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A numerical investigation about the effects of Reynolds number on the flow around an appended axisymmetric body of revolution

Published online by Cambridge University Press:  17 December 2019

Antonio Posa Open the ORCID record for Antonio Posa [Opens in a new window]  and
Elias Balaras Open the ORCID record for Elias Balaras [Opens in a new window]
Antonio Posa*
Affiliation:
CNR-INM, National Research Council of Italy, Institute of Marine Engineering, via di Vallerano 139, 00128Roma, Italy Department of Mechanical and Aerospace Engineering, The George Washington University, 800 22nd Street, N.W., Washington, DC20052, USA
Elias Balaras
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, 800 22nd Street, N.W., Washington, DC20052, USA
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Large-eddy simulations for the case of an axisymmetric body of revolution with appendages are considered. The geometry is the benchmark case of the DARPA suboff body. The paper focuses on the effects of the Reynolds number on the structure of the boundary layer in the stern area as well as the near wake. For this purpose we compare results for two Reynolds numbers (based on the length of the body, $L$, and the free-stream velocity, $U_{\infty }$): $Re_{L}=12\times 10^{6}$ and $Re_{L}=1.2\times 10^{6}$. Results are in good agreement with published experiments at the same Reynolds numbers. The boundary layer thickness over the stern increases substantially at both simulated Reynolds numbers, due to the adverse pressure gradient at the rear of the body. However, for the high Reynolds number case, a weaker peak of turbulent kinetic energy develops in the outer layer over the stern. Nonetheless, the associated bimodal distribution of the turbulent stresses in the wake is already very similar a few diameters downstream of the tail. First- and second-order moments demonstrate that junction vortices at the stern bring higher velocities and turbulence at the root of the appendages for both Reynolds numbers, with a more evident signature at $Re_{L}=12\times 10^{6}$. An azimuthal readjustment of turbulent kinetic energy occurs in the wake, becoming more axisymmetric, with increasing values in the planes aligned with the stern appendages, due to turbulence coming from both the stern boundary layer and junction vortices.

JFM classification

Turbulent Flows: Turbulent boundary layers Wakes/Jets: Wakes Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A41
Copyright
© 2019 Cambridge University Press

