Physics-based modelling of turbulence in wind-turbine wakes turbulence in neutral atmospheric boundary layers

Abstract

So-called engineering or analytical wind farm flow solvers typically build upon two submodels: one for the velocity deficit and one for the wake-added turbulence intensity. While velocity deficit modelling has received considerable attention, wake-added turbulence models are less prevalent in comparison. Yet, accurate estimates of local turbulence intensity are essential for predicting flow interactions and energy yield, as turbine wakes are both sensitive to and sources of turbulence. Existing wake-added turbulence models are typically empirical or assume axial symmetry despite the inherently three-dimensional nature of turbulent wake fields. In this work, we present a physics-based model for wake-added turbulence intensity. Our approach is based on the analysis of the turbulent kinetic energy and the streamwise Reynolds stress budget, incorporating classical RANS modelling assumptions and far-wake approximations. The resulting model maintains a simple and practical form, demonstrating strong agreement with LES and wind tunnel measurements. Our model provides a more physically consistent and predictive tool for wind farm flow modelling and performance estimation.

Figures (29)

• Figure 1: Normalised velocity (left) and streamwise normal Reynolds stress (right) inflow profiles for all considered roughness lengths.
• Figure 2: case lateral and vertical profiles of the velocity deficit $\Delta \overline{u}{}$, the wake-added $k_w$ and the wake-added $\overline{u'u'}{}_w$ profiles in the wake of the porous disk in a smooth boundary layer, normalised by their minimum or maximum values.
• Figure 3: blackNormalised lateral (top) and vertical (bottom) profiles of the wake-added budget terms for the case. Normalised lateral (top) and vertical (bottom) profiles of the wake-added budget terms for the case.
• Figure 4: Comparison of the modelled and -based lateral and vertical wake eddy viscosity profiles inside the wake for the case.
• Figure 5: blackLateral and vertical profiles of the dissipation time scale for the SBL (top) and RBL (bottom) cases at two different downwind locations. Reference results at $x=-3D$ are shown as blue dashed lines. Lateral and vertical profiles of the dissipation time scale for the SBL (top) and RBL (bottom) cases at two different downwind locations. Reference results at $x=-3D$ are shown as blue dashed lines.