 (left). SIMA underestimates the low-frequency surge forces, and by 26.6% at surge natural frequency. CFD also underpredicts the surge forces by 16.2% at the surge natural frequency. On the other hand, CFD results have more significant wave energy (within 20%) at low frequencies.  Fig. 17 (right) presents the low-frequency surge force spectra considering different force contributions in SIMA. All of the components of the measured irregular wave are treated linearly in SIMA. The surge natural frequency is below the cut-off frequency, so there is no significant linear wave excitation (SIMA 1) at surge natural frequency. The difference-frequency QTF (SIMA 2) has a slight influence on the low-frequency surge force. The surge force at surge natural frequency is mainly from integration of the Morison drag force to the linear free surface (SIMA 4). The axial drag forces on the heave plates have no effect on the low-frequency surge force (SIMA 5 vs SIMA 4).
The heave force spectra are compared in Fig. 18 (left). SIMA underestimates the low-frequency heave forces, and by 20.5% at the heave natural frequency. The CFD model shows better predictions of heave forces, however, there is also significantly less wave energy (18%) at the heave natural frequency in the CFD model. It is important to note that the laminar flow model used in CFD simulation cannot correctly capture the flow around the heave plate. A large part of the heave force comes from linear potential flow theory (SIMA 1), see right part of Fig. 18. The difference-frequency QTF (SIMA 2) and the normal drag forces (SIMA 3 and 4) have minor effects on the heave force. The axial drag forces on the heave plates (SIMA 5) increase the heave force by 89.5% at the heave natural frequency.

H. Li and E.E. Bachynski
Renewable Energy 171 (2021) 709e727 Fig. 19 (left) compares the low-frequency pitch moment spectra. Similar to the surge and heave forces, SIMA underpredicts the pitch moment. This is consistent with previous results showing five times smaller load responses at the pitch natural frequency of a mooring FWT seen in simulations using the engineering tools compared to the experimental measurements [5]. The CFD model underpredicts the low-frequency pitch moment by about 10%. Again, this underprediction may in fact be more severe than it seems, as the CFD model includes more wave energy at low frequencies.
The comparisons of low-frequency pitch moment spectra with different force contributions in SIMA are shown in Fig. 19 (right). The pitch moment from the difference-frequency QTF (SIMA 2) is significant. In addition, the normal drag forces (SIMA 3) and integrations to the linear free surface (SIMA 4) have little effect on the pitch moment at low frequencies. The axial drag forces on the heave plates (SIMA 5) increase the moment at very low frequencies, but the results remain lower than experimental measurements.

Conclusions
Nonlinear wave loads are important for designing the floater and mooring system for FWTs. In this paper, nonlinear diffraction wave loads on a semi-submersible FWT are studied using two numerical approaches based on CFD and potential flow theory as well as experimental measurements.
Based on the comparisons under a regular wave, good agreement (within 10%) between numerical models and experiment is achieved for wave-frequency loads. For higher order wave loads, CFD correctly estimates the phase, and CFD with the turbulence model generally give the best results. The lower heave force and pitch moment in the laminar flow may be due to the lack of simulation for weak flow separation occurring around heave plate. SIMA (potential flow with Morison drag) has large discrepancies in prediction of phase and amplitude of higher order wave loads. The dominant higher order components in SIMA are related to treating a nonlinear wave measurement as a linear input, which leads to phase discrepancy against CFD and experimental measurements. The normal drag force of columns and cross braces in SIMA model has significant contributions to the surge force while the axial drag forces on the heave plates increase the heave force and the pitch moment. The proper drag coefficient can decrease the amplitude discrepancy in higher order loads, but a phase difference nonetheless exists in the SIMA results. This discrepancy demonstrates the limitation of potential flow theory with Morison-type drag for estimating high order diffraction wave loads.
Regarding the low-frequency wave loads on the fixed structure under an irregular wave, both CFD and SIMA underpredict the loads, but the discrepancy for CFD results is smaller. In SIMA, all of the components of the measured irregular wave are treated linearly. The difference-frequency QTF has significant contributions to the pitch moment. Normal drag forces on the columns and cross braces lead to an increased surge force at surge natural frequency. In addition, the axial drag forces on the heave plates largely increase the heave force at heave and pitch natural frequencies, but only contribute to the pitch moment at very low frequencies. Due to excessive numerical damping of the wave using a turbulence model in CFD, only laminar flow was considered in the irregular waves. Further developments of hybrid methods with CFD with a turbulence model and potential flow theory models are needed.      In order to better understand the effects of the multimember arrangement of the semisubmersible, surge forces on each column are extracted. Higher order surge forces on the starboard column are larger than those on the upstream column in the CFD simulations under this regular wave (12.1 s), but this conclusion is frequency-dependent (based on potential flow simulations at additional frequencies). Furthermore, the total surge force on the upper column is larger than the force on the heave plate, and this discrepancy increases for shorter waves.
The effects of 5 mean pitch angle on the nonlinear wave loads are also investigated in regular waves, using the same global coordinate system as in the upright condition. In the trimmed condition, the surge force and pitch moment increase while the heave force decreases. Furthermore, this 5 mean pitch angle reduces the higher order surge and heave forces while increasing the higher order pitch moment. In SIMA, the axial drag forces on the heave plates increase the third harmonic heave force and pitch moment, but decrease the third harmonic surge force, which is due to the phase difference between vertical and horizontal water particle velocity. Considering the effect of changed volume, the surge and heave forces decrease, and the pitch moment slightly increases under trimmed position.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.How many led shop light fixtures are produced by Halcon LED Lighting per month?
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