本研究使用計算流體力學對成大拖航試驗水槽延長加深水段與舊有水段之間深度變化的斜坡槽底對船模阻力試驗造成的影響進行研究，本文將使用開源的計算流體力學軟體OpenFOAM進行模擬分析，使用RANS方程式求解，使用SST (Shear Stress Volume of Fraction) k-ω紊流模型，並使用VOF (Volume of Fluid) 方法描述表面的自由液面，以及由韓國船舶與海洋工程研究所 (Korean Research Institude of Ships Ocean Engineering , KRISO) 公開的KCS (Korean Contanier Ship) 船型進行模擬，因為KCS船型有豐富的試驗與模擬資料可供比對，並且船型屬於排水量型的貨櫃輪，且受槽底深度改變的影響會比吃水較小的船型來的大。
不同於傳統的CFD模擬會將計算域設為入流面與出流面，由入流面給定的流體速度來還原實驗中船的移動與水的相對速度；本研究將計算域的邊界條件設為壁面，並藉由使用重疊網格的系統來賦予模型向前移動的速度，重疊網格可以將移動的模型區域與背景的水槽網格區域分離出來單獨擁有自己的設定，因此可以使得含有船模的動網格區域單獨向前移動，以模擬試驗時拖航台車帶著船模移動的情形，並且在背景網格建立起深度改變的水槽模型，在移動的船模通過槽底的斜坡之時便可以觀察到水面的波形變化。
從計算的結果可得知，船模在通過成大拖航水槽的斜坡槽底時，阻力係數與升力並無明顯變化，而從表面產生的凱爾文波來看，表面波的波型受斜坡槽底的影響也不明寫，故推測該斜坡槽底對於排水量型的船模阻力試驗影響甚微。

This study presents a novel approach for Computational Fluid Dynamics (CFD) simulations in towing tanks with varying depths. Unlike traditional methods, it uses a moving ship mesh to directly impart velocity to the surrounding fluid, replicating a ship’s motion in a confined numerical towing tank. The KCS ship model’s resistance coefficient and surface wave patterns were analyzed as it passed over a sloped bottom connecting deep (5 m) and shallow (3.5 m) water sections. Simulation results, validated against experimental data, showed errors within acceptable limits.
Using dynamic mesh technology (overset mesh) and fine grids, the simulations achieved high accuracy. The slope caused minimal disturbance to resistance and flow characteristics, even at various Froude numbers (Fr=0.108 to Fr=0.283). Slight underestimations at low speeds and overestimations at high speeds were attributed to wall effects in the tank.
The findings confirm the effectiveness of the overset mesh, the precision of fine grids, and the minimal impact of the sloped bottom on ship resistance tests. This validates the reliability of the method and demonstrates the NCKU towing tank’s suitability for advanced experimental applications.

[1] B. E. Launder and D. B. Spalding, "The numerical computation of turbulent flows," in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion: Elsevier, 1983, pp. 96-116.
[2] L. Larsson, V. C. Patel, and G. Dyne, "Ship viscous flow," in Proceedings of 1990 SSPA-CTH-IIHR Workshop.
[3] D. C. Wilcox, "Reassessment of the scale-determining equation for advanced turbulence models," AIAA journal, vol. 26, no. 11, pp. 1299-1310, 1988.
[4] F. R. Menter, "Two-equation eddy-viscosity turbulence models for engineering applications," AIAA journal, vol. 32, no. 8, pp. 1598-1605, 1994.
[5] Y. Ahmed and C. G. Soares, "Simulation of free surface flow around a VLCC hull using viscous and potential flow methods," Ocean Engineering, vol. 36, no. 9-10, pp. 691-696, 2009.
[6] L. Larsson, F. Stern, and V. Bertram, "Benchmarking of computational fluid dynamics for ship flows: the Gothenburg 2000 workshop," Journal of Ship Research, vol. 47, no. 01, pp. 63-81, 2003.
[7] C. W. Hirt and B. D. Nichols, "Volume of fluid (VOF) method for the dynamics of free boundaries," Journal of computational physics, vol. 39, no. 1, pp. 201-225, 1981.
[8] Y. H. Ozdemir, T. Cosgun, A. Dogrul, and B. Barlas, "A numerical application to predict the resistance and wave pattern of KRISO container ship," Brodogradnja: An International Journal of Naval Architecture and Ocean Engineering for Research and Development, vol. 67, no. 2, pp. 47-65, 2016.
[9] J. H. Seo, D. M. Seol, J. H. Lee, and S. H. Rhee, "Flexible CFD meshing strategy for prediction of ship resistance and propulsion performance," International Journal of Naval Architecture and Ocean Engineering, vol. 2, no. 3, pp. 139-145, 2010.
[10] P. Tisovska, "Description of the overset mesh approach in ESI version of OpenFOAM," Proceedings of the CFD with OpenSource Software, 2019.
[11] G. Decorte, G. Lombaert, and J. Monbaliu, "A first assessment of the interdependency of mesh motion and free surface models in OpenFOAM regarding wave-structure interaction," in MARINE VIII: proceedings of the VIII International Conference on Computational Methods in Marine Engineering, 2019: CIMNE, pp. 795-806.
[12] A. De Marco, S. Mancini, S. Miranda, R. Scognamiglio, and L. Vitiello, "Experimental and numerical hydrodynamic analysis of a stepped planing hull," Applied Ocean Research, vol. 64, pp. 135-154, 2017.
[13] B. Ibrahim and H. Zekri, "Numerical assessment of symmetric wedge water-entry impact using OpenFOAM," European Journal of Pure and Applied Mathematics, vol. 15, no. 4, pp. 1998-2010, 2022.
[14] W. Shi, M. Li, and Z. Yuan, "Investigation of the ship–seabed interaction with a high‑fidelity CFD approach," Journal of Marine Science and Technology, 2021.
[15] Z. Shen, "Development of overset grid technique for hull-propeller-rudder interactions," Doctoral Thesis Shanghai Jiao Tong University, 2014.
[16] ITTC, "'"Resistance Test" " ITTC - Recommended Procedures and Guidelines, 7.5-02-02-01, 2011.
[17] K. Tamura, "Study on the blockage correction," Journal of the Society of Naval Architects of Japan, vol. 1972, no. 131, pp. 17-28, 1972.
[18] 張奕峰, "On the Improvement of Blockage Correction ans Wall Effect of Ship Model Resistance Test," Master Thesis, System and Naval Mechatronic Engineering, National Cheng Kung Univesity, 2017.
[19] Tokyo 2015 Workshop Organizing Committee, "A Workshop on CFD in Ship Hydrodynamics KRISO Container Ship (KCS)," Tokyo 2015 Workshop, Case 2.1, 2015. [Online]. Available: https://www.t2015.nmri.go.jp/Instructions_KCS/Case_2.1/Case_2-1.html
[20] ITTC, "Uncertainty Analysis in CFD Verification and Validation Methodology and Procedures," ITTC – Recommended Procedures and Guidelines, 7.5-03-01-01, 2017.
[21] W. Kim, S. Van, and D. Kim, "Measurement of flows around modern commercial ship models," Experiments in fluids, vol. 31, no. 5, pp. 567-578, 2001.