Very simple eddy viscosity models compute a global value for from the mean velocity and a geometric length scale using an empirical formula. Because no additional transport equations are solved, these models are termed ‘zero equation.’

The zero equation model in Ansys CFX uses an algebraic equation to calculate the viscous contribution from turbulent eddies. A constant turbulent eddy viscosity is calculated for the entire flow domain.

The turbulence viscosity is modeled as the product of a turbulent velocity scale, , and a turbulence length scale, , as proposed by Prandtl and Kolmogorov,

(2–17)

where is a proportionality constant. The velocity scale is taken to be the maximum velocity in the fluid domain. The length scale is derived using the formula:

(2–18)

where is the fluid domain volume. This model has little physical foundation and is not recommended.