Output Surface

The Output Surface statistics provide time-evolving, raw and reduced descriptive statistics evaluated over the output surface. For each enabled variable, the solver reports surface-based minimum, mean, and maximum values, as well as integrated surface quantities where applicable, such as total area and volumetric flux. This output produces a tab-separated ASCII .txt file named OutputSurface_{DynamicName}.txt, where the dynamic name corresponds to the name of the Output Surface in the Model Tree.

The data is written as a time series, where each row corresponds to a simulation time and each column corresponds to a statistic listed in the table below. Each row in the output file corresponds to a new statistics output time and is appended at the Statistics Output Write Interval.

The reported quantities fall into several categories:

• Geometric Metrics: Total area describes the size of the output surface.

• Flux Metrics: Surface-integrated flux quantifies the volumetric flow passing through the surface, with sign determined by the surface normal direction.

• Kinematic Metrics: Velocity and vorticity (including component-wise values) describe the motion and rotation of the fluid at the surface.

• Turbulence and Dissipation Metrics: Energy dissipation rate, turbulent kinetic energy, and sub-grid turbulent viscosity characterize turbulence behavior at the surface.

• Stress and Deformation Metrics: Strain rate and resolved shear stress quantify deformation and stress along the surface.

• Thermodynamic and Material Properties: Pressure, density, viscosity, and temperature describe the physical state of the fluid, including multiphase effects.

• Multiphase and Particle Metrics: Fluid and particle volume fractions and particle-set kLa describe phase distribution and interphase transport across the surface.

• Scalar and Custom Variable Metrics: Scalar fields and user-defined variables provide additional transported or model-defined quantities.

• Age Metrics: Mean age and its extrema characterize residence time behavior of the fluid at the surface.

• Extrema and Statistical Metrics: Maximum, mean, and minimum values describe the range and distribution of quantities over the surface.

• Time-Averaged Metrics: Time-averaged quantities provide smoothed representations of behavior for steady-state or statistically converged analysis.

Statistics Table

The index table below shows the statistics that will appear in the Output Surface output file. Within this table, each statistic corresponds to a column in the output table that evolves with the time column.