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References

Alin, N., Bensow, R. E., Fureby, C., Huuva, T. & Svennberg, U. 2010 Current capabilities of DES and LES for submarines at straight course. J. Ship Res. 54 (3), 184–196.Google Scholar
Amiri, M. M., Esperana, P. T., Vitola, M. A. & Sphaier, S. H. 2018 How does the free surface affect the hydrodynamics of a shallowly submerged submarine? Appl. Ocean Res. 76, 34–50.CrossRefGoogle Scholar
Balaras, E. 2004 Modeling complex boundaries using an external force field on fixed cartesian grids in large-eddy simulations. Comput. Fluids 33 (3), 375–404.CrossRefGoogle Scholar
Balaras, E., Schroeder, S. & Posa, A. 2015 Large-eddy simulations of submarine propellers. J. Ship Res. 59 (4), 227–237.CrossRefGoogle Scholar
Beratlis, N., Squires, K. & Balaras, E. 2012 Numerical investigation of magnus effect on dimpled spheres. J. Turbul. 13, N15.CrossRefGoogle Scholar
Bhushan, S., Alam, M. F. & Walters, D. K. 2013 Evaluation of hybrid RANS/LES models for prediction of flow around surface combatant and Suboff geometries. Comput. Fluids 88, 834–849.CrossRefGoogle Scholar
Boger, D. A. & Dreyer, J. J. 2006 Prediction of hydrodynamic forces and moments for underwater vehicles using overset grids. In Collection of Technical Papers – 44th AIAA Aerospace Sciences Meeting, 9–12 January 2006, Reno, Nevada, USA, American Institute of Aeronautics and Astronautics.Google Scholar
Budak, G. & Beji, S. 2016 Computational resistance analyses of a generic submarine hull form and its geometric variants. J. Ocean Technol. 11 (2), 77–86.Google Scholar
Cao, L., Zhu, J. & Zeng, G. 2016 Viscous-flow calculations of submarine maneuvering hydrodynamic coefficients and flow field based on same grid topology. J. Appl. Fluid Mech. 9 (2), 817–826.Google Scholar
Chase, N. & Carrica, P. M. 2013 Submarine propeller computations and application to self-propulsion of DARPA Suboff. Ocean Engng 60, 68–80.CrossRefGoogle Scholar
Chase, N., Michael, T. & Carrica, P. M. 2013 Overset simulation of a submarine and propeller in towed, self-propelled and maneuvering conditions. Intl Shipbuilding Prog. 60 (1–4), 171–205.Google Scholar
Feng, D., Wang, X., Jiang, F. & Zhang, Z. 2015 Large eddy simulation of DARPA SUBOFF for Re = 2. 65 × 107. J. Coast. Res. 73, 687–691.CrossRefGoogle Scholar
Gao, T., Wang, Y., Pang, Y., Chen, Q. & Tang, Y. 2018 A time-efficient CFD approach for hydrodynamic coefficient determination and model simplification of submarine. Ocean Engng 154, 16–26.CrossRefGoogle Scholar
Givler, R. C., Gartling, D. K., Engelman, M. S. & Haroutunian, V. 1991 Navier–Stokes simulations of flow past three-dimensional submarine models. Comput. Meth. Appl. Mech. Engng 87 (2–3), 175–200.CrossRefGoogle Scholar
Gorski, J. J., Coleman, R. M. & Haussling, H. J.1990 Computation of incompressible flow around the DARPA SUBOFF bodies. Tech. Rep. David Taylor Research Center, Bethesda, MD.CrossRefGoogle Scholar
Huang, T., Liu, H. L., Groves, N., Forlini, T., Blanton, J. & Gowing, S. 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, 23–28 August 1992, Seoul, South Korea, US Office of Naval Research.Google Scholar
Jiménez, J. M., Hultmark, M. & Smits, A. J. 2010a The intermediate wake of a body of revolution at high Reynolds numbers. J. Fluid Mech. 659, 516–539.CrossRefGoogle Scholar
Jiménez, J. M., Reynolds, R. T. & Smits, A. J. 2010b The effects of fins on the intermediate wake of a submarine model. Trans. ASME J. Fluids Engng 132 (3), 0311021–0311027.CrossRefGoogle Scholar
Kim, S.-E. & Rhee, B. 2016 Eddy-resolving simulation of turbulent flows around undersea vehicles – a quest for a practical approach. In Proceedings of the 31st Symposium on Naval Hydrodynamics, 11–16 September 2016, Monterey, CA, USA, US Office of Naval Research.Google Scholar
Kumar, P. & Mahesh, K. 2018a Large-eddy simulation of flow over an axisymmetric body of revolution. J. Fluid Mech. 853, 537–563.CrossRefGoogle Scholar
Kumar, P. & Mahesh, K. 2018b Large eddy simulation of flow over axisymmetric hull. In Proceedings of the 32nd Symposium on Naval Hydrodynamics, 5–10 August 2018, Hamburg, Germany, US Office of Naval Research.Google Scholar
Mahesh, K., Kumar, P., Gnanaskandan, A. & Nitzkorski, Z. 2015 LES applied to ship research. J. Ship Res. 59 (4), 238–245.CrossRefGoogle Scholar
