Abstract
A novel fast-running model is developed to predict the three-dimensional (3D)
distribution of turbulent kinetic energy (TKE) in axisymmetric wake flows. This
is achieved by mathematically solving the partial differential equation of the
TKE transport using the Green's function method. The developed solution reduces
to a double integral that can be computed numerically for a wake prescribed by
any arbitrary velocity profile. It is shown that the solution can be further
simplified to a single integral for wakes with Gaussian-like velocity-deficit
profiles. Model results are compared and validated against detailed 3D laser
Doppler anemometry data measured within the wake flow of a model wind turbine
in a laboratory environment. This shows a remarkably good agreement in both the
magnitude and shape of the radial TKE profiles at the turbine hub height. The
wind-tunnel data also provide insights into the evolution of important
turbulent flow quantities such as turbulent viscosity, mixing length, and the
TKE dissipation rate within a wind turbine wake.