Influence of Full and Symmetrical Domains on the Numerical Flow around a SUBOFF Submarine Model using OpenFOAM

Document Type : Regular Article

Authors

1 Department of Systems & Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan

2 Department of Marine Engineering, Hang Tuah University, Surabaya, Indonesia

Abstract

In this research, we consider the influence of two kinds of domain on the numerical flow around a submarine model. A fully appended SUBOFF submarine model was used, and the structure and characteristics of the flow were investigated under a full domain and a symmetrical domain arrangement. The numerical simulation was carried out using the OpenFOAM software, and the flow was numerically modelled as single-phase and incompressible. The SST k-ω turbulence model was used in both domains, together with an insensitive Spalding wall function to represent the boundary layer near the wall. The results showed that simulations in both the full and symmetrical domains could accurately predict the total resistance. Compared to the symmetrical domain, the resistance value obtained with the full domain was more precise; the symmetrical domain under coarse grid conditions had an error value of 1.34%, whereas the full domain using the same grid size had an error value of 0.6%. Hence, the full domain was superior in terms of predicting the resistance with a coarse grid. Next, the pressure coefficient comparison at the leading edge of the rudder was calculated, where = 0.92, and the symmetric domain was found to have a value of 0.0747 whereas the full domain had a value of 0.236. Compared with the results from experiment (=0.302), the symmetric domain appears to give an underestimate for the pressure distribution at this position. In addition, the flow structures and properties in both domains differ, particularly in terms of the vortical structures generated by the sail and rudders. The simulation results for the full domain reveal that the flow around the SUBOFF model is asymmetric. The full domain was able to capture the flow structures in more detail than the symmetrical domain, and represented the velocity distribution at the propeller plane better. As a result, the full domain must be considered when carrying out propeller analysis and self-propulsion simulations.

