為提升潛艇的續航能力，本研究藉由運用數值方法對潛艇附屬件布局進行最佳化，降低航行時所產生之阻力及升力，增進潛艇的使用效益。選定已廣泛運用、具可信實驗數據供參照的「SUBOFF」潛艇作為研究對象，使用三維計算流體力學模擬軟體進行模擬，並透過格點數測試驗證模擬之準確性。再以其帆罩及控制面之位置及高度為輸入參數、潛艇阻力及升力為目標函數，採用基因演算法進行分組最佳化，並討論不同參數變化對阻力及升力的影響。潛艇最小阻力771.649 N，較最佳化前減少6.15 %。另分別對潛艇受到下方來流(-10°)及上方來流(10°)進行最佳化，阻力分別較最佳化前減少了11.66%及14.38%。推論在來流角度變化的情形下，最佳化的結果將更為顯著，且變化趨勢與正向來流相同。最後經回歸分析得升力與輸入參數之判定係數僅0.089，而阻力則達0.910為高度相關，推論升力值與附屬件位置及高度並無顯著相關。
本研究建立了外形設計的最佳化流程，可以藉由數值模型的調整及納入更多性能參數，達到更完整、全面以及通用的載具外形最佳化設計工具，減少傳統設計上耗費的大量時間與金錢成本。

To enhance the endurance of submarines, this study employs numerical methods to optimize the layout of submarine appendages, aiming to reduce resistance and lift generated during navigation. The "SUBOFF" submarine, widely used and supported by reliable experimental data, is selected as the research subject. Three-dimensional computational fluid dynamics simulation software is applied for modeling, and the accuracy of the simulation is verified through mesh independence check. Taking the positions and heights of the sail and control surfaces as input parameters and submarine resistance and lift as object functions. This study use genetic algorithm for optimization, then discuss the influence of variety parameters on resistance and lift. The obtained minimum submarine resistance is 771.649 N, representing a 6.15% reduction compared to the pre-optimization state. Regression analysis reveals a coefficient of determination only 0.089 for lift with respect to input parameters, and for resistance shows a high correlation with a coefficient of determination of 0.910. It is inferred that lift is not significantly correlated with the positions and heights of the appendages.

[1] R. Burcher, & Rydill, L., Geometric form and arrangements, in Concepts in Submarine Design, Cambridge University Press, pp. 131-150, 1994.
[2] M. Renilson, Submarine hydrodynamics, 2 ed, Vol. 31, Springer, 2015.
[3] C. Zheng, et al., "An experimental investigation of drag and noise reduction from a circular cylinder using longitudinal grooves," Physics of Fluids, Vol. 33(11), 2021.
[4] A. Sharma, Introduction to computational fluid dynamics: development, application and analysis, Springer Nature, 2021.
[5] M. Mackay and R. Defence, The standard submarine model: a survey of static hydrodynamic experiments and semiempirical predictions, Citeseer, 2003.
[6] J.-Y. Park, N. Kim, and Y.-K. Shin, "Experimental study on hydrodynamic coefficients for high-incidence-angle maneuver of a submarine," International Journal of Naval Architecture and Ocean Engineering, Vol. 9(1), pp. 100-113, 2017.
[7] F. Gao, X. Gu, and D. Jeng, "Physical modeling of untrenched submarine pipeline instability," Ocean Engineering, Vol. 30(10), pp. 1283-1304, 2003.
[8] N. C. Groves, et al., Geometric Characteristics of DARPA Suboff Models: (DTRC Model Nos. 5470 and 5471), David Taylor Research Center, 1989.
[9] H. L. Liu, et al., Summary of DARPA Suboff Experimental Program Data, Naval surface warfare center carderock Division bethesda md hydromechanics directorate, 1998.
[10] R. F. Roddy, "Investigation of the stability and control characteristics of several configurations of the DARPA SUBOFF model (DTRC Model 5470) from captive-model experiments," David Taylor Research Center, Ship Hydromechanics Department, DTRC/SHD-1298-08, 1990.
[11] S. Sezen, et al., "Investigation of self-propulsion of DARPA Suboff by RANS method," Ocean Engineering, Vol. 150, pp. 258-271, 2018.
[12] X. Huang, et al., "Reducing underwater radiated noise of a SUBOFF model propelled by a pump-jet without tip clearance: Numerical simulation," Ocean Engineering, Vol. 243, 2022.
[13] M. Moonesun, Y. Korol, and H. Dalayeli, "CFD Analysis on the Bare Hull Form of Submarines for Minimizing the Resistance," International Journal of Maritime Technology, Vol. 3, pp. 1-16, 2015.
[14] M. Moonesun, et al., "Optimization on submarine stern design," Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, Vol. 231(1), pp. 109-119, 2017.
