[Shingo Iwashita]

I conducted the simulation of unsteady aerodynamic force of flat plate, using dynamic mesh and UDF. The condition of analysis is following picture. U=2m/sec, B=1.0m and B/D=1000. And Turbulence model is LES Smagorinsky-Lilly (Cs=0.1)
The figure below is explanation of analysis.

And Here is model settings in Ansys fluent.
model.pngDynamic mesh setting.jpgDynamic mesh setting2.jpg
Unsteady aerodynamic force is calculated by following formula.
and
L~, M~ : Unsteady lift and moment force.
ρ: density of air 1.225kg/m^3
y: position of flat plate, and y-dot is speed of plat plate,
ω: angular velocity(rad/sec)

LyR(real) and LyI(imag) on the complex plane, represent the phase difference against flat plate motion . MyR and MzR is also.
Following figure describes the concept of unsteady aerodynamic force.


Finally, I got the results as following. Black line is theoretical value by theodorsen function. The result of moment is correct, but LyR has large error. Only phase of Lift force is not correct.The theodorsen function says when U/Bf(Non-dimensional wind speed)=0, both LyR and LyI =0 , which means no lift force when U=0(m/sec).But actually, lift force work on oscillating flat plate in no wind by my analysis model.

Following figure describes that the U/Bf is smaller(ω is faster) the phase error of LyR is bigger.

Please tell me what causes this error if anybody knows about this problem.
Regards