Drag Coefficient Modification The average force in IL direction will be influenced by VIV. CF vibrations will normally lead to increased drag, while pure IL response may give increased or decreased drag depending on amplitude and frequency. VIVANA will in its present version apply the CF amplitude to calculate drag magnification for pure CF and combined CF and IL oscillations. Drag modification for pure IL cases is found by considering response frequency and amplitude. 1. Drag amplification for CF and combined CF and IL response The drag coefficient of a cross section that vibrates in CF direction will be larger than for the fixed cylinder case. A simple way to describe the drag magnification is to find an empirical equation that gives a reasonably good fit to measured data. Two such equations have been published, and both apply the oscillation amplitude as the only parameter. The discrepancy between the two equations is most likely to be caused by use of different data, and the fact that other parameters like IL amplitude, Reynolds number and oscillation frequency are important. The drag amplification factors DAF are given as: Option 1. Blevins, (1990): \[DAF_{i,Blevins}=1+2.1(\frac{A}{D})_i\] Option 2. Vandiver et, (1983): \[DAF_{i,Vandiver}=1+1.043(\frac{2A_{rms}}{D})_i^{0.65}\] The drag coefficient will hence be given by \[C_d(\frac{A}{D})_i=C_d(A=0)_i\:DAF(\frac{A}{D})_i\] where \(\mathrm {\displaystyle C_d(\frac{A}{D})_i\quad }\) Amplified drag coefficient at element \(\mathrm {i}\), CF amplitude \(\mathrm {A}\) and diameter \(\mathrm {D}\) \(\mathrm {C_d(A=0)\quad }\) User specified drag coefficient valid for a fixed cylinder \(\mathrm {A_{rms,i}\quad }\) rms-value of the response at element \(\mathrm {i}\) The user can specify that results from one of these equations or both are stored on the .res or .mpf files. 2. Drag adjustment for pure in-line VIV VIVANA calculates drag amplification for pure in-line VIV by using the results from Aronsen’s pure IL experiments, see Blevins, (1990). These results give \(\mathrm {C_D}\) for simultaneous values of the non-dimensional oscillation frequency and amplitude, \(\mathrm {C_{D,IL}(\hat{f},A/D)}\), see Table 1. The tests were carried out for constant diameter and flow velocity that gave a constant Reynolds number of \(\mathrm {24~000}\). The drag coefficient for a non-vibrating cylinder was found to be \(\mathrm {1.33}\) from the same test apparatus. 2.1. Drag coefficients for pure in-line VIV. Table 1. Drag coefficients for pure in-line VIV, from Aronsen (2007) \(\mathrm {\hat{f}}\) \(\mathrm {\displaystyle \frac{A}{D}=0.00}\) \(\mathrm {\displaystyle \frac{A}{D}=0.05}\) \(\mathrm {\displaystyle \frac{A}{D}=0.10}\) \(\mathrm {\displaystyle \frac{A}{D}=0.15}\) \(\mathrm {\displaystyle \frac{A}{D}=0.20}\) \(\mathrm {\displaystyle \frac{A}{D}=0.25}\) \(\mathrm {\displaystyle \frac{A}{D}=0.30}\) 0.20 1.33 1.40 1.40 1.40 1.60 1.60 1.80 0.25 1.33 1.40 1.40 1.48 1.75 1.80 1.80 0.30 1.33 1.40 1.70 1.85 1.80 1.80 1.80 0.35 1.33 1.70 1.80 1.80 1.40 1.15 1.00 0.40 1.33 1.60 1.40 1.10 0.95 0.90 0.80 0.45 1.33 1.35 1.05 0.85 0.80 0.75 0.70 0.50 1.33 1.25 0.95 0.80 0.70 0.70 0.70 0.55 1.33 1.20 0.85 0.70 0.75 0.60 0.65 0.60 1.33 1.10 0.75 0.60 0.58 0.58 0.59 0.65 1.33 1.10 0.70 0.57 0.55 0.55 0.55 0.70 1.33 1.00 0.67 0.55 0.53 0.54 0.54 0.75 1.33 0.95 0.64 0.55 0.50 0.52 0.53 0.80 1.33 0.90 0.60 0.51 0.47 0.50 0.48 0.85 1.33 0.80 0.57 0.47 0.46 0.48 0.50 0.90 1.33 0.80 0.57 0.47 0.45 0.47 0.49 The drag amplification factor for in-line VIV is now found as \[DAF_{IL}=\frac{C_{D,IL}(\hat{f},A/D)}{1.33}\]