# Mach Number exceeds 0.3 for large wind turbines (15MW)

Dear All,

I am interested in running the design load cases for IEA-15-240-RWT-UMaineSemi in OpenFAST. For turbulent wind speeds more than 12 m/s (Figure 1), the values of relative velocities at the blade tip are reaching values greater than 103 m/s (Figure 2), which in-turn leads to a Mach number greater 0.3 (Figure 2). As the Mach number exceeds 0.3, the BEM solver in OpenFAST is giving a warning message saying “Theory is invalid” (Figure 3). Even after the system reaches the steady state condition the Mach number exceeds 0.3 (which is evident from Figure 2). I have double-checked the initial conditions based on some suggestions in the Forum (15MW MaineSemi-sub floater simulation shows tower strike - #6 by Jason.Jonkman), but I am still getting the same warning message. Could you please help me in resolving this issue?

Regards
Ramya

Dear Ramya,

Can you share plots of the rotor speed, blade-pitch angle, and blade and tower deflections? Are they reasonable for the conditions simulated?

Best regards,

Dear Jason,
Thanks for your reply. As requested, I am sharing the plots for the Rotor speed, Blade1-Pitch angle, Blade1 Out-of plane and In-plane tip deflections, Tower top fore-aft and side-to-side deflections for turbulent wind speed of 12m/s. I have compared the mean values of the Rotor speed and the Blade1-pitch angles with the Figure 3-1 of the IEA 15-MW RWT specifications report (nrel.gov/docs/fy20osti/75698.pdf) and I found the values to be reasonable.

Regards
Ramya

Hello Ramya,

The design max tip speed of the IEA Wind 15-MW is 95 m/s. At standard atmospheric conditions, that is already a Mach number of about 95/340 = 0.279. So, it is quite reasonable that the relative velocity of the incoming flow at the tip can exceed Mach 0.3, especially in the floating case where we have seen some rotor over-speeds in the controller sometimes.

Hope that helps,
Garrett

Dear Garrett,

Thanks for the prompt reply. As the Mach numbers are exceeding 0.3 and the BEM theory is not valid, it’s not clear to me how the force calculation can be done in OpenFAST. I understand that one approach is to apply correction factors (e.g.: Prandtl-Glauert corrections) on the lift and drag coefficients to incorporate the effect of compressibility at the blade tip. However, I am not sure if the correction factors can be incorporated in OpenFAST or if there is any other approach to accurately calculate the forces at the blade tip in OpenFAST?

Regards
Ramya

Dear Ramya,

The unsteady airfoil aerodynamics module of AeroDyn v15 does employ some Mach-dependent quantities, e.g., Mach-dependent time constants and compressibility correction factors. However, it also warns that the theory is invalid at Mach = 0.3 and fatally aborts when Mach = 1.0. The BEM theory is likely also not valid above Mach 0.3. I would say that the solution is probably generally OK up to Mach = 0.3, but I would be concerned if 0.3 is greatly exceeded for extended periods of time.

Best regards,

Dear Jason,

Thank you for the clarification.

Regards
Ramya