Theory

Monin Obukhov Neutral

Javier Sanz Rodrigo's picture
Submitted by Javier Sanz Rodrigo on May 4, 2015 - 3:58pm

Scope

The benchmark is open to participants of the Wakebench project using surface layer models. This is the first element of the building-block approach so it should be mandatory if you intend to participate in other test cases down the line.

The benchmark consists on empty domain (flat terrain) simulations of the neutral surface boundary layer in steady-state conditions. 

Objectives

Demonstrate that the flow model, when run in M-O conditions, is able to reproduce the analytical expressions of the profiles predicted by the theory for neutral conditions. At the same time, it will be possible to check the compatibility of the wall treatment with the flow model for a range of surface roughness conditions.

Data Accessibility

The benchmark is offered to participants of the IEA Task 31 Wakebench. In the future it will be open for public access.

Input data

The conditions for simulating the M-O profiles in neutral conditions are:

  • von karman constant: κ = 0.4

  • Roughness length: z0 = [0.0002, 0.03, 0.4] m

  • Obukhov length: L = ∞

  • Use dry air with a density ρ = 1.225 kg/m3 and dynamic viscosity μ = 1.73e-5 kg/ms

Validation data

The validation data will consist on normalized M-O profiles obtained from analytical functions.

Monin Obukhov Stratified

Javier Sanz Rodrigo's picture
Submitted by Javier Sanz Rodrigo on May 4, 2015 - 3:56pm

Scope

The benchmark is open to participants of the Wakebench project using surface layer models with stratification. This is the first element of the building-block approach so it should be mandatory if you intend to participate in other test cases down the line where thermal stratification is present.

The benchmark consists on empty domain (flat terrain) simulations of the thermally stratified surface boundary layer in steady-state conditions. 

Objectives

Demonstrate that the flow model, when run in M-O conditions, is able to reproduce the analytical expressions of the profiles predicted by the theory for stratified flow. At the same time, it will be possible to check the compatibility of the wall treatment with the flow model for a range of heat flux conditions.

Data Accessibility

The benchmark is offered to participants of the IEA Task 31 Wakebench. In the future it will be open for public access.

Input data

The conditions for simulating the M-O profiles in stratified conditions are:

  • von karman constant: κ = 0.4

  • Roughness length: z0 = 0.03 m.

  • Obukhov length: L = [-100, ∞, 100] m

  • Use dry air with a density ρ = 1.225 kg/m3 and dynamic viscosity μ = 1.73e-5 kg/ms.

Axisymmetric Wake Neutral

Jonathan Naughton's picture
Submitted by Jonathan Naughton on May 4, 2015 - 2:27pm

Scope

The benchmark is open to participants of the Wakebench project using flow models to calculate wind turbine wakes. Completion of the benchmark will demonstrate that a simulation approach is capable of capturing the physics necessary to predict behavior of an isolated wake.

Objectives

Evaluate models using a theoretical solution to assure that they can capture an important component of wind turbine wake flows.

Data Accessibility

The benchmark is offered to participants of the IEA Task 31 Wakebench. In the future it will be open for public access

Input data

The wake profiles being compared should meet the following criteria required for equilibrium similarity:

  • x/θ > 100, and
  • U0δ*/ν > 500

Validation data

The validation exercises to be performed consist of the following comparisons.

  • Demonstrate the wake width grows as x1/3

Note that a is an adjustable parameter that depends on a particular simulation boundary conditions

Infinite Wind Farm Neutral

Simon-Philippe Breton's picture
Submitted by Simon-Philippe ... on May 4, 2015 - 2:16pm

Scope

The benchmark is opened to participants of the Wakebench project using flow models to model wakes of wind turbines aligned in a row in search for an asymptotic deficit state. Two cases are suggested to be modeled:

a) a large (but finite) number of turbines

b) an idealized case with an “infinite” number of turbines, where simulations are made either considering periodic boundary conditions in the streamwise direction, or using analytical models (see e.g. Peña and Rathmann 2013 [1]) to predict the flow in the limit of an infinite number of turbines.

Case a) is compared to case b) to determine how many turbines are needed to reach an asymptotic wake state (and to verify that the same final converged wake state is reached).

Objectives

Completion of the benchmark will inform on the number of turbines necessary for an asymptotic deficit state to be reached (which might depend on the quantity that is analyzed), as well as on the flow characteristics associated to this state. The dependency on the distance between the turbines as well as the ambient level of turbulence intensity will be investigated.