Thank you for your reply but I still have some questions.
I set my mesh and inflow parameters as follows:
1)The real radius of inlet boundary is R_real = 1 cm. The radius of inlet boundary shown in Gmsh is R_Gmsh = 1. Hence we calculate the characteristic length to be L_scal = R_real / R_Gmsh = 1 cm.
R_Gmsh is the non-dimensional radius.
2) We define the characteristic flow velocity to be the maximum value of the flow velocity U_scal = U_max = 23 cm/s.
U/U_scal is the non-dimensional flow velocity
3) Next we calculate the characteristic time to the divison of L_scal and U_scal, i.e. T_scal = L_scal / U_scal = 0.044 s.
T/T_scal is the non-dimensional time. Since the whole period lasts for 0.71 s, the non-dimensional period is 0.71/0.044 = 16.14.
4)Based on (1),(2) and (3), assume the flow density rho = 1.05 g/cm^3, fluid viscosity mu = 0.04 g/(cm*s), we can get the Reynolds number Re = rho * U_scal * L_scal / mu = 598 and the non-dimensional kinematic viscosity nu = 1/Re = 0.0017
With the above parameters "T = 16.14, R = 1, nu = 0.0017" , we calculate womersley numbers "alpha_n", the fourier coefficients "A" of the non-dimensional flow velocity together with the transformed fourier coefficients "\tilde{A}" as the fomulas in the tutorial.
However, when I set radius=1 in womersley boundary condition, the result seems wrong. The simulation blow up in half way and here I visualize the result in earlier time step. The first figure shows the geometry with inflow velocity. The second figure visualize velocity by arrows. In this result, I believe the red part of figure 1 should be bigger to fill out the inlet, which means setting radius=1 may not big enough in womersley boundary condition. Also, we can see some flow in going back from inlet, which is wrong because the inflow in my case should always move into the geometry but not move out from the inlet. So my question is, if radius=1 is not right, then how can I set the radius of Wommersley boundary condition ? Or is there some other problem in the set up which may cause this mistake? Thank you for your help!
Figure 1
Figure 2
Best,
Shan