Analytical asymptotic solutions for heat transfer during transient compression filling of spherical and cylindrical pressure vessels in the limit of small Reynolds number

摘要

Taking the limit of small Reynolds number for a vessel being filled with compressed gas, the energy equation was found to asymptote to the unsteady heat conduction equation with heat generation and variable density. This equation was solved analytically for cylindrical and spherical geometry. Assuming the density changes linearly with time, a solution is obtained which is identical in form to the constant density solution if the Fourier number is denned using the log-mean density rather than the instantaneous density. At steady state conditions, the Nus-selt number based on the diameter for cylinders with aspect ratios larger than 1 rapidly approaches an integer solution of Nu_D = 8. For cylinders with aspect ratios less than 1, the Nusselt number based on the cylinder length (height) characteristic dimension rapidly approaches Nu_L = 6. It is shown experimentally and numerically that during compression filling, the heat transfer asymptotically approaches this analytical solution at low Reynolds numbers.