Static Inlet Outlet

The Inlet/Outlet statistics provide time-resolved, surface-integrated quantities describing fluid, scalar, and thermal transport across boundary regions. These outputs capture flow rates, phase composition, pressure, velocity, and transported quantities (e.g., scalar, temperature, age). A tab-separated ASCII .txt file is created for each Static Inlet Outlet. The name of this file is InletOutlet_{DynamicName}.txt, where the dynamic name corresponds to the name of the Static Inlet Outlet in the Model Tree. The output files are updated at the Statistics Output Write Interval.

The reported quantities fall into several categories:

• Flow and Throughput Metrics: Flow rates and realized flow quantities describe volumetric and mass transport across the boundary.

• Velocity and Pressure Metrics: Velocity components and pressure values characterize the local flow conditions at the boundary.

• Phase and Composition Metrics: Volume fraction and density values describe the phase distribution and mixture properties.

• Scalar Transport Metrics: Scalar field flow rates and statistics describe transport of species or dissolved quantities across the boundary.

• Thermal Metrics: Temperature and thermal flux quantities describe energy transport into and out of the system.

• Age and Residence Metrics: Age and flux-age quantities describe residence time characteristics of fluid entering or leaving the domain.

• Geometric Metrics: Area defines the effective boundary surface resolved by the mesh.

Statistics Table

The index table below shows the statistics that can appear in the Static Inlet Outlet output file. Within this table, each statistic corresponds to a column in the output table that evolves with the time column.

Statistics	Units	Details	Output Condition
Time	s	simulation time
[dynamic] Flow Rate	m^3/s	total flow rate of fluid 1, positive indicates fluid entering system
[dynamic] Flow Rate	m^3/s	total flow rate of fluid 2, positive indicates fluid entering system
[dynamic] Volume Fraction	vf	spatial mean of fluid 1 volume fraction
[dynamic] Volume Fraction	vf	spatial mean of fluid 2 volume fraction
Age	s	spatial mean of fluid mean age	Mean Age
Area	m^2	total area resolved by mesh
Flow Rate	m^3/s	total flow rate, positive indicates fluid entering system
Flux Age	s	spatial mean of mean age for fluid entering/leaving	Mean Age
LB Density	Dimensionless	spatial mean of lattice-Boltzmann density
LB Mass Flow Rate	Dimensionless	total flow rate of lattice-Boltzmann mass
Pressure	Pa	spatial mean of pressure
Pressure Before Buffer	Pa	spatial mean of pressure, values taken beyond buffer length exclude its pressure drop effect
Realized Flow Rate	m^3/s	total flow rate measured using lattice-Boltzmann density flux, positive indicates fluid entering system
Realized Velocity X	m/s	spatial mean of fluid velocity measured using lattice-Boltzmann density flux
Realized Velocity Y	m/s	spatial mean of fluid velocity measured using lattice-Boltzmann density flux
Realized Velocity Z	m/s	spatial mean of fluid velocity measured using lattice-Boltzmann density flux
Scalar Field Flow Rate	[dynamic]	total flow rate of scalar field entering/leaving, positive indicates scalar entering system
Scalar Field Mean	[dynamic]	spatial mean of scalar field
Scalar Field StdDev	[dynamic]	spatial standard deviation of scalar field
Thermal Field Flux Temperature	K	spatial mean of thermal field temperature for fluid entering/leaving
Thermal Field Temperature	K	spatial mean of thermal field temperature
Velocity X	m/s	spatial mean of fluid velocity
Velocity Y	m/s	spatial mean of fluid velocity
Velocity Z	m/s	spatial mean of fluid velocity
Volume Fraction	vf	spatial mean of fluid volume fraction

Usage and Interpretation

Flow and Throughput Metrics

The flow rate quantities (e.g., Flow Rate, Realized Flow Rate, LB Mass Flow Rate) describe the volumetric or mass transport across the boundary. These are computed as surface integrals over the inlet or outlet region

\[Q = \sum_k (\mathbf{u}_k \cdot \mathbf{n}_k) \, A_k,\]

where \(uk\) is the local velocity, \(nk\) is the outward normal, and \(Ak\) is the face area.

Positive values indicate flow entering the system, while negative values indicate flow leaving.

The Realized Flow Rate and LB Mass Flow Rate are computed using lattice-Boltzmann density fluxes, providing a measure of the transported mass consistent with the solver formulation.

