mass & area average
in visualise when I do quantitative calculation, I see area average and mass average.
what are these ,could someone please explain
Re: mass & area average
The area average of a scalar is calculated by integrating the scalar times the area divided by the total area over the region. A mass averaged quantity is obtained by integrating the scalar time mass flow divided by total mass flow over the region.
area_ave = int( Phi*dA ) / A
mass_ave = int( Phi*dm ) / M
With an area average, the spacially dominant quantity will have the greatest influence on the result. A mass average is a bit more difficult to conceptualize. Mass averaging will return the quantity which is dominant in the flow.
When considering which to use, think conservation. Area averaging pressure results in summing the forces and dividing by the total area, ie area averaged pressure is is the same as total force over total area.
On the other hand, a flow quantity such as Total Pressure or Enthalpy is not spacially conserved. If you need an average of these, you must take the mass_average. A good example is to consider the flow downstream of a turbine blade; if you take the area average, the low total pressure of wake may have undue influence, since there is not much mass flow through it. If you take the mass average, the mean flow will dominate the result.
Hope this clears things up.
Why area avg require direction then?
I read your post which cleared at least some doubts.
But i wonder, why area avg quantity (pressure for instance) required us to give direction.? what does it signify.?
Give none instead of (x,y,or z) direction
I don't quite understand the concept of mass flow averaging v/s area averaging. The math formulae are solid and I have no doubt about that.
I'm trying to understand from a physical point of view, when to use what in any given situation. From your example, "When considering which to use, think conservation. Area averaging pressure results in summing the forces and dividing by the total area, ie area averaged pressure is is the same as total force over total area." What pressure am I area averaging? total pressure??
And could you give me another example that might shed some light on the mass flow averaging concept?
Robin has not posted on this forum for 5 years unfortunately.
But to answer your question - think about the physical thing you are doing. Pressure acts on a surface, total pressure only exists in the middle of a flow. At a stationary surface the total pressure and pressure are the same as there is no dynamic component. So if you are trying to get a representative pressure on an inlet then total pressure is probably better, but if you are trying to get a representative pressure over a surface then static pressure is the one to choose.
Cool!!! Thanks Mr Horrocks, that helps me a lot ... now to see if I understood your concept correctly, since static pressure acts on a stationary surface, I would choose to area average it (mass flow averaging static pressure on the same stationary surface would give me the same value as area averaging it).
However, for calculating total pressure at the inlet/ outlet, mass averaging total pressure would give me relatively more accurate information. Area averaging total pressure at the inlet will not take into account the dynamic component.
Let me know if I'm thinking correctly.
The is no flow across a surface in most cases so doing a massflow average on a surface is not meaningful (for most applications)
If I was trying to get a representative pressure over an inlet or outlet I would probably use an areaAve of static pressure. massflowAve is good to use for things like temperature, enthalpy and additional variables as you are then summing up the energy content (or additional variable content) over the boundary.
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