Distributed roughness induced transition on wind-turbine airfoils simulated by four-equation k-ω-γ-Ar transition model

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The original k-ω-γ transition model has been modified to consider the effects of distributed surface roughness.

Some modifications about free stream turbulence intensity Tu are also proposed.

The modifications are based on fully local variables as well as a substantial physical foundation.

The validation on several wind turbine airfoils with distributed surface roughness has achieved satisfactory results.

The present model can be used in the design as well as the energy output prediction of wind turbines.


The fourth transport equation for “roughness amplification” factor Ar, which depends on equivalent sand grain roughness height ks, has been combined with the original three-equation k-ω-γ transition model. According to linear stability theory, the effective length scale of original k-ω-γ model is amplified through Ar, which could enhance the 1st mode time scale and lead to earlier transition. The new model is calibrated and validated by several cases with available experimental data, including flat plate, some wind-turbine airfoils with different patterns of distributed surface roughness. After careful comparisons with the measurements, the new four-equation transition model performs very well and satisfactory results have been achieved.


Distributed roughness induced transition

Four-equation transition model

Wind turbine


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