Computational Multiphysics Modeling of Instability Staged Combustion Propulsion, Radiative Convective Ablative/TPS Interfacial Heat Transfer, Supersonic Retro Propulsive Landing Dynamics for Reusable Heavy Lift Architectures and Subcooled Liquid Management in High Pressure Rocket Engine and Booster Return Trajectories

To understand the work described in this paper, one must first grasp the immense physical challenge of sending humans back to the Moon and eventually to Mars. The goal is not merely to launch a rocket, but to build a vehicle that can fly to space, return to Earth, land softly, and fly again, all while carrying a crew and a massive amount of fuel. This requires solving four distinct but connected problems. First, the engine must burn fuel so intensely that it creates enough power to lift a heavy ship, yet remain stable enough not to shake itself apart. Second, the vehicle's skin must survive the searing heat of re-entering the atmosphere, where air friction turns the surface into a glowing furnace, without melting or cracking. Third, the massive booster that launches the ship must be caught mid-air by a giant tower arm, a maneuver that demands precise timing and a cushioning system that absorbs a huge impact without breaking. Finally, the fuel tanks must keep their liquid contents from boiling away into gas while the ship waits in the cold vacuum of space for weeks, a process that could leave the ship stranded without enough power to reach its destination.

Viraj Gajera, an engineer at the New York Institute of Technology, has created a set of computer models to explore how these four problems might be solved. The paper does not present new hardware or physical test results; instead, it offers a rigorous, physics-based simulation of the engineering hurdles facing SpaceX's Starship system and its role in NASA's Artemis program. By building simplified but accurate digital representations of the engine, the heat shield, the catch mechanism, and the fuel tanks, the author demonstrates how different design choices affect performance. The work serves as a foundational step, proving that specific mathematical approaches can predict how these complex systems behave before they are built, providing a clear roadmap for the more detailed testing that will follow.

The first area of focus is the Raptor engine, the heart of the Starship system. This engine uses a complex cycle where both the liquid oxygen and liquid methane fuel are turned into gas before they enter the main combustion chamber. This design allows for extremely high pressure, which generates tremendous thrust, but it also makes the engine difficult to control. The author built a computer model to calculate the shape of the engine's nozzle, the part that directs the exhaust gases to create thrust. By solving the equations that govern how gas flows through a narrowing and then widening tube, the model determined the precise curve needed to accelerate the exhaust to supersonic speeds. The simulation showed that for the engine's specific operating pressure, the nozzle should expand to a certain size to maximize efficiency. While this is a simplified view that ignores some of the messy details of real-world gas flow, it provides a solid starting point for designing the actual metal shape of the engine, ensuring that the thrust is directed correctly to lift the heavy vehicle.

Next, the paper examines the thermal protection system, the thousands of ceramic tiles that cover the ship's belly to protect it from the heat of re-entry. When the vehicle plunges back into the atmosphere, the air compresses and heats up to temperatures exceeding 1,400 degrees Celsius. The tiles must absorb this heat and radiate it away without letting it pass through to the steel skin of the ship, which would melt. The author created a digital model of a single tile stack, simulating how heat moves through the layers over time. The simulation applied a pulse of intense heat to the surface and tracked how the temperature changed inside the material. The results showed that a 50-millimeter thick layer of the silica-based tile material was sufficient to keep the steel underneath relatively cool, rising by only about 20 degrees Celsius even while the surface reached over 1,000 degrees. This confirms that the basic design of the tile system works in principle, though the model also noted that real-world issues like cracks forming between tiles or mechanical stress would require more complex testing to fully understand.

The third challenge involves the "Mechazilla" catch system, where a giant tower arm grabs the returning booster. This is a high-stakes maneuver: the booster, weighing hundreds of tonnes, must be caught by two arms moving along a track, with the engines still firing just meters away. The author modeled this event as a simple spring and damper system, similar to how a car's suspension absorbs a bump. The goal was to find the right amount of stiffness for the cushioning mechanism on the arms. If the arms are too stiff, the impact will be too hard and could damage the structure; if they are too soft, the booster might bounce or take too long to stop. Using a computer search to test thousands of possibilities, the model identified a specific stiffness that would minimize the peak force felt by the tower. The simulation suggested that a relatively soft, compliant cushion is best, allowing the arms to absorb the energy of the catch over a slightly longer period, thereby protecting the massive structure from a sudden, violent shock.

Finally, the paper addresses the issue of fuel management in space. To reach the Moon, the Starship lander must be refueled in Earth orbit by a series of tanker flights. However, the fuel is kept at extremely cold temperatures, and any heat leaking into the tanks causes the liquid to boil off into gas, which must be vented or results in a loss of fuel. The author built a model to estimate how much fuel would be lost over a typical mission timeline, depending on how well the tanks are insulated. The simulation varied the number of layers in the insulation blanket and calculated the rate of fuel loss over a twenty-day period. The results highlighted a critical trade-off: even with excellent insulation, the longer the ship waits in orbit, the more fuel is lost. This finding underscores the importance of the catch system described earlier; by enabling rapid reuse of the boosters and tankers, the program can launch more frequently and reduce the total time the fuel sits in orbit, thereby minimizing the amount lost to boiling.

Throughout the paper, the author is careful to distinguish between these simplified computer calculations and the complex reality of building a rocket. The models presented are reduced-order, meaning they strip away many of the three-dimensional details and chaotic behaviors found in the real world to focus on the core physics. The author explicitly states that these results are not final designs but rather a necessary first step. To move from these simulations to a flying vehicle, engineers would need to use advanced software to create full 3D models, run detailed fluid dynamics simulations, and conduct physical tests on real hardware. The value of this work lies in its clarity: it takes four of the most difficult engineering problems facing the next generation of spaceflight and breaks them down into manageable, solvable pieces. By showing how specific design choices—like the shape of a nozzle, the thickness of a tile, the stiffness of a catch arm, or the layers of insulation—directly influence the outcome, the paper provides a clear, logical path forward for turning the ambitious vision of a reusable lunar transport system into a reality.