On the hydrodynamic stability of an imploding rotating circular cylindrical liquid liner

Abstract

The hydrodynamic stability of an imploding cylindrical liquid liner is analytically and numerically investigated. Such dynamic system can be used to compress gas trapped by the liner, as one may seek in a hydrogen fusion reactor. For such system it is vital for the liner to stay intact at least up to the turnaround point, which marks the point of maximum compression of the inner gas. New two-dimensional linear stability of Bell-type equation and Wentzel-Kramers-Brillouin (WKB) approximations are derived to account for the rotation of the liner. Excellent agreement is achieved between computational fluid dynamics (CFD) and 1D analysis for the trajectory of the unperturbed liner. Very good agreement is also achieved between the Bell type linear stability solution and the CFD until non-linear effects take hold near the turnaround point. The WKB approximation also agrees well but only at the early stage of the liner motion. Viscosity, surface tension and inner gas stability waves are found to have a small effect for a liner’s radial compression of up to ten. It is seen that the rotation has little effect on the perturbation amplitude during the accelerating stage of the liner, which is dominated by a slow oscillatory growth of a Bell-Plesset type at the studied conditions. However, at the decelerating stage towards the turnaround point, Rayleigh–Taylor rapid perturbation growth is suppressed at sufficiently large rotation rates. Hence, when coupled with non-linear saturation effects, the liner stays much intact until the turnaround point for radial compression ratios of up to ten. New simple linear stability limits are derived and are analysed.