Skip to main navigation menu Skip to main content Skip to site footer

Vol. 25 No. 42 (2016)

Papers

Comparative study of fluid flow across orifice plate using Stokes and Navier-Stokes equations

https://doi.org/10.19053/01211129.4633

Published 2016-05-03

  • Miryam Lucía Guerra-Mazo
    • ,
  • María Vilma García-Buitrago
    • ,
  • Elizabeth Rodríguez-Acevedo

Miryam Lucía Guerra-Mazo
Instituto Tecnológico Metropolitano (Medellín – Antioquia, Colombia).

María Vilma García-Buitrago
Instituto Tecnológico Metropolitano (Medellín – Antioquia, Colombia).

Elizabeth Rodríguez-Acevedo
Instituto Tecnológico Metropolitano (Medellín – Antioquia, Colombia).

Abstract

This paper presents the results of a comparison between Stokes and Navier-Stokes equations, in order to simulate the flow of liquid water at atmosferic conditions, through a concentric orifice plate. From experimental data taken from the fluids bank, the simulations of both equations were evaluated, using free software Freefem++CS, which is based on the finite elements method. The evaluated variables are velocity and pression in a time interval. When analyzing the results obtained with the simulations and comparing them with the experimental data, it was found that the Navier-Stokes equations represent better the system, than the Stokes equation.

Keywords

mathematical model, orifice plate, simulation, Stokes and Navier-Stokes equations

PDF (Español) HTML (Español)

References

  1. J. M. Cimbala and Y. A. Cengel, “Flujo en Tuberías”, Mecánica de Fluidos: Fundamentos y Aplicaciones. V.C. Olguin. Mexico: McGraw Hill, pp. 321-398, 2006.
  2. R. L. Mott, “Medición del Flujo”, Mecánica de Fluidos. J. E. Brito. Mexico: Pearson Education, pp. 473-499, 2006.
  3. B. Manshoor, F. C. Nicolleau and S. B. Beck, “The fractal flow conditioner for orifIce plate flow meters”, Flow Measurement and Instrumentation, vol. 22 (3), pp. 208-214, Jun. 2011. DOI: http://dx.doi.org/10.1016/j.flowmeasinst.2011.02.003. DOI: https://doi.org/10.1016/j.flowmeasinst.2011.02.003
  4. J. Banks, J. S. Carson, B. L. Nelson and D. M. Nicol, Discrete-event system simulation. USA: Prentice Hall, 2009.
  5. F. Hecht, O. Piro and A. Le Hyaric, “Freefem++,” 2014. [Online]. Disponible: http://www.freefem.org/ff++/ftp/freefem++doc.pdf.
  6. R. Lewandowski, “The mathematical analysis of the coupling of a turbulent kinetic energy equation to the Navier-Stokes equation with an eddy viscosity”, Nonlinear Analysis, Theory, Methods & Applications, vol. 28 (2), pp. 393-417, Jan. 1997. DOI: http://dx.doi.org/10.1016/0362-546X(95)00149-P. DOI: https://doi.org/10.1016/0362-546X(95)00149-P
  7. M. M. Rhaman and K. M. Helal, “Numerical Simulations of unsteady Navier-Stokes Equations for incompressionable newtonian fluid using FreeFem++ based on Finite Element Method”, Annals of Pure and Applied Mathematics, vol. 6 (1), pp. 70-84, May. 2014.
  8. C. L. Felter, J. H. Walther and C. Henriksen, “Moving least squares simulation of free surface flows”, Computers & Fluids, vol. 91, pp. 47-56, Mar. 2014. DOI: http://dx.doi.org/10.1016/j.compfluid.2013.12.006. DOI: https://doi.org/10.1016/j.compfluid.2013.12.006
  9. Z. Li, K. Ito and M. C. Lai, “An augmented approach for Stokes equations with a discontinuous viscosity and singular forces”, Computers & Fluids, vol. 36 (3), pp. 622-635, Mar. 2007. DOI: http://dx.doi.org/10.1016/j.compfluid.2006.03.003. DOI: https://doi.org/10.1016/j.compfluid.2006.03.003
  10. T. Geenen, M. ur Rehman, S. P. MacLachlan et al., “Scalable robust solvers for unstructured FE geodynamic modeling applications: Solving the Stokes equation for models with large localized viscosity contrasts”, Geochemistry, Geophysics, Geosystems. An Electronical Journal of the earth sciences, vol. 10 (9), pp. 1-12, Sep. 2009. DOI: https://doi.org/10.1029/2009GC002526
  11. A. Mojtabi and M. O. Deville, “One-dimensional linear advection–diffusion equation: Analytical and finite element solutions”, Computers & Fluids, vol. 107, pp. 189-195, Jan. 2015. DOI: http://dx.doi.org/10.1016/j.compfluid.2014.11.006. DOI: https://doi.org/10.1016/j.compfluid.2014.11.006
  12. J. Volker, K. Kaiser and J. Novo, “Finite Element Methods for the Incompressible Stokes Equations with Variable Viscosity”, Zeitschrift fûr Angewandte Mathematik und Mechanik, vol. 96 (2), pp. 205-216, 2016. DOI: http://dx.doi.org/10.1002/zamm.201400291. DOI: https://doi.org/10.1002/zamm.201400291
  13. P. Gómez-Palacio, “Solución de la ecuación de Stokes”, Revista Universidad EAFIT, vol. 46, pp. 90-102, 2010.
  14. E. Engineering, Análisis y Simulación de la dinámica de fluidos computacionales-CFD a fluidos internos [Online]. Disponible: http://evaeng.com/analisis-y-simulacion-de-ladinamica-de-los-fluidos-computacionales-cfda-flujos-internos/.
  15. C. M. Institute, Navier-Stokes equation [Online]. Disponible: http://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation.
  16. J. L. Vázquez, Fundamentos matemáticos de la mecánica de fluidos. Madrid: Universidad Autónoma de Madrid, 2003.
  17. P. K. Kundu, I. M. Cohen and D. R. Dowling, Fluids Mechanics. Elsevier, 2012.

Downloads

Download data is not yet available.

Similar Articles

You may also start an advanced similarity search for this article.