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Verification and Validation of Numerical Simulations of Displacement Type Vessels

Year 2021, Volume , Issue 219, 77 - 95, 30.06.2021

Abstract

It is crucial to reduce the power need and fuel consumption of ships, thus eco-friendly ship design can be achieved. This goal can be achieved with the accurate prediction of the hydrodynamic performance of ships. In this manner, numerical and experimental methods are widely used by many researchers. Experimental studies are based on towing tank tests while the numerical methods are based on viscous and potential flow assumptions. In this study, it is aimed to investigate different types of ship models to provide a comprehensive data set. A numerical approach solving RANS (Reynolds-averaged Navier-Stokes) equations was employed for two container ships and a naval surface combatant to show the precision and accuracy of the numerical method. These vessels are KRISO container ship (KCS), Duisburg test case (DTC) and ONR Tumblehome (ONRT) developed by the Office of Naval Research. The flow around these vessels was investigated by taking the free surface into account. The flow analyses were carried out in calm water conditions and the ships were set to be free to sinkage and trim. For the verification study, the GCI method, which is recommended by ITTC (International Towing Tank Conference) and AIAA (American Institute of Aeronautics and Astronautics), was employed. Fine, medium and coarse cases were generated with different grid sizes and time step sizes. These cases were generated by using a constant refinement ratio\ \left(\sqrt2\right). The numerical analyses for the verification purpose were conducted at the design Froude number of each model ship. The uncertainty values were obtained for the total resistance. Following this, a comprehensive validation study was conducted for each ship model in a wide range of Froude numbers, covering low and moderate speeds. The validation was done by comparing the numerical results with the available experimental data. In addition to this, the results were compared with other existing numerical results in the literature. The validation was done in terms of total resistance, sinkage and trim parameters. This study showed that the computational fluid dynamics (CFD) method can sufficiently estimate the ship’s hydrodynamic performance. Within these results, when there is a lack of experimental data for comparison, the numerical method is again reliable having low spatial and temporal uncertainty values.

