A Structural Analysis of the 1st Stage Reaction Chamber and Supporting Thrust Structure in Support of Project Icarus

Over this past summer, I was in the pursuit of my Master’s thesis subject. I’ve always been interested in space exploration and settlement, and my graduate advisor, Haym Benaroya, informed me of Project Icarus. This definitely gained my interest, and he subsequently sent me the final report on Project Daedulus. After reading through the Project Daedulus trade study, I was sold on working on Project Icarus.

As a mechanical engineer, my industrial background is as a design/build engineer, taking projects from conceptual designs to detailed design and analysis leading to fully-tested and functioning prototypes. I decided to take this approach to the first stage reaction chamber and supporting thrust structure of the Project Daedulus spacecraft. The figure below shows the spacecraft configuration of my analysis (courtesy of Adriann Mann).

Icarus spacecraft configuration derived from the Daedulus design

In my mind, the requirements were clear for what this reaction chamber and thrust structure needed to survive under operation and potential failure modes (derived from the Daedulus calculations). From here, I undertook an analysis factoring in vibration and thermal loading, as well as manufacturing considerations.

Project Icarus has some near-term linear extrapolation on technology, such as nuclear fusion propulsion. However, I narrowed my focus on the specific task at hand, the first stage reaction chamber and thrust structure. My first key question was if we were to start building this tomorrow, how would we do it? Only from this would we know where we need to focus more research and development in regards to the reaction chamber.

My first task was to see what material the reaction chamber would be made of. In the Daedulus study, certain alloys were suggested with the necessary properties for the reaction chamber (low density, high temperature capability, high electrical conductivity, etc.). From here, I searched through governing present-day military and commercial standards to find a starting point on what material we could use. From this, I determined that Molybdenum TZM, ASTM B386, Type 363 (Vacuum arc-cast), 4-step internal nitriding after commercial procurement, fit the bill. This alloy had the initial properties we were looking for, but of course would need to be refined further for our application as well as analyzed more in depth.

Now that I had a material in mind, I started building the reaction chamber structure via Computer Aided Drafting tools and Finite Element Modeling tools. My approach was to analyze the foundation before adding peripheral structure, ie analyze the reaction chamber before analyzing the thrust structure. If the foundation is weak, the structure will fall.

I assigned the appropriate material properties to my simulations to see how our newly defined material will hold up to our conditions. The reaction chamber was modeled to Daedulus parameters. The figure below shows my Finite Element Modeling simulation conditions on the reaction chamber. The magenta arrows show the equivalent 1.696 million pounds-force tensile load resulting from the fusion reactions. The green arrows show the fixture condition. The figure on the right shows the meshed model.


Figure 2: Finite Element Model Initial Conditions and Meshed Model

Finite Element Model Initial Conditions and Meshed Model


The next step was to analyze the general stress results from the operational loading. The figure below shows the von Mises stress (resultant stress). It is very important to keep the stresses under the yield strength of the material, which is 100,000 psi (100 ksi) in the case of the TZM alloy assigned to the reaction chamber.


von Mises Stress Results for Operational Loading on 1st Stage Reaction Chamber

von Mises Stress Results for Operational Loading on 1st Stage Reaction Chamber


The resultant stresses are well below the 100 ksi yield strength. However, we assumed that the reaction chamber was fixed at the bottom for this model, which was a good starting point but may not accurately represent the fixture conditions to the rest of the spacecraft. This will be explored a little later, but first we must see how the reaction chamber reacts in a failure scenario, if the load becomes compressive when a fuel pellet fails to ignite. The figure below shows the initial conditions of the simulation model as well as the general von Mises stress results.


Initial Conditions and von Mises Stress Results for Failure Loading on 1st Stage Reaction Chamber

Initial Conditions and von Mises Stress Results for Failure Loading on 1st Stage Reaction Chamber


The loading for the failure condition is the same magnitude but in the opposite direction, as evidenced by the magenta arrows above. Here, as well, the general stresses are well below the yield strength of the material.

Before adding more elements on to the reaction chamber, we were interested in seeing what the modal analysis showed for the reaction chamber, as we expect a 250 Hz repetition rate for the Icarus spacecraft. The goal is to mitigate any resonance interaction, as there is almost no way to damp vibration in space. The figure below shows the modal analysis results for the reaction chamber.


Figure 5


The modal analysis is highly dependent on fixture conditions and geometry. The fundamental frequency for this configuration is seen around 7.85 Hz.

The next building block that we added to the structure was the interface to the pellet injector. The figure below, courtesy of the Daedulus study, shows a schematic of operation with the pellet injector.


Figure 6


Per the Daedulus study, the dimensions of the pellet injector interface are miniscule when compared to the rest of the spacecraft. The figure below shows the solid model and FEM results with the scale pellet injector interface.


Figure 7


The stresses are shown to be well over 100 ksi, into the millions of psi range with this configuration. The FEM solver also gives an error of model stability with this configuration. This means that we need to adjust the interface reacting the thrust load to greater dimensions. The figure below shows the pellet injector interface after iteration. The solid model is on the left and the Finite Element Model in on the right.


Figure 8


The von Mises stress results are shown in the figure below. The stresses are shown to be below the 100 ksi yield strength at room temperature.


Figure 9


The figure below shows the resultant displacement results from the tensile loading on the reaction chamber with pellet injector interface. From the strain patterns, it can be seen that an integrally backed thrust structure is necessary to support the reaction chamber.


Figure 10


The next addition to our structure is an integrally backed thrust structure. The figure below shows the bracing structure to support the loading on the reaction chamber. It consists of 12 lateral braces and one bottom brace. The figure on the left shows the solid model, the figure in the middle is the exploded model, and the figure on the right is the Finite Element Model.


Figure 11


The figure below shows the von Mises stress results for this configuration.


Figure 12


A modal analysis was then conducted to ascertain the effects of adding the pellet injector interface and thrust structure. The figure below shows the results of the modal analysis.


Figure 13


It can be seen that by fixing the reaction chamber structure on the pellet injector interface to the rest of the spacecraft, coupled with the geometry changes and addition of new parts, result in the natural modes and frequencies being significantly lower than with the reaction chamber by itself fixed on the bottom.

From this point in my research and analysis, I am adding the Induction Loop and supporting structure, as well as the Field coils and their supporting structure. The figure below shows the work in progress for this modeling and analysis.

Figure 14


Once the Field Coil and Induction Loop structure are added, my next step would be to reduce the resulting operational stresses to the 30 ksi range maximum. This is due to the fact that the yield strength of TZM at our 1600 degree K operational temperature is in the 30 ksi range, as well as us having over 30 billion cycles on the reaction chamber, which are magnitudes higher than traditional fatigue analyses.

Of course, this is a summary and not all of the details of my analysis and methodology are presented here, but I would be more than happy to provide more details on request.