different between the various averaging
 

Hi, Is there anyone can tell me the difference between the mass averaging, area averaging, theta_averaing, I mean the physical meaning.

I am runing a case of centrifugal pump, and want to get the velocity and pressure average value in some special regions, but I do not understand the physical meaning of these three averaging methods.

thanks

Re: different between the various averaging
 

Dear Huewei,

I will try to explain my answer by an example.

consider this very simple case:

2 face's

face 1 face 2 area A 1 2 massflow m 1 1 x variable 1 0.5

area average = (A1*x1+A2*x2)/(A1+A2)= (1*1+2*0.5)/(1+2)= 2/3

mass average = (m1*x1+m2*x2)/(m1+m2)= (1*1+1*0.5)/(1+1)= 3/4

When calculating a pressure difference (both static and dynamic) you must use the mass average - it comes from the energy equation.

For averaging the velocity the area average should be ok.

Regards Jan

Re: different between the various averaging
 

A mass average is calculating by taking the mass-integral of the scalar and dividing by the total mass-flow. Area averaged quantities are calculated by taking the area-integral and dividing by the total area. Theta averaged quantities are taken by integrating over the entire angular extent and dividing by the total angle (typically used by averaging along lines of constant radii to estimating mixed-out quantities for a downstream component).

Whether to use mass averaging or area averaging depends on how a quantity is conserved.

i) If you are concerned with a conserved quantity, such as momentum or total pressure, a mass average is appropriate because it is the mass integrated quantity which is conserved.

ii) If you are looking at static pressure, it is the area integral (force) which is conserved and thus the area average should be used.

Robin

Hello,

I have a problem when calculating the mass average of the circumferential velocity component cu i found its value higher than the mass average of the absolute velocity c , how?!!!!!!

Can any on help me to know the reason.

Thanks