References

  • Bertram, V. (2014). Practical Ship Hydrodynamics (2nd ed.). Elsevier Science.
  • Can, U., Delen, C., & Bal, S. (2020). "Effective wake estimation of KCS hull at full-scale by GEOSIM method based on CFD". Ocean Engineering, 218, 108052. doi:10.1016/j.oceaneng.2020.108052.
  • Carrica, P. M., Fu, H., & Stern, F. (2011). "Computations of self-propulsion free to sink and trim and of motions in head waves of the KRISO Container Ship (KCS) model". Applied Ocean Research, 33(4), 309–320. doi:10.1016/j.apor.2011.07.003.
  • Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., & Raad, P. E. (2008). "Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications". Journal of Fluids Engineering, 130(7), 078001. doi:10.1115/1.2960953.
  • Cook, S. S. (2011). Effects of headwinds on towing tank resistance and PMM tests for ONR Tumblehome [MSc Thesis, University of Iowa]. Available from Iowa Research Online. doi:10.17077/etd.9t68ik1e.
  • Cosner, R., Oberkampf, B., Rumsey, C., Rahaim, C., & Shih, T. (2006). "AIAA Committee on Standards for Computational Fluid Dynamics: Status and Plans". In 44th AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2006-889
  • Delen, C., & Bal, S. (2019, September 9). "Uncertainty analysis of numerical and experimental resistance tests for ONR Tumblehome". International Maritime Association of the Mediterranean IMAM 2019, Varna, Bulgaria.
  • Delen, C., Can, U., & Bal, S. (2020). "Prediction of Resistance and Self-Propulsion Characteristics of a Full-Scale Naval Ship by CFD-Based GEOSIM Method". Journal of Ship Research, 16. doi:10.5957/JOSR.03200022
  • Dogrul, A., Song, S., & Demirel, Y. K. (2020). "Scale effect on ship resistance components and form factor". Ocean Engineering, 209, 107428. doi:10.1016/j.oceaneng.2020.107428
  • Eça, L., Vaz, G., Toxopeus, S. L., & Hoekstra, M. (2019). "Numerical Errors in Unsteady Flow Simulations". Journal of Verification, Validation and Uncertainty Quantification, 4(021001). doi:10.1115/1.4043975
  • Guo, H., Zou, Z., Liu, Y., & Wang, F. (2018). "Investigation on hull-propeller-rudder interaction by RANS simulation of captive model tests for a twin-screw ship". Ocean Engineering, 162, 259–273. doi:10.1016/j.oceaneng.2018.05.035
  • Hino, T., Stern, F., Larsson, L., Visonneau, M., Hirata, N., & Kim, J. (Eds.). (2021). Numerical Ship Hydrodynamics: An Assessment of the Tokyo 2015 Workshop. Springer International Publishing. doi:10.1007/978-3-030-47572-7
  • ITTC. (1957). Report of Resistance Committee. Proceedings of 8th ITTC, Madrid, Spain.
  • ITTC. (2014a). 7.5-03-01-01 Uncertainty Analysis in CFD, Verification and Validation Methodology and Procedures. In ITTC - Recommended Procedures and Guidelines.
  • ITTC. (2014b). 7.5-03-02-03 Practical Guidelines for Ship CFD Applications. In ITTC - Recommended Procedures and Guidelines.
  • Kahramanoglu, E., Cakici, F., & Dogrul, A. (2020). "Numerical Prediction of the Vertical Responses of Planing Hulls in Regular Head Waves". Journal of Marine Science and Engineering, 8(6), 455. doi:10.3390/jmse8060455
  • Kim, W. J., Van, S. H., & Kim, D. H. (2001). "Measurement of flows around modern commercial ship models". Experiments in Fluids, 31(5), 567–578. doi:10.1007/s003480100332
  • Kinaci, O. K., Gokce, M. K., & Delen, C. (2020). "Resistance experiments and self-propulsion estimations of Duisburg Test Case at 1/100 scale". Ship Technology Research, 67(2), 109–120. doi:10.1080/09377255.2020.1729454
  • Kok, Z., Duffy, J., Chai, S., Jin, Y., & Javanmardi, M. (2020). "Numerical investigation of scale effect in self-propelled container ship squat". Applied Ocean Research, 99, 102143. doi:10.1016/j.apor.2020.102143
  • Larsson, L., & Zou, L. (2014). "Evaluation of Resistance, Sinkage and Trim, Self Propulsion and Wave Pattern Predictions". In L. Larsson, F. Stern, & M. Visonneau (Eds.), Numerical Ship Hydrodynamics (pp. 17–64). Springer Netherlands. doi:10.1007/978-94-007-7189-5_2
