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 In this last iteration I've managed to utilise the cooling flow up to 5 kg/s liquid methane, while keeping the max. shield temperature reasonable for HASTELLOY, keeping enough structural strenght and oxidation resistance. The 3D simulation model is designed to provide correct enough results, while keeping it simple, which is nececesey for the reentry simulation itself.
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This is just a very small part of the Starship reentry simulations I've performed. Wide range of conditions - different shield shapes, angle of attacks (AOA), velocities, atm. pressures and so on. CONCLUSION - ALL THEY BURN TILES AND CRINGE STEEL !!! THE TILES BASED SHIELD IS COMPLETELY DOOMED!!! ...what those people are thinking???
  After performing multiple flow reentry simulations with wide reentry conditions I have not other choice, but to conclude that using a tiles based shield is completely impossible. It would not be safe even for one reentry as the temperatures on the tiles surface of more than 50% of the shield area well exceeds 3000 K. At that point I am mildly said baffled, why this option was even considered. On the other hand I've proved without a doubt, that an internally cooled shield is the only viable solution. My simulations and calculations proved that 10kg/s to 15kg/s cooling methane would be enough to keep the shield temperature below 1400 K in the most heated areas. As well I've proved that expelling methane through holes in the shield is far worse than keeping the cold methane inside the shield "jacket" and expelling it through the upper part of the shield. With this information I will allow myself to make a prediction - If SpaceX does not scrap completely and fast this d...
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 In this simulation I've tried to optimize the cooling methane flow by introducing several baffles. This makes the heat transfer from the shield to the cooling methane more efficient "trapping" the methane longer in the shield jacket. As a result the fresh 100K cold methane gas is heated up to 330K, which is about 7 KW cooling power in a 50 mm shield slice. If we approximate this to the full Starship length we get minimum necessary cooling power of  about 8400KW. Same reentry conditions - V=6000m/s and Patm.=15 Pascals. If we consider the methane liquid-vapor phase transfer energy I think that 10 tons of methane should be enough for a 15 min. long reentry cooling. However this is on optimistic side and 15 tons methane should provide enough safety margin.
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 Simulation of a cylindrical shaped shield reentry with V=6000m/s, P=15 Pa. Flow of  0.02 kg/s 100K cold methane is injected on 50 mm slice. This does not take into account the phase transferee energy of methane - 510KJ/kg.K. If we take into account the phase transferee energy, even 0.01 kg/s could be enough. For 60 meters length of Starship we have 12kg/s total methane consumption for cooling. If we consider 15 min. reentry we get 10.8 tons methane in total, but to be on the safer side I think 20 tons would be wiser. If  HASTELLOY   alloy is used for the shield it could withstand multiple reentries as it keeps enough strength and oxidation resistance at 1300K. However,  for a reentry shield  I consider the cylindrical shape mildly said inappropriate. 
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 This is a cross section of the shield with simplified but principally correct geometry. The liquid methane is ejected through a single "pipe" directly over the most heated part of the shield. The methane vapor is ejected through a gas "trap" (View A) in radial direction towards the upper part - after many experiments this redirection of the vapor seems most logical, as it helps cooling the upper part without creating excessive force in the reentry direction. The temperature of the exhausted methane is still low enough - about 170-180 K
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 Much more refined fluid simulation of Starship reentry with liquid-vapor cooling. About 5 0000 000 fluid and solid cells and 8 hours CPU time. The shield temperature is acceptable, despite that it will still glow red. About 20kg/s methane without considering the  methane  phase transferer energy - 510 KJ/Kg.K. The simulation study does not allow that. If we consider the  phase transferer energy, the total methane consumption will decrease significantly. As well the heat transfer efficiency in the shield can be further optimized. Considering about 20 minutes reentry cooling I can approximate that 20 tons of methane should be enough for a first /still risky/ reentry attempt. The necessary cooling power is approximately 3000 kW .