Research Article

### Mathematical Model of Roll Decay Motion for a Surfaced Submarine

Year 2021, Issue: 219, 107 - 123, 30.06.2021

### Abstract

Among all ship motions, the most critical one is the roll motion for a submarine. The excessive roll motion can be harmful to both ship's crew and equipment, especially in surfaced condition. For this reason, it is important to predict the roll motion during the design stage to overcome excessive roll amplitudes. A mathematical model of the roll motion can be used to predict the motion responses of a submarine. Estimation of the roll damping is the most critical part to develop the mathematical model for a better prediction of the roll motion. The roll damping can be obtained experimentally, numerically and empirically. Experimental methods are expensive and time-consuming and empirical methods cannot be applied for all ship types. For this reason, numerical methods are frequently used due to the development of computer technologies in recent years, being economical and fast. In this study, the mathematical model of roll decay motion for a submarine at surfaced condition was obtained. The roll damping term was obtained numerically by carrying out roll decay simulations using a commercial Computational Fluid Dynamic (CFD) code. The inertia and restoring terms were obtained empirically by using the submarine geometry. The mathematical model was obtained and the roll decay motion of the surfaced submarine was calculated with a 20 degrees initial roll angle at zero speed and 5 kn, 7.5 kn and 10 kn forward speeds. The results were compared with numerical results and a good agreement was observed.

### References

• Cakici, F, Kahramanoglu, E., & Alkan, A. D. (2017). Numerical Prediction of Vertical Ship Motions and Added Resistance. International Journal of Maritime Engineering, 159(A4). https://doi.org/10.3940/rina.ijme.2017.a4.450
• Cakici, Ferdi, Kahramanoglu, E., Duman, S., & Alkan, A. D. (2018). A new URANS based approach on the prediction of vertical motions of a surface combatant in head waves. Ocean Engineering, 162, 21-33. https://doi.org/10.1016/j.oceaneng.2018.05.020
• Gokce, M.K., Kinaci, O.K. (2018). Numerical simulations of free roll decay of DTMB 5415. Ocean Engineering , 159, 539-551
• Hedberg, Sara. (2006). Investigation of Submarine Roll Behaviour. Masters Thesis, KTH Royal Institute of Technology, Sweden
• Himeno, Y. (1981). Prediction of ship roll damping-state of the art. U. Michigan Dept. of Naval Arch. and Marine Engineering, Report 239
• Ikeda, Y., Himeno, Y., Tanaka, N. (1978). A prediction method for ship roll damping. Report of the department of naval architecture, University of Osaka Prefecture, No. 00405
• ITTC. (2011). Recommended Procedures and Guidelines-Practical Guidelines for Ship CFD Applications
• Kahramanoglu, E., Yıldız, B., Çakıcı, F., & Yilmaz, H. (2020). Numerical roll damping prediction of a planing hull. Ships and Offshore Structures, 1-10. https://doi.org/10.1080/17445302.2020.1730088
• Letter, Brendan. (2009). Numerical and Experimental Roll Response and Decay of a Surfaced Submarine. Bachelor Thesis, University of Tasmania, Australia
• Thornhill, E., Hermanski, G. (2008). Numerical And Experimental Analysis of Surfaced Submarine Roll Decay Behaviour. Journal of Ocean Technology, 3(1), 91-100

