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Unlike uniform motion, when an object moves underwater with variable speed, it experiences additional resistance from the water, commonly referred to as added mass force. At present, several methods exist to solve this force, including theoretical, experimental, and simulation approaches. This paper addresses the challenge of determining the added mass force for irregularly shaped small objects undergoing variable speed motion underwater, proposing a method to obtain the added mass force through numerical simulation. It employs regression analysis and parameter separation analysis to solve the added mass force, added mass, viscous drag coefficient, and pressure drag coefficient. The results indicate that an added mass force exists during both the acceleration and deceleration of the object, with little difference between them. Under the same velocity conditions, significant differences exist in pressure drag forces, while differences in viscous drag forces are not significant. This suggests that the primary source of added mass force is pressure drag, with viscous drag having little effect on it. During acceleration, the surrounding fluid accelerates with the object, increasing the pressure drag with a high-pressure area concentrating at the object’s front, forming an added mass force that is directed backward. By contrast, during deceleration, the fluid at the object’s front tends to detach, and the fluid at the rear rushes forward, leading to a smaller high-pressure area at the front and a larger one at the rear, reducing the pressure drag and forming an added mass force that is directed forward. By comparing the added mass of a standard ellipsoid obtained from numerical simulation with theoretical values, the regression analysis method is proven to be highly accurate and entirely applicable for solving the added mass of underwater vehicles.

Viscous drag, nonlinear in nature, is an important aspect of the fluid−structure interaction modelling and is usually not taken into account when the fluid is assumed to be inviscid. Potential flow solvers can competently compute radiation damping, which is related to the radiated wave field. However, the drag damping primarily related to the viscous effects is usually neglected in the radiation/diffraction problems solved by the boundary element method (BEM), also known as the boundary integral element method (BIEM). This drag force can have a significant impact in the case of structures extending much deeper below the free surface, or for those that are completely submerged. In this paper, the drag coefficient C d was quantified for the heave and surge response of a structure which consists of a moored horizontally oriented domed cylinder with two surface piercing square columns located at the top surface. The domed cylinder is the primary part and is submerged. The drag coefficient is estimated using the experimental measurements related to harmonic monochromatic wave−structure interaction. Finally, this estimated drag coefficient was used in the modified time domain model, which includes the nonlinear viscous correction term, and the resulting device response in heave and surge directions is presented for an irregular incoming wave field. The comparison of the numerical model and the experiments validates the estimated C d values obtained earlier. Prior to the time domain model, frequency-dependent parameters such as added mass, radiation damping, and excitation force were computed using three mainstream potential flow packages (that is, ANSYS AQWA, WAMIT, and NEMOH), and a comparison is presented. The effect of free surface on the drag coefficient is investigated through differences in C d values between heave and surge modes.

This paper analyses the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier–Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show that when the wave steepness is doubled, the response reduction is: (i) 3% due to the nonlinear mooring response and the Froude–Krylov force; (ii) 1–4% due to viscous forces; and (iii) 18–19% due to induced drag and non-linear added mass and radiation forces. The effect of the induced drag is shown to be largely scale-independent. It is caused by local pressure variations due to vortex generation below the body, which reduce the total pressure force on the hull. Euler simulations are shown to be scale-independent and the scale effects of the WEC are limited by the purely viscous contribution (1–4%) for the two waves studied. We recommend that experimental model scale test campaigns of WECs should be accompanied by RANS simulations, and the analysis complemented by scale-independent Euler simulations to quantify the scale-dependent part of the nonlinear effects.