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Dikuza

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- TL;DR Summary
- Looking for an example to calculate lift and drag coefficients for hypersonic flow over a blunt-body

Hello, this is a very specific question so any help is much appreciated!

GOAL: I'm trying to get a first-pass analytical approximation for the lift and drag coefficients for hypersonic flow over a blunt-body capsule spacecraft (similar to NASA's Apollo or SpaceX's Dragon) during atmospheric reentry from LEO.

METHOD: I understand that modified Newtonian fluid theory is the best (most accurate for its simplicity) approach before considering any computationally-demanding and time-consuming CFD simulations. The basis of this theory is to integrate the pressure coefficient over the portion of the 3D body that is exposed to air flow ("non-shadowed region") using the equation Cp = Cp(max)*sin^2(theta).

ISSUE: I've done a fair amount of research, however, not having an extensive background in aerodynamics am struggling with how exactly this is applied. For a given vehicle shape, angle of attack, and mach number, how exactly is this done? Every paper I read (3 of which I've referenced below as examples) seem to skip over the actual calculations and reference some code that's been written or use an existing program like CBAERO that I don't have access to. I've also found a couple of the original documents from the 60's ( https://ntrs.nasa.gov/api/citations/19660012440/downloads/19660012440.pdf) that go over this but are pretty hard to follow. Has anyone done this before and could walk me through the process or point me to an example calculation for my scenario or code? If this approach is reportedly simpler than CFD and used as a means of quick design iteration, I would think it's not super difficult but I'm lost with the complex integrations and limits.

SOURCES:

https://engineering.purdue.edu/~mjgrant/48th-aiaa-aerospace-science.pdf: "After analytic relations are developed, they are output to a Matlab-based aerodynamics module."

https://www.intechopen.com/chapters/21789]https://www.intechopen.com/chapters/21789: "A computer program is written to compute the aerodynamic coefficients using the Newtonian sine-squared law" https://www.researchgate.net/publication/269802955_Application_of_Modified_Newton_Flow_Model_to_Earth_Reentry_Capsules: "A Fortran code has been written, making benefit of existing in-house library"

GOAL: I'm trying to get a first-pass analytical approximation for the lift and drag coefficients for hypersonic flow over a blunt-body capsule spacecraft (similar to NASA's Apollo or SpaceX's Dragon) during atmospheric reentry from LEO.

METHOD: I understand that modified Newtonian fluid theory is the best (most accurate for its simplicity) approach before considering any computationally-demanding and time-consuming CFD simulations. The basis of this theory is to integrate the pressure coefficient over the portion of the 3D body that is exposed to air flow ("non-shadowed region") using the equation Cp = Cp(max)*sin^2(theta).

ISSUE: I've done a fair amount of research, however, not having an extensive background in aerodynamics am struggling with how exactly this is applied. For a given vehicle shape, angle of attack, and mach number, how exactly is this done? Every paper I read (3 of which I've referenced below as examples) seem to skip over the actual calculations and reference some code that's been written or use an existing program like CBAERO that I don't have access to. I've also found a couple of the original documents from the 60's ( https://ntrs.nasa.gov/api/citations/19660012440/downloads/19660012440.pdf) that go over this but are pretty hard to follow. Has anyone done this before and could walk me through the process or point me to an example calculation for my scenario or code? If this approach is reportedly simpler than CFD and used as a means of quick design iteration, I would think it's not super difficult but I'm lost with the complex integrations and limits.

SOURCES:

https://engineering.purdue.edu/~mjgrant/48th-aiaa-aerospace-science.pdf: "After analytic relations are developed, they are output to a Matlab-based aerodynamics module."

https://www.intechopen.com/chapters/21789]https://www.intechopen.com/chapters/21789: "A computer program is written to compute the aerodynamic coefficients using the Newtonian sine-squared law" https://www.researchgate.net/publication/269802955_Application_of_Modified_Newton_Flow_Model_to_Earth_Reentry_Capsules: "A Fortran code has been written, making benefit of existing in-house library"