  • Menter, F. R. (1994). "Two-equation eddy-viscosity turbulence models for engineering applications". AIAA Journal, 32(8), 1598–1605. doi:10.2514/3.12149
  • Menter, Florian R. (2009). "Review of the shear-stress transport turbulence model experience from an industrial perspective". International Journal of Computational Fluid Dynamics, 23(4), 305–316. doi:10.1080/10618560902773387
  • Moctar, O. el, Shigunov, V., & Zorn, T. (2012). "Duisburg Test Case: Post-Panamax Container Ship for Benchmarking". Ship Technology Research, 59(3), 50–64. doi:10.1179/str.2012.59.3.004
  • Ozdemir, Y. H., Cosgun, T., Dogrul, A., & Barlas, B. (2016). "A Numerical Application to Predict The Resistance and Wave Pattern of KRISO Container Ship". Brodogradnja : Teorija i Praksa Brodogradnje i Pomorske Tehnike, 67(2), 47–65. doi:10.21278/brod67204
  • Pereira, F. S., Eça, L., & Vaz, G. (2017). "Verification and Validation exercises for the flow around the KVLCC2 tanker at model and full-scale Reynolds numbers". Ocean Engineering, 129, 133–148. doi:10.1016/j.oceaneng.2016.11.005
  • Richardson, L. F. (1911). "The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam". Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 210, 307–357.
  • Roache, Patrick J. (1998). "Verification of Codes and Calculations". AIAA Journal, 36(5), 696–702. doi:10.2514/2.457
  • Roache, P.J. (1997). "Quantification of uncertainty in computational fluid dynamics". Annual Review of Fluid Mechanics, 29, 123–160. Scopus. doi:10.1146/annurev.fluid.29.1.123
  • Sezen, S., Dogrul, A., Delen, C., & Bal, S. (2018). "Investigation of self-propulsion of DARPA Suboff by RANS method". Ocean Engineering, 150, 258–271. doi:10.1016/j.oceaneng.2017.12.051
  • Shen, Z., Wan, D., & Carrica, P. M. (2015). "Dynamic overset grids in OpenFOAM with application to KCS self-propulsion and maneuvering. Ocean Engineering, 108, 287–306. doi:10.1016/j.oceaneng.2015.07.035
  • Stern, F., Wilson, R. V., Coleman, H. W., & Paterson, E. G. (2001). Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures". Journal of Fluids Engineering, 123(4), 793–802. doi:10.1115/1.1412235
  • Terziev, M., Tezdogan, T., Oguz, E., Gourlay, T., Demirel, Y. K., & Incecik, A. (2018). "Numerical investigation of the behaviour and performance of ships advancing through restricted shallow waters". Journal of Fluids and Structures, 76, 185–215. doi:10.1016/j.jfluidstructs.2017.10.003
  • Tezdogan, T., Demirel, Y. K., Kellett, P., Khorasanchi, M., Incecik, A., & Turan, O. (2015). "Full-scale unsteady RANS CFD simulations of ship behaviour and performance in head seas due to slow steaming". Ocean Engineering, 97, 186–206. doi:10.1016/j.oceaneng.2015.01.011
  • Tezdogan, T., Incecik, A., & Turan, O. (2016). "A numerical investigation of the squat and resistance of ships advancing through a canal using CFD". Journal of Marine Science and Technology, 1–16. doi:10.1007/s00773-015-0334-1
  • Van, S., Ahn, H., Lee, Y., Kim, C., Hwang, S., Kim, J., Kim, K., & Park, I. (2011). "Resistance characteristics and form factor evaluation for geosim models of KVLCC2 and KCS". Proceeding of 2nd International Conference on Advanced Model Measurement Technology for EU Maritime Industry, 282–293.
  • Van, S. H., Kim, W. J., Yoon, H. S., Lee, Y. Y., & Park, I. R. (2006). "Flow measurement around a model ship with propeller and rudder". Experiments in Fluids, 40(4), 533–545. doi:10.1007/s00348-005-0093-6
  • Wilcox, D. C. (2008). "Formulation of the k-w Turbulence Model Revisited". AIAA Journal, 46(11), 2823–2838. doi:10.2514/1.36541
  • Xing, T., & Stern, F. (2010). "Factors of Safety for Richardson Extrapolation". Journal of Fluids Engineering, 132(061403). doi:10.1115/1.4001771
  • Zhang, Z. (2010). "Verification and validation for RANS simulation of KCS container ship without/with propeller". Journal of Hydrodynamics, Ser. B, 22(5, Supplement 1), 932–939. doi:10.1016/S1001-6058(10)60055-8

