Free Vortex Wake Method
A free vortex wake method is available in Bladed to compute the aerodynamic loading on the turbine rotor. The loading is computed by discretising the blades into multiple aerodynamic blade sections similar to the blade element momentum (BEM) method. Instead of using momentum theory to compute the flow induction at the blade, during operation, the rotor wake is explicitly resolved using vortex sheets that trial from each blade as shown in Figure 1.
The theoretical background and calculation procedure of the free wake method is summarised in a series of articles. The basic lifting line theory is explained to give the reader knowledge of the fundamental equations used during the calculation and principles that form the basis of the method. The vortex wake is constructed from shed and trailing elements and the initial vortex strength of newly added elements must be set. The evolution of the vortex wake geometry and its convection downstream are determined by a time-marching algorithm in Bladed according to a user specified time step size.
The advantages of the vortex wake method are that it does not require engineering correction models unlike the BEM method. Instead the vortex wake method resolves the induction calculation directly and is a more theoretically accurate method. The vortex wake method also overcomes some of the limitations of the BEM method such as in cases of highly yawed flow.
Verification and Analysis of Vortex Wake Calculation
The results of the free vortex method in Bladed have been compared to other calculation methods implemented in a range of other software packages including: blade element momentum, vortex wake and computational fluid dynamic methods. Comparisons have also been made to measurement data. Notable studies that demonstrate the vortex wake method giving good results when compare to other calculation methods and also measurement data are (Bangga, 2023), (Boorsma, 2020), and (Boorsma, 2024).
In addition, further studies have been completed using a series of Bladed demonstration models. Figure 2 demonstrates the fatigue load reduction observed when using the vortex wake method compared to the BEM method for two large wind turbine models. The first set of results is for the bottom fixed IEA 22 MW reference wind turbine (RWT). The 10 minutes simulations are based on a subset of DLC 1.2 simulations analysed at a single mean wind speed of 9 m/s with 10 different wind seeds. The maximum fatigue load reduction observed, as a consequence of using the vortex wake method, is 9.19 %. The second fatigue load comparison is completed using a full range of DLC 1.2 simulations for the floating IEA 15 MW RWT covering all operational wind speeds and 6 wind seeds each. The simulation duration is set to one hour and includes wave as well as turbulent wind. The maximum fatigue load reduction, as a consequence of using the vortex wake method, is 14.1 %.
Controlling the Convergence and Accuracy of the Vortex Wake
The resolution of the vortex wake is important for an accurate and converged solution to the rotor aerodynamic loads. A number of wake steps is required for a converged solution to be reached as all elements in the vortex wake contribute to the induced velocity at the rotor plane. However, a highly resolved vortex wake will be detrimental to simulation performance as a greater number of vortex elements and wake nodes results in greater computational demand. There are a few options to improve the speed of the calculation by maximising the use of computing hardware to achieve reasonable simulation run time.
The number of wake nodes that are present in the vortex wake is limited by the number of wake steps \(N\). After \(N\) wake steps the nodes and vortex elements will be removed from the vortex wake and not contribute to the induction calculation at the blade sections.
To further reduce computational demand, the update of the induced velocity used to convect the wake nodes downwind can be limited to wake nodes close to the rotor. After a given number of free wake steps \(N_w\) the wake is frozen such that the induction remains constant until the wake node and vortex elements are removed after \(N\) wake steps.
The resolution of the vortex wake is also governed by the wake time step \(\delta t\) used to compute the updated wake node positions during the evolution of the vortex wake geometry. The user can adopt a larger time step for an initial simulation time period of \(T\). The time \(T\) is referred to as the fine time step start time. When the simulation time \(t=T\) then the user specified time step \(\delta t\) will be used and is fixed for the remainder of the calculation.
Dynamic Stall Model
When using a free vortex wake method a dynamic stall model is only used to capture the dynamics of detached flow states. These include terms that represent flow separation and vortex lift contributions. It is unnecessary for the dynamic stall models to represent the attached flow states as these are captured by the free vortex wake method instead so the dynamic stall attached flow states are excluded.
Limitations
Some current limitations of the vortex wake methodology should be noted by the user:
For multi-rotor simulations the induction calculation for each rotor is only a function of it's own wake. In other words, the impact on the aerodynamic performance due to the interaction of multiple wakes is not accounted for.
Users cannot run steady or linearisation calculations using the vortex wake method for computing aerodynamic loading. This includes: aerodynamic information, performance coefficient, steady power curve, steady operational loads, steady parked loads, and all the model linearisation calculations such as Campbell diagram, model linearisation & blade stability and so on.
Last updated 13-12-2024