Windenergie 2 - Wake 2

12 November 2025, Po Wen Cheng

Questions at the beginning

• What happens to the wind field behind the wind turbine?
  • The velocity decreases
  • The turbulence intensity increases
• What happens to the wind turbine in the wake of other wind turbines?
  • Power production increases
  • Fatigue load increases
• Higher turbulence intensity
  • Leads to faster recovery of the wake deficit
• Highly stable atmospheric boundary layer
  • Leads to slower recovery of the wake deficit
• Which of the wind farm is likely to be experiencing a stable ABL (atmospheric boundary layer)?
  • The one with shorter wake effects
• Wich is the shape of the wake behind a wind turbine measured at the distance of 7D?
  • No double gaussian shape in the far wake
  • Double gaussian shape in the near wake, right behind the turbine
• Which parameters have large influence on the wake recovery?
  1. Thrust coefficient
  2. Turbulence intensity
  3. Temperature profile
• Where can we find the highest turbulence intensity in the near wake?
  • Toward the edge of the wake / edge of the rotor

Wake models

• Empirical models
  • Estimate the variation of the ake-center velocity deficit
• Kinematic models
  • Simple assumptions from first principles: energy conservation, impulse conservation
• Field wake models
  • Derived based on governing equations of flow, Navier-Stokes

Empirical model

The correlation of the velocity deficit in a far wake can be appoximated with:

$$ \frac{\Delta v}{v_{hub}} = A \cdot (\frac{R}{x})^n $$

Empirical data can be fitted to this equation

Kinematic wake models

• Jensen wake model (simple, but still used most of the time)
  • It is a one dimensional kinematic wake model, based on a linear expanding wake, that incoporates the rotor diameter and the thrust coefficient as parameters
  • Assume uniform inflow and uniform wake deficit
  • Wake expansion is linear with distance
• Larsen wake model
  • Kinematic model based on the Prandtl turbulent boundary layer equation
  • Assumes incompressible, stationary, acissymmetric flow
  • Describes rotationally symmetric wake
• Frandsen wake model
  • Three regimes:
    • turbines are exposed to multiple-wake-flow and an analytical analytical link between the expansion of the multiple-wake and the asymptotic flow speed deficit is derived
    • wakes from neighboring rows merge and the wakes can only expand vertically upward
    • wind farm is infinitely large and flow is in balance with the boundary layer
• Bastankhah and Porté-Agel wake model (currently most used model)
  • Applies mass and momentum conservation while neglecting the viscosity and pressure terms in equations
  • Velocity deficit is characterized by a gaussian shape

Field wake models

Based on time- or space averaged Navier-Stokes equations. They can solve the implicit equation to find the magnitude of the velocity over the entire flow field

• Ainslie eddy viscosity wake model
  • Simplifictaion: rotationally symmetric
• Numerical wake models
  • Very difficult to model interaction between atmospheric boundary layer, thermal effect, atmospheric stability
  • Useful to help understand wake physics (wake revovery, mixing)

Dynamic wake meandering model

A more enhanced model than the wake induced turbulence models is the dynamic wake meandering model. Here the three following effects are considered:

1. Velocity deficit: reduced wind speed due to extraction of kinetic energy
2. Meandering: deficit profile moves in space
3. Added turbulence: blade and hub create vortices that add turbulence