Deplasman Tipi Gemiler için Sayısal Analizlerin Gerçeklemesi ve Doğrulaması

Year 2021, Volume , Issue 219, 77 - 95, 30.06.2021

Abstract

Gemilerde güç ihtiyacı ve yakıt tüketimini en aza indirmek çok önemlidir, bu sayede daha çevreci gemiler elde edilmiş olur. Bu hedef, gemilerin hidrodinamik performansının tahmin edilmesi ile elde edilebilir. Bu bağlamda, çeşitli araştırmacılar tarafından deneysel ve sayısal yöntemler yaygın olarak kullanılmaktadır. Deneysel çalışmalar model deneylerine dayanırken sayısal yöntemler viskoz ve potansiyel akış kabullerine dayanmaktadır. Bu çalışmada çeşitli tipte gemiler sayısal olarak incelenerek hem gerçekleme hem de doğrulama adına kapsamlı bir veri setinin sunulması amaçlanmıştır. Sayısal yöntemin doğruluğunu ve hassasiyetini göstermek adına iki konteyner gemisi ve bir muharip suüstü gemisi için RANS denklemlerini çözen sayısal bir yaklaşım kullanılmıştır. Bu gemiler KRISO konteyner gemisi (KCS), Duisburg test gemisi (DTC) ve ONR (Office of Naval Research) tarafından geliştirilen teknedir. Bu gemiler etrafındaki akış incelenirken serbest yüzey etkileri hesaba katılmıştır. Akış analizleri sakin su koşullarında gerçekleştirilmiştir ve gemiler paralel batma ve trim hareketine karşı serbest bırakılmıştır. Belirsizlik çalışması için ITTC ve AIAA tarafından önerilen GCI yöntemi kullanılmıştır. Sık, orta ve seyrek olacak şekilde ağ boyutu ve zaman adımı açısından farklı analiz setleri kurgulanmıştır. Bu analiz setleri sabit bir iyileştirme oranıyla \left(\sqrt\mathbf{2}\right) oluşturulmuştur. Belirsizlik amaçlı sayısal analizler her bir geminin dizayn Froude sayısında gerçekleştirilmiştir. Belirsizlik değerleri toplam direnç açısından elde edilmiştir. Bunu takiben, düşük ve orta hızları kapsayacak şekilde geniş bir Froude sayısı aralığında her bir model gemi için kapsamlı bir doğrulama çalışması yapılmıştır. Doğrulama, sayısal sonuçların erişilebilen deneysel sonuçlarla kıyaslanmasıyla yapılmıştır. Buna ek olarak, sonuçlar literatürde mevcut diğer sayısal sonuçlarla karşılaştırılmıştır. Doğrulama, toplam direnç, paralel batma ve trim açısı parametreleri üzerinden yapılmıştır. Bu çalışma, hesaplamalı akışkanlar dinamiği (HAD) yönteminin gemi hidrodinamik performansını yeterli düzeyde tahmin edebildiğini göstermiştir. Bu sonuçlara göre karşılaştırma için deneysel veri eksikliğinde sayısal yöntem düşük belirsizlik değerleriyle güvenilirdir.