Velocity and Pressure Metrics

Velocity quantities (e.g., Velocity X/Y/Z, Realized Velocity X/Y/Z) represent spatial averages over the boundary,

\[\langle \mathbf{u} \rangle = \frac{1}{A_{\text{tot}}} \sum_k \mathbf{u}_k \, A_k.\]

Pressure quantities (e.g., Pressure, Pressure Before Buffer) are also area-weighted averages,

\[\langle p \rangle = \frac{1}{A_{\text{tot}}} \sum_k p_k \, A_k.\]

The Pressure Before Buffer excludes pressure drop contributions from buffer regions, providing a more representative upstream/downstream value.

Phase and Composition Metrics

Phase quantities (e.g., Volume Fraction, LB Density) describe the composition of fluid crossing the boundary

\[\langle \alpha \rangle = \frac{1}{A_{\text{tot}}} \sum_k \alpha_k \, A_k,\]

where \(\sum_k\) is the local volume fraction.

These metrics are critical in multiphase systems for determining which phases are entering or leaving and in what proportions

Scalar Transport Metrics

Scalar transport quantities (e.g., Scalar Field Flow Rate, Scalar Field Mean, Scalar Field StdDev) describe the transport of scalar quantities across the boundary.

The scalar flow rate represents the net convective transport of the scalar across the boundary,

\[\dot{m}_{\phi} = \sum_k \left( \phi_k \, \mathbf{u}_k \cdot \mathbf{n}_k \right) A_k,\]

where \(ϕk\) is the scalar value in voxel \(k\), \(\mathbf{u}_k\) is the velocity vector, \(\mathbf{n}_k\) is the outward surface normal vector, and \(A_k\) is the voxel face area. The summation over \(k\) is taken over all voxels defining the inlet or outlet surface.

The scalar mean is computed as an area-weighted average over the boundary

\[\bar{\phi} = \frac{\sum_k \phi_k A_k}{\sum_k A_k},\]

where \(A_k\) is the surface area associated with voxel \(k\).

The scalar standard deviation is computed as the area-weighted standard deviation

\[\sigma_{\phi} = \sqrt{\frac{\sum_k A_k \left(\phi_k - \bar{\phi}\right)^2}{\sum_k A_k}},\]

where \(\bar{\phi}\) is the area-weighted scalar mean.

Thermal Metrics

Thermal quantities (e.g., Thermal Field Temperature, Thermal Field Flux Temperature) describe temperature and energy transport across the boundary.

The mean temperature is computed as the area-weighted average

\[\langle \mathbf{T} \rangle = \frac{1}{A_{\text{tot}}} \sum_k \mathbf{T}_k \, A_k,\]

where the summation \(k\) is taken over all voxels defining the inlet or outlet surface, \(T_k\) is the local temperature, and \(A_{\text{tot}} = \sum_k A_k\).

Flux-based temperature metrics represent the temperature of fluid actually entering or leaving the boundary, weighted by the local flow rate. This quantity corresponds to the mixing-cup average temperature and is computed as

\[\langle T \rangle_{\text{flux}} = \frac{\sum_k T_k \left(\mathbf{u}_k \cdot \mathbf{n}_k\right) A_k} {\sum_k \left(\mathbf{u}_k \cdot \mathbf{n}_k\right) A_k}.\]

The flux temperature therefore represents the effective bulk temperature of the flowing stream, with faster-moving regions contributing proportionally more strongly to the average.

Age and Residence Metrics

Age-related quantities (e.g., Age, Flux Age) describe the residence time of fluid crossing the boundary.

The mean age is computed as an area-weighted average

\[\langle t_{\text{age}} \rangle = \frac{1}{A_{\text{tot}}} \sum_k t_{\text{age},k} \, A_k.\]

The Flux Age represents a flow-weighted average

\[\langle t_{\text{age}} \rangle_{\text{flux}} = \frac{\sum_k t_{\text{age},k} \, (\mathbf{u}_k \cdot \mathbf{n}_k) \, A_k} {\sum_k (\mathbf{u}_k \cdot \mathbf{n}_k) \, A_k}.\]

These metrics are useful for residence time analysis and tracking how long fluid has remained in the system prior to exiting.

Geometric Metrics

The boundary area is computed as

\[A_{\text{tot}} = \sum_k A_k.\]

This represents the effective surface area of the inlet/outlet and is used to normalize all spatially averaged quantities.