when I want to implement a solver for calculation of the induction factor in Blade Element Momentum method using DMST modeling I have a problem. the process of the calculation of the induction factor is an iterative process. I should guess an induction factor and using that induction factor I should calculate the thrust coefficient from Blade element theory. then I should equalize that with the equation of thrust coefficient from Momentum theory (I use Gluaert correction too).the equation is such:
if : 0 < a < 0.4 : C_TH = 4a(1-a)
if : 0.4 < a < 1 : C_TH = 4a(1-0.25a(5-3a))
if the a calculated from this equation is equal with the guessed induction factor that is used in Blade element theory the guessed induction factor will eb accepted, unless we should update our guess and repeat these process.
I have used Gradient Descent algorithm , induction factor seed with 1e-06 increment But they did not work.
can you please suggest the best algorithms to do this iterative process?
Best regards!
Yazdan Abbasmosleh