stable Regime ◽  
Proper Orthogonal

A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.

Symmetry Considerations When Using Proper Orthogonal Decomposition for Predicting Wind Turbine Yaw Loads

2006 ◽  
Vol 128 (4) ◽  
pp. 574-579 ◽  
Author(s):  
Korn Saranyasoontorn ◽  
Lance Manuel
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Random Fields ◽  
Orthogonal Decomposition ◽  
Extreme Statistics ◽  
Full Field ◽  
Monotonic Convergence ◽  
Inflow Turbulence ◽  
Low Dimensional ◽  
Proper Orthogonal

In an earlier study, the authors discussed the efficiency of low-dimensional representations of inflow turbulence random fields in predicting statistics of wind turbine loads that included blade and tower bending moments. Both root-mean-square and 10-min extreme statistics for these loads were approximated very well when time-domain simulations were carried out on a 600kW two-bladed turbine and only a limited number of inflow “modes” were employed using proper orthogonal decomposition (POD). Here, turbine yaw loads are considered and the conventional ordering of POD modes is seen to be not as efficient in predicting full-field load statistics for the same turbine. Based on symmetry arguments, reasons for a different treatment of yaw loads are presented and reasons for observed deviation from the expected monotonic convergence to full-field load statistics with increasing POD mode number are illustrated.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

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