Question about code snippet of subroutine inductionFactors2 from AeroDyn module

Wind & Water Computer-Aided Engineering Software Tools
1

Dear all,
Here is the code snippet from inductionFactors2 (inductionFactors2, aerodyn module, Openfast v3.5.3),

!..
! compute axial induction factor:
!..
sigma_p = Bchord/(TwoPi_R8r) ! local solidity
k = sigma_pcn/(4.0_R8KiFsphisphi)*drdz

! “corrections”
VxCorrected = Vxcos(cantAngle)+xVelCorr
kCorrectionFactor = 1.0_R8Ki + xVelCorr/(Vxcos(real(cantAngle,R8Ki)))
kpCorrectionFactor = kCorrectionFactor
k = k*kCorrectionFactor**2

my question is why kCorrectionFactor takes that form？
When dealing with a rigid system, Vx is zero, which make kCorrectionFactor goes to infinite, so does factor k. That leads to the breakdown of momentum theory no mater what inflow velocity is.
I think kCorrectionFactor should be calculated according to following equation,
kCorrectionFactor = 1 / (1−"Vx∗cos(cantAngle)" /“xVelCorr” )
in which ‘minus’ comes from the local blade coordinate system illustrated in Aerodyn Manual,
When Vx is positive, it reduce the relative Vwind.
Here is the derivation process of kCorrectionFactor，

4
42521×1379 227 KB

Best regards,

2

Dear @Shaozhuo.Luo

In the current implementation xVelCorr is zero. You are correct that Vx could be zero, and we could potentially “protect” the calculation of kCorrectionFactor to avoid it being infinite. I do believe that most compilers would return kCorrectionFactor =1

Let us know if my interepretation is incorect and if you observe weird behavior.

best regards,

Emmanuel

3

Thanks for your help.

Best regards