POLYFLOW - Some useful evolution functions for the power index of a viscosity law.
Evolution strategies are usually recommended when the viscosity law (Bird-Carreau or power laws) involves a low index. However, the selection of an evolution function and its parameters can sometimes enter in conflict with other evolution functions applied on other parameters.
When the evolution is only required on the power index:
- assign the required value to the power index n
- select f(S) = 1/S
- select Sini as the required value n, and Sfin to 1
When the above evolution scheme enters in conflict with other functions:
- assign the value 1 to the power index n
- select f(S) = a + b.S + c.S^2 + d.S^3, with a = -1, b = -2(1-n), c = 1-n
- select Sini = 0 and Sfin = 1 (default values)
- a quick inspection shows that n will decrease from 1 to the assigned value.
Other evolutoni functions may be created along the same idea, and are mainly a metter of algebra.