Statistics	Units	Details	When Appears
Time	s	simulation time
Age Max	s	fluid mean age	Mean Age
Age Mean	s	fluid mean age	Mean Age
Age Min	s	fluid mean age	Mean Age
Avg Turb KE Max	J/kg	time-averaged turbulent kinetic energy
Avg Turb KE Mean	J/kg	time-averaged turbulent kinetic energy
Avg Turb KE Min	J/kg	time-averaged turbulent kinetic energy
Custom Variable Max	[dynamic]	custom variable magnitude
Custom Variable Max	[dynamic]	custom variable magnitude
Custom Variable Mean	[dynamic]	custom variable magnitude
Custom Variable Mean	[dynamic]	custom variable magnitude
Custom Variable Min	[dynamic]	custom variable magnitude
Custom Variable Min	[dynamic]	custom variable magnitude
Custom Variable X Max	[dynamic]	custom variable value
Custom Variable X Mean	[dynamic]	custom variable value
Custom Variable X Min	[dynamic]	custom variable value
Custom Variable Y Max	[dynamic]	custom variable value
Custom Variable Y Mean	[dynamic]	custom variable value
Custom Variable Y Min	[dynamic]	custom variable value
Custom Variable Z Max	[dynamic]	custom variable value
Custom Variable Z Mean	[dynamic]	custom variable value
Custom Variable Z Min	[dynamic]	custom variable value
Density Max	kg/m^3	density after accounting for multiphase, particles, bubbles, and scalar fields
Density Mean	kg/m^3	density after accounting for multiphase, particles, bubbles, and scalar fields
Density Min	kg/m^3	density after accounting for multiphase, particles, bubbles, and scalar fields
Energy Dissipation Rate Max	W/kg	energy dissipation rate including both resolved and unresolved components
Energy Dissipation Rate Mean	W/kg	energy dissipation rate including both resolved and unresolved components
Energy Dissipation Rate Min	W/kg	energy dissipation rate including both resolved and unresolved components
Fluid Viscosity Max	m^2/s	fluid kinematic viscosity
Fluid Viscosity Mean	m^2/s	fluid kinematic viscosity
Fluid Viscosity Min	m^2/s	fluid kinematic viscosity
Fluid Volume Fraction Max	vf	fluid volume fraction
Fluid Volume Fraction Mean	vf	fluid volume fraction
Fluid Volume Fraction Min	vf	fluid volume fraction
Flux	m^3/s	total fluid flux through output surface, positive indicates flow in direction of the mesh’s triangle normals
Particle Set kLa Max	1/s	kLa for particle set
Particle Set kLa Mean	1/s	kLa for particle set
Particle Set kLa Min	1/s	kLa for particle set
Particle Set Volume Fraction Max	vf	volume fraction for particle set
Particle Set Volume Fraction Mean	vf	volume fraction for particle set
Particle Set Volume Fraction Min	vf	volume fraction for particle set
Pressure Max	Pa	pressure
Pressure Mean	Pa	pressure
Pressure Min	Pa	pressure
Resolved Shear Stress Max	Pa	resolved shear stress magnitude
Resolved Shear Stress Mean	Pa	resolved shear stress magnitude
Resolved Shear Stress Min	Pa	resolved shear stress magnitude
Resolved Strain Rate Max	1/s	strain rate magnitude not including unresolved strain
Resolved Strain Rate Mean	1/s	strain rate magnitude not including unresolved strain
Resolved Strain Rate Min	1/s	strain rate magnitude not including unresolved strain
Scalar Field Max	[dynamic]	scalar field value
Scalar Field Mean	[dynamic]	scalar field value
Scalar Field Min	[dynamic]	scalar field value
Sub-Grid Turbulent Viscosity Max	m^2/s	sub-grid turbulent viscosity from LES model
Sub-Grid Turbulent Viscosity Mean	m^2/s	sub-grid turbulent viscosity from LES model
Sub-Grid Turbulent Viscosity Min	m^2/s	sub-grid turbulent viscosity from LES model
Temperature Max	K	fluid temperature
Temperature Mean	K	fluid temperature
Temperature Min	K	fluid temperature
Time-Avg Energy Dissipation Rate Max	W/kg	time-averaged energy dissipation rate including both resolved and unresolved components
Time-Avg Energy Dissipation Rate Mean	W/kg	time-averaged energy dissipation rate including both resolved and unresolved components
Time-Avg Energy Dissipation Rate Min	W/kg	time-averaged energy dissipation rate including both resolved and unresolved components
Time-Avg Pressure Max	Pa	time-averaged pressure
Time-Avg Pressure Mean	Pa	time-averaged pressure
Time-Avg Pressure Min	Pa	time-averaged pressure
Time-Avg Resovled Shear Stress Max	Pa	time-averaged resolved shear stress magnitude
Time-Avg Resovled Shear Stress Mean	Pa	time-averaged resolved shear stress magnitude
Time-Avg Resovled Shear Stress Min	Pa	time-averaged resolved shear stress magnitude
Time-Avg Strain Rate Max	1/s	time-averaged strain rate magnitude
Time-Avg Strain Rate Mean	1/s	time-averaged strain rate magnitude
Time-Avg Strain Rate Min	1/s	time-averaged strain rate magnitude
Time-Avg Velocity Magnitude Max	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity Magnitude Mean	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity Magnitude Min	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity Max	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity Mean	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity Min	m/s	time-averaged fluid velocity magnitude
Time-Avg Velocity X Max	m/s	time-averaged fluid velocity
Time-Avg Velocity X Mean	m/s	time-averaged fluid velocity
Time-Avg Velocity X Min	m/s	time-averaged fluid velocity
Time-Avg Velocity Y Max	m/s	time-averaged fluid velocity
Time-Avg Velocity Y Mean	m/s	time-averaged fluid velocity
Time-Avg Velocity Y Min	m/s	time-averaged fluid velocity
Time-Avg Velocity Z Max	m/s	time-averaged fluid velocity
Time-Avg Velocity Z Mean	m/s	time-averaged fluid velocity
Time-Avg Velocity Z Min	m/s	time-averaged fluid velocity
Total Area	m^2	total area
Velocity Magnitude Max	m/s	magnitude of fluid velocity
Velocity Magnitude Mean	m/s	magnitude of fluid velocity
Velocity Magnitude Min	m/s	magnitude of fluid velocity
Velocity Max	m/s	magnitude of fluid velocity
Velocity Mean	m/s	magnitude of fluid velocity
Velocity Min	m/s	magnitude of fluid velocity
Velocity X Max	m/s	fluid velocity
Velocity X Mean	m/s	fluid velocity
Velocity X Min	m/s	fluid velocity
Velocity Y Max	m/s	fluid velocity
Velocity Y Mean	m/s	fluid velocity
Velocity Y Min	m/s	fluid velocity
Velocity Z Max	m/s	fluid velocity
Velocity Z Mean	m/s	fluid velocity
Velocity Z Min	m/s	fluid velocity
Vorticity Magnitude Max	1/s	vorticity magnitude
Vorticity Magnitude Mean	1/s	vorticity magnitude
Vorticity Magnitude Min	1/s	vorticity magnitude
Vorticity Max	1/s	vorticity magnitude
Vorticity Mean	1/s	vorticity magnitude
Vorticity Min	1/s	vorticity magnitude
Vorticity X Max	1/s	vorticity
Vorticity X Mean	1/s	vorticity
Vorticity X Min	1/s	vorticity
Vorticity Y Max	1/s	vorticity
Vorticity Y Mean	1/s	vorticity
Vorticity Y Min	1/s	vorticity
Vorticity Z Max	1/s	vorticity
Vorticity Z Mean	1/s	vorticity
Vorticity Z Min	1/s	vorticity

