Efficient Turbulence Modeling for CFD Wake Simulations

Wind turbine wakes can cause 10-20% annual energy losses in wind farms, and wake turbulence can decrease the lifetime of wind turbine blades. One way of estimating these effects is the use of computational fluid dynamics (CFD) to simulate wind turbines wakes in the atmospheric boundary layer. Since this flow is in the high Reynolds number regime, it is mainly dictated by turbulence.

As a result, the turbulence modeling in CFD dominates the wake characteristics, especially in Reynolds-averaged Navier-Stokes (RANS). The present work is dedicated to study and develop RANS-based turbulence models, that can accurately and efficiently simulate wind turbine wakes. The linear k-ε eddy viscosity model (EVM) is a popular turbulence model in RANS; however, it underpredicts the velocity wake deficit and cannot predict the anisotropic Reynolds-stresses in the wake.

In the current work, nonlinear eddy viscosity models (NLEVM) are applied to wind turbine wakes. NLEVMs can model anisotropic turbulence through a nonlinear stress-strain relation, and they can improve the velocity deficit by the use of a variable eddy viscosity coefficient, that delays the wake recovery.

Unfortunately, all tested NLEVMs show numerically unstable behavior for fine grids, which inhibits a grid dependency study for numerical verification. Therefore, a simpler EVM is proposed, labeled as the k-ε - fp EVM, that has a linear stress-strain relation, but still has a variable eddy viscosity coefficient.

The k-ε - fp EVM is numerically verified with a grid dependency study. With respect to the standard k-ε EVM, the k-ε- fp EVM compares better with measurements of the velocity deficit, especially in the near wake, which translates to improved power deficits of the first wind turbines in a row. When the CFD metholody is applied to a large wind farm, the simulated results cannot be compared directly with wind farm measurements that have a high uncertainty in the measured reference wind direction.

When this uncertainty is used to post-process the CFD results, a fairer comparison with measurements is achieved.