How Can Ablative Cooling in A Solid Propellant Rocket Engine Be Accurately Modelled in Order to Optimise Performance?

Abstract

This essay investigates the use of ablative cooling in solid propellant rocket engines. It begins by exploring the mechanisms by which ablation occurs. It then demonstrates how heat transfer to an ablator can be modelled, and how this can be used to find ablator recession rate and hence the necessary ablator thickness for a rocket engine. It does so by considering simplified mathematical models. These are then compared to the more complex models that have recently been developed. The different variables involved and how they might be used or calculated are discussed. The next section of the essay ties this theoretical knowledge and modelling into practical engineering use by considering the impact ablation has on performance. MATLAB is used to demonstrate how an expanding throat diameter of the nozzle can decrease thrust and specific impulse, and that this can greatly decrease payload capacities. Other variables involved in creating a thrust profile for a solid propellant rocket engine are considered. Finally, the essay will look at how to choose an optimal ablator. It goes through the universally desirable characteristics and uses the Space Shuttle SRMs as an example of disadvantages that may not initially be considered when selecting an ablator.

Introduction

I. INTRODUCTION

Rocket engines are some of the most complex pieces of machinery humans have constructed. They essentially control high energy explosions in order to provide the thrust required to lift a payload into space.

The combustion temperatures as a result of the reactions between the fuel and oxidiser typically range from 2700K to 3600K; substantially higher than the melting point of the metals from which the rocket nozzle is made. In order to preserve the structural integrity of the nozzle wall, the wall temperatures must be far below the melting points of the metals. Various cooling techniques have been implemented to rapidly cool the engine and prevent rocket failure, the most common of which are regenerative cooling and ablative cooling. 1 2

Regenerative cooling is currently the most common method used for liquid propellant rocket engines. It works by flowing propellant (which is often cryogenic) through the walls of the combustion chamber to transfer heat away rapidly. It enables the walls of engine to be fairly thin, which reduces the weight, hence increasing the specific impulse of the engine. It will also continue to function until the propellant runs out.

Furthermore, it can be integrated into an expander cycle. This is where the fuel boils while passing through the combustion chamber walls, and then spins a turbine, harnessing extra energy. 2

Ablative cooling is a much simpler way of cooling an engine, as there is simply a layer of ablative material coating the engine wall, which vaporises as the hot exhaust gases pass by it, taking heat with it.

This method is much simpler to implement in an engine as there are no moving parts, however it does have several disadvantages. As the ablative layer erodes away, the nozzle expansion ratio changes, reducing the thrust output of the engine. This also means that these engines are not reusable, which can add significant risk to a mission as the same engine can’t be tested and then flown. A notable example of this is the Apollo Lunar Ascent engine which wasn’t fired until it was actually on the moon. Despite this, it’s simplicity makes it extremely useful for smaller engines such as those on missiles, and also solid propellant rocket engines as there is no propellant to run around the combustion chamber. 2

Conclusion

Overall, it is clear that regenerative cooling is the method of choice for liquid propellant engines for a reason. It is far simpler to model and much more accurate predictions can be made. Ablation is still not particularly well understood, and the lack of a clear mathematical model is evidence for this. Many models, such as the Q* method rely on experimental data which comes with several disadvantages. The more sophisticated models often don’t consider certain processes, and there is a large difference in models used by different engineers. However, advances in computational modelling seem to provide close enough estimates that engineers are still able to safely implement ablative cooling systems. With the use of a model evaluating a greater number of physical and chemical processes, more data can be produced, enabling performance to be optimised. The drawbacks of ablation can hence be lessened by assessing it’s impact of a rocket’s thrust profile, and making necessary changes to minimise these.

Copyright

Copyright © 2022 Sassan Bhanji. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.