A two-dimensional high-order explicit analytical solution model for symmetric wedges entering water

Abstract

The slamming phenomenon is a highly concerned fluid structure coupling problem in the engineering field. Based on the original MLM(Modified Logvinovich Mode), an explicit solution for the higher-order MLM slamming model is derived. The second-order velocity potential, pressure distribution and slamming force can be quickly evaluated. The derived second-order MLM slamming model is compared with the first-order solution and numerical results. Sensitivity analysis reveals that for small angles ($\beta \le {15}^{\circ }$), both first-order and second-order MLM solutions can provide sufficiently accurate slamming solutions. However, for larger deadrise angles ($\beta >{15}^{\circ }$), the second-order solution becomes increasingly significant. The excess second-order pressure cannot be ignored, achieving a $60\%$ proportion. The accuracy of the first-order MLM solutions cannot be guaranteed for large $\beta$ cases, with an error of up to $48\%$, with the difference in slamming force growing more pronounced as $\beta$ increases. For larger $\beta$ values, the second-order MLM solution is more consistent with the numerical results, while the accuracy of the first-order MLM solution decreases. The study concludes that the second-order MLM model expands the applicability of the MLM slamming model to larger deadrise angles, providing a new method for rapid assessment of slamming problems in structures with large $\beta$.