**4. Experiment Validation**

The experiments were carried out in the large-scale cross-sectional wave flume of Zhejiang University Ocean College in Zhoushan in December 2017. The flume was 75 m in length, 2 m in height, and 1.8 m in width, as shown in Figure 11a; the AUH was preadjusted to neutral buoyancy and then placed in the flume. A diagrammatic sketch of the wave-flume cross-section within the AUH is shown in Figure 11b. There was a wave maker at the end of the flume that could generate regular and irregular waves within a 0.5–5.0 s wave-period range and 0.02–0.6 m wave-height range. The waves in frequency range of 0.2–1.0 rad/s were made in the experiment to simulate a moderate sea state for recovering AUH in waves. The perspective view of the wave flume is shown in Figure 11c. The simulations of the wave flume and AUH with discrete panels, boundary conditions, and wave propagation direction for validation study is as shown in Figure 11d.

**Figure 11.** (**a**) AUH set in experiment wave flume in lateral view; (**b**) diagrammatic sketch of AUH in wave flume in frontal view; (**c**) wave flume with total length of 75 m; (**d**) simulation model of the wave flume and AUH.

The purpose of this experiment was to verify the accuracy of the numerical calculation results of the AUH wave force. Water depth h was 1.2 m, and distance *hS* from bottom to the center of gravity was 0.6 m. Wave period *Tw* was set as 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 s, and wave height *Hw* was set as 0.1 and 0.2 m. A WT901BLE-type attitude sensor was used to record AUH motion angle and angular-velocity information. Sensor measurement stability was 0.05◦, and output frequency was 10 Hz.

The rolling angle of the AUH for different wave periods and heights was measured. Figure 12a–c shows the rolling angles of AUH change over time in three conditions: (1) *Tw* = 2s, *Hw* = 0.2m, (2) *Tw* = 2.5s, *Hw* = 0.2m, and (3) *Tw* = 5s, *Hw* = 0.1m. The rolling-angle response was more regular in high-frequency waves when compared to that in low-frequency waves.

 **Figure 12.** AUH rolling response in regular waves.

At the same time, AUH Numerical Simulation 1 in the restricted flume was conducted as shown in Figure 13. The boundary conditions were set in accordance with the experiment. Due to ANSYS-AQWA being potential-based hydrodynamic-simulation software, damping influence was neglected. Damping has grea<sup>t</sup> influence on the rolling motion of the AUH, i.e., viscous damping forces playing an important role while the AUH is in the condition where the lower wave frequency implies the greater wavelength encountered. The factor of damping was taken into account in Numerical Simulation 2, which increased the accuracy of the numerical simulation of the rolling direction. The improved effectiveness is obvious especially at low frequencies, as in Table 4. The proposed damping term for the vertical axisymmetrical AUH can be expressed as

$$D\_{critical} = 2\sqrt{mK} = 2\sqrt{(I\_{xx} + \Delta I\_{xx})K\_{Roll}} \tag{16}$$

where *Dcritical* represents critical damping; *Ixx* represents rolling inertia mass; *KRoll* represents rolling stiffness matrix; and *K* and Δ*Ixx* represent the stiffness of corresponding degrees of freedom and added mass inertia mass, respectively.

**Figure 13.** Comparison of RAO variations in roll versus wave frequency using the panel methods and experiment data.


**Table 4.** Comparison between experiment data and numerical results.

A comparison between numerical results of the AUH rolling RAO and the experiment data is shown in Figure 13 and Table 4. The overall trend of the AUH motion RAO in rolling was relatively consistent. From Table 4 we know that in wave-frequency range 0.2–1.0 Hz, the average error of the AUH rolling RAO was 21% in different wave frequencies, and minimum error was 3.4% in 2.9 Hz. Within the limits of experimental error and sensor precision, viscous force was not considered in the numerical calculation. Thus, the tolerance error was acceptable to prove the numerical results as a valid and rational. Study 1 was further optimized, and the results of Study 2 were more accurate by adding the damping term, as shown in Equation (16). This process reduced the error from 21.03% to 9.95%.
