Numerical investigation of natural convection in slope longitudinal air layer

Mathematics. Physics. Mechanics


Аuthors

Pivovarov D. E.

Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia

e-mail: pivovar@ipmnet.ru

Abstract

It is the numerical investigation of the natural convection flow pattern and heat transfer rate inside rectangular box heated from below and cooled from above with insulated sidewalls. The box is inclined from horizontal to vertical position and back round the shortest side. This is the longitudinal configuration of the inclined layer for which the transversal rolls are typical.
Direct numerical simulation (DNS) of Navier-Stokes equations for incompressible fluid is applied. The numerical method is based on a second-order central difference approximation in space and on integration for time by a third-order semi-implicit Runge–Kutta method. Spatial discretization retains some important properties of the Navier–Stokes equations, including energy conservation by the nonlinear and pressure-gradient terms. The scheme is supplied with a local error estimation and time-step control algorithm.
The hysteresis with subject to changing the inclination of the box has been confirmed. Different convection interactions have been detected. It is noted that there are oscillations of flow for some angles at high Rayleigh numbers. The comparison of regime diagram for spatial and plane flow showed the discrepancy in number of rolls and the borders of their number change.
The study is limited by laminar regime for incompressible fluid for which Boussinesq approximation is right. The observable fluid was air. The Rayleigh number is varied between 103 and 105 and the angle range from 0 up to 90°.
This is the study of spatial pattern and heat transfer rate of convection interactions in the longitudinal layer defined by the aspect ratios of the box. The diagram of the interactions regime was sketched.

Keywords:

Navier-Stokes equation, Boussinesq approximation, modeling, natural convection, bifurcations, hysteresis, slope layer

