Vast:

Introduction

On the first day of my internship at Vast in the summer of 2023, I was told to "go figure out sloshing". At the time I had no idea what sloshing even was, but soon learned about the real danger that it poses to launch vehicles and spacecraft. In everyday life, sloshing can be the innocuous movement of coffee in a cup, but for space applications, this liquid movement can spell disaster if it is too strong or occurs at the wrong frequency, interfering with control algorithms or resonating with structural modes. Below, I have included an "Introduction to Sloshing" video that I made to further explain this. 

For Vast,  I was responsible for determining the risks that sloshing posed to the Haven-1 space station. Specifically, I needed to produce a parametric model of sloshing in the propellant tanks that could be inputted into the larger GNC model of Haven-1 for a variety of environments and factors. 

*Due to NDA, I can only include a limited amount of technical details 

Introduction to Sloshing Video

Methods

In order to develop a model of sloshing, I first consulted outside experts and literature, which led me to "The New Dynamic Behavior of Liquids in Moving Containers" written by Franklin T. Dodge based on NASA SP-106 and affectionately known as the "Slosh Bible" by those in the field.  Sloshing is a complex phenomenon that involves fluid mechanics, harmonic motion, and potential flow theory. As such, computational analysis methods are resource-intensive and sometimes unreliable, especially in microgravity conditions. 

The most popular method to represent sloshing is through an equivalent mechanical model, such as a pendulum or spring-mass system. I used the framework outlined in Dodge's paper to create a parametric pendulum model for sloshing in our specific tanks. Inputs to this model included tank geometry, acceleration profile, fluids density, fluid viscosity, and fill level. Using my model, I analyzed full propellant tanks at launch (high-G) and partially filled tanks in orbit (low-G). Another important factor was temperature, because the specific propellants used for Haven-1, nitrous and ethane, experience significant density changes with temperature, which in turn determines fill level. My model accounted for these relations and simplified them to produce intelligible graphs. 

Results

Through my sloshing analysis program, I determined that sloshing posed little risk to Haven-1, even without the implementation of propellant management devices, due to its range of natural frequencies being far below those of the control system and structural bending modes of the spacecraft. 

However, I also applied my program to another Vast spacecraft, Orbiter SN3, and identified a mission-threatening design issue. Due to the placement and planned fill level of the propellant tanks, the spacecraft had a high risk of tumbling out of control after separation. This was because its center of mass was going to be outside its bounding box of control authority, meaning the spacecraft could not compensate with its reaction or attitude control system. My proposed solution involved rearranging the tanks and the fluid management system so that sloshing would be decreased and the center of mass shift would be reduced by <50%