Method for CFD Simulation of Propellant Slosh in a Spherical Tank

Propellant sloshing can impart unwanted disturbances to spacecraft, especially if the spacecraft controller is driving the system at the slosh frequency.This paper describes the work performed by the authors in simulating propellant slosh in a spherical tank using computational fluid dynamics (CFD).ANSYS-CFX is the CFD package used to perform the analysis.A 42 in spherical tank is studied with various fill fractions.Results are provided for the forces on the walls and the frequency of the slosh.Snapshots of slosh animation give a qualitative understanding of the propellant slosh.The results show that maximum slosh forces occur at a tank fill fraction of 0.4 and 0.6 due to the amount of mass participating in the slosh and the room available for sloshing to occur.The slosh frequency increases as the tank fill fraction increases. I. IntroductionS LOSH behavior is observed when a bucket of water is carried from one location to another.As the person carrying the bucket walks, the back and forth the motion of the person's hand motion causes the water to move back and forth in the bucket (slosh).When the bucket is set down, the water continues to slosh back and forth within the bucket and the forces exerted on the bucket walls cause the bucket to rock back and forth or shake.This same phenomenon occurs with a spacecraft's propellant when maneuvers are performed in space.During a spacecraft maneuver propellant slosh can be excited by the spacecraft control system.The control system then uses thrusters to control the slosh resulting in the use of propellant.In some cases control maneuvers can excite the slosh further.In extreme cases, slosh can result in mission failure.For spinning spacecraft a nutation can be introduced by sloshing propellant.Problems with slosh have occurred on A TS-V, Intelsat IV series spacecraft, NEAR Shoemaker mission, and Gravity Probe B.1 As the ratio between propellant and dry mass increases, the impact of slosh also increases, causing a significant effect on attitude control, performance, and stability.For missions requiring large amounts of propellant for orbit insertion, orbit maintenance, or momentum unload, it is imperative that slosh dynamics are well understood.Slosh dynamics in a low gravity environment are very nonlinear and cannot easily be modeled.Computational fluid dynamics (CFD) can be used to provide an accurate description of the fluid dynamics?,3Due to CFD being computationally expensive, other computationally inexpensive modeling techniques can be used to provide a first order description of the slosh dynamics.The most common first order model is an equivalent mechanical model such as a pendulum mode1. 4 Equivalent mechanical models can be used to design controllers and determine stability margins.Because CFD results are used to create these simpler models, it is important that the CFD results accurately describe the resulting forces and torques on the propellant tank wall.In addition, accurate CFD results will also provide better estimates of the modal frequency and viscous damping of the sloshing.Because of the cost of writing a CFD code it is often more cost effective to use proven commercially available codes such as ANSYS-CFX.In the following sections, a method for simulating sloshing in a spherical tank with a diameter of 42 inches, using ANSYS-CFX, in a constant accelerating environment, and with a constant rate, is presented.For completeness, various tank fill fractions are simulated.The results provided are not compared to experimental data, but are reviewed by professionals who are familiar with the forces applied to a spacecraft to verify that the results are reasonable and realistic.