How would you make someone (who has a good understanding of CFD) understand that CFD codes use Semi-empirical methods instead of empirical as for the turbulence model. what are the upsides/downsides ? thanks

What do you call "semi-empirical" and "empirical"? Which turbulent model is purely empirical? Even the most simple models that I am aware of apply some sort of analytical relation (such as mixing-length theory and boundary-layer theory).

On a high level you could argue that all methods (analytical or numerical) based on conservation laws are "semi-empirical", because conservation itself is a fundamental empirical observation.

hi, well i am using Kameleon fire Ex , which is a safety CFD code... form what i understand empirical methods, based on experimental correlations, are only applicable to simple geometries. KFX uses a semi-empirical method that does not simulate the details of the turbulent motion but only the effect of the turbulence on the mean-flow. the basic concept is to apply the conversation laws for mass momentum and energy averaged over a time scale long compared with that of the turbulent motion. I do use turbulence mixing lenght and turbulence intensity the model is the k-e one.