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September 30, 2014, 12:39 
Local mach number

#1 
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Hi,
I am currently doing some programming work on a CFD software, however while my programming skills are good, I have a limited knowledge of physics. The programming work itself do not really require me to understand the fluid dynamics, however to demonstrate the work it would be nice to have a better idea of what is happening. As a result I have a few questions, and I hope someone could help me explaining this in a very dumbed down version. The questions relates to Mach numbers, which are shown as a result of CFD computations. For example I have done a simulation on the ONERA M6 wing. Viewing the result in Paraview gives me the wing itself, coloured dependent on several values, including the mach number and pressure. The results looks similar to the following image. For the pressure it looks about the same however reversed. My question is related to what these results actually show. I gather the the Mach number representing the speed of the object in relation to the local speed of sound, where Mach 1 = local speed of sound. The input for the simulation is a freestream Mach number of ~0.8. Given that the input is a specific speed (not aboslute speed but relative to the speed of sound), I am unsure what the mach number resulting of the simulation is. I hoped that someone here could help me clarify? Is the Mach numbers for different parts of an object different due to local circumstances affecting what the speed of sounds is (e.g. differences in fluid densities, temperature, etc)? Or is the Mach number in this circumstance actually the Mach number of the fluid passing the object rather than the Mach number of the object itself? Secondly as two bonus questions: What can we use the knowledge of the local Mach numbers for? Similar to the Mach numbers the result can also show pressure numbers. They are fairly close to being the opposite of the Mach numbers. In the relation of an aircraft wing for example, is this the pressure that the air is pushing onto the wing? E.g. the actual force to the area? I hope someone would be able to explain a dumbed down version of this. Thanks a lot, much appreciated and I excuse my ignorance! 

October 1, 2014, 08:51 

#2 
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The local Mach number is just that  the Mach number of the fluid at a point in space, dependent on the fluid properties at that point in space. Simulations of external flows typically involve a reference Mach number which is usually computed from freestream values of u and a (the fluid velocity and the speed of sound) if the flow is moving over the wing, or conversely the body velocity and the farfield speed of sound if the body is moving into still air. But the local Mach number is the local fluid velocity divided by the local speed of sound.
For a perfect gas the local Mach number can be thought of as another fluid property that makes it easy to visualize certain behaviors. For example, the location of shock waves and Mach bubbles can be visualized quickly using the local Mach number. Isentropic relations make it easy to evaluate total temperature and pressure if we have the local Mach number and static temperature and pressure. There is an entire field of aerodynamics behind the full answer to your questions. I recommend starting here http://www.grc.nasa.gov/WWW/K12/airplane/bgc.html for some good basic information. 

October 1, 2014, 09:15 

#3 
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Many thanks for taking time to reply! Much appreciated.
So the Mach numbers illustrated in the picture in the original post, is the Mach numbers of the passing fluid at that part of the wing? 

October 1, 2014, 10:20 

#4 
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I can't see your picture but I would assume from your description that the Mach numbers are the Mach numbers of the fluid as it passes the wing.


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