[15] T. Gao, et al., "Hull shape optimization for autonomous underwater vehicles using CFD," Engineering Applications of Computational Fluid Mechanics, Vol. 10(1), pp. 599-607, 2016.
[16] K. Zhang, L. Wang, and H. Chen. Position Optimization of Underwater Vehicle Appendage Based on Modular Grid. in OCEANS - MTS/IEEE Kobe Techno-Oceans (OTO). 2018.
[17] W. Luo and W. Lyu, "An application of multidisciplinary design optimization to the hydrodynamic performances of underwater robots," Ocean Engineering, Vol. 104, pp. 686-697, 2015.
[18] G. John, et al., Turbulence Models Commonly Used in CFD, in Applications of Computational Fluid Dynamics Simulation and Modeling, IntechOpen, 2021.
[19] T. Karthik and F. Durst, "Turbulence models and their applications," 10th Indo German Winter Academy, pp. 1-52, 2011.
[20] R. Shaheed, A. Mohammadian, and H. Kheirkhah Gildeh, "A comparison of standard k–ε and realizable k–ε turbulence models in curved and confluent channels," Environmental Fluid Mechanics, Vol. 19(2), pp. 543-568, 2019.
[21] K. Takahashi and P. K. Sahoo, "Fundamental CFD Study on the Hydrodynamic Performance of the DARPA SUBOFF Submarine," ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering, Vol. 2, 2019.
[22] ANSYS, ANSYS FLUENT Theory Guide. ANSYS Inc.
[23] F. Moukalled, et al., The finite volume method, Springer, 2016.
[24] M. Murayama and K. Yamamoto, "Comparison study of drag prediction by structured and unstructured mesh method," Journal of Aircraft, Vol. 45(3), pp. 799-822, 2008.
[25] M. Uy and J. K. Telford. Optimization by design of experiment techniques. in 2009 IEEE Aerospace conference. 2009. IEEE.
[26] J. Antony, Design of experiments for engineers and scientists, Elsevier, 2023.
[27] T. J. Santner, B. J. Williams, and W. I. Notz, Space-Filling Designs for Computer Experiments, The Design and Analysis of Computer Experiments, New York, Springer New York, 2018.
[28] W. J. Hill and W. G. Hunter, "A review of response surface methodology: a literature survey," Technometrics, Vol. 8(4), pp. 571-590, 1966.
[29] C. M. Anderson-Cook, C. M. Borror, and D. C. Montgomery, "Response surface design evaluation and comparison," Journal of Statistical Planning and Inference, Vol. 139(2), pp. 629-641, 2009.
[30] A. I. Khuri and S. Mukhopadhyay, "Response surface methodology," WIREs Computational Statistics, Vol. 2(2), pp. 128-149, 2010.
[31] S. M. Thede, "An introduction to genetic algorithms," Journal of Computing Sciences in Colleges, Vol. 20(1), pp. 115-123, 2004.
[32] A. Lambora, K. Gupta, and K. Chopra. Genetic Algorithm- A Literature Review. in 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon). 2019.
[33] S. Mirjalili, Genetic Algorithm, in Evolutionary Algorithms and Neural Networks: Theory and Applications, Springer International Publishing: Cham, pp. 43-55, 2019.
[34] J. Andre, P. Siarry, and T. Dognon, "An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization," Advances in Engineering Software, Vol. 32(1), pp. 49-60, 2001.
[35] N. M. Razali and J. Geraghty. Genetic algorithm performance with different selection strategies in solving TSP. in Proceedings of the world congress on engineering. 2011. International Association of Engineers Hong Kong, China.
[36] ANSYS, DesignXplorer User's Guide. ANSYS, Inc.
[37] P. Ngatchou, A. Zarei, and A. El-Sharkawi. Pareto Multi Objective Optimization. in Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems. 2005.
[38] P. Joubert, "Some aspects of submarine design: part 1: Hydrodynamics," Australian Department of Defence, 2004.
[39] N. Graphics. Submarine of the world. [cited November 2023]; Available from: https://imgur.com/K9HeDSD.
[40] Aokomoriuta. Wall function. [cited January 2024]; Available from: https://en.wikipedia.org/wiki/File:Law_of_the_wall_(English).svg.
[41] F. Pauw. Central Composite design. [cited November 2023]; Available from: https://develve.net/Central%20Composite%20design.html#3.
[42] Mike1979. Type 214 submarine. [cited November 2023]; Available from: https://en.wikipedia.org/wiki/Type_214_submarine#/media/File:Type_214_submarine.svg.
[43] Mike1979. Dolphin class submarine. [cited November 2023]; Available from: https://en.wikipedia.org/wiki/Dolphin-class_submarine#/media/File:Dolphin_class_submarine.svg.