References

  • Bertram, V. (2014). Practical Ship Hydrodynamics (2nd ed.). Elsevier Science.
  • Can, U., Delen, C., & Bal, S. (2020). "Effective wake estimation of KCS hull at full-scale by GEOSIM method based on CFD". Ocean Engineering, 218, 108052. doi:10.1016/j.oceaneng.2020.108052.
  • Carrica, P. M., Fu, H., & Stern, F. (2011). "Computations of self-propulsion free to sink and trim and of motions in head waves of the KRISO Container Ship (KCS) model". Applied Ocean Research, 33(4), 309–320. doi:10.1016/j.apor.2011.07.003.
  • Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., & Raad, P. E. (2008). "Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications". Journal of Fluids Engineering, 130(7), 078001. doi:10.1115/1.2960953.
  • Cook, S. S. (2011). Effects of headwinds on towing tank resistance and PMM tests for ONR Tumblehome [MSc Thesis, University of Iowa]. Available from Iowa Research Online. doi:10.17077/etd.9t68ik1e.
  • Cosner, R., Oberkampf, B., Rumsey, C., Rahaim, C., & Shih, T. (2006). "AIAA Committee on Standards for Computational Fluid Dynamics: Status and Plans". In 44th AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2006-889
  • Delen, C., & Bal, S. (2019, September 9). "Uncertainty analysis of numerical and experimental resistance tests for ONR Tumblehome". International Maritime Association of the Mediterranean IMAM 2019, Varna, Bulgaria.
  • Delen, C., Can, U., & Bal, S. (2020). "Prediction of Resistance and Self-Propulsion Characteristics of a Full-Scale Naval Ship by CFD-Based GEOSIM Method". Journal of Ship Research, 16. doi:10.5957/JOSR.03200022
  • Dogrul, A., Song, S., & Demirel, Y. K. (2020). "Scale effect on ship resistance components and form factor". Ocean Engineering, 209, 107428. doi:10.1016/j.oceaneng.2020.107428
  • Eça, L., Vaz, G., Toxopeus, S. L., & Hoekstra, M. (2019). "Numerical Errors in Unsteady Flow Simulations". Journal of Verification, Validation and Uncertainty Quantification, 4(021001). doi:10.1115/1.4043975
  • Guo, H., Zou, Z., Liu, Y., & Wang, F. (2018). "Investigation on hull-propeller-rudder interaction by RANS simulation of captive model tests for a twin-screw ship". Ocean Engineering, 162, 259–273. doi:10.1016/j.oceaneng.2018.05.035
  • Hino, T., Stern, F., Larsson, L., Visonneau, M., Hirata, N., & Kim, J. (Eds.). (2021). Numerical Ship Hydrodynamics: An Assessment of the Tokyo 2015 Workshop. Springer International Publishing. doi:10.1007/978-3-030-47572-7
  • ITTC. (1957). Report of Resistance Committee. Proceedings of 8th ITTC, Madrid, Spain.
  • ITTC. (2014a). 7.5-03-01-01 Uncertainty Analysis in CFD, Verification and Validation Methodology and Procedures. In ITTC - Recommended Procedures and Guidelines.
  • ITTC. (2014b). 7.5-03-02-03 Practical Guidelines for Ship CFD Applications. In ITTC - Recommended Procedures and Guidelines.
  • Kahramanoglu, E., Cakici, F., & Dogrul, A. (2020). "Numerical Prediction of the Vertical Responses of Planing Hulls in Regular Head Waves". Journal of Marine Science and Engineering, 8(6), 455. doi:10.3390/jmse8060455
  • Kim, W. J., Van, S. H., & Kim, D. H. (2001). "Measurement of flows around modern commercial ship models". Experiments in Fluids, 31(5), 567–578. doi:10.1007/s003480100332
  • Kinaci, O. K., Gokce, M. K., & Delen, C. (2020). "Resistance experiments and self-propulsion estimations of Duisburg Test Case at 1/100 scale". Ship Technology Research, 67(2), 109–120. doi:10.1080/09377255.2020.1729454
  • Kok, Z., Duffy, J., Chai, S., Jin, Y., & Javanmardi, M. (2020). "Numerical investigation of scale effect in self-propelled container ship squat". Applied Ocean Research, 99, 102143. doi:10.1016/j.apor.2020.102143
  • Larsson, L., & Zou, L. (2014). "Evaluation of Resistance, Sinkage and Trim, Self Propulsion and Wave Pattern Predictions". In L. Larsson, F. Stern, & M. Visonneau (Eds.), Numerical Ship Hydrodynamics (pp. 17–64). Springer Netherlands. doi:10.1007/978-94-007-7189-5_2