Usage and Interpretation

The reported statistics describe fluid properties evaluated along a user-defined output surface. These quantities are computed as surface integrals, surface averages, or extrema over the surface \(A\), and are written as time-evolving values. They provide localized insight into transport, flow behavior, and multiphase interactions across internal sections of the domain.

Unless otherwise noted, surface-averaged quantities are defined as

\[\langle \phi \rangle_A = \frac{1}{A} \int_A \phi(x)\, dA\]

where \(A = \int_A dA\) is the total surface area.

Geometric and Flux Metrics

Geometric and flux quantities describe the size of the surface and the transport of fluid across it. The total surface area is given by \(A = \int_A dA\). The volumetric flux through the surface is defined as

\[Q = \int_A \mathbf{u}(x) \cdot \mathbf{n}\, dA\]

where \(𝐮\) is the velocity and \(𝐧\) is the outward-facing surface normal. The sign of \(Q\) reflects the direction of flow relative to the surface orientation. These metrics are useful for computing flow rates, residence times, and inlet/outlet balances.

Kinematic Metrics

Kinematic quantities describe the motion and rotation of the fluid along the surface. The mean velocity magnitude is computed as

\[\langle \lvert \mathbf{u} \rvert \rangle_A = \frac{1}{A} \int_A \lvert \mathbf{u}(x) \rvert\, dA\]

while component-wise averages follow similarly, e.g.,

\[\langle u_i \rangle_A = \frac{1}{A} \int_A u_i(x)\, dA\]

The vorticity is defined as \(\omega = \nabla \times \mathbf{u}\), with surface-averaged magnitude

\[\langle \lvert \omega \rvert \rangle_A = \frac{1}{A} \int_A \lvert \nabla \times \mathbf{u} \rvert\, dA\]

These metrics characterize flow directionality, rotation, and the presence of coherent structures at the surface.

