Farklı Ağ Elemanı Boyutlarının ve Türbülans Modellerinin Düz Levha Sürtünme Direnci Üzerindeki Etkisinin Sayısal Olarak İncelenmesi

Yıl 2023, Sayı: 223, 29 - 46, 24.08.2023

Erhan Aksu

https://doi.org/10.54926/gdt.1248594

Öz

Geminin hız gereksinimini karşılayacak makine gücünü belirlemek için gemi direncinin doğru bir şekilde tahmin edilmesinde kullanılan model deneyleri yönteminde model deneylerinin sonuçları ölçeklendirilerek modelden gemiye aktarılır ve gemi direnci belirlenir. Bu aktarımda uygulanan işlem adımlarında düz bir levhanın sürtünme direncinin belirlenmesi önemli bir rol oynamaktadır. Bu çalışmada iki boyutta düz bir levha üzerindeki akış 7 farklı Reynolds sayısı aralığında hesaplamalı akışkanlar dinamiği kullanılarak standart k-ε (gelişmiş duvar yaklaşımı ile) ve SST k-ω türbülans modelleri ile analiz edilmiştir. Analizler neticesinde yerel ve toplam sürtünme katsayıları ampirik bağıntılarla karşılaştırılmış, farklı ağ boyutlarının sayısal çözümler üzerinde etkisi incelenmiş ve türbülans modelleri karşılaştırılmıştır. Öncelikle akış yönünde eleman sayısı ve ilk ağ elemanın duvardan olan mesafesinin değiştirildiği ağ yapıları oluşturulmuştur. Bu ağ yapılarının seçilen türbülans modellerinde sürtünme direnç katsayıları ile olan ilişkisini belirleyebilmek için en düşük ve en yüksek hızda analizler gerçekleştirilmiştir. Analizler neticesinde akış yönündeki eleman sayısının toplam direnç katsayısı üzerinde etkisinin çok az olduğu görülmüştür. Buna karşın ilk ağ elemanın duvardan olan mesafesi özellikle düşük Reynolds sayısında gerçekleştirilen analizlerde etkilidir. En düşük ve en yüksek hızlarda gerçekleştirilen analizlerde yerel sürtünme direnç katsayısı eğrisinin ampirik bağıntılarla olan uyumlu olduğu ağ yapısında tüm hızlar için analizler gerçekleştirilmiştir. Sonuç olarak toplam sürtünme direnç katsayısı ve maksimum sınır tabaka kalınlıkları SST k-ω türbülans modeline göre standart k-ε (gelişmiş duvar yaklaşımı ile) türbülans modelinde daha büyük çıkmaktadır.

Anahtar Kelimeler

Düz levha, sürtünme direnci, hesaplamalı akışkanlar dinamiği, ağ yapısı

Numerical Investigation of the Effect of Different Grid Element Sizes and Turbulence Models on the Friction Resistance of Flat Plates

Öz

In the model testing method, the results of the model testing are scaled and transferred from the model to the ship, and the ship resistance is determined to accurately estimate the resistance of the ship to determine the engine power that meets the speed requirement of the ship. The evaluation of the frictional resistance of a flat plate is critical to the process steps used in this transfer. In this study, the flow on a flat plate is analyzed in two dimensions using computational fluid dynamics in the 7 different Reynolds numbers with standard k-ε (with an enhanced wall treatment) and SST k-ω turbulence models. As a result of the analyzes, local and total friction coefficients are compared with empirical relationships, the effect of different grid sizes on numerical solutions is investigated and turbulence models are compared. In the first step, structures are developed where the number of elements in the flow direction and the distance of the first grid element from the wall are modified. The lowest and highest velocity analysis is performed to determine the relationship of these grid structures to the resistance coefficients in the selected turbulence models. The analysis shows that the number of elements in the flow direction has little impact on the total resistance coefficient. However, the distance from the wall of the first grid element is particularly effective in analyzing the low Reynolds number. Analyzes are performed for all velocities in the grid structure where the local frictional resistance coefficient curve is compatible with empirical correlations in the analyzes performed at the lowest and highest velocities. As a result, the total frictional drag coefficient and maximum boundary layer thicknesses are larger in the standard k-ε turbulence model (with an enhanced wall treatment) than in the SST k-ω turbulence model.

