Calculating Heat Shield Thickness for Atmospheric Entry

[habibi]

Hi all,

I'm working on a project where I want to evaluate the performance of different microstructures of a material as candidates for an atmospheric entry heat shield. I have thermal conductivities for these materials, as well as atmospheric conditions and a required temperature gradient across the heat shield, so I'd like to make some rough calculations for the thickness required of each material. From there I can make comments on the size and weight required. I'm not sure how to calculate the heat flux through the materials in order to determine their thickness, does anyone know how I might go about that?

I know that I'm not taking a lot into account (like ablation, convection of pyrolysis gases, radiation, etc) but I just want some rough numbers on how these microstructures affect the TPS requirements for a heat shield. Thanks!

[AIkonoklazt]

I've never played Kerbal Space Program before.

Is it fun?

[npts2020]

Once you know the expected temperature to be reached at reentry and how hot you want to allow the inside temps to get, it is a simple matter of looking up the thermal conductivity of the material under consideration and using the formula contained here... https://www.toppr.com/guides/physics-formulas/thermal-conductivity-formula/

[mistermack]

On 12/4/2023 at 5:47 AM, npts2020 said:

Once you know the expected temperature to be reached at reentry and how hot you want to allow the inside temps to get, it is a simple matter of looking up the thermal conductivity of the material under consideration and using the formula contained here... https://www.toppr.com/guides/physics-formulas/thermal-conductivity-formula/

I don't think it would be as simple as that. The formula would be ok for static conditions, but surely the pressures and turbulence of re-entry, and how they vary with time would hugely complicate the calculation. Also, it's not just the temperature reached, but the time it stays at the highest temperature, and how fast it rises and falls. Also, the cooling effect on the cold side, how that varies with pressure and altitude. 

It's more likely that you would need to use data from previous re-entries and build models and try to match it all up.