Mass flow rate: calculation v/s computation

beguxa · April 21, 2010, 08:33

Hi all,
In my simulations density (Rho) is constant. I have computed mass flow rate (M) through an interior face using standard mass flow rate calculation option from fluent. Then I calculated mass averaged velocity (Vm), area weighted averaged velocity (Va) and facet averaged velocity (Vf). To recheck, I calculated the mass flow rate as M' = Rho*A*V. By using all the three above mentioned velocities in the above formula I am not able to get both mass flow rates the same (i.e. M' and M are not equal). Which is the apropriate value of velocity that one should consider to re-calculate accurately the mass flow rate?
I guess, the mass flow rate is computed in fluent as summation of (Rho*A*V) values at all the facets. Could any body throw some light on this issue?

Thanks.
-aditya

AJoubert · March 23, 2013, 11:31

Hi beguxa, I believe the velocity you want to use is actually the axial velocity. When running my current simulation of flow rate through a nozzle I used surface integrals in the report menu to get an accurate reading but when calculating the flow through use of a custom field function the velocity which returned the same value for flow rate was the axial velocity.

jthiakz · March 24, 2013, 04:44

you can use standard massflow option in fluent. but to check this use velocity normal to the surface in your calculation. I think both should agree.

oj.bulmer · March 28, 2013, 12:04

beguxa, There are subtle differences in all four values.

For correct mass flow rate, we want addition of all the mass flow rates going into the every surface element of your surface.

Let's compare all four approaches with this bold statement.

Area averaged velocity is calculated as $\frac{1}{A} \int vdA$ . This is a good representation of average velocity over the surface. But depending on velocity distribution and mesh, smaller mesh elements may have higher velocities and vice versa, so this doesn't equate to bold sentence at the beginning.

Facet average is calculated as $\frac{\sum v} {n}$ , where n is no. of facets in the surface. If your mesh is not uniform and if there are more mesh elements in regions of high velocity, your facet average velocity will be unnecessarily higher than the average velocity. You can't multiply this with area and still get the definition of bold statement at the beginning.

Mass weighted average is $\frac{\int v \rho | \overline{v}.\overline{dA}|}{\int \rho | \overline{v}.\overline{dA}|}$ . We are slowly getting closer now, since there is a slight reference of actual mass going into every element - $\int \rho | \overline{v}.\overline{dA}|$ - in the denominator. But again since it is "weighted" it bears same limitations as above.

Mass flow rate is calculated as: $\int \rho \overline{v}.\overline{dA}$ . This definition is closest to the bold statement at the beginning. And hence is recommended.

Although, if mesh is of high quality, structured and if solution is fully converged, the differences between these should become smaller. But in real world, with often-used unstructured meshes, this is not always possible.

OJ

Behnam Ghadimi · June 8, 2013, 17:17

Dear beguxa
If you define a variable in the Define> Custom Field Functions... as Density*Velocity, and then integrated this variable in the report>surface integral using the "integral" in the "Report type" you can observe that this value is equal to the mass flow rate in your desired surface, which is reported by FLUENT post processing from Report> FLuxes

Che.Shuguang · December 2, 2018, 22:02

beguxa，What is your final conclusion about your question? I have encountered a problem similar to yours. Thank you!

April 21, 2010, 08:33	Mass flow rate: calculation v/s computation	#1
beguxa New Member Annon Join Date: Apr 2010 Posts: 18 Rep Power: 16	Hi all, In my simulations density (Rho) is constant. I have computed mass flow rate (M) through an interior face using standard mass flow rate calculation option from fluent. Then I calculated mass averaged velocity (Vm), area weighted averaged velocity (Va) and facet averaged velocity (Vf). To recheck, I calculated the mass flow rate as M' = RhoAV. By using all the three above mentioned velocities in the above formula I am not able to get both mass flow rates the same (i.e. M' and M are not equal). Which is the apropriate value of velocity that one should consider to re-calculate accurately the mass flow rate? I guess, the mass flow rate is computed in fluent as summation of (RhoAV) values at all the facets. Could any body throw some light on this issue? Thanks. -aditya

March 28, 2013, 12:04		#4
oj.bulmer Senior Member OJ Join Date: Apr 2012 Location: United Kindom Posts: 473 Rep Power: 20	beguxa, There are subtle differences in all four values. For correct mass flow rate, we want addition of all the mass flow rates going into the every surface element of your surface. Let's compare all four approaches with this bold statement. Area averaged velocity is calculated as $\frac{1}{A} \int vdA$ . This is a good representation of average velocity over the surface. But depending on velocity distribution and mesh, smaller mesh elements may have higher velocities and vice versa, so this doesn't equate to bold sentence at the beginning. Facet average is calculated as $\frac{\sum v} {n}$ , where n is no. of facets in the surface. If your mesh is not uniform and if there are more mesh elements in regions of high velocity, your facet average velocity will be unnecessarily higher than the average velocity. You can't multiply this with area and still get the definition of bold statement at the beginning. Mass weighted average is $\frac{\int v \rho \| \overline{v}.\overline{dA}\|}{\int \rho \| \overline{v}.\overline{dA}\|}$ . We are slowly getting closer now, since there is a slight reference of actual mass going into every element - $\int \rho \| \overline{v}.\overline{dA}\|$ - in the denominator. But again since it is "weighted" it bears same limitations as above. Mass flow rate is calculated as: $\int \rho \overline{v}.\overline{dA}$ . This definition is closest to the bold statement at the beginning. And hence is recommended. Although, if mesh is of high quality, structured and if solution is fully converged, the differences between these should become smaller. But in real world, with often-used unstructured meshes, this is not always possible. OJ delaneyluke, Behnam Ghadimi, chek321 and 1 others like this.

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March 23, 2013, 11:31		#2
AJoubert New Member Andre Joubert Join Date: Mar 2013 Posts: 4 Rep Power: 13	Hi beguxa, I believe the velocity you want to use is actually the axial velocity. When running my current simulation of flow rate through a nozzle I used surface integrals in the report menu to get an accurate reading but when calculating the flow through use of a custom field function the velocity which returned the same value for flow rate was the axial velocity.

March 24, 2013, 04:44		#3
jthiakz Member Thiagu Join Date: Oct 2012 Location: India Posts: 60 Rep Power: 14	you can use standard massflow option in fluent. but to check this use velocity normal to the surface in your calculation. I think both should agree.

June 8, 2013, 17:17		#5
Behnam Ghadimi New Member behnam Join Date: Sep 2011 Location: Iran Posts: 20 Rep Power: 15	Dear beguxa If you define a variable in the Define> Custom Field Functions... as Density*Velocity, and then integrated this variable in the report>surface integral using the "integral" in the "Report type" you can observe that this value is equal to the mass flow rate in your desired surface, which is reported by FLUENT post processing from Report> FLuxes

December 2, 2018, 22:02		#6
Che.Shuguang New Member che.shugang Join Date: Oct 2018 Posts: 2 Rep Power: 0	beguxa，What is your final conclusion about your question? I have encountered a problem similar to yours. Thank you!