Numerical simulation of the motion of a wedge-shaped two-mass vibration-driven robot in a viscous fluid

Authors

DOI:

https://doi.org/10.7242/1999-6691/2016.9.1.1

Keywords:

vibration-driven robot, numerical simulation, motion regimes, viscous fluid, Navier-Stokes equations, OpenFOAM

Abstract

The translational motion of a two-mass mechanical system in a viscous incompressible fluid is considered. The system consists of a closed wedge-shaped body placed in a liquid and a movable internal mass oscillated harmonically inside the shell. The motion of the whole system is ensured by the periodic oscillations of the internal mass. The asymmetry in the shell shape generates different reactions of the fluid at different phases of motion (forward and backward), providing the directional translational motion of the system in the liquid. The described mechanical system simulates a vibration-driven robot - a mobile device able to move in the fluid without moving external parts. The problem of an interaction between the robot and the viscous fluid is solved using direct numerical simulation. Studies are carried out in a range of low Reynolds numbers (Re < 250), where the hypothesis of a plane-parallel laminar flow is applicable. A computational scheme is constructed on the basis of an open-source software package OpenFOAM. The results of this work show that the fluid-shell interaction is a complex phenomenon associated with switching between flow regimes. The flow structure formed by the robot motion has a strong influence on the characteristics of the movement, including the direction of the movement. Furthermore, the high nonlinearity of the processes leads to the formation of significantly different regimes of robot motion at the same parameters of internal mass oscillations.

Downloads

Download data is not yet available.

References

Гулиа Н.В. Инерция. - М.: Наука, 1982. - 150 с.
2. Черноусько Ф.Л. О движении тела, содержащего подвижную внутреннюю массу // ДАН. - 2005. - Т. 405, № 1. - С. 56-60.
3. Черноусько Ф.Л. Анализ и оптимизация движения тела, управляемого посредством подвижной внутренней массы // ПММ. - 2006. - Т. 70, № 6. - С. 915-941. DOI
4. Черноусько Ф.Л. Оптимальные периодические движения двухмассовой системы в сопротивляющейся среде // ПММ. - 2008. - Т. 72, № 2. - С. 202-215. DOI
5. Болотник Н.Н., Фигурина Т.Ю., Черноусько Ф.Л. Оптимальное управление прямолинейным движением системы двух тел в сопротивляющейся среде // ПММ. - 2012. - Т. 76, № 1. - С. 3-22. DOI
6. Болотник Н.Н., Фигурина Т.Ю. Оптимальное управление прямолинейным движением твердого тела по шероховатой плоскости посредством перемещения двух внутренних масс // ПММ. - 2008. - Т. 72, № 2. - С. 216-229. DOI
7. Zimmermann K., Bohm V., Zeidis I. Vibration-driven mobile robots based on magneto-sensitive elastomers // IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 3-7 July, 2011. - P. 730-735. DOI
8. Akbarimajd A., Sotoudeh N. Design and motion analysis of vibration-driven small robot Rizeh // Adv. Robotics. - 2014. - Vol. 28, no. 2. - P. 105-117. DOI
9. Егоров А.Г., Захарова О.С. Оптимальное по энергетическим затратам движение виброробота в среде с сопротивлением // ПММ. - 2010. - Т. 74, № 4. - С. 620-632. DOI
10. Егоров А.Г., Захарова О.С. Оптимальное квазистационарное движение виброробота в вязкой жидкости // Изв. ВУЗов. Математика. - 2012. - № 2. - C. 57-64. DOI
11. OpenFOAM User Guide, version 2.2.1. http://www.openfoam.org/docs/user/ (дата обращения: 11.11.2015).
12. http://openfoamwiki.net/index.php/Main_Page (дата обращения: 11.11.2015).
13. https://unihub.ru/about (дата обращения: 11.11.2015).
14. Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flows / PhD thesis. - London: Imperial College, University of London, 1996. - 394 p.
15. 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, no. 2. - P. 431-449. DOI
16. Versteeg H.K., Malalasekera W. An introduction to computational fluid dynamics. The finite volume method. - New York: Longman, 1995. - 257 p.
17. Нуриев А.Н., Зайцева О.Н. Решение задачи об осциллирующем движении цилиндра в вязкой жидкости в пакете OpenFOAM // Вестник Казанского технологического ун-та. - 2013. - Т. 16, № 8. - С. 116-123.
18. Issa R.I. Solution of the implicitly discretised fluid flow equations by operator-splitting // J. Comput. Phys. - 1985. - Vol. 62, no. 1. - P. 40-65. DOI
19. Behrens T. OpenFOAM’s basic solvers for linear systems of equations.
20. Zeitoun O., Ali M., Nuhait A. Convective heat transfer around a triangular cylinder in an air cross flow // Int. J. Therm. Sci. - 2011. - Vol. 50, no. 9. - P. 1685-1697. DOI
21. De A.K., Dalal A. Numerical simulation of unconfined flow past a triangular cylinder // Int. J. Numer. Meth. Fl. - 2006. - Vol. 52, no. 7. - P. 801-821. DOI
22. Martinez G. Caractéristiques dynamiques et thermiques de l’écoulement autour d’un cylindre circulaire à nombre de Reynolds modéré / Thèse de Docteur-Ingénieur. - Institut National Polytechnique de Toulouse, 1979.

