Turbulence modeling for wind turbine wakes in non-neutral and anisotropic conditions

When a wind turbine extracts kinetic energy from the air, it leaves behind a wake of low kinetic energy and this wake can persist for a long distance downstream. This means that if the wind direction is aligned between two turbines, then the downwind turbine will produce less electricity and in wind farms the annual energy loss can amount to 10-20%.

Furthermore, the flow in the wake is highly turbulent, so not only does the impacted turbine produce less energy, it also experiences higher fatigue loads, which decreases the expected lifetime of it. One of the most common approaches to estimate wake effects is computational fluid dynamics (CFD), where the Navier-Stokes equations are solved numerically on computers.

However, in atmospheric flows there is such a large gap between the smallest and largest turbulence scales that it is impossible to simulate wind turbine wakes directly even on the largest supercomputers and one must therefore use a turbulence model instead. In this work the focus is on the numerical solution of the Reynolds-Averaged Navier-Stokes (RANS) equations, which describe the mean flow and where the quality of the turbulence model is of utmost importance, because all turbulence scales are in fact modeled.

The first part of the work concerns the development of a simple two-equation RANS turbulence model for simulation of wakes in non-neutral conditions, where buoyancy effects can not be neglected. Such conditions are rather common and can have large effects on wakes, hence it is important also to be able to model these conditions in simulations.

However, from a practical point of view it is also important to have a simple model with few parameters and with low computational cost, which is why the Monin-Obukhov similarity theory (MOST) was considered for the parametrization of the non-neutral inflow. The turbulence model is based on the so-called “k–ε–fP model” but with some additions, which makes it consistent with MOST.

The final model was found to predict reasonable velocity deficits, while the turbulence intensity and second moments were more poorly predicted, when comparing with various large-eddy simulation (LES) datasets. In the second part, an explicit algebraic Reynolds stress model (EARSM) is investigated for the use of RANS simulations of wind turbine wakes in neutral conditions.

This type of turbulence model has a more solid physical basis as it is derived directly from the full differential Reynolds stress model (DRSM), but at the same time has a comparable computational cost to the popular two-equation models. It is capable of predicting more complex flow phenomena such as secondary flows and anisotropic turbulence, where the latter is typically present in atmospheric flows.

While other EARSMs previously have been shown to be numerically unstable for wind turbine wake flows, the EARSM used in the current study is observed to be robust and enhance predictions of second order turbulence statistics such as the turbulence intensity