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Simulation of the wedge-shaped vibration-driven robot motion in the viscous fluid forced by different laws of internal mass movement in the package OpenFOAM

https://doi.org/10.15514/ISPRAS-2017-29(1)-7

Abstract

The work is devoted to the study of the two-mass vibration-driven system motion in the viscous fluid. The system consists of a closed wedge-shaped body, placed in a fluid, and a movable internal mass, oscillated harmonically inside the shell. The described mechanical system simulates a vibration-driven robot. The complex model of the robot interaction with the medium is considered, where fluid motion is described by the full unsteady Navier-Stokes equations. The problems of improving the efficiency of vibration-driven robot motion by choosing a special law internal mass movement are investigated. For these purposes, a comparative analysis of the characteristics of the motion and flow regimes around the robot are carried out for the simple harmonic law of the internal mass motion and the special two-phase law of the internal mass motion. The analysis of the flows around the robot and their influence on the characteristics (the average speed and the efficiency) of the movement is carried out. The numerical solution of the problem is carried out in the OpenFOAM open-source software package. The numerical scheme is implemented on the basis of the finite-volume discretization approach. For joint solution the Navier-Stokes equations and the mechanical system, which describes the interaction of components of vibration-driven robot and viscous media, a special iteration scheme is constructed. Results of the study show that the directional movement of the wedge-shaped vibration-driven robot is possible for both harmonic and two-phase laws of internal mass motion. In each of the cases it is possible to find stable regimes of motion observed in a wide range of Reynolds numbers. Analysis of average speed and efficiency of regimes allows finding the optimal parameters of vibration-driven robot motion.

About the Authors

A. N. Nuriev
Nizhny Novgorod State University; Kazan Federal University
Russian Federation


A. I. Yunusova
Kazan State Technological University
Russian Federation


O. N. Zaitseva
Kazan Federal University
Russian Federation


References

1. Chernous'ko F. L. The optimal periodic motions of a two-mass system in a resistant medium. PMM [ J. Appl. Math. Mech.], 72, 2008, pp. 202-215 (in Russian).

2. Bolotnik N.N., Figurina T.Y., Chernous'ko F.L. Optimal control of the rectilinear motion of a two-body system in a resistive medium. PMM [J. Appl. Math. Mech], 76, 2012, pp. 3-22 (in Russian).

3. Lighthill M.J. On the Squirming Motion of Nearly Spherical Deformable Bodies through Liquids at Very Small Reynolds Numbers. Comm. Pure Appl. Math, 5(2), 1952, pp. 109-118.

4. Saffman P.G. The Self-Propulsion of a Deformable Body in a Perfect Fluid. J. Fluid Mech., 28(2), 1967, pp. 385-389.

5. Ramodanov S.M., Tenenev V.A., Treschev D.V. Self-propulsion of a Body with Rigid Surface and Variable Coefficient of Lift in a Perfect Fluid. Regul. Chaotic Dyn., 17(6), 2012, pp. 547-558.

6. Chernous’ko F.L. On the motion of a body containing a movable internal mass. Dokl. RAN [Dokl. Phys.], 450(1), 2005, pp. 56-60 (in Russian).

7. Chernous’ko F.L. Analysis and optimization of the motion of a body controlled by means of a movable internal mass. PMM [J. Appl. Math. Mech.], 70(6), 2006, pp. 915-941 (in Russian).

8. Volkova L.Yu., Jatsun S.F. Control of the Three-Mass Robot Moving in the Liquid Environment. Nelinejnaja dinamika [J. Nonlin. Dyn.], 7(4), 2011, pp. 845-857 (in Russian).

9. Childress S., Spagnolie S.E., Tokieda T.A. Bug on a Raft: Recoil Locomotion in a Viscous Fluid. J. Fluid Mech., 669, 2011, pp. 527-556.

10. Auziņš J., Beresņevičs V., Kaktabulis I., Kuļikovskis G. Dynamics of Water Vehicle with Internal Vibrating Gyrodrive. Vibration Problems ICOVP 2011. Supplement: The 10th International Conference on Vibration Problems, Czech Republic, Prague, 5-8 September.

11. Vetchanin E. The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid. Regular and Chaotic Dynamics, 18, 2013, pp. 100-117.

12. Egorov A.G., Zakharova O.S. The energyoptimal motion of a vibrationdriven robot in a resistive medium. PMM [J. Appl. Math. Mech.], 74(4), 2010, pp. 620-632 (in Russian).

13. Egorov A.G., Zakharova O.S. Optimal quasistationar motion of vibrationdriven robot in a viscous liquid. Izvestija VUZov. Matematika [Russian Mathematics (Iz. VUZ)], 2, 2012, pp. 57-64 (in Russian).

14. Egorov A.G., Zakharova O.S. The Energy-Optimal Motion of a Vibration-Driven Robot in a Medium with a Inherited Law of Resistance. Izvestija RAN. Teorija i sistemy upravlenija [J. of Computer and Systems Sciences International], 3, 2015, pp. 168-176 (in Russian).

15. Nuriev A. N., Zakharova O.S. Simulation of the wedge-shaped two-mass vibration-driven robot motion in a viscous fluid. [Computational Continuum Mechanics], 9, 2016, pp. 5-15 (in Russian).

16. Open foam (the open source cfd toolbox): User guide version 2.2.1, URL: http://www.openfoam.org/docs/user/, 2.07.2016.

17. Unihub.ru, Available at: https://unihub.ru/about, accessed 2.07.2016.

18. Jasak H., Weller H.G., Gosman A D. High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int. J. Numer. Meth. Fluids, 1999, vol.31, pp. 431-449.

19. Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, London: Imperial College, University of London, 1996.

20. Issa R.I. Solution of implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys., 1986, vol. 62, pp. 40-65.

21. Behrens T. Openfoam's basic solvers for linear systems of equations. Technical Report, Technical University of Denmark, Lingby Available at: http://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2008/TimBehrens/tibeh-report-fin.pdf, accessed 10.10.2016.

22. Nuriev A. N., Zaytseva O.N., Moscheva E.E., Yunusova A.I. Structure of secondary flow around cylinder triangular, performs harmonic oscillations in a viscous incompressible fluid. Vestn. Kaz. tehnologicheskogo universiteta [Heald of Kazan Technological University], 16, 2015, pp. 239-242 (in Russian).

23. Martinez G. Caractristiques dynamiques et thermiques de l'coulement autour d'un cylindre circulaire a nombres de reynolds moderes. Ph.D. thesis,I.N.P. Toulouse, 1979

24. De A. K., Dalal A. Numerical simulation of unconfined flow past a triangular cylinder. Int. J. Numer. Meth. Fluids, 2006, No. 52, p. 801-821.


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For citations:


Nuriev A.N., Yunusova A.I., Zaitseva O.N. Simulation of the wedge-shaped vibration-driven robot motion in the viscous fluid forced by different laws of internal mass movement in the package OpenFOAM. Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2017;29(1):101-118. (In Russ.) https://doi.org/10.15514/ISPRAS-2017-29(1)-7



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ISSN 2079-8156 (Print)
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