It is well known that surface tension of a liquid has a decisive role in flow dynamics and the eventual equilibrium state, especially in confined flows under low gravity conditions and also in free surface flows. One such instance of a combination of these two cases where surface tension plays an important role is in the microgravity environment of a spacecraft propellant tank. In this specific case both propellant acquisition and residual propellant estimation are critical to the mission objectives particularly in the end-of-life phase. While there have been a few studies pertaining to the equilibrium state in given geometric configurations, the transient flow leading to final state from an initial arbitrary distribution of propellant is rarely described. The present study is aimed at analysing the dynamic behaviour of the liquids under reduced gravity through numerical simulation and also addresses the specific case of propellant flow transient in a cone-in-a-sphere type of tank configuration proposed by Lal and Raghunandan which is likely to result in both improved acquisition and life time estimation of spacecraft. While addressing this specific problem, the present work aims to study the transient nature of such surface tension driven flows in a general form as applicable to other similar problems also. Volume of Fluid (VOF) method for multiphase model in ANSYS FLUENT was adapted with suitable changes for generating numerical solutions to this problem. Simulations were run for three different cone angles of 17o, 21o & 28o with a flat liquid surface for full scale models to measure the rise height and time of rise. Two scaled models of ½ and 1/10th of the original dimensions with the same liquid configuration of the 28o cone angle case were simulated to see if the time scales involved would come down for experimental feasibility. A third simulation of the 1/10th scale model was run with the liquid spread in the tank to imitate the general conditions found in the propellant tank in microgravity. To understand the behaviour of liquids in the microgravity state to changing physical parameters, a set of simulations was run using liquid phases as water and hydrazine with different physical parameters of temperature and surface tension. The theory put forward by Lal and Raghunandan was found to stand firm. In the case of the cone angle of 28o it was observed that in the final equilibrium state the liquid collected towards the apex of the cone with the larger volume fraction of liquid accumulating inside the cone. An addition of a cylindrical section at the bottom of the cone seems to help although not uniformly for all case. The equilibrium settling times for all the three cone angle cases were in the order of 300 to 600 seconds for simulations on a spherical tank of diameter two metres which was close to the actual tank dimension used on spacecraft. Scaled down simulations of 1/10th and ½ the tank geometry with both flat liquid surfaces and spread out liquid volumes showed that the smaller models had equilibrium settling times which were considerably lower (in the order of tens of seconds) than the full scale models. Although smaller, these time scales are larger than the maximum time scales available in drop tower tests which provide a maximum free fall time of around 9 to 10 seconds. Validation of the proposed configuration by flying an aircraft in a parabolic flight path is a possibility that could be explored for the scaled down models since the zero-g duration for these flights is on an average between 15-20 seconds.