Pressure rise during unsteady natural convection of hydrogen vapor in a vertical cylinder with isothermal bottom boundary


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 problem of pressure rise of hydrogen vapor in the presence of natural convection in a vertical cylinder with isothermal bottom boundary is considered using homobaricity approach. Several analytical solutions for pressure and average Nusselt number is received for cylinder with thermally isolated bottom boundary and cylinder with isothermal bottom boundary on steady state regime. The original numerical algorithm for low Mach number flows is developed for the case of axial symmetry. Moreover, the analysis of grid and time convergence of this method is made in this article. This method is shown good agreement with analytical solution for the case of the cylinder with thermally isolated bottom boundary. The numerical simulation of unsteady heating of cylinder is made in vide range of laminar Rayleigh numbers and aspect ratios. The initial conditions for this calculation approximately modeled vapor storage in the rocket fuel tank. The flow patterns and temperature isolines for different time moments and Rayleigh number and aspect ratio values are shown. The influence of natural convention inten­sity and cylinder height on pressure rise is investigated. The method of asymptotic estimate for the upper limit of pressure rise during fuel storage is given.

Keywords:

laminar natural convection, nonstationary convection, homobaricity, ideal gas, Boussinesq approach, low Mach number approach, vertical cylinder, fuel storage

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