Comparison Between the FLUIDICS Experiment and Direct Numerical Simulations of Fluid Sloshing in Spherical Tanks Under Microgravity Conditions

The fluids behaviour within a spherical tank under microgravity conditions is investigated through a comparison between the original data from the FLUIDICS experiment carried out in the ISS and Direct Numerical Simulations for two-phase flows. The study case consists in the rotation of a spherical tank around a fixed axis. The tank is filled with a liquid with physical properties similar to those of liquid propellants and gases used in the space industry. Two tanks with different filling ratios have been tested in space. Cameras and sensors allow extracting the fluids dynamics and the temporal evolution of the force and torque exerted by the fluids on the tank wall. Several manoeuvres corresponding to different angular velocities and angular accelerations are submitted on both tanks. The velocity profile is divided into four phases: from zero, the angular velocity around the vertical axis increases linearly until it reaches the required constant value for which the fluids stabilise in the second phase, then the angular velocity decreases until it recovers zero. Numerical simulations are computed with the home-made code DIVA which is based on the Level Set method coupled with the Ghost Fluid Method. The force in the radial direction gives the value of the centrifugal force during the constant angular velocity phase. The average centrifugal force is well predicted by the simulations, the comparison with the experimental data exhibits errors lower than 3% for the half-filled tank. Considering the vertical torque, the effect of the Euler acceleration is clearly visible through the important peaks of opposite sign observed during the acceleration and the deceleration phases. Moreover, the oscillations of the gas bubble during the second phase can be observed from the torque evolution. Their magnitude decreases throughout time until the steady state is reached. The measured and predicted temporal evolutions match together until the magnitude of the oscillations reaches the noise level of the data. The bubble oscillations are much more damped for the tank containing a larger amount of liquid (75%). The frequency of these oscillations are investigated applying the Fourier transform of the torque signals and by looking at the videos taken during the experiment. Similar oscillation frequencies are observed with the experimental setup and the numerical simulations, even for the manoeuvre with the lower Bond numbers. We verify that the oscillation frequency increases with the angular velocity. Finally, the comparison exhibits that the numerical simulations provide an accurate prediction of the fluids behaviours in microgravity conditions for this range of Bond numbers.