Planar and Spatial kinematic for vortex fluid flow behaviour by using perturbation parameter

Jérémie Gaston SAMBOU; Edouard DIOUF

doi:https://doi.org/10.14445/22315373/IJMTT-V67I5P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 5 | Year 2021 | Article Id. IJMTT-V67I5P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I5P506

Planar and Spatial kinematic for vortex fluid flow behaviour by using perturbation parameter

Jérémie Gaston SAMBOU, Edouard DIOUF

Abstract

Our aim in this research paper is to elaborate two new kinematics of deformation of a particle fluid in a planar and spatial vortex for mathematical modelization of these natural phenomenons. Incompressibility condition, Rotational and divergence of velocity tensor are calculated in every case and in also two examples of fluid flow. The pressure is interpret by using a Bernoulli theorem. As results, we have: the same incompressible condition in the case of horizontal accelerated flow than in the case of a shearing flow and we have the pressure which decreases in the two motion. We have the same rotational between the planar vortex flow and the spatial vortex flow, what means that there is no influence of the z component in the rotional of these two vortex flows when ε=1. And we also show that for specific values of ε and Θ, we have the same values in calculated expressions between the planar vortex flow and the spatial vortex flow.

Keywords

Kinematic of deformation , isotropic elementary invariants, Incompressible deformation, Vortex flow, Rotational, Divergence, Bernoulli theorem.

References

[1] C. Pailler-Mattei, "Les fluides: concepts et propriétés", Cours du Professeur C. Pailler-Mattei.Tutorat Santé Lyon Sud (2016-2017).
[2] M. S. Ullah, A. Tarammim, M. J. Uddin."A Study of Two Dimensional Unsteady MHD Free Convection Flow over a Vertical Plate in the Presence of Radiation". Open Journal of Fluid Dynamics. Vol.11 No.1, March 2021.
[3] A. Ivanchin. "Viscous Fluid Flowing around the Plate: Turbulence". Open Journal of Fluid Dynamics, 10, 291-316. doi: 10.4236/ojfd.2020.104018.
[4] J. S. Caltagirone, S. Vincent2. "A Kinematics Scalar Projection Method (KSP) for Incompressible Flows with Variable Density".Open Journal of Fluid Dynamics, 5, 171-182. doi: 10.4236/ojfd.2015.52019.
[5] M. Aldhabani, S. M. Sayed. "Travelling Wave Solutions for Three Dimensional Incompressible MHD Equations". Journal of Applied Mathematics and Physics, 6, 114-121. doi: 10.4236/jamp.2018.61011.
[6] E. M. Solouma, M. M. Wageeda, Y. Gh. Gouda, M. Bary. "Studying Scalar Curvature of Two Dimensional Kinematic Surfaces Obtained by Using Similarity Kinematic of a Deltoid". Applied Mathematics, 6, 1353- 1361. doi: 10.4236/am.2015.68128.
[7] D. Volchenkov, B. E. Bläsing, T. Schack. "Spatio-Temporal Kinematic Decomposition of Movements". Engineering, 6, 385-398. doi: 10.4236/eng. 2014.68041.
[8] Z. Liu, H. Chen. "Mechanical Design and Kinematic Simulation of Automated Assembly System for Relay" World Journal of Mechanics, 6, 1-7. doi: 10.4236/wjm.2016.61001.

Citation :

Jérémie Gaston SAMBOU, Edouard DIOUF, "Planar and Spatial kinematic for vortex fluid flow behaviour by using perturbation parameter," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 5, pp. 49-62, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I5P506