Keywords


Atta, T., Z. Ali, S. F. Ali and E. Uddin (2019). Hydrodynamic design and performance analysis of underwater vehicles using CFD. Central European Symposium on Thermophysics 2019 (CEST).##
Barth, T. J. and D. C. Jespersen (1989). The design and application of upwind schemes on unstructured meshes. 27th Aerospace Sciences Meeting.##
Boache, J. (1994). Perspective: A method for uniform reporting of grid refinement studies. Journal of Fluid Engineering 116, 405-413.##
Catalano, P., W. Meng, G. Iaccarino and P. Moin (2003). Numerical simulation of the flow around a circular cylinder at high Reynolds numbers. International Journal of Heat and Fluid Flow 24(4), 463-69.##
Constantinescu, G. and K. Squires (2004). Numerical investigations of flow over a sphere in the subcritical and supercritical regimes. Physics of Fluids 16(5), 1449-66.##
Doğrul, A. (2019). Hydrodynamic investigation of a submarine moving under free surface. Journal of ETA Maritime Science 7(3), 212-27.##
Ellis, C. L., D. B. Clarke, D. Butler and P. Brandner (2016). Complementary CFD study of generic submarine model tests in a cavitation tunnel. In 20th Australasian Fluid Mechanics Conference (20AFMC) (pp. 1-4).##
Gao, W., N. Daniel, L. Zhenxia and L. Yaguo (2018). Numerical investigation of flow around one finite circular cylinder with two free ends. Ocean Engineering 156, 373-80.##
Huang, T., H. Liu, N. Groves, T. Forlini, J. Blanton and S. Growing (1992). Measurements of flows over an axisymmetric body with various appendages in a wind tunnel: The DARPA SUBOFF experimental program. In Proceedings of the 19th Symposium on Naval Hydrodynamics, Seoul, Korea.##
Islam, H. and C. G. Soares (2019). Uncertainty analysis in ship resistance prediction using OpenFOAM. Ocean Engineering 191, 105805.##
ITTC (2011). Practical guidelines for ship cfd applications. In ITTC—Recommended Procedures and Guidelines, 26th ITTC Executive Committee, Rio de Janeiro, Brazil, Chapter 7.5-03-02-03.##
ITTC (2017). Uncertainly analysis in CFD verification and validation methodology and procedures. In ITTC—Recommended Procedures and Guidelines; 28th ITTC Executive Committee. Chapter 7.5-03-01-01.##
ITTC (2021). Guideline for VIV Testing. In ITTC—Recommended Procedures and Guidelines. In Ocean Engineering Committee of the 29th ITTC: France in Virtual. Chapter 7.5-02-03-10.##
Lin, H. and C. Li (2020). The investigation of a sliding mesh model for hydrodynamic analysis of a SUBOFF model in turbulent flow fields. Journal of Marine Science and Engineering 8(10), 1-19.##
Lungu, A. (2019). DES-based computation of the flow around the DARPA SUBOFF. In IOP Conference Series: Materials Science and Engineering, Institute of Physics Publishing.##
Menter, R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8), 1598-1605.##
Pan, Y., H. Zhang and Q. Zhou (2012). Numerical Prediction of Submarine Hydrodynamic Coefficients using CFD Simulation. Journal of Hydrodynamics 24(6), 840–847.##
Pantokratoras, A. (2017). Progress in Computational Fluid Dynamics. Steady Flow of Power-Law Fluids across a Circular Rotating Cylinder.##
Paredes, J., T. Maria, H. Quintuña and R. Datla (2021). Numerical flow characterization around a Type 209 submarine using OpenFOAM. Fluids 6(2).##
Paudel, S. and N. Saenger (2017). Grid refinement study for three dimensional CFD model involving incompressible free surface flow and rotating object. Computers and Fluids 143, 134-40.##
Pereira, S., G. Vaz, L. Eça, and S. Girimaji (2018). Simulation of the flow around a circular cylinder at Re=3900 with partially-averaged Navier-Stokes equations. International Journal of Heat and Fluid Flow 69, 234-46.##
Permadi, N. V. A. and E. Sugianto (2022). CFD Simulation Model for Optimum Design of B-Series Propeller using Multiple Reference Frame (MRF). CFD Letters 14(11), 22-39.##
Pook, D. A., D. B. Clarke, M. Jones, H. Quick and D. Ranmuthugala (2018, December). RANS based CFD prediction of submarine hydrodynamic loads. In 21st Australasian Fluid Mechanics Conference, Adelaide, Australia.##
Qiu, Y., K. Shi, X. Hou and F. Wei (2007). Validation of numerical simulation of the flow over submarine geometries with full appendages. Chuanbo Lixue Journal of Ship Mechanics 11, 341-350.##
Rajani, N., A. Kandasamy and S. Majumdar (2009). Numerical simulation of laminar flow past a circular cylinder. Applied Mathematical Modelling 33(3), 1228-47.##
Roache, J. (1997). Quantification of uncertainty in computational fluid dynamics. Annual review of fluid Mechanics 29(1), 123-160.##
Roache, J. (1998). Verification of codes and calculations. AIAA Journal 36(5), 696-702.##
Rocha, A. L., L. Eça and G. Vaz (2017). On the numerical convergence properties of the calculation of the flow around the KVLCC2 tanker in unstructured grids. In MARINE VII: proceedings of the VII International Conference on Computational Methods in Marine Engineering (pp. 336-352). CIMNE.##
Roy, J. (2005). Review of code and solution verification procedures for computational simulation. Journal of Computational Physics 205(1), 131-56.##
Sadikin, A., Y. Nurul, K. Abdullah and M. Mohammed (2014). Numerical study of flow past a solid sphere at moderate reynolds number. In Applied Mechanics and Materials, Trans Tech Publications Ltd.##
Sugianto, E., J. H. Chen and N. V. A. Permadi (2022). Effect of monohull type and catamaran hull type on ocean waste collection behavior using OpenFOAM. Water 14(17), 2623.##
Takahashi, K. and S. Prasanta (2019). Fundamental CFD Study on the hydrodynamic performance of the DARPA SUBOFF submarine. In Volume 2: CFD and FSI, American Society of Mechanical Engineers.##
Toxopeus, S. (2008). Viscous-flow calculations for bare hull DARPA SUBOFF submarine at incidence. International Shipbuilding Progress 55(3), 227-51.##
Ueda, H. and O. Hinze (1975). Fine-structure turbulence in the wall region of a turbulent boundary layer. Journal of Fluid Mechanics 67(1), 125-43.##
Versteeg, H. K. and W. Malalasekera (2007). An introduction to computational fluid dynamics - the finite volume method.##
Yen, C. H., U. J. Hui, Y. Y. We, A. Sadikin, N. Nordin, I. Taib, K. Abdullah, A. N. Mohammed, A. Sapit and M. W. M. Razali (2017). Numerical study of flow past a solid sphere at high Reynolds number. IOP Conference Series. https://doi.org/
10.1088/1757-899x/243/1/012042##
Yin, G. and M. C. Ong (2020). On the wake flow behind a sphere in a pipe flow at low Reynolds numbers. Physics of Fluids 32(10), 103605. https://doi.org/10.1063/5.0017349##