Adapted two-equation turbulence closures for actuator disk RANS simulations of wind & tidal turbine wakes

Highlights

Existing 2-equation turbulence models over predict wake recovery rate.

The kω SST model captures initial wake recovery well by limiting eddy viscosity.

Introduced a novel model for production of turbulence from tip vortex breakdown.

Achieved excellent agreement with experimental data of wake velocity and turbulence.

Tested cases with two rotors/flume tanks, with three inflow turbulence intensities, and several array configurations.

Abstract

Reliable methods for modelling wake recovery within a farm of wind or tidal turbines are critical for obtaining accurate estimates of annual energy production, and for detailed farm layout optimization. These are important objectives for maximizing energy yield while minimizing costs. Computational fluid dynamics (CFD) simulation is rapidly being adopted as a tool for flow modelling in wind and tidal farms, gaining favour over more traditional and simpler empirically-determined wake models. The most practical methodology for CFD simulations of turbine farms uses an actuator disk (AD) representation for each rotor, which imposes the rotor forces by adding source terms to the governing equations rather than explicitly resolving the flow over the turbine blades. It is well understood that when using the AD approach, standard turbulence models tend to predict faster wake recovery than is observed in real flows. Thus, the standard CFD turbulence models must be adapted for use with the AD methodology. Additionally, because of the manner in which the AD approach distributes the rotor forces, it cannot resolve the system of discrete vortices trailed from the blade tips.

This article presents two contributions to improving AD simulations of wind/tidal turbine wakes. The first is identifying that the well-established kω SST turbulence model is appropriate for AD simulations because it mitigates the problem of over-predicting the initial wake recovery rate. The second contribution is a method to include the typically un-modelled production of turbulent kinetic energy due to the breakdown of trailed vortices. This method was tuned to minimize the wake error for three experimental test cases with different rotors and different ambient turbulence intensities {3,10,15}%. The new model was validated and compared to existing turbulence methods for the wake of a second rotor in a tandem array configuration with different separation distances and ambient turbulence intensities. The different models were assessed using an error metric designed to estimate the error in predicting the power production of a turbine array. The reduction of this error by the new model varied from case to case, but was on the order of 3.5–10%, compared to the standard kε model.

Keywords

  • Actuator disk;
  • Wind;
  • Tidal;
  • Turbine;
  • Turbulence;
  • RANS

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