scholarly journals Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes

2017 ◽  
Vol 375 (2091) ◽  
pp. 20160108 ◽  
Author(s):  
M. Debnath ◽  
C. Santoni ◽  
S. Leonardi ◽  
G. V. Iungo
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Atmospheric Boundary Layer ◽  
Wind Turbine ◽  
Turbine Blades ◽  
Dynamic Mode ◽  
Decomposition Techniques ◽  
Modal Decomposition ◽  
Tip Vortices ◽  
Reduced Order

The dynamics of the velocity field resulting from the interaction between the atmospheric boundary layer and a wind turbine array can affect significantly the performance of a wind power plant and the durability of wind turbines. In this work, dynamics in wind turbine wakes and instabilities of helicoidal tip vortices are detected and characterized through modal decomposition techniques. The dataset under examination consists of snapshots of the velocity field obtained from large-eddy simulations (LES) of an isolated wind turbine, for which aerodynamic forcing exerted by the turbine blades on the atmospheric boundary layer is mimicked through the actuator line model. Particular attention is paid to the interaction between the downstream evolution of the helicoidal tip vortices and the alternate vortex shedding from the turbine tower. The LES dataset is interrogated through different modal decomposition techniques, such as proper orthogonal decomposition and dynamic mode decomposition. The dominant wake dynamics are selected for the formulation of a reduced order model, which consists in a linear time-marching algorithm where temporal evolution of flow dynamics is obtained from the previous temporal realization multiplied by a time-invariant operator. This article is part of the themed issue ‘Wind energy in complex terrains’.

scholarly journals Data Driven Modal Decomposition of the Wake behind an NREL-5MW Wind Turbine

2021 ◽  
Vol 6 (4) ◽  
pp. 44
Author(s):  
Stefania Cherubini ◽  
Giovanni De Cillis ◽  
Onofrio Semeraro ◽  
Stefano Leonardi ◽  
Pietro De Palma
Keyword(s):  
Flow Field ◽  
Wind Turbine ◽  
Large Scale ◽  
Reduced Order Model ◽  
Dynamic Mode Decomposition ◽  
Speed Ratio ◽  
Dynamic Mode ◽  
Order Model ◽  
Modal Decomposition ◽  
Reduced Order

The wake produced by a utility-scale wind turbine invested by a laminar, uniform inflow is analyzed by means of two different modal decompositions, the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), in its sparsity-promoting variant. The turbine considered is the NREL-5MW at tip-speed ratio λ=7 and a diameter-based Reynolds number of the order 108. The flow is simulated through large eddy simulation, where the forces exerted by the blades are modeled using the actuator line method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by both modal decompositions are compared and some differences emerge that can be of great importance for the formulation of a reduced-order model. In particular, a high-frequency mode directly related to the tip vortices is found using both methods, but it is ranked differently. The other dominant modes are composed by large-scale low-frequency structures, but with different frequency content and spatial structure. The most energetic 200 POD modes account for ≈20% only of the flow kinetic energy. While using the same number of DMD modes, it is possible to reconstruct the flow field to within 80% accuracy. Despite the similarities between the set of modes, the comparison between these modal-decomposition techniques points out that an energy-based criterion such as that used in the POD may not be suitable for formulating a reduced-order model of wind turbine wakes, while the sparsity-promoting DMD appears able to perform well in reconstructing the flow field with only a few modes.

scholarly journals Mutual inductance instability of the tip vortices behind a wind turbine

2014 ◽  
Vol 755 ◽  
pp. 705-731 ◽  
Author(s):  
Sasan Sarmast ◽  
Reza Dadfar ◽  
Robert F. Mikkelsen ◽  
Philipp Schlatter ◽  
Stefan Ivanell ◽  
...  
Keyword(s):  
Growth Rate ◽  
Wind Turbine ◽  
Numerical Study ◽  
Operating Conditions ◽  
Analytical Relationship ◽  
Dynamic Mode ◽  
Spatial Structures ◽  
Tip Vortices ◽  
Positive Growth ◽  
The Stability

AbstractTwo modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier–Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tjæreborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120° symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360° wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\pi /2$ and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

Study of Dynamical Instabilities in Siemens Liquid Spray Injectors Using Complementary Modal Decomposition Techniques

2019 ◽  
Author(s):  
Adesile Ajisafe ◽  
Midhat Talibi ◽  
Andrea Ducci ◽  
Ramanarayanan Balachandran ◽  
Nishant Parsania ◽  
...  
Keyword(s):  
High Speed ◽  
Dynamical Behaviour ◽  
Operating Conditions ◽  
Dynamic Mode Decomposition ◽  
Fuel Spray ◽  
Chamber Pressure ◽  
Dynamic Mode ◽  
Decomposition Techniques ◽  
Planar Imaging ◽  
Modal Decomposition

Abstract Liquid fuel spray characterisation is essential for understanding the mechanisms underlying fuel energy release and pollutant formation. Careful selection of operating conditions can promote flow instabilities in the fuel spray which can enhance atomisation and fuel mixing, thereby resulting in more efficient combustion. However, the inherent instabilities present in the spray could have adverse effect on the combustor dynamics. Hence, it is important to better understand the dynamical behaviour of the spray, and particularly at representative operating conditions. This work describes an experimental investigation of dynamical behaviour of pressure-swirl atomisers used in Siemens industrial gas turbine combustors, at a range of chamber pressures and fuel injection pressures, using high speed laser planar imaging. Two modal decomposition techniques — Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) — are applied and compared to assess the spray dynamics. Results indicate that both POD and DMD are able to capture periodic structures occurring in the spray at different spatial length scales. The characteristic frequencies estimated from both the methods are in good agreement with each other. Both techniques are able to identify coherent structures with variable size, shape and level of staggering, which are observed to be dependent on the pressure difference across the atomiser and the chamber pressure. The spatio-temporally resolved data and the results could be used for spray model development and validation. Furthermore, the methods employed could be applied to other fuel atomisers, and more complicated conditions involving cross flow and higher chamber temperatures.

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