Laminar natural convection of gas in closed square cavity


Аuthors

Cherkasov S. G.*, Laptev I. V.**, Ananyev A. V.***, Gorodnov A. O.****

Keldysh Research Centre, 8, Onezhskaya str., Moscow, 125438, Russia

*e-mail: sgcherkasov@yandex.ru
**e-mail: laptev@kerc.msk.ru
***e-mail: anatoly.v.ananyev@gmail.com
****e-mail: an.ol.gorodnov@gmail.com

Abstract

The article considers the steady state problem of laminar natural convection of ideal gas with linear dependence between thermal conductivity and viscosity coefficients and temperature in closed square cavity between two vertical walls with large temperature difference and two thermally isolated horizontal walls using homobaricity approximation. It presents the dimensionless form of equations, and analyzes limiting transition of these equations in case of smallness of the characteristic temperature drops. The control volume method was applied for the obtained equations approximation in case of small Mach numbers conditions. Analysis of mesh convergence of the applied numerical method was performed. Comparison of numerical modeling results for such problem with constant gas properties with the well‑known data obtained by generalizing the great number of calculations made by various authors on the similar meshes, demonstrated good matching of the results. As a result of numerical modeling the problem was solved in a wide range of the key parameters, such Rayleigh number and characteristic temperature drop. Temperature fields and flow lines for various Rayleigh number values and temperature parameter are shown. The obtained results were compared with Boussinesq limit when temperature drops in the area were small. Conditions of transition to Boussinesq limit and effect of characteristic temperature selecting on this limiting transition were clarified. The best option for the characteristic temperature selection for describing the heat and mass exchange processes was substantiated. The dependence between thicknesses of near‑wall boundary layer and temperature parameter were obtained. Criteria of Boussinesq limit applicability for heat and mass exchange description in case of the above said type of the problems was substantiated.

Keywords:

laminar natural convection, homobaricity, ideal gas, Boussinesq approach, low Mach number approach

References

  1. Agafonov D.V., Cherkasov S.G. The effect of the variability of density on the propagation of heat in a gas. High Temperature, 2002, vol. 40, no. 4, pp. 617–622.

  2. Cherkasov S.G., Cherkasova А.S. Odnomernyj teploperenos v gaze s uchetom effektov, obuslovlennykh teplovym rasshireniem [One-dimensional heat transfer in gases and effects due to thermal expansion]. Izvestiya RАN. Energetika – Proceedings of the Russian Academy of Sciences. Power Engineering, 2007, no. 1, pp. 47–54. In Russ.

  3. Cherkasov S.G., Mironov V.V., Tlevcejev V.V. Teoreticheskoe issledovanie nestatsionarnogo teploobmena v zamknutom gazovom ob''eme pri otsutstvii massovykh sil [Theoretical research of non-stationary heat-exchange in closed gas volume at the absence of mass forces]. Izvestiya RАN. Energetika – Proceedings of the Russian Academy of Sciences. Power Engineering, 2012, no. 4, pp. 139–150. In Russ.

  4. Cherkasov S.G., Mironov V.V. Ob usloviyakh primenimosti uravneniya teploprovodnosti dlya opisaniya odnomernogo nestatsionarnogo teploperenosa v szhimaemoj tekuchej srede [About conditions of application of thermal conductivity equation for the description of one-dimensional non-stationary heat transfer in compressible fluid medium]. Izvestiya RАN. Energetika – Proceedings of the Russian Academy of Sciences. Power Engineering, 2012, no. 4, pp. 134–138. In Russ.

  5. Lapin Yu.V., Strelets M.Kh. Vnutrennie techeniya gazovykh smesej [Internal flows of gas mixtures]. Moscow, Nauka, 1989. 368 p. In Russ.

  6. Cherkasov S.G. Some special features of description of thermal and dynamic processes in gases in the approximation of homobaricity. High Temperature, 2010, vol. 48, no. 3, pp. 444–448.

  7. Belyayev A.Yn., Ivanov A.V., Egorov S.D., Voyteshonok V.S., Mironov V.M. Pathways to solve the problem of cryogenic rocket propellant long storage in space. Proc. Int. Aerospace Congress. Moscow. Russia. August 15-19, 1994, vol. 1, pp. 558–562.

  8. Landau L.D., Lifshitz E.M. Fluid mechanics (Course of theoretical physics; v. 6). Pergamon Press, 1987. 547 p.

  9. Polezhaev V.I., Buneh А.V., Verezub N.А., Glushko G.S., Gryaznov V.L., Dubovik K.G., Nikitin S.А., Prostomolotov А.I. Matematicheskoe modelirovanie konvektivnogo teplo-massoobmena na osnove uravnenij Nav’e–Stoksa [Mathematical modeling of convective heat-mass transfer on the basis of the Navier–Stokes equations]. Moscow, Nauka, 1987. 272 p. In Russ.

  10. Gray D.D., Giorgini A. The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer, 1976, vol. 19, pp. 545–551.

  11. Niculin D.A, Strelets M.Kh. Numerical modeling of nonsteady natural-convection of homogeneous compressible gas in a closed nonadiabatic region. High Temperature, 1984, vol. 22, no. 5, pp. 707–713.

  12. Chenoweth D. R., Paolucci S. Natural convection in an enclosed vertical air layer with large horizontal temperature difference. J. Fluid Mech., 1986, vol. 169, pp. 173–210.

  13. Cherkasov S.G., Laptev I.V. Uproshhennyj raschet laminarnogo svobodno-konvektivnogo sloya v gaze [Simplified approach for natural convection laminar boundary layer calculation]. Teplovye protsessy v tekhnike – Thermal processes in engineering, 2017, vol. 9, no. 4, pp. 146–153. In Russ.

  14. Vargaftik N.B. Spravochnik po teplofizicheskim svojstvam gazov i zhidkostej [Reference book on thermophysical properties of gases and liquids]. Moscow: Nauka, 1972. 720 p. In Russ.

  15. Gorodnov А.O., Laptev I.V., Cherkasov S.G. Modelirovanie estestvennoj konvektsii szhimaemogo gaza v zamknutoj oblasti [Simulation of natural convection of a compressible gas in a closed region]. Sbornik tezisov yubilejnoj konferentsii Natsional’nogo komiteta RАN po teplo- imassoobmenu “Fundamental’nyei prikladnye problem teplomassoobmena” i “Problem ygazodinamiki I teplomassoobmena v ehnergeticheskikh ustanovkakh” – Extended abstracts of both jubilee conference “Fundamental and applied problems in heat and mass transfer” and “Problems of gas dynamics, heat and mass transfer in power plants”, Publishing house MPEI, 2017, vol. 1, pp. 103–104. In Russ.

  16. Paolucci S. On the filtering of sound from the Navier–Stokes equations. Sandia National Laboratories report SAND 82-8257, 1982. 52 p.

  17. Qu´er´e P.L. Modelling of natural convection flows with large temperature differences: A benchmark problem for low Mach number solvers. Part 1, reference solutions. ESAIM: Mathematical Modelling and Numerical Analysis. 2005, vol. 39, no. 3, pp. 609–616.

  18. Roux B., Grondin J. C., Bontoux P., Gilly B. On a high-order accurate method for the numerical study of natural convection in a vertical square cavity. Numerical Heat Transfer, 1978, vol. 1, pp. 331–349.

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