Mass Flow

The mass flow report is represented in the simulation tree by a node which has properties and is subject to the report node’s pop-up menu.

The total mass flow through a boundary is computed as:

图 1. EQUATION_DISPLAY

\dot{m} = \int ρ v \cdot ⅆ a = \sum_{f}^{} ρ_{f} v_{f} \cdot a_{f}

(442)

where $ρ_{f}$ is the face density, $v_{f}$ is the face velocity vector and $a_{f}$ is the face area vector. The sign convention is such that a positive value of $\dot{m}$ implies that mass flow is out of the domain.

注	When the Mass Flow and Mass Flow Averaged reports are run on derived parts with moving meshes as inputs, they behave as though the derived part were instantaneously fixed to the mesh, and use the fluid velocity relative to the Region mesh to compute mass flow.

Mass Flow in Harmonic Balance

When the Harmonic Balance model is selected, the total mass flow through a boundary is computed as:

图 2. EQUATION_DISPLAY

\dot{m} = \underset{f}{\sum_{} {\tilde{m}}_{f}}

(443)

where ${\tilde{m}}_{f}$ is the face flux at the boundary face that depends on the representation used:

Volume mesh representation: ${\tilde{m}}_{f} = {\hat{m}}_{0 f}$ where ${\hat{m}}_{0 f}$ is the time-mean value of the face flux (that is, face flux Fourier mode 0).
Harmonic Balance solution view representation:: ${\tilde{m}}_{f}$ is the variant of the face flux correponding to the selection in the HB Solution View node. Examples include Face Flux at Physical Time of 5 s and Face Flux Fourier Mode 1 Real.

${\tilde{m}}_{f}$ is calculated as:

图 3. EQUATION_DISPLAY

{\tilde{m}}_{f} = {[C \cdot m_{f}^{*}]}_{component}

(444)

where:

$C$ is a complex HB operator (row vector), the contents of which depends on whether you choose a Fourier Mode component or an instantaneous time solution at a specific blade passage.
$m_{f}^{*}$ is a time-level vector (column vector) of mass flow rates at the given face $f$ .
${[]}_{component}$ is one of the components of the resulting complex number inside the square bracketsꟷthat is, Real, Imaginary, Magnitude or Phase.

Note that the operator $C$ is invariant across the blade row. Hence:

图 4. EQUATION_DISPLAY

\sum_{f} C \cdot m_{f}^{*} = C \cdot \sum_{f} m_{f}^{*}

(445)

Mass Flow Report Properties


Units	Units that are used for specifying the quantity.
Parts	A list of parts that is used as the source for this report. Uses the in-place part selector for editing.

Mass Flow Report Expert Properties


Representation	Selects a representation. Additional selections appear as representations that are added to the simulation.
Smooth Values	When this property is activated, the report is calculated using node (interpolated) values of the chosen quantity rather than cell values.
Account for Idealization	Applies idealizations related to the chosen parts before computing. For details, see Obtaining Whole Domain Reports through Idealizations.