How to Approximate Aerodynamic Coefficients? (Lift/Drag)

In summary: Shock-expansion theory is good when you have a symmetric body and can neglect the pressure on the opposite side of the body. The tangent-wedge/cone approximation is good for more complicated shapes where the pressure is not constant along the body.
  • #1
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"
 
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  • #2
You might take a look in newer resources like "Hypersonic and High-Temperature Gas Dynamics" by John Anderson. Since it's a textbook, it's goal is to inform a reader how to do things like this.

You may also need to employ something like shock-expansion theory or the tangent-wedge/cone approximation depending on your shape (they're also fairly easy to implement and are in the above book).
 
  • Informative
Likes berkeman

1. How do you calculate lift and drag coefficients?

To calculate lift and drag coefficients, you need to first measure the forces acting on the object in a wind tunnel or through computational fluid dynamics (CFD) simulations. Then, you can use the following equations:

Lift coefficient (CL) = Lift force / (dynamic pressure * reference area)

Drag coefficient (CD) = Drag force / (dynamic pressure * reference area)

2. What is the reference area for calculating aerodynamic coefficients?

The reference area is the projected area of the object in the direction of the fluid flow. This can vary depending on the shape and orientation of the object. For example, for an airfoil, the reference area is the area of the airfoil's cross-section.

3. How do you approximate aerodynamic coefficients for complex shapes?

For complex shapes, it is not possible to calculate aerodynamic coefficients analytically. In this case, CFD simulations are used to approximate the coefficients. These simulations use numerical methods to solve the Navier-Stokes equations, which describe the motion of fluids.

4. What factors can affect the accuracy of approximated aerodynamic coefficients?

The accuracy of approximated aerodynamic coefficients can be affected by several factors, such as the shape and surface roughness of the object, the airspeed, and the fluid properties. Additionally, the accuracy of the CFD simulations or wind tunnel measurements can also impact the accuracy of the coefficients.

5. How can aerodynamic coefficients be used in practical applications?

Aerodynamic coefficients are essential in the design and analysis of aircraft, cars, and other objects that experience fluid flow. They can be used to predict the lift and drag forces acting on the object, which can then be used to improve the efficiency and performance of the object. Aerodynamic coefficients are also used in the development of flight control systems and for predicting the stability and maneuverability of an object.

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