  • Menter, F. R. (1994). "Two-equation eddy-viscosity turbulence models for engineering applications". AIAA Journal, 32(8), 1598–1605. doi:10.2514/3.12149
  • Menter, Florian R. (2009). "Review of the shear-stress transport turbulence model experience from an industrial perspective". International Journal of Computational Fluid Dynamics, 23(4), 305–316. doi:10.1080/10618560902773387
  • Moctar, O. el, Shigunov, V., & Zorn, T. (2012). "Duisburg Test Case: Post-Panamax Container Ship for Benchmarking". Ship Technology Research, 59(3), 50–64. doi:10.1179/str.2012.59.3.004
  • Ozdemir, Y. H., Cosgun, T., Dogrul, A., & Barlas, B. (2016). "A Numerical Application to Predict The Resistance and Wave Pattern of KRISO Container Ship". Brodogradnja : Teorija i Praksa Brodogradnje i Pomorske Tehnike, 67(2), 47–65. doi:10.21278/brod67204
  • Pereira, F. S., Eça, L., & Vaz, G. (2017). "Verification and Validation exercises for the flow around the KVLCC2 tanker at model and full-scale Reynolds numbers". Ocean Engineering, 129, 133–148. doi:10.1016/j.oceaneng.2016.11.005
  • Richardson, L. F. (1911). "The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam". Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 210, 307–357.
  • Roache, Patrick J. (1998). "Verification of Codes and Calculations". AIAA Journal, 36(5), 696–702. doi:10.2514/2.457
  • Roache, P.J. (1997). "Quantification of uncertainty in computational fluid dynamics". Annual Review of Fluid Mechanics, 29, 123–160. Scopus. doi:10.1146/annurev.fluid.29.1.123
  • Sezen, S., Dogrul, A., Delen, C., & Bal, S. (2018). "Investigation of self-propulsion of DARPA Suboff by RANS method". Ocean Engineering, 150, 258–271. doi:10.1016/j.oceaneng.2017.12.051
  • Shen, Z., Wan, D., & Carrica, P. M. (2015). "Dynamic overset grids in OpenFOAM with application to KCS self-propulsion and maneuvering. Ocean Engineering, 108, 287–306. doi:10.1016/j.oceaneng.2015.07.035
  • Stern, F., Wilson, R. V., Coleman, H. W., & Paterson, E. G. (2001). Comprehensive Approach to Verification and Validation of CFD Simulations—Part 1: Methodology and Procedures". Journal of Fluids Engineering, 123(4), 793–802. doi:10.1115/1.1412235
  • Terziev, M., Tezdogan, T., Oguz, E., Gourlay, T., Demirel, Y. K., & Incecik, A. (2018). "Numerical investigation of the behaviour and performance of ships advancing through restricted shallow waters". Journal of Fluids and Structures, 76, 185–215. doi:10.1016/j.jfluidstructs.2017.10.003
  • Tezdogan, T., Demirel, Y. K., Kellett, P., Khorasanchi, M., Incecik, A., & Turan, O. (2015). "Full-scale unsteady RANS CFD simulations of ship behaviour and performance in head seas due to slow steaming". Ocean Engineering, 97, 186–206. doi:10.1016/j.oceaneng.2015.01.011
  • Tezdogan, T., Incecik, A., & Turan, O. (2016). "A numerical investigation of the squat and resistance of ships advancing through a canal using CFD". Journal of Marine Science and Technology, 1–16. doi:10.1007/s00773-015-0334-1
  • Van, S., Ahn, H., Lee, Y., Kim, C., Hwang, S., Kim, J., Kim, K., & Park, I. (2011). "Resistance characteristics and form factor evaluation for geosim models of KVLCC2 and KCS". Proceeding of 2nd International Conference on Advanced Model Measurement Technology for EU Maritime Industry, 282–293.
  • Van, S. H., Kim, W. J., Yoon, H. S., Lee, Y. Y., & Park, I. R. (2006). "Flow measurement around a model ship with propeller and rudder". Experiments in Fluids, 40(4), 533–545. doi:10.1007/s00348-005-0093-6
  • Wilcox, D. C. (2008). "Formulation of the k-w Turbulence Model Revisited". AIAA Journal, 46(11), 2823–2838. doi:10.2514/1.36541
  • Xing, T., & Stern, F. (2010). "Factors of Safety for Richardson Extrapolation". Journal of Fluids Engineering, 132(061403). doi:10.1115/1.4001771
  • Zhang, Z. (2010). "Verification and validation for RANS simulation of KCS container ship without/with propeller". Journal of Hydrodynamics, Ser. B, 22(5, Supplement 1), 932–939. doi:10.1016/S1001-6058(10)60055-8

