Dimensionless Parameters
1. Reynolds number
The Reynolds number classifies dynamically similar flows, i.e. flows that have geometrically similar streamlines around bodies of identical shapes when the incoming flow direction is the same. The condition for similarity is that the ratio of inertia force to friction force is constant at all corresponding points. The Reynolds number at a position \(\mathrm {s}\) along the structure is defined as
where \(\mathrm {v(T)}\) is the temperature dependant kinematic viscosity, found from Faltinsen (1990), see Figure 1. The \(\mathrm {s}\) coordinate follows the length of the structure in its deformed position.
2. Strouhal number
The Strouhal number is related to the vortex shedding frequency \(\mathrm {f_v}\) for a fixed cylinder, and defined by
Note that the vortex shedding frequency in the general case will change when VIV occurs, but the Strouhal number should not be referred to a vibrating cylinder. The Strouhal number is used for an initial evaluation and identification of a preliminary list of possible response frequencies.
Figure 2 shows the builtin curve for \(\mathrm {St(Re)}\) in VIVANA. The curve is valid for a circular cylinder with some roughness and is taken from Faltinsen (1990). The user may specify another curve or keep the Strouhal number independent of the Reynolds number.
The selected curve for \(\mathrm {St(Re)}\) (see Figure 2) is assumed to be the best possible alternative for the present use of the Strouhal number, namely to find an initial value for the response frequency in an iteration. Experience shows that even if the vortex shedding frequency for a fixed, smooth cylinder might be significantly higher in the critical flow regime than what is indicated on the curve, the response frequency will drop to a level more like the rough cylinder case.
The vortex shedding frequency along a nonvibrating structure can be found from
Note that the Strouhal number is used to correct the nondimensional frequency in order to apply the builtin or user given curves for hydrodynamic coefficients for vibrating cylinders correctly.
3. Nondimensional frequency
The nondimensional frequency \(\mathrm {\hat{f}}\) is used as a controlling parameter for added mass and excitation force coefficients. The nondimensional frequency is defined by
The builtin data for added mass and excitation force are given as function of the nondimensional frequency. These data are found from experiments at a given Reynolds number, and hence also for a given Strouhal number. The data will, however, be applied for other flow conditions, which means that they must be corrected. This correction is automatically performed in VIVANA by correcting the nondimensional frequency according to change of Strouhal number:
\(\mathrm {St_E}\) is the Strouhal number valid for the experiments from which the applied coefficients are found, and \(\mathrm {St}\) is the actual Strouhal number (see Section 2). This correction will ensure that the ratio between the oscillation frequency and vortex shedding frequency for the fixed cylinder is the same for the actual application as for the empirical basis. If the builtin data are used, \(\mathrm {St_E}\) is defined as \(\mathrm {0.2}\), and the correction will be performed accordingly. See also Appendix A.
Note that:

Both builtin and user specified parameters for added mass and excitation coefficients are assumed to be valid for \(\mathrm {St_E}=0.2\) and corrected accordingly.

The nondimensional frequency for CF and IL components is referred to the respective oscillation frequencies. Hence, \(\mathrm {\hat{f}_{IL}=2\hat{f}_{CF}}\) for the same flow condition since the IL response frequency always is assumed to be two times the CF frequency.