Numerical Solution of the Blunt Body in Supersonic Flow Problem
 

Hi,

I want to do a CFD code to solve the blunt body problem in supersonic flow. I'll probably pick a sphere in supersonic flow. I want to find the
shock wave location and the static pressure at the surface of the sphere.
This will be a 2D problem. Are the Euler equations enough for this, or do I
need to go Navier-Stokes? Also, since I don't know beforehand the shape
and location of the bow shock wave, the code has to find it itself. Will
the Euler equations handle that? I will be using the finite difference approach. I'll be coding this in Matlab since it is the language I know. I will post the code in the Matlab Central page. Any help with the questions I have are appreciated. Thanks.

Hi, since you seem to be solving an inviscid flow problem, the Euler equations should be enough. Take a look at this document: http://www.dtic.mil/cgi-bin/GetTRDoc...f&AD=AD0846913. There you will find the proper equations and transformation.

The best way to handle the detached shock wave in the finite difference method is to use the time-dependent technique. I am also trying to solve this problem. I am using the MacCormarck's predictor-corrector time marching technique.

Hi andres17,

I'm also very interested in your program with the EULER equations in Matlab. Is it possible to have a look at the code??

Best regards
Kathrin

Hi Kathrin,
I haven't solved the blunt body problem either, however I've solved the Prandtl-Meyer expansion wave problem form Anderson's book (chapter 8). It is based on Euler equations. You can find it here: http://www.mathworks.es/matlabcentra...on-wave-solver
Hope this helps.

Hi Ivan,

coincidentally I've seen your Prandtl-code working, yesterday. But for large angles (i. e. 20°) the iteration just stopped at about 250 iterations. Do you know why?

Nevertheless, for comparisons I need the mentoined algorithm from andres17. Of course, I can do it my own with the deteiled desciption in chapter 5 (Anderson, John David: Hypersonic and High Temperature Gas Dynamics. New York: McGraw-Hill, 1989.) But I hoped that someone already accomplished the EULER equation as a MATLAB-Code and shares it...

By the way, I've an other problem, where I don't find a solution - even in the case of a simple steamline. Can you help me here: http://www.cfd-online.com/Forums/mai...swatitsch.html ??

Best regard
Kathrin

Hi Kathrin,
Yes, the Prandtl-Meyer code is very sensitive to angle variations. It is a very primitive implementation and does not work as a general solver. In fact, the computation blows up most of the times when changing the parameters, as you may have seen. It is my first CFD code, but is very good way to understand the physics of Euler equations and the MacCormack's predictor corrector technique.

Anyway, at the end of chapter 8 of Anderson's CFD book (pag. 410), he says that when the leading egde of the expansion wave exits the computational domain through the upper boundary, and not through the right boundary, the boundary conditions of the upper boundary must be changed. That's why it doesn't work for large angles, because the boundary condition I set was simply the specification of uniform conditions equal to those in the upstream uniform flow. Maybe in a future I will try to improve the code.

Regarding the blunt body problem, I have read the explanation in chapter 5 of Hypersonic and... but I still have some doubts about how to start the problem. I will take a look at it more closely this summer.

I have read your post about Mach-number-independence Oswatitsch but I don't know Crocco's theorem and I have never implemented a time dependent MacCormack method, so, by now, I'm not able to help you with it. But as I said before, I will try to solve the blunt body in a few days. If it works I will inform you.

Just a last thing, do you know where could I find this document? A time dependent computational method for blunt body flows, AIAA Journal, Vol 4, No. 12. Dec, 1966. Moretti, G. and Abbett, M. I think it describes all the necessary points to solve the problem.

Best regards
Ivan

Hi Ivan,

OK, that explains why the Prandtl-Code only holds for certain angles. But the code looks really good.

To your question:

I found this paper from Abbett concerning the algothm https://www.unibw.de/mb/fakultaet/we...download/down2

and that concerning different boundary condions at the wall https://www.unibw.de/mb/fakultaet/we...download/down1

I can leave these files uploaded for about 24 hours. Could you please tell me when you got them??

You're right, I think the desciption in the paper, you were looking for, is quite helpful. As you said, it would be very nice if you would tell me, when you got a solution for this problem.

Greetings
Kathrin

Thank you very much for the documents Kathrin, I have already downloaded them.
As I said, as soon as I finish the course (3-4 weeks) I will start with the blunt body problem. I will tell you about it then.
Best regards,
Ivan

Hello Ivan,

I just started to develop the space-marching technique for EULER in the purely supersonic case. Have you already made any progesses with the time-dependent technique for sub- and supersonic flows?

Best regards
Kathrin

Hi Kathrin,
I'm sorry for not answering until today, I've been on holiday and I couldn't send any message.
I have made several progresses with the numerical solution of the blunt body problem. I've wirten a Matlab code followin both the documents we talked about and Ansderson's books. However, I have not been able to obtain a converged solution of the problem. After a huge number of time steps the calculation blows up. Anyway, the code works pretty well and I believe in a few days I will manage to run it until the end.
Have obtained any solution as well?

Greetings,
Ivan

Hello Ivan,

I wrote the code for a steady (!) EULER-case and used the space-marching MacCormack-method from Anderson. However, I got nearly the same problem: the calculations blow up, too, and I was unable to find the mistake, although the code is rather simple. :-(

Hi,
I am still working on the time marching solution, but I haven't managed to obtain a steady solution yet, however the results are improving little by little.
Which space marching problem are you solving? The one in Anderson's hypersonic book? I can have a look at it if you want
Best regards
Iván

Hi Ivan,

that sounds good.

How do I create an attachement so that only you can open it or which is only visible for a certain period of time?

It's written on MATLAB R2012 A.

Greetings

OK, thanks, I will take a look at it and try to find out any error, however it will be difficult.
Good luck
Iván

Hi Kathrin
I want to calculate the aerodynamic forces for re-entry capsule, can i use your code "EULER steady hypersonic" for this purpose?
If it is possible put your email address for me due future calls.

Hi gomnam,

you can use this program as a very simple way of solving your problem but this code is just valid for completely supersonic fields. And it was one one of my first trials. So, there are some mistakes in it.
By now, for my Phd. I developed a new and very fast Euler-code that works for both sub- and supersonic regions behind the shock, including chemical reactions.

Best regards

Hi Kathrin again
How is Arrangement of implementation subprograms in "EULER steady hypersonic" zipfile? and How can run these subprograms as one program in matlab?
its 2D solver or 3D solver?
thanks for your attention

Hey,

I am trying to implement a Mac Cormack technique to solve the blunt body problem using finite-differences but it doesn't work for for than 30 iterations before temperature becomes negative somewhere. (specifically at the third node from the wall).

Anyone who can give me ideas on what can/is causing this error?

Hello, I am interested to solve blunt body problem with the help of fdm. I am trying to obtain conditions at initial time for this problem. Please suggest me that how to find these conditions at initial time.

Take your initial condition to be the free stream value at the Mach number you are solving for. In essence you are inserting the body at a given instant in the free stream flow immediately.

Your Euler code should 'generate' the shock in front of the body provided you have the appropriate Upwind scheme and you are marching in time. <- Recommended

If you are using central differences, keep an eye on your time-step and insert artificial viscosity <- This is NOT recommended.

Good luck!