The effect of the wall heat capacity on the temperature stratification and pressure rise during natural convection of hydrogen vapor in a vertical cylindrical vessel


Gorodnov A. O.*, Laptev I. V.**

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



As of today, Russian space industry announced several projects of new launch vessels, such as super heavy class rocket and the rocket with reusable stages, operated on liquefied natural gas as a fuel. Moreover, other countries, such as USA, China and the ESA members, announced plans of future missions to Mars and Moon. A considerable part of the future space missions depends on the possibility of effective long-term storage of cryogenic fuel components under lowered gravity conditions. The important role of cryogens in space flights is being determined by their widespread application as a fuel and in life support systems.

Due to cryogens’ very low temperatures, the tanks for their storage are extremely sensitive to the thermal flows from the environment caused by solar radiation, aerodynamic heating and conductive transference from the other parts of a spacecraft. External heating and the presence of microgravity lead to pressure raise and free-convective motions in the storage tank. The pressure rise rate is being accelerated by temperature stratification effect. This effect has been demonstrated in many ground and space experiments.

One of the most important problem in experimental cryogenic storage studies is scale factor. Most of experimental data was obtained with small-size fuel tanks. This leads to the problem of geometric similarity violation of the fuel tank wall thickness compared to the real rocket storage tanks. To estimate the impact of this dissimilarity, the article considers the problem of the wall’s thermal capacity and thermal conductivity impact on temperature stratification and pressure rise at the vapor non-stationary thermal convection in the closed cylindrical vessel.

Low Mach numbers approximation is being used to describe evolution of the vapor temperature, velocity, density and other parameters. Boundary conditions, defining parameters range, physical properties of vapor and a wall material simulate conditions of the experiment on drainage-free hydrogen storage.

A series of computations at various wall thickness values was performed using numerical method proposed by Quazzani and Garrabos. The computation data demonstrates considerable reduction in the pressure rise rate, temperature stratification value and convection intensity with the wall thickness increase. The obtained results demonstrate the possibility of considerable underrating of the pressure rise rate and other heat exchange parameters on the steam blanket of the tank, when the wall’s real thermal capacity and thermal conductivity are not being accounted for.


natural convection, low Mach number approach, homo-baricity approximating, drainage-free storage, steam blanket


  1. Ward W.D. et al. Evaluation of AS-203 Low-Gravity Orbital Experiment, NASA CR 94045 (Chrysler Corp. Space Div. Technical Report BB-3.4.3-5-101), 13 January 1967.

  2. 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.

  3. Van Dresar N.T., Lin C.S., Hasan M.M. Self_pressurization of a flightweight liquid hydrogen tank: Effect of fill level at low wall heat flux, AIAA Paper, 1992. DOI: 10.2514/6.1992-818

  4. Hastings L.J., Flachbart R.H., Martin J.J., Hedayat A., Fazah M., Lak T., Nguyen H., Bailey J.W. Spray Bar Zero-Gravity Vent System for On-Orbit Liquid Hydrogen Storage, NASA TM-2006-212926, 2006. URL:

  5. Seo M., Jeong S. Analysis of self-pressurization phenomenon of cryogenic fluid storage tank with thermal diffusion model, Cryogenics, 2010, vol. 50, no. 9, pp. 549 - 555. DOI: 10.1016/j.cryogenics.2010.02.021

  6. Khusnetdinov I.R. Trudy MAI, 2014, no. 73. URL:

  7. Partola I.S. Trudy MAI, 2011, no. 46. URL:

  8. Polezhaev V.I., Bune A.V., Verezub N.A. et al. Matematicheskoe modelirovanie konvektivnogo teplomassoobmena na osnove uravnenii Nav'e-Stoksa (Mathematical modelling of convective heat and mass exchange basув oт Navier-Stokes equations), Moscow, Nauka, 1987, 270 p.

  9. Polezhaev V.I., Cherkasov S.G. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza, 1983, no. 4, pp. 148 - 157.

  10. Polezhaev V.I. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza, 1972, no. 4, pp. 77 - 88.

  11. Moiseeva L.A., Cherkasov S.G. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza, 1996, no. 2, pp. 66 - 72.

  12. Lin W., Armfield S.W. Direct simulation of natural convection cooling in a vertical circular cylinder, International Journal of Heat and Mass Transfer, 1999, vol. 42, no. 22, pp. 4117 – 4130.