References

  1. Polezhaev V.I., Myakshina M.N., Nikitin S.A. Heat transfer due to buoyancy-driven convective interaction in enclosures: Fundamentals and applications, International Journal of Heat and Mass Transfer, 2012, vol. 55, no. 1–3, pp. 156–165.
  2. Graaf J.D., Held E.V.D., The relation between the heat transfer and the convection phenomena in enclosed plane air layers, Applied Scientific Research, 1953, vol. 3, no. 6, pp. 393–409.
  3. Birikh R.V., Gershuni G.Z., Zhukhovitskii E.M., Rudakov R.N. Prikladnaya matematika i mekhanika, 1969, vol. 32, no. 2, pp. 256–263.
  4. Gershuni G.Z., Zhukhovitskii E.M. Prikladnaya matematika i mekhanika, 1969, vol. 33, no. 5, pp. 855–860.
  5. Hart J.E. Stability of the flow in a differentially heated inclined box, Journal of Fluid Mechanics, 1971, vol. 47, no. 3, pp. 547–576.
  6. Buchberg H., Catton I., Edwards D.K. Natural Convection in Enclosed Spaces—A Review of Application to Solar Energy Collection, Journal of Heat Transfer, 1976, vol. 98, no. 2, pp. 182–188.
  7. Catton I. Natural Convection in Enclosures, Proceedings of the Sixth Int. Heat Trans. Conference, Toronto, W.D.C, Hemisphere, 1978, vol. 6, pp.13–31.
  8. Inaba H., Fukuda T. An Experimental Study of Natural Convection in an Inclined Rectangular Cavity Filled With Water at Its Density Extremum, Journal of Heat Transfer, 1984, vol. 106, no. 1, pp. 109–115.
  9. ElSherbiny S.M., Raithby G.D., Hollands K.G.T. Heat Transfer by Natural Convection Across Vertical and Inclined Air Layers, Journal of Heat Transfer, 1982, vol. 104, no. 1, pp. 96–102.
  10. Symons J.G., Peck M.K. Natural Convection Heat Transfer Through Inclined Longitudinal Slots, Journal of Heat Transfer, 1984, vol. 106, no. 4, pp.824–829.
  11. Ozoe H., Sayama H., Churchill S.W. Natural convection patterns in a long inclined rectangular box heated from below: Part I. Three-directional photography, International Journal of Heat and Mass Transfer, 1977, vol. 20, no. 2, pp. 123–129.
  12. Khatuntseva O.N. Elektronnyi zhurnal “Fiziko-khimicheskaya kinetika v gazovoi dinamike”, 2012, vol. 13, available at:http://www.chemphys.edu.ru/media/files/2012-02-29-001.pdf. (accessed 29.02.2012).
  13. Yang H.Q., Yang K.T., Lloyd J.R. Laminar natural-convection flow transitions in tilted three-dimensional longitudinal rectangular enclosures, International Journal of Heat and Mass Transfer, 1987, vol. 30, no. 8, pp. 1637–1644.
  14. Soong C.Y., Tzeng P.Y., Chiang D.C., Sheu T.S. Numerical study on mode-transition of natural convection in differentially heated inclined enclosures, International Journal of Heat and Mass Transfer, 1996, vol. 39, no. 14, pp. 2869–2882.
  15. Pivovarov D.E., Polezhaev V.I. Trudy XVII Shkoly-seminara molodykh uchenykh i spetsialistov pod rukovodstvom akademika RAN A.I. Leont'eva "Problemy gazodinamiki i teplomassoobmena v aerokosmicheskikh tekhnologiyakh ", Moscow, Izdatel'skij dom MJeI, 2009, vol. 2, pp. 113–116.
  16. Khezzar L., Siginer D., Vinogradov I. Natural convection in inclined two dimensional rectangular cavities, Heat and Mass Transfer, 2012, vol. 48, no. 2, pp. 227–239.
  17. Singh A.K., Roy S., Basak T. Visualization of Heat Transport during Natural Convection in a Tilted Square Cavity: Effect of Isothermal and Nonisothermal Heating, Numerical Heat Transfer, Part A: Applications, 2012, vol. 61, no. 6, pp. 417–441.
  18. Azwadi C.S.N., Fairus M.Y.M., Syahrullail S. Virtual Study of Natural Convection Heat Transfer in an Inclined Square Cavity, Journal of Applied Sciences, 2010, vol. 10, no. 4, pp. 331–336.
  19. Munir F.A., Sidik N.A.C., Ibrahim N.I.N. Numerical Simulation of Natural Convection in an Inclined Square Cavity, Journal of Applied Sciences, 2011, vol.11, no. 2, pp. 373–378.
  20. Nikitin N.V. Third-order-accurate semi-implicit runge-kutta scheme for incompressible navier-stokes equations, International Journal for Numerical Methods in Fluids, 2006, vol. 51, no. 2, pp. 221–233.
  21. Nikitin N.V. Finite-difference method for incompressible Navier–Stokes equations in arbitrary orthogonal curvilinear coordinates, Journal of Computational Physics, 2006, vol. 217, no. 2, pp. 759–781.
  22. Nikitin N.V. Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki, 2006, vol. 46, no. 3, pp. 509–525.
  23. Pivovarov D.E. Problemy gazodinamiki i teplomassoobmena v novykh energeticheskikh tekhnologiyakh: Tezisy dokladov XVIII Shkoly-seminara molodykh uchenykh i spetsialistov pod rukovodstvom akad. RAN A.I. Leont'eva, Moscow, Izdatel'skij dom MJeI, 2011, pp. 79–80.
  24. Bessonov O.A., Brailovskaya V.A., Nikitin S.A., Polezhaev V.I, Matematicheskoe modelirovanie, 1999, vol. 11, no. 12, pp. 51–58.
  25. Arnold J.N., Catton I., Edwards D.K. Experimental Investigation of Natural Convection in Inclined Rectangular Regions of Differing Aspect Ratios, Journal of Heat Transfer, 1976, vol. 98, no. 1, pp. 67–71.

Download

mai.ru — informational site MAI

Copyright © 2000-2021 by MAI

Вход