Turbulence and Dissipation Metrics

Turbulence quantities describe both resolved and modeled turbulent behavior at the surface. The turbulent kinetic energy is defined as

\[k = \frac{1}{2} \langle \mathbf{u}' \cdot \mathbf{u}' \rangle\]

and its surface mean is

\[\langle k \rangle_A = \frac{1}{A} \int_A k(x)\, dA\]

The energy dissipation rate is given by

\[\varepsilon = \nu \left( \frac{\partial u_i}{\partial x_j} \frac{\partial u_i}{\partial x_j} \right)\]

with surface mean

\[\langle \varepsilon \rangle_A = \frac{1}{A} \int_A \varepsilon(x)\, dA\]

The sub-grid turbulent viscosity \(𝜈_t\) is similarly averaged as

\[\langle \nu_t \rangle_A = \frac{1}{A} \int_A \nu_t(x)\, dA\]

These quantities are used to understand mixing, turbulence intensity, and scale-dependent transport behavior at the surface.

Stress and Deformation Metrics

Stress and deformation metrics quantify how the fluid is being sheared and deformed along the surface. The strain rate tensor is defined as

\[S_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right)\]

with magnitude

\[\lvert S \rvert = \sqrt{2 S_{ij} S_{ij}}\]

and surface mean

\[\langle \lvert S \rvert \rangle_A = \frac{1}{A} \int_A \lvert S(x) \rvert\, dA\]

The resolved shear stress magnitude is related to viscous stress, typically

\[\tau = \mu \lvert S \rvert\]

with surface mean

\[\langle \tau \rangle_A = \frac{1}{A} \int_A \mu(x)\, \lvert S(x) \rvert\, dA\]

These metrics describe deformation rates, shear-driven mixing, and stress distributions.

Thermodynamic and Material Properties

Thermodynamic and material properties describe the physical state of the fluid at the surface. Surface-averaged pressure is

\[\langle p \rangle_A = \frac{1}{A} \int_A p(x)\, dA\]

while density and viscosity are

\[\langle \rho \rangle_A = \frac{1}{A} \int_A \rho(x)\, dA, \quad \langle \nu \rangle_A = \frac{1}{A} \int_A \nu(x)\, dA\]

Multiphase and Particle Metrics

Multiphase quantities describe the distribution of phases and interphase transport at the surface. The fluid volume fraction is averaged as

\[\langle \alpha_f \rangle_A = \frac{1}{A} \int_A \alpha_f(x)\, dA\]

and particle volume fraction similarly as

\[\langle \alpha_f \rangle_A = \frac{1}{A} \int_A \alpha_f(x)\, dA\]

The particle-set mass transfer coefficient (kLa) is averaged as

\[\langle k_L a \rangle_A = \frac{1}{A} \int_A k_L a(x)\, dA\]

These metrics are used to interpret phase distribution, interfacial area effects, and transport between phases.

Scalar and Custom Variable Metrics

Scalar fields and user-defined variables are treated generically. For any scalar field \(𝜙\), the surface mean is

\[\langle \phi \rangle_A = \frac{1}{A} \int_A \phi(x)\, dA\]

Component-wise values follow similarly. These quantities allow users to track transported species, reaction progress, or custom model outputs.

Age Metrics

Age metrics describe residence time behavior at the surface. The mean age is defined as

\[\langle t_{\text{age}} \rangle_A = \frac{1}{A} \int_A t_{\text{age}}(x)\, dA\]

with extrema defined pointwise as

\[t_{\text{age,max}} = \max_{x \in A} t_{\text{age}}(x), \quad t_{\text{age,min}} = \min_{x \in A} t_{\text{age}}(x)\]

Extrema and Statistical Metrics

Extrema quantities are computed pointwise over the surface as

\[\phi_{\text{max}} = \max_{x \in A} \phi(x), \quad \phi_{\text{min}} = \min_{x \in A} \phi(x)\]

These values identify peak conditions and variability across the surface.

Time-Averaged Metrics

Time-averaged quantities provide smoothed representations of surface behavior. These are computed as

\[\bar{\phi}(t) = \frac{1}{T} \int_{t-T}^{t} \phi(\tau)\, d\tau.\]