Mutual inductance instability of the tip vortices behind a wind turbine

Two 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 Tj ae reborg 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 degrees symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360 degrees 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 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

Unsteady Two-Dimensional Orifice Flow: A Large-Size Experimental Investigation

Orifice flows were used as water clocks since the Antiquity up to the 16-th century. Today orifices and nozzles are used for measuring discharges. Most works were conducted with steady flow conditions and there is little information on the unsteady flow pattern. In this study, the writers describe an experimental investigation of an unsteady orifice flow discharging vertically. The study was conducted in a large-size facility with a rectangular orifice (0.75-m by 0.07-m) discharging up to 1.2 m3 in about 10 seconds. The study presents new information on the unsteady flow patterns, the discharge capacity and the velocity field in the reservoir. The results are compared with 'classical' orifice flow results

A Fast Panel Code for Complex Actuator Disk Flows

A fast, linear scaling vortex method is presented to study inviscid incompressible flow problems involving one or more actuator disks. Building upon previous efforts that were limited to axi-symmetric flow cases, the proposed methodology is able to handle arbitrary configurations with no symmetry constraints. Applications include the conceptual study of wake interaction mechanisms in wind farms, and the correction of wind tunnel blockage effects in test sections of arbitrary shape. Actuator disks represent wind turbines through the shedding of a deformable vortex wake, discretized with a plaid of triangular distributed dipole singularities. An iterative method is adopted to align the wake with the local flow field, which is reconstructed from the vorticity field with a Green function approach. Interactions are computed with a Fast Multipole Method (FMM), effectively overcoming the quadratic scaling of computational time associated with traditional panel methods. When compared to direct computation, the use of an FMM algorithm reduced solution time by a factor 30 when studying the wake of a single actuator disk with 60000 panels. In the same case, the mass flux of the actuator streamtube was conserved to 0:002%. Finally, the presence of round and square impermeable walls around the actuator is considered to demonstrate the code applicability to wind tunnel wall interference correction problems

Reduced-order model predictions of wind turbines via mode decomposition and sparse sampling

Wind turbine wakes are dominated by several energetic turbulent coherent structures that oscillate at specific Strouhal numbers. Implications on wind power harvesting of these dynamics, induced features require accurate unsteady modeling. Dynamic mode decomposition (DMD), a data-driven modal analysis, has demonstrated the ability to identify flow features based on specific frequencies. In this work, the selection of modes and data-driven DMD models pertaining to wakes with constant Strouhal number coherent structures are investigated using physically-informed criteria and sparse sampling. Both criteria are applied to data derived from the large-eddy simulation of a wind turbine wake. Modes related to tip vortices and hub vortex system are identified. Sparse identification shows remarkable ability to select the optimal modes for reduced-order modeling. Error becomes nearly independent of the number of modes when using fewer than 10% of the modes