vivyd.models.TamuraModel#
- class TamuraModel(*, diam=0.18, St=0.18, c_m=0.05, k_m=39.47841760435743, m_lin=25.0, rho=1.25, u_inf=1.0, fm=1.16, Cd=1.2, zeta=0.038, Cl0=0.4, l_star=1.1)[source]#
Bases:
VIVModelTamura & Matsui (1980) wake-oscillator model for vortex-induced vibrations on circular cylinders [TM80]. By identifying the lift and transverse drag forces, the mechanical equation of motion of the cylinder is written as
\[\ddot{y} + \frac{c}{m} \dot{y} + \frac{k}{m} y = - \frac{\rho U_\infty^2 D}{2 m_\text{lin}} \left(f_m \left(q + \frac{\dot{y}}{U_\infty} \right) + C_D \frac{\dot{y}}{U_\infty} \right),\]and the equation of the wake is written as
\[\ddot{q} + 2 \zeta \omega_s \left(4 \frac{f_m^2}{C_{L 0}^2} q^2 - 1 \right) \dot{q} + \omega_s^2 \left(q + \frac{\dot{y}}{U_\infty} \right) = - \frac{\ddot{y}}{D \left(\displaystyle \frac{1}{2} + l^* \right)},\]with
\[\omega_s = 2 \pi \text{St} \frac{U_\infty}{D}.\]- Parameters:
diam (float, optional) – Diameter of the cylinder, \(D\). Default is 0.18 m.
St (float, optional) – Strouhal number, \(\text{St}\). Default is 0.18.
c_m (float, optional) – Specific mechanical damping, \(c/m\). Default is 0.05.
k_m (float, optional) – Specific mechanical stiffness, \(k/m\). Default is \(4 \pi^2\).
m_lin (float, optional) – Mass per unit length of the cylinder, \(m_\text{lin}\). Default is 25.0 kg/m.
rho (float, optional) – Density of the fluid, \(\rho\). Default is 1.25 kg/m³.
u_inf (float, optional) – Free-stream velocity, \(U_\infty\). Default is 1.0 m/s.
fm (float, optional) – Magnus force coefficient, \(f_m\). Default is 1.16.
Cd (float, optional) – Drag coefficient, \(C_D\). Default is 1.2.
zeta (float, optional) – Damping ratio, \(\zeta\). Default is 0.038.
Cl0 (float, optional) – Lift coefficient at zero angle of attack, \(C_{L 0}\). Default is 0.4.
l_star (float, optional) – Dimensionless length of the wake lamina, \(l^* = l / D\). Default is 1.1.
Attributes#
- TamuraModel.diam: float#
Diameter of the cylinder, \(D\).
- TamuraModel.St: float#
Strouhal number, \(\text{St}\).
- TamuraModel.c_m: float#
Specific mechanical damping, \(c/m\).
- TamuraModel.k_m: float#
Specific mechanical stiffness, \(k/m\).
- TamuraModel.m_lin: float#
Mass per unit length of the cylinder, \(m_\text{lin}\).
- TamuraModel.rho: float#
Density of the fluid, \(\rho\).
- TamuraModel.u_inf: float#
Free-stream velocity, \(U_\infty\).
- TamuraModel.fm: float#
Magnus force coefficient, \(f_m\).
- TamuraModel.Cd: float#
Drag coefficient, \(C_D\).
- TamuraModel.zeta: float#
Damping ratio, \(\zeta\).
- TamuraModel.Cl0: float#
Lift coefficient at zero angle of attack, \(C_{L 0}\).
- TamuraModel.l_star: float#
Dimensionless length of the wake lamina, \(l^* = l / D\).
- property TamuraModel.n: float#
Dimensionless mass ratio, \(n = \dfrac{\rho D^2}{2 m_\text{lin}}\).
- property TamuraModel.m_star: float#
Coefficient \(m^* = \dfrac{1}{0.5 + l^*}\).
- property TamuraModel.St_star: float#
Angular Strouhal number, \(\text{St}^* = 2 \pi \text{St}\).
- property TamuraModel.ws: float#
Strouhal’s vortex shedding pulsation, \(\omega_s = 2 \pi \text{St} \dfrac{U_\infty}{D}\).
- property TamuraModel.generalized_params: dict[str, float]#
A dictionary containing the parameters of the model in a format compatible with the constructor of
GeneralizedModel.
Methods#
- TamuraModel.to_generalized()[source]#
- Returns:
A generalized model instance equivalent to the present model.
- Return type: