When the turbulent model theory is used to solve the turbulent boundary layer
 

When the turbulent model theory is used to solve the turbulent boundary
layer, can the algebra stress model (ASM) be used? Why?

The algebraic stress model is a turbulence model. You're asking when a turbulence model is being used, if a turbulence model can be used.

If you're asking whether a turbulence model can be used on a turbulent boundary layer, the answer is it should or else it's not a good turbulence model.

If you're asking whether the algebraic stress model is a good model for a turbulent boundary layer, the answer is it depends. It's a model, not the best one, your mileage will vary.