CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Mach-number-independence Oswatitsch

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Search this Thread Display Modes
Old   June 3, 2012, 09:37
Question Mach-number-independence Oswatitsch
New Member
Join Date: Jun 2012
Posts: 9
Rep Power: 13
Kathrin is on a distinguished road
for my studies, I've to develop a solution method for the mach-number-independence principle which is valid for very high mach-numbers. In my case I assume
- ideal gas,
- inviscid flow,
- flow over a blunt body,
- 2D flow,
- steady flow (at the end of the iteration),
- shock fitting.

In nondimensional form the systems consists of Crocco's theorem (a combination of the momentum equation and the first and second law of thermodynamics) with two equations for {Ma\rightarrow\infty}

{\left( {\begin{array}{*{20}{c}}u\\v\end{array}} \right)_t} = \dfrac{{1}}{{2\kappa }}\left( {1 - V^2} \right)\left( {\begin{array}{*{20}{c}}{s{_x}}\\{s{_y}}\end{array}} \right) + ({v_x} - {u_y})\left( {\begin{array}{*{20}{c}}v\\{ - u}\end{array}} \right)

and the gas dynamic equation which is a combination of the momentum and the coninuity equation and yields for

    (u u_t + v v_t  - \frac{1}{\rho}\frac{\kappa-1}{2}(1-V^2) \rho_t)&+ 
    (u^2 - \frac{\kappa  - 1}{2}(1-V^2))u_x + \\
(v^2 - \frac{\kappa  - 1}{2}(1-V^2))v_y &+
    u v (u_y + v_x) = 0

with entropy s, x-component of velocity u, y-component of velocity v, density \rho and V^2 = u^2 + v^2 with its spatial x and y and time derivatives t. I complement the sytems with the equation of state and the entropy equation which can be calculated in a seperate way.

I know that the system is elliptic and hyperbolic in space depending on the local velocity. So a time-dependent method must be applied. I already used MacCormack (without artificial viscosity) for a very simple case which was a 1-D streamline but the system didn't converged and became unstable.

Can anybody help me to find the mistake or has anybody even already implemented these equations???
Kathrin is offline   Reply With Quote


hypersonic, maccormack, oswatitsch, time dependent

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
[mesh manipulation] Mesh Refinement Luiz Eduardo Bittencourt Sampaio (Sampaio) OpenFOAM Meshing & Mesh Conversion 42 January 8, 2017 12:55
[snappyHexMesh] SnappyHexMesh for internal Flow vishwa OpenFOAM Meshing & Mesh Conversion 24 June 27, 2016 08:54
Problem with decomposePar tool vinz OpenFOAM Pre-Processing 18 January 26, 2011 02:17
Strong oscillation at transonic mach number martingariepy FLUENT 2 May 12, 2009 11:40
[Commercial meshers] Trimmed cell and embedded refinement mesh conversion issues michele OpenFOAM Meshing & Mesh Conversion 2 July 15, 2005 04:15

All times are GMT -4. The time now is 23:23.