A Free Convection in Thin Spherical Shells as a Key to a Precise Estimation of the Titan Montgolfiere Heat Performance

Division of Engineering and Applied Science, California Institute of Technology

A precise assessment of heat transfer characteristics of the turbulent natural convection flow inside narrow spherical shells is critical for design of various engineering applications where the shell plays a role of insulator separating between hot interior and cold environment. Titan Montgolfiere, built to operate at a cryogenic environment, is one of the most representative examples when optimally designed shell can drastically decrease costs and increase payload of a certain scientific mission.

An extensive numerical study of laminar and turbulent free convection flow inside thin spherical shells with isothermal cold and hot boundaries and internal/external radius ratios in the range of 0.85≤ ri/ro≤0.95 is presented. The accuracy of the results has been verified by grid independence analysis and DNS-LES comparisons of the flow characteristics for the typical cases. The functional Nu-Ra dependency is investigated for the range of 103≤Ra≤1010 covering laminar, transitional and fully turbulent flow regimes. The RANS modeling for even higher Rayleigh numbers is discussed as well. For thin shells, we observe considerable deviations from the existing engineering correlations. The deviations tend to increase for transitional and fully turbulent flows. A new correlation for Nu-Ra dependency for the thin spherical shell geometry is suggested.