Appendix B: Numerical Values for Excitation Coefficients

Default lift coefficients

Pure cross-flow loading (IRSTYP = 1): The default curves cover the \(\mathrm {\hat{f}}\) range of \(\mathrm {0.120-0.310}\). (Internal VIVANA data FHLC_DEF, AD0_DEF, ADMAX_DEF, CLM_DEF, CL0_DEF)

Table 1. Coefficients (after VIVANA version 4.0, Passano et al. (2012))
\(\mathrm {\hat{f}_{CF}}\)	\(\begin{array}{l}(\frac{A}{D})_{CF}\quad \mathrm {for}\\C_{e,CF}=0\end{array}\)	\(\begin{array}{l}(\frac{A}{D})_{CF}\quad \mathrm {for}\\C_{e,CF}=\mathrm {max}\end{array}\)	\(C_{e,CF,\mathrm {max}}\)	\(\begin{array}{l}C_{e,CF}\quad \mathrm {for}\\\frac{A}{D}=0\end{array}\)
.120	.200	.100	.100	.050
.125	.400	.200	.100	.060
.135	.500	.270	.100	.080
.140	.550	.350	.140	.110
.150	.600	.450	.200	.180
.160	.700	.500	.350	.240
.165	.800	.500	.500	.300
.170	.900	.430	.800	.400
.175	.820	.400	.700	.200
.180	.780	.400	.500	.150
.185	.750	.400	.550	.160
.190	.650	.400	.600	.170
.200	.580	.380	.650	.200
.210	.550	.350	.600	.250
.250	.400	.200	.350	.200
.300	.200	.100	.200	.150
.310	.180	.090	.100	.150

The default lift curves after VIVANA version 4.0 are changed based on the study Passano et al. (2012). The default pure cross-flow loading curves used before VIVANA 4.0 were slightly different:

Table 2. Coefficients (before VIVANA version 4.0).
\(\mathrm {\hat{f}_{CF}}\)	\(\begin{array}{l}(\frac{A}{D})_{CF}\quad \mathrm {for}\\C_{e,CF}=0\end{array}\)	\(\begin{array}{l}(\frac{A}{D})_{CF}\quad \mathrm {for}\\C_{e,CF}=\mathrm {max}\end{array}\)	\(C_{e,CF,\mathrm {max}}\)	\(\begin{array}{l}C_{e,CF}\quad \mathrm {for}\\\frac{A}{D}=0\end{array}\)
.120	.149	.100	.100	.000
.125	.266	.200	.100	.000
.127	.400	.214	.100	.016
.130	.451	.235	.100	.040
.135	.505	.270	.100	.080
.140	.530	.350	.140	.110
.150	.588	.450	.200	.180
.160	.658	.500	.350	.240
.165	.746	.500	.500	.300
.168	.890	.460	.780	.350
.172	.900	.430	.800	.400
.175	.837	.400	.700	.200
.180	.761	.400	.400	.100
.185	.706	.400	.300	.000
.190	.666	.400	.200	.000
.200	.615	.380	.100	.000
.210	.592	.350	.100	.000
.220	.575	.313	.100	.000
.230	.539	.275	.100	.000
.240	.504	.238	.100	.000
.250	.420	.200	.100	.000
.270	.312	.160	.100	.000
.280	.247	.140	.100	.000
.290	.186	.120	.100	.000
.300	.160	.100	.100	.000
.310	.136	.090	.100	.000

Pure in-line loading (IRSTYP = 2): The default curves cover the \(\mathrm {\hat{f}}\) range of \(\mathrm {0.200-0.900}\). (Internal VIVANA data FHLC_IL_DEF, AD0_IL_DEF, ADMAX_IL_DEF, CLM_IL_DEF, CL0_IL_DEF)

Table 3. Coefficients
\(\mathrm {\hat{f}_{CF}}\)	\(\begin{array}{l}(\frac{A}{D})_{IL}\quad \mathrm {for}\\C_{e,IL}=0\end{array}\)	\(\begin{array}{l}(\frac{A}{D})_{IL}\quad \mathrm {for}\\C_{e,IL}=\mathrm {max}\end{array}\)	\(C_{e,IL,\mathrm {max}}\)	\(\begin{array}{l}C_{e,IL}\quad \mathrm {for}\\\frac{A}{D}=0\end{array}\)
.200	.000	.000	.000	.000
.250	.000	.000	.000	.000
.275	.070	.050	.010	.000
.300	.110	.070	.070	.000
.325	.100	.060	.100	.000
.350	.070	.045	.050	.000
.375	.130	.050	.100	.000
.400	.115	.080	.070	.000
.425	.120	.070	.140	.000
.450	.110	.060	.130	.000
.500	.080	.050	.130	.000
.550	.075	.045	.130	.000
.600	.068	.035	.110	.000
.650	.050	.030	.060	.000
.700	.035	.020	.040	.000
.750	.028	.010	.020	.000
.800	.000	.000	.000	.000
.850	.000	.000	.000	.000
.900	.000	.000	.000	.000

Cross-flow and in-line loading (IRSTYP = 3).

CF: As for IRSTYP = 1. The default curves cover the \(\mathrm {\hat{f}}\) range of \(\mathrm {0.12-0.310}\).

IL: Default curve cover the \(\mathrm {\hat{f}}\) range from \(\mathrm {0.250-0.400}\). (Internal VIVANA data FHLC_IL2_DEF, AD0_IL2_DEF, ADMAX_IL2_DEF, CLM_IL2_DEF, CL0_IL2_DEF)

Table 4 gives the parameters on the VIVANA CF format as function of the CF non-dimensional frequency. The IL non-dimensional frequency is 2 times this value. Passano et al. (2012)

Table 4. Coefficients
\(\mathrm {\hat{f}_{CF}}\)	\(\mathrm {\hat{f}_{IL}}\)	\(\begin{array}{l}(\frac{A}{D})_{IL}\quad \mathrm {for}\\C_{e,IL}=0\end{array}\)	\((\frac{A}{D})_{IL,\mathrm {max}}\)	\(C_{e,IL,\mathrm {max}}\)	\(\begin{array}{l}C_{e,IL}\quad \mathrm {for}\\\frac{A}{D}=0\end{array}\)
0.1	0.200	0.210	0.080	0.250	0.010
0.125	0.250	0.230	0.110	0.300	0.020
0.15	0.300	0.260	0.110	0.400	0.020
0.156	0.312	0.260	0.110	0.470	0.020
0.167	0.334	0.260	0.100	0.470	0.020
0.173	0.346	0.240	0.070	0.450	0.010
0.183	0.366	0.120	0.050	0.400	0.010
0.2	0.400	0.100	0.040	0.350	0.010
0.25	0.500	0.070	0.040	0.250	0.010
0.3	0.600	0.070	0.040	0.200	0.010

these curves must be regarded as preliminary and subjected to revision as soon as we have better results from our experiments.