Numerical modeling of a solid sphere free fall into the water

Аuthors

Konstantinov S. G.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: slk.konstantinov@gmail.com

Abstract

A solid body motion trajectory depends significantly on its hydrodynamic characteristics. Thus, an important problem consists in determining aero-hydrodynamic forces and moments, impacting the body depending on its special position and media properties. Application of modern computing techniques, allowing accounting for complex physical pattern of the body flow-around in viscous turbulent flow of liquid and compressible gas, becomes highly relevant for determining dynamic characteristics of a solid body free falling and immersing into the water.

Computational Fluid Dynamics (CFD) methods, constructed on the solution of the Navier-Stokes equations, allow simulate the fluid and gas flows dynamics with account for the viscosity, compressibility and detachment phenomena effect.

The main problem while the CFD methods application is the simulation of turbulent flows. Until now, universal turbulence models, capable of accounting for all the scales of turbulence have not been developed. Thus, with regard to computing resources costs, the Reynolds-averaged Navier-Stokes (RANS) equations closed by a particular turbulence model are widely employed. With this approach, the numerical experiment accuracy depends largely on the correct choice of the turbulence model.

To assess the validity of the RANS method, the aerodynamic characteristics of the sphere were computed using three most widely used turbulence models, i.e. Spalart-Allmaras, k-SST and k-e, realizable in the ANSYS FLUENT program.

Comparative testing of turbulence models based on aerodynamic characteristics computing of the sphere while airflow over a wide range of Reynolds numbers revealed that the computing results obtained from the Spalart-Allmaras and k-SST turbulence models are closest to the experimental data.

To determine the aero-hydrodynamic characteristics of a sphere free falling into water, as well as the trajectory of incidence and immersion, calculations were performed using the RANS method with the k-ω SST turbulence model and Volume of fluid (VOF) and Six degrees of freedom (6DOF) models contained in the program ANSYS FLUENT.

Based on computing results, the sphere hydrodynamic characteristics, trajectory and sinking speed were determined. The patterns of the total velocity in the calculated area were obtained, and visualization of the cavity formation process in the water while immersion of the sphere with hydrophobic properties was demonstrated. The numerical modeling results of the sphere immersion into the water were compared with the experimental data.

The results of sphere aero-hydrodynamic characteristics computing and numerical modeling of the sphere immersion into the water demonstrated satisfactory agreement with experimental data, which indicates the fidelity of the physico-mathematical model of the applied method.

The implemented method can be employed in the aircraft building industry to solve problems related to determination of the dynamic characteristics of seaplanes and helicopters capable of being driven and moving along the water surface with account for the impact of the incoming airflow, currents and free surface waves.

Keywords:

aerodynamic characteristics sphere, numerical modeling, methods RANS, model VOF, model 6DOF

References

1. Van-Daik M. Al’bom techenii zhidkosti i gaza (Album of fluid and gas flows), Moscow, Mir, 1986, 184 p.

2. Devnin S.I. Aerogidromekhanika plokhoobtekaemykh konstruktsii (Aerohydromechanics of poorly streamlined structures), Leningrad, Sudostroenie, 1983, 332 p.

3. Ignatkin Ju. M., Konstantinov S.G. Trudy MAI, 2012, no 57, available at: http://trudymai.ru/eng/published.php?ID=30875

4. Kozelkov A.S. et al. Trudy Nizhegorodskogo gosudarstvennogo tekhnicheskogo universiteta imeni R.E. Alekseeva, 2015, no. 2 (109), pp. 49 – 69.

5. Le Kuok Din, Semenchikov N. V., Jakovlevskij O.V., Chang Kuang Dyk. Trudy MAI, 2012, no 52, available at: http://trudymai.ru/eng/published.php?ID=29590

6. Fletcher K. Vychislitel’nye metody v dinamike zhidkostei. (Computational methods in the dynamics of liquids), Moscow, Mir, 1991, 504 p.

7. Frik P.G. Turbulentnost’: modeli i podkhody (Turbulence: models and approaches), Perm, PGTU, 1998, 108 p.

8. Shlikhting G. Teoriya pogranichnogo sloya (The boundary layer theory), Moscow, Nauka, 1974, 712 p.

9. ANSYS FLUENT 6.3. Theory Manual. 2005. Fluent Inc. Central Source Park, 10 Cavendish Court, Lebanon, NH 03766, USA, available at: http://www.fluent.com

10. Aristoff J.M., & Bush J. W.M. Water entry of small hydrophobic spheres, Journal of Fluid Mechanics, 2009, vol. 619, pp. 45 – 78.

11. Asfar K. and Moore S. Rigid-body water impact at shallow angles of incidence, Proceedings of the international offshore mechanics and arctic engineering symposium, ASME, Virginia Polytechnic Inst. State Univ., Blacksburg, VA, USA, 1987, vol. 2, pp. 105 – 112.

12. Duez C., Ybert C., Clanet C., & Bocquet L. Making a splash with water repellency, Nature Physics, 2007, no. 3, pp. 180 – 183.

13. Ferziger J.H., Peric M. Computational methods for fluid dynamics, Springer-Verlag, Berlin, 1996, 356 p.

14. May A. & Hoover W.R. A study of the water-entry cavity. Unclassified NOLTR 63 – 264, United States Naval Ordinance Laboratory, White Oak, Maryland, USA, 1963.

15. Menter F.R. Zonal two equation turbulence models for aerody namic flows, 24th Fluid Dynamics Conference, July 6-9, 1993, Orlando, Florida, available at: https://cfd.spbstu.ru/agarbaruk/doc/1993_Menter_Zonal%20Two%20Equation%20k-w%20Turbulence%20Models%20for%20Aerodynamic%20Flows(2).pdf

16. Salvi R. Navier-Stokes equations theory and numerical methods, Marcel Dekker, Inc., 2002, vol. 223, 308 p.

17. Spalart P.R., Allmaras S.R. A One-equation turbulence model for aerodynamics, Conference Reno, Nevada, USA, 1999, pp. 92–439.

18. Tadd T. Truscott, Brenden P. Epps, Alexandra H. Techet. Unsteady forces on spheres during free-surface water entry, Journal of Fluid Mechanics, Cambridge University Press, 2012, vol. 704, pp. 173 – 210.

19. Wilcox D.C. Turbulence modeling for CFD, California, DCW Industries, Inc., 1994, 460 p.

20. Sun Zhao, CaoWei, and Wang Cong. Numerical Investigation of Water Entry of Half Hydrophilic and Half Hydrophobic Spheres, Mathematical Problems in Engineering, volume 2016, Article ID 5265818, available at: http://dx.doi.org/10.1155/2016/5265818

Download