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[andreas.gebhardt]

Hi everyone,

I have a question concerning the example in lesson 6 ((288) Method of Characteristics — Lesson 6 - YouTube) on how to calculate the flow field of a CD nozzle with MOC. The lecturer starts in this example with point 2 that is situated in the throat of the CD nozzle. When I try to start my calculation at this point it fails, as the characteristic line is perpendicular to the flow. In the example the characteristitc line is not perpendicular but has a certain angle. How can I find this angle? 

In the further course nu of point 5 is calculated by using the characteristic line C+ of point 3 and theta 5 of the expansion arc. I would assume, that theta and nu are already known on the expansion arc as they have the same value. I've also found this assumption in an open source NASA code

If this assumption is correct wouldn't it be much easier to start the calculation with the characteristic lines on the expansion arc?

I hope this makes any sense and somebody could help me out on this topic.

Best regards

Andreas Gebhardt

[EdnaMorgan]

Hello Andreas,

It seems you have identified an interesting point in the method of characteristics (MOC) applied to the CD nozzle flow field calculation. Let's address your concerns:

1. Characteristic Line Angle at the Nozzle Throat (Point 2):

   • In the MOC method, the characteristic lines represent the direction of the flow velocity. The angle of the characteristic lines at the throat (Point 2) is influenced by the geometry of the nozzle. The angle can be determined by considering the local slope of the nozzle wall at that point. If the characteristic line is perpendicular to the flow, there might be a geometric consideration or a simplification in the example.

2. Assumption about θ and ν on the Expansion Arc (Point 5):

   • Your assumption that θ and ν have the same value on the expansion arc is correct. This is a common assumption and simplification in certain flow situations. The angle θ represents the nozzle wall angle, and in expansion regions, it's often assumed that the flow follows the nozzle contour, making θ and ν equal.

3. Starting Calculation with Expansion Arc:

   • Starting the calculation with characteristic lines on the expansion arc is indeed a valid approach. It might simplify the calculation and provide a clearer starting point. However, the choice of starting point can depend on the specific requirements of the problem or the preference of the analyst.

Your observations and assumptions align with common practices in the method of characteristics. If the characteristic line at the nozzle throat seems problematic, it's worth revisiting the geometric considerations and possibly consulting additional resources or literature for insights into the specific example you are studying.

If you have access to the NASA code and it employs a similar assumption, it could be valuable to study the code and see how they handle these aspects. Additionally, reaching out to the community or forums related to computational fluid dynamics (CFD) or nozzle design might provide further clarification.

Best regards, Name Combiner Online Tool