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Verifying Mass Balance in Fluent

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Old   March 27, 2014, 18:18
Default Verifying Mass Balance in Fluent
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Ken Noble
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Hello,

I apologize if this has been addressed elsewhere, it seems a likely issue to be discussed but I have not found it anywhere on this forum, my question is very fundamental - I am by all means a novice to CFD.

I am have been investigating whether ANSYS Fluent is useful in modeling the pressure drop of low pressure steam (near 200 mbarA). I am confident in my geometry, my mesh and my model, however I noticed that the mass flow rate is not the same as density*area*velocity (velocity normal to the boundary condition). The difference is around 2% for a complex problem, so I made a simple test geometry to see if the discrepancy persists (and indeed it does, albeit in a smaller magnitude) so it seems prudent to discuss the simple geometry here.

The model is a 10m long by 1.3m diameter cylinder (3D flow). One of the ends is a velocity inlet, the other is an outflow.
The mesh is generated in workbench with an automated inflation layer, mesh size is around 2million elements with max skewness of near 0.8
The velocity and turbulence of the inlet boundary condition is specified
Dry steam at 220 mbarA is considered for a material (density is 0.143 kg/m^3, viscosity is 1.1e-05 kg/m-s).
Realizable k-epsilon model with standard near wall treatment is employed
Solution scheme is coupled with following spatial discretization: second order momentum, TKE, TDR. Standard pressure, least squares cell-based gradient.

Ran for a few hundred calculations and attained convergence.

The "mass flow rate" result of my outflow and my velocity inlet are very near identical (4.6267643 kg/s at the inlet compared to -4.6267605 at the outflow). This is attained by specifying a mass flow rate report.

The centerline of the cylinder is parellel to the y-axis of the geometry, so only the component of the flow velocity in the y direction can be considered as entering or leaving the system (since flow cannot leave through the walls).

Under the definition that mass flow is density*area*v where v is the component of velocity normal to the cross-section of area (y velocity)

A_inlet = A_outflow = 1.3260244 m^2
rho_inlet = rho_outflow = 0.14300001 kg/m^3
v_inlet = 24.4 m/s (mass weighted average, y velocity)
v_outlfow = 24.942724 m/s (mass weighted average, y velocity)
v_inlet = 24.4 m/s (area weighted average, y velocity)
v_outflow = 24.393316 m/s (area weighted average, y velocity)

It seems to me for the purpose of calculating the mass flow rate it is appropriate to use the area weighted average to determine the velocity. As can be seen, the resultant mass flow rate is

m_dot,inlet = 4.62676 (agrees)
m_dot,outlet = 4.62549 (does not agree)

This seems a small discrepancy, but is frustrating that I cannot implement the definition of mass flow rate to verify the mass flow rate which ANSYS reports.

Can anyone help explain what is going on? Does y velocity not mean the velocity of the flow in the y direction? What am I missing?

Many thanks in advance.
-Ken
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