Recent investigations have successfully demonstrated closed-form analytical solutions of spontaneous capillary flows in idealized cylindrical containers with interior corners. In this work, the theory is extended and applied to complex containers modeling spacecraft fuel tanks employing propellant-management devices (PMDs) consisting of networks of vanes. The specific problem investigated is one of spontaneous rewetting of a typical partially filled liquid-fuel/cryogen tank with PMD after thrust resettling. The transients of this flow impact the logistics of orbital maneuvers and potentially tank thermal control. The general procedure to compute the initial condition for the closed-form transient flows is first outlined and then solved for several complex cylindrical tanks exhibiting symmetry. The utility and limitations of the technique as a design tool are discussed in a summary, which also highlights comparisons with NASA flight data of a model propellant tank with PMD