  13. Pivovarov D.E. Trudy MAI, 2013, no. 68. URL:

  14. Fedyushkin A.I., Puntus A.A. Trudy MAI, 2018, no. 102. URL:

  15. Ai M.V., Temnov A.R. Trudy MAI, 2015, no. 79. URL:

  16. Miroshnichenko I.V., Sheremet M.A. Turbulent natural convection combined with thermal surface radiation inside an inclined cavity having local heater, International Journal of Thermal Sciences, 2018, vol. 124, pp. 122 - 130.

  17. Martyushev S.G., Sheremet M.A. Conjugate natural convection combined with surface thermal radiation in a three-dimensional enclosure with a heat source, International Journal of Heat and Mass Transfer, 2014, vol. 73, pp. 340 - 353. DOI: 10.1016/j.ijheatmasstransfer.2014.02.009

  18. Gray D.D., Giorgini A. The validity of the boussinesq approximation for liquids and gases, International Journal of Heat and Mass Transfer, 1976, vol. 19, no.5, pp. 545 – 551. DOI: 10.1016/0017-9310(76)90168-X

  19. Nekhamkina O.A., Nikulin D.A., Strelets M.Kh. Teplofizika vysokikh temperatur, 1989, vol. 27, no. 6, pp. 1115 - 1125.

  20. Paolucci S. On the filtering of sound from the Navier-Stokes equations, Sandia National Laboratories, Livermore, Rep. SAND824257, December 1982. URL:

  21. Lapin Yu.V., Strelets M.Kh. Vnutrennie techeniya gazovykh smesei (Internal flows of gas mixtures), Moscow, Nauka, 1989, 368 p.

  22. Soboleva E.B. Chislennoe modelirovanie dinamiki okolokriticheskoi zhidkosti v tverdoi poristoi matritse (Numerical modelling of near-critical fluid dynamics in solid porous medium), Moscow, Institut problem mekhaniki RAN, 2006, 58 p.

  23. Beysens D., Chatain D., Nikolayev V.S., Ouazzani J., Garrabos Y. Possibility of long-distance heat transport in weightlessness using supercritical fluids, Physical Review E, 2010, vol. 82, no. 6. DOI: 10.1103/PhysRevE.82.061126

  24. Chenoweth D.R., Paolucci S. Natural convection in an enclosed vertical air layer with large horizontal temperature difference, Journal of Fluid Mechanics, 1986, vol. 169, pp. 173 – 210. URL:

  25. Chenoweth D.R., Paolucci S. Gas flow in vertical slots with large horizontal temperature difference, Physics Fluids, 1985, vol. 28, no. 8, pp. 2365 - 2374.

  26. Cherkasov S.G., Laptev I.V. Teplovye protsessy v tekhnike, 2017, no. 4, pp. 146 - 153.

  27. Cherkasov S.G., Anan’ev A.V., Moiseeva L.A. Limitations of the Boussinesq Model on the Example of Laminary Natural Convection of Gas between Vertical Isothermal Walls, High Temperature, 2018, vol. 56, no. 6, pp. 878 – 883. DOI: 10.1134/S0018151X18060081

  28. Cherkasov S.G., Laptev I.V., Anan'ev A.V., Gorodnov A.O. Teplovye protsessy v tekhnike, 2019, vol. 11, no. 5, pp. 203 – 215.

  29. Ferziger J.H., Peric M. Computational methods for fluid dynamics, Springer, 2002. DOI: 10.1007/978-3-642-56026-2

  30. Patankar S. Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, New York, 1980, 197 p.

  31. Quazzani J., Garrabos Y. A new numerical algorithm for low Mach number supercritical fluid, Preprint Elsevier, 23 Apr. 2007. URL:

  32. Vargaftik. N.B. Spravochnik po teplofizicheskim svoistvam gazov i zhidkostei (Handbook of physical properties of liquids and gases), Moscow, Nauka, 1972, 721 p.

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