Manshadi, M. D., Hejranfar, K. & Farajollahi, A. H. 2017 Effect of vortex generators on hydrodynamic behavior of an underwater axisymmetric hull at high angles of attack. J. Vis. 20 (3), 559–579.CrossRefGoogle Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62 (3), 183–200.CrossRefGoogle Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21 (3), 251–269.CrossRefGoogle Scholar
Pan, Y. C., Zhang, H. X. & Zhou, Q. D. 2012 Numerical prediction of submarine hydrodynamic coefficients using CFD simulation. J. Hydrodynam. B 24 (6), 840–847.CrossRefGoogle Scholar
Posa, A. & Balaras, E. 2016a A numerical investigation of the wake of an axisymmetric body with appendages. J. Fluid Mech. 792, 470–498.CrossRefGoogle Scholar
Posa, A. & Balaras, E. 2016b Large-eddy simulations of the DARPA SUBOFF model in towed and propelled configurations. In Proceedings of the 31st Symposium on Naval Hydrodynamics, 11–16 September 2016, Monterey, CA, USA, US Office of Naval Research.Google Scholar
Posa, A. & Balaras, E. 2018 Large-eddy simulations of a notional submarine in towed and self-propelled configurations. Comput. Fluids 165, 116–126.CrossRefGoogle Scholar
Posa, A., Broglia, R. & Balaras, E. 2019a Analysis of the influence of an upstream rudder over the wake features of a submarine propeller. In Proceedings of the Sixth International Symposium on Marine Propulsors, 26–30 May 2019, Rome, Italy, National Research Council of Italy, Institute of Marine Engineering.Google Scholar
Posa, A., Broglia, R. & Balaras, E. 2019b LES study of the wake features of a propeller in presence of an upstream rudder. Comput. Fluids 192, 104247.CrossRefGoogle Scholar
Posa, A., Broglia, R., Felli, M., Falchi, M. & Balaras, E. 2018 Numerical investigation of the wake of a propeller by large-eddy simulation. In Proceedings of the 32nd Symposium on Naval Hydrodynamics, 5–10 August 2018, Hamburg, Germany, US Office of Naval Research.Google Scholar
Posa, A., Broglia, R., Felli, M., Falchi, M. & Balaras, E. 2019c Characterization of the wake of a submarine propeller via large-eddy simulation. Comput. Fluids 184, 138–152.CrossRefGoogle Scholar
Rossi, T. & Toivanen, J. 1999 A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20 (5), 1778–1793.CrossRefGoogle Scholar
Schroeder, S., Posa, A. & Balaras, E. 2014 Tip vortex evolution of a marine propeller including the effects of an upstream appendage. In Proceedings of the 30th Symposium on Naval Hydrodynamics, 2–7 November 2014, Hobart, Australia, US Office of Naval Research.Google Scholar
Shariati, S. K. & Mousavizadegan, S. H. 2017 The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface. Appl. Ocean Res. 67, 31–43.CrossRefGoogle Scholar
Shi, B., Yang, X., Jin, G., He, G. & Wang, S. 2019 Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method. Appl. Math. Mech. 40 (3), 305–320.CrossRefGoogle Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. J. Appl. Mech. 28 (3), 455–458.CrossRefGoogle Scholar
Toxopeus, S. 2008 Viscous-flow calculations for bare hull DARPA SUBOFF submarine at incidence. Intl Shipbuilding Prog. 55 (3), 227–251.Google Scholar
Vaz, G., Toxopeus, S. & Holmes, S. 2010 Calculation of manoeuvring forces on submarines using two viscous-flow solvers. In Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering – OMAE, 6–11 June 2010, Shanghai, China, The American Society of Mechanical Engineers.Google Scholar
Wang, S., Shi, B., Li, Y. & He, G. 2016 A large eddy simulation of flows around an underwater vehicle model using an immersed boundary method. Theor. Appl. Mech. Lett. 6 (6), 302–305.CrossRefGoogle Scholar
Wang, Y., Gao, T., Pang, Y. & Tang, Y. 2018 Investigation and optimization of appendage influence on the hydrodynamic performance of AUVs. J. Mar. Sci. Technol. 24, 297–305.CrossRefGoogle Scholar
Yang, J. & Balaras, E. 2006 An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 215 (1), 12–40.CrossRefGoogle Scholar
Yao, H., Zhang, H., Liu, H. & Jiang, W. 2017 Numerical study of flow-excited noise of a submarine with full appendages considering fluid structure interaction using the boundary element method. Engng Anal. Bound. Elem. 77, 1–9.CrossRefGoogle Scholar
Zhang, D., Chao, L. & Pan, G. 2019 Analysis of hydrodynamic interaction impacts on a two-AUV system. Ships Offshore Struct. 14 (1), 23–34.CrossRefGoogle Scholar
Zhihua, L., Ying, X. & Chengxu, T. 2011 Numerical simulation and control of horseshoe vortex around an appendage-body junction. J. Fluids Struct. 27 (1), 23–42.CrossRefGoogle Scholar
Zhihua, L., Ying, X. & Chengxu, T. 2012 Method to control unsteady force of submarine propeller based on the control of horseshoe vortex. J. Ship Res. 56 (1), 12–22.CrossRefGoogle Scholar