Anahtar Kelimeler

Flat plate, friction resistance, computational fluid dynamics, grid structure

Kaynakça

• 1957 "Proceedings of the 8th ITTC." Madrid, Spain 1957, published by Canal de Experiencias Hidrodinamicas, El Pardo, Madrid.
• Anderson, J. D. J. P. t. (2005). "Ludwig Prandtl’s boundary layer.", Physics today , 58(12): 42-48.
• Bose, N., et al. (2002). "Final Report and Recommendations to the 23rd ITTC." Proceedings of the 23rd ITTC.
• Boussinesq, J. (1877). Essai sur la théorie des eaux courantes, Imprimerie nationale Campana, E., et al. (2008). The Resistance Committee-Final Report and recommendations to the 25th ITTC. 25th International Towing Tank Conference.
• Coles, D. (1956). "The law of the wake in the turbulent boundary layer." Journal of Fluid Mechanics 1(2): 191-226. Date, J. C. and S. R. Turnock (1999). A study into the techniques needed to accurately predict skin friction using RANS solvers with validation against Froude's historical flat plate experimental data.
• Eça, L., et al. (2008). "The numerical friction line." Journal of marine science and technology, 13(4): 328-345.
• Fluent, A. (2015). Ansys Fluent Theory guide, ANSYS Inc.
• Froude, W. (1872). "Experiments on the surface-friction experienced by a plane moving through water." British Association for the Advancement of Science 42: 118-124.
• Froude, W. (1874). Report to the lords commissioners of the admiralty on experiments for the determination of the frictional resistance of water on a surface, under various conditions, performed at Chelston cross, under the authority of their lordships, Taylor & Francis.
• Froude, W., et al. (1955). The Papers of William Froude, 1810-1879: With a Memoir by Sir Westcott Abell and an Evaluation of William Froude's Work by RWL Gawn: Collected Into One Volume, Institution of Naval Architects.
• Glegg, S. and W. Devenport (2017). Chapter 8 - Turbulence and stochastic processes. Aeroacoustics of Low Mach Number Flows. S. Glegg and W. Devenport, Academic Press: 163-184. Gorski, J., et al. (2011). The resistance committee-final report and recommendations to the 26th ittc. Proceeding of 26th Iternational Towing Tank Conference. Grigson, C. (1999). "A planar friction algorithm and its use in analysing hull resistance." Trans RINA. Hughes, G. (1954). "Friction and form resistance in turbulent flow, and a proposed formulation for use in model and ship correlation." National Physical Laboratory, NPL, Ship Division, Presented at the Institution of Naval Architects, Paper No. 7, London, April, RINA Transactions 1954-16.
• Katsui, T. (2005). The proposal of a new friction line. Fifth Osaka colloquium on advanced CFD applications to ship flow and hull form design, Osaka, Japan, 2005. Korkmaz, K., Werner, S., Bensow, R. (2019). Numerical Friction Lines For CFD Based Form Factor Determination. In MARINE VIII: proceedings of the VIII International Conference on Computational Methods in Marine Engineering (pp. 694-705). CIMNE.
• Launder, B. E. and Spalding, D. B. (1983). The numerıcal computatıon of turbulent flows. Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion. S. V. Patankar, A. Pollard, A. K. Singhal and S. P. Vanka, Pergamon: 96-116. Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA journal, 32(8), 1598-1605. Molland, A. F., et al. (2017). Ship resistance and propulsion, Cambridge university press. Park, D.-W. (2015). "A study on the effect of flat plate friction resistance on speed performance prediction of full scale." International Journal of Naval Architecture and Ocean Engineering 7(1): 195-211. Schlichting, H. (1979). Boundary layer theory, 7th edn. McGrawHill, New York.
• Schoenherr, K. E. (1932). "Resistance of flat surfaces moving through a fluid." Trans. Soc. Nav. Archit. Mar. Eng. 40: 279-313. Schultz-Grunow, F. (1941). New frictional resistance law for smooth plates, National Advisory Commitee for Aeronautics. Von Kármán, T. J. Z. A. M. M. (1921). "Uber laminare und turbulente Reibung." 1: 233-252. Wang, Z.-z., et al. (2015). "A numerical flat plate friction line and its application." Journal of Hydrodynamics, Ser. B 27(3): 383-393. White, F. M. (2006). Viscous fluid flow, third ed. McGraw-Hill, New York. Zeng, Q., et al. (2019). "A modification of the ITTC57 correlation line for shallow water." Journal of Marine Science and Technology 24(2): 642-657.