Learning Forum

[jiangtao.lu]

I have a multiphase problem, and am checking mass- and volume-weight average definition. 

In Theory Guide, mass average is below, and explitcitly say rho_i is the mixture density. In this case, V_i is clearly to be the total volume.

the volume aveage is blow. Is V_i the total volume also? If so, I do not understand...

If we consider a variable in phase k in a multiphase problme. Shouldn't we consider the phase fraction? Namely the following equations? 

and

Even if we take one step back for the average of the total volume, the phase fraction should still be in the numerator, isn't it? 

[Federico Alzamora Previtali]

Hello,

variables with subscript _i are cell values, so you are summing over the total number of cells the corresponding quantities, which give you the total quantities.

Hence, V is the total volume, V_i is the volume of cell i. Finally, rho_i is indeed the mixture density, for cell i.

 

[jiangtao.lu]

thanks. Now the definition is clear, then my point is such calculation is nonsense, if we do not include the phase volume fraction of cell i for a multiphase problem.  

[Federico Alzamora Previtali]

Which equations from the Theory Guide are you looking at? If you are referring to Eqs. 26.35 and 26.32 (from 23R1 Theory Guide), then these are general mass weighted and volume weighted averages equations. You are correct to say that for a multiphase problem, the volume fraction of the phase should be included.

[jiangtao.lu]

thanks for reply. Yes, I am looking at these two equations in Theory Guide, which are used in 36.2.1.2 Volume Report Definitions and 36.8.1 Generating a Volume Integral Reoport in User Guide.

Thanks for confirming these calculations are invalid for multiphase problems. 

 

[Federico Alzamora Previtali]

Right, these two equations are general formulations, not specific for multiphase.