Details

Primary Language English
Subjects Engineering
Journal Section Issue
Authors

Sarih SARI
YILDIZ TEKNİK ÜNİVERSİTESİ
0000-0002-0665-5046
Türkiye


Ali DOĞRUL (Primary Author)
MİLLİ SAVUNMA ÜNİVERSİTESİ, DENİZ HARP OKULU
0000-0003-3236-555X
Türkiye

Publication Date June 30, 2021
Published in Issue Year 2021, Volume , Issue 219

Cite

Bibtex @research article { gdt927147, journal = {Gemi ve Deniz Teknolojisi}, issn = {1300-1973}, eissn = {2651-530X}, address = {}, publisher = {TMMOB Gemi Mühendisleri Odası}, year = {2021}, volume = {}, pages = {77 - 95}, doi = {}, title = {Verification and Validation of Numerical Simulations of Displacement Type Vessels}, key = {cite}, author = {Sarı, Sarih and Doğrul, Ali} }
APA Sarı, S. & Doğrul, A. (2021). Verification and Validation of Numerical Simulations of Displacement Type Vessels . Gemi ve Deniz Teknolojisi , (219) , 77-95 . Retrieved from https://dergipark.org.tr/en/pub/gdt/issue/63160/927147
MLA Sarı, S. , Doğrul, A. "Verification and Validation of Numerical Simulations of Displacement Type Vessels" . Gemi ve Deniz Teknolojisi (2021 ): 77-95 <https://dergipark.org.tr/en/pub/gdt/issue/63160/927147>
Chicago Sarı, S. , Doğrul, A. "Verification and Validation of Numerical Simulations of Displacement Type Vessels". Gemi ve Deniz Teknolojisi (2021 ): 77-95
RIS TY - JOUR T1 - Verification and Validation of Numerical Simulations of Displacement Type Vessels AU - Sarih Sarı , Ali Doğrul Y1 - 2021 PY - 2021 N1 - DO - T2 - Gemi ve Deniz Teknolojisi JF - Journal JO - JOR SP - 77 EP - 95 VL - IS - 219 SN - 1300-1973-2651-530X M3 - UR - Y2 - 2021 ER -
EndNote %0 Gemi ve Deniz Teknolojisi Verification and Validation of Numerical Simulations of Displacement Type Vessels %A Sarih Sarı , Ali Doğrul %T Verification and Validation of Numerical Simulations of Displacement Type Vessels %D 2021 %J Gemi ve Deniz Teknolojisi %P 1300-1973-2651-530X %V %N 219 %R %U
ISNAD Sarı, Sarih , Doğrul, Ali . "Verification and Validation of Numerical Simulations of Displacement Type Vessels". Gemi ve Deniz Teknolojisi / 219 (June 2021): 77-95 .
AMA Sarı S. , Doğrul A. Verification and Validation of Numerical Simulations of Displacement Type Vessels. Gemi ve Deniz Teknolojisi. 2021; (219): 77-95.
Vancouver Sarı S. , Doğrul A. Verification and Validation of Numerical Simulations of Displacement Type Vessels. Gemi ve Deniz Teknolojisi. 2021; (219): 77-95.
IEEE S. Sarı and A. Doğrul , "Verification and Validation of Numerical Simulations of Displacement Type Vessels", Gemi ve Deniz Teknolojisi, no. 219, pp. 77-95, Jun. 2021