### Satıhtaki Bir Denizaltının Yalpa Salınım Hareketinin Matematiksel Modeli

Year 2021, Issue: 219, 107 - 123, 30.06.2021

### Abstract

Bir denizaltı için yalpa hareketi diğer gemi hareketlerinin arasında en kritik olanıdır. Özellikle satıh durumunda, aşırı yalpa hareketi denizaltı mürettebatı ve ekipmanı için tehlikeli olabilir. Bu sebeple, aşırı genlikli yalpa hareketlerine maruz kalınmaması için dizayn aşamasında yalpa hareketinin analiz edilmesi gereklidir. Hareket genliklerini elde etmek için yalpa hareketinin matematiksel modeli kullanılabilir. Yalpa hareketinin matematiksel modelinin oluşturulmasında en önemli kısım yalpa sönümünün tahminidir. Yalpa sönümü deneysel, sayısal ve ampirik olarak elde edilebilir. Deneysel yöntemler pahalı ve zaman alıcı, ampirik ifadeler ise her gemi tipi için uygun değildir. Bu sebeple, son zamanlarda bilgisayar teknolojisindeki gelişiminde etkisiyle daha hızlı ve ucuz bir yöntem olan sayısal metotlar sıklıkla kullanılmaktadır. Bu çalışmada, satıhtaki bir denizaltının serbest yalpa hareketinin matematiksel modeli elde edilmiştir. Yalpa sönüm terimi denizaltının serbest yalpa salınım hareketinin ticari bir Hesaplamalı Akışkanlar Dinamiği (HAD) kodu ile sayısal olarak modellenmesi ile elde edilmiştir. Atalet ve doğrultma terimleri ise denizaltı geometrisi kullanılarak ampirik olarak hesaplanmıştır. Matematiksel model elde edilmiştir ve 20 derece serbest bırakma açısındaki denizaltı yalpa salınım hareketi sıfır hızda ve 5 kn, 7.5 kn ve 10 kn ileri hızda hesaplanmıştır. Elde edilen sonuçlar sayısal analiz sonuçları ile karşılaştırılmış ve uyumlu sonuçlar gözlemlenmiştir.

### References

• Cakici, F, Kahramanoglu, E., & Alkan, A. D. (2017). Numerical Prediction of Vertical Ship Motions and Added Resistance. International Journal of Maritime Engineering, 159(A4). https://doi.org/10.3940/rina.ijme.2017.a4.450
• Cakici, Ferdi, Kahramanoglu, E., Duman, S., & Alkan, A. D. (2018). A new URANS based approach on the prediction of vertical motions of a surface combatant in head waves. Ocean Engineering, 162, 21-33. https://doi.org/10.1016/j.oceaneng.2018.05.020
• Gokce, M.K., Kinaci, O.K. (2018). Numerical simulations of free roll decay of DTMB 5415. Ocean Engineering , 159, 539-551
• Hedberg, Sara. (2006). Investigation of Submarine Roll Behaviour. Masters Thesis, KTH Royal Institute of Technology, Sweden
• Himeno, Y. (1981). Prediction of ship roll damping-state of the art. U. Michigan Dept. of Naval Arch. and Marine Engineering, Report 239
• Ikeda, Y., Himeno, Y., Tanaka, N. (1978). A prediction method for ship roll damping. Report of the department of naval architecture, University of Osaka Prefecture, No. 00405
• ITTC. (2011). Recommended Procedures and Guidelines-Practical Guidelines for Ship CFD Applications
• Kahramanoglu, E., Yıldız, B., Çakıcı, F., & Yilmaz, H. (2020). Numerical roll damping prediction of a planing hull. Ships and Offshore Structures, 1-10. https://doi.org/10.1080/17445302.2020.1730088
• Letter, Brendan. (2009). Numerical and Experimental Roll Response and Decay of a Surfaced Submarine. Bachelor Thesis, University of Tasmania, Australia
• Thornhill, E., Hermanski, G. (2008). Numerical And Experimental Analysis of Surfaced Submarine Roll Decay Behaviour. Journal of Ocean Technology, 3(1), 91-100
There are 12 citations in total.

### Details

Primary Language English Engineering Articles Muhammed Cansız This is me YILDIZ TECHNICAL UNIVERSITY Türkiye Burak Yıldız YILDIZ TECHNICAL UNIVERSITY Türkiye June 30, 2021 Year 2021 Issue: 219

### Cite

 APA Cansız, M., & Yıldız, B. (2021). Mathematical Model of Roll Decay Motion for a Surfaced Submarine. Gemi Ve Deniz Teknolojisi(219), 107-123.