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## A collateral question about rockets

My question is about the rocket aerodynamics. I'm getting in a course of CFD (computational fluid dynamics) in my university. We have to do a project for this quarter. And I thought in modelling (with Matlab) the supersonic aerodynamics of the Soyuz/ST rocket. I'm only going to test the leading fairing. I have made yet the mesh generation in Matlab (it took me a lot of time) with an elliptic generator. But now I'm analysing the on flight conditions of the free stream, at a height of 100km. I'm not sure if Navier Stokes equations are valid at such heights, where density is too small. If anybody has coursed aerospace studies, have you ever made something similar and with which equations?. I have read N-S equations are not valid for the re-entry of space vehicles due to the low density. If they are not valid, which equations are used?. I need some advice before proceeding further.

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 Recognitions: Gold Member Science Advisor Staff Emeritus Hi Clausius. N-S are not valid. For upper atmospheres, you need to look at Newtonian Flow. I don't know of any software which currently handles that (maybe STK?). Basically, you'll need to have random impacts of single atoms and molecules and consider the momentum transferred. This should be doable, but will take an enormous amount of work to get coded, as far as I can see. Now, if it's low enough for a shock wave to form, I'm totally at a loss how to model it. If you find out, let me know. This is one thing we needed to scrap from the report for our space tourism project. We tried doing it in FEMLAB, wasted entirely too much time, and then found out the equations we were using weren't valid for that situation.
 Recognitions: Gold Member Science Advisor Thanks. I have not another possibility than using N-S equations. In part because I don't know a Newtonian formulation as you referred to. As far as I know I think Fluent cannot deal with low density flows. I have heard about the Lagrangian formulation in which is modelled the movement of each particle as you said. But surely it needs a lot of computing time! Anyway, I have the curves of acceleration (U-h and U-t) of the rocket. So that I have to choose some height valid for N-S equations. Currently I'm linearizing around a height of 50 Km (at the Stratopause). There $$\rho=0.96*10^{-3} kg/m^3$$ as the Standard Atmosphere figures state. Which height do you think is the threshold for the validity of the N-S equations?