###

Gulia N.V. Inercia. - M.: Nauka, 1982. - 150 s.
2. Cernous’ko F.L. O dvizenii tela, soderzasego podviznuu vnutrennuu massu // DAN. - 2005. - T. 405, No 1. - S. 56-60.
3. Cernous’ko F.L. Analiz i optimizacia dvizenia tela, upravlaemogo posredstvom podviznoj vnutrennej massy // PMM. - 2006. - T. 70, No 6. - S. 915-941. DOI
4. Cernous’ko F.L. Optimal’nye periodiceskie dvizenia dvuhmassovoj sistemy v soprotivlausejsa srede // PMM. - 2008. - T. 72, No 2. - S. 202-215. DOI
5. Bolotnik N.N., Figurina T.U., Cernous’ko F.L. Optimal’noe upravlenie pramolinejnym dvizeniem sistemy dvuh tel v soprotivlausejsa srede // PMM. - 2012. - T. 76, No 1. - S. 3-22. DOI
6. Bolotnik N.N., Figurina T.U. Optimal’noe upravlenie pramolinejnym dvizeniem tverdogo tela po serohovatoj ploskosti posredstvom peremesenia dvuh vnutrennih mass // PMM. - 2008. - T. 72, No 2. - S. 216-229. DOI
7. Zimmermann K., Bohm V., Zeidis I. Vibration-driven mobile robots based on magneto-sensitive elastomers // IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 3-7 July, 2011. - P. 730-735. DOI
8. Akbarimajd A., Sotoudeh N. Design and motion analysis of vibration-driven small robot Rizeh // Adv. Robotics. - 2014. - Vol. 28, no. 2. - P. 105-117. DOI
9. Egorov A.G., Zaharova O.S. Optimal’noe po energeticeskim zatratam dvizenie vibrorobota v srede s soprotivleniem // PMM. - 2010. - T. 74, No 4. - S. 620-632. DOI
10. Egorov A.G., Zaharova O.S. Optimal’noe kvazistacionarnoe dvizenie vibrorobota v vazkoj zidkosti // Izv. VUZov. Matematika. - 2012. - No 2. - C. 57-64. DOI
11. OpenFOAM User Guide, version 2.2.1. http://www.openfoam.org/docs/user/ (data obrasenia: 11.11.2015).
12. http://openfoamwiki.net/index.php/Main_Page (data obrasenia: 11.11.2015).
13. https://unihub.ru/about (data obrasenia: 11.11.2015).
14. Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flows / PhD thesis. - London: Imperial College, University of London, 1996. - 394 p.
15. 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, no. 2. - P. 431-449. DOI
16. Versteeg H.K., Malalasekera W. An introduction to computational fluid dynamics. The finite volume method. - New York: Longman, 1995. - 257 p.
17. Nuriev A.N., Zajceva O.N. Resenie zadaci ob oscilliruusem dvizenii cilindra v vazkoj zidkosti v pakete OpenFOAM // Vestnik Kazanskogo tehnologiceskogo un-ta. - 2013. - T. 16, No 8. - S. 116-123.
18. Issa R.I. Solution of the implicitly discretised fluid flow equations by operator-splitting // J. Comput. Phys. - 1985. - Vol. 62, no. 1. - P. 40-65. DOI
19. Behrens T. OpenFOAM’s basic solvers for linear systems of equations.
20. Zeitoun O., Ali M., Nuhait A. Convective heat transfer around a triangular cylinder in an air cross flow // Int. J. Therm. Sci. - 2011. - Vol. 50, no. 9. - P. 1685-1697. DOI
21. De A.K., Dalal A. Numerical simulation of unconfined flow past a triangular cylinder // Int. J. Numer. Meth. Fl. - 2006. - Vol. 52, no. 7. - P. 801-821. DOI
22. Martinez G. Caracteristiques dynamiques et thermiques de l’ecoulement autour d’un cylindre circulaire a nombre de Reynolds modere / These de Docteur-Ingenieur. - Institut National Polytechnique de Toulouse, 1979.

Downloads

Published

2016-03-30

Issue

Section

Articles

How to Cite

Nuriev, A. N., & Zakharova, O. S. (2016). Numerical simulation of the motion of a wedge-shaped two-mass vibration-driven robot in a viscous fluid. Computational Continuum Mechanics, 9(1), 5-15. https://doi.org/10.7242/1999-6691/2016.9.1.1