Fluid¶

The Fluid statistics provide time-resolved, volume-integrated and spatially averaged quantities describing the state of the fluid within the simulation domain. These outputs capture global measures of mass, momentum, energy, and turbulence, enabling system-level analysis of flow behavior. The name of this file is Fluid.txt. The data is written as a time series, with each row corresponding to a simulation time and appended at the Statistics Output Write Interval.

The reported quantities fall into several categories:

Volume and Inventory Metrics: Fluid volume, domain volume, and phase-specific volumes describe how much fluid is present and how it is distributed across phases.
Conversion Metrics: Fluid-to-particle and particle-to-fluid conversion rates track interphase transformations between Eulerian fluid and Lagrangian particles.
Energy Metrics: Kinetic and potential energy quantify the total energy content of the fluid.
Flow and Kinematic Metrics: Velocity, vorticity, and strain rate describe the motion and deformation of the fluid.
Turbulence and Dissipation Metrics: Energy dissipation rate, turbulent viscosity, and turbulent kinetic energy characterize resolved and sub-grid turbulence behavior.
Thermodynamic and Material Properties: Pressure, viscosity, and density metrics describe the physical state of the fluid.
Extrema and Stability Metrics: Maximum velocity and lattice-Boltzmann density bounds provide indicators of numerical stability and flow intensity.
Time-Averaged Metrics: Time-averaged quantities provide smoothed representations of system behavior for steady-state analysis.

Statistics Table¶

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

Statistics	Units	Details
Time	s	simulation time
[dynamic] Volume	m^3	total volume of 1st fluid phase
[dynamic] Volume	m^3	total volume of 2nd fluid phase
[dynamic] Volume LB	m^3	total volume of 1st fluid phase adjusted by lattice Boltzmann density
Domain Volume	m^3	total volume of region available for fluid to occupy
Fluid to Particle Number Conversion Rate	number/s	rate at which fluid is being converted to particles
Fluid to Particle Volume Conversion Rate	m^3/s	rate at which fluid is being converted to particles
Fluid Volume	m^3	total volume of fluid
Fluid Volume LB	m^3	total fluid volume adjusted by lattice Boltzmann density
Kinetic Energy	J	total kinetic energy of fluid
LB Density Max	Dimensionless	max lattice Boltzmann density
LB Density Min	Dimensionless	min lattice Boltzmann density
Max Velocity	m/s	max fluid velocity magnitude
Mean Energy Dissipation Rate	W/kg	spatial mean of energy dissipation rate including both resolved and unresolved components
Mean Fluid Viscosity	m^2/s	spatial mean of fluid kinematic viscosity
Mean Pressure	Pa	spatial mean of pressure
Mean Resolved Shear Stress	Pa	spatial mean of resolved shear stress
Mean Strain Rate	1/s	spatial mean of strain rate magnitude
Mean Sub-Grid Turbulent Viscosity	m^2/s	spatial mean of sub-grid turbulent viscosity from LES model
Mean Time-Avg Energy Dissipation Rate	W/kg	spatial mean of time-averaged energy dissipation rate including both resolved and unresolved components
Mean Time-Avg Pressure	Pa	spatial mean of time-averaged pressure
Mean Time-Avg Resolved Shear Stress	Pa	spatial mean of time-averaged resolved shear stress
Mean Time-Avg Strain Rate	1/s	spatial mean of time-averaged strain rate magnitude
Mean Turbulent Kinetic Energy	J/kg	spatial mean of time-averaged turbulent kinetic energy
Mean Velocity	m/s	spatial mean of fluid velocity
Mean Vorticity	1/s	spatial mean of vorticity
Particle to Fluid Number Conversion Rate	number/s	rate at which particles are being converted to fluid
Particle to Fluid Volume Conversion Rate	m^3/s	rate at which particles are being converted to fluid
Potential Energy	J	total potential energy of fluid relative to initial state at time 0
Time-Avg Mean Velocity	m/s	time-averaged spatial mean of fluid velocity

Usage and Interpretation¶

Volume and Inventory Metrics

The volume quantities (e.g., Volume, Fluid Volume, Domain Volume) describe how much fluid is present in the system and how it is distributed across phases.

The total fluid volume is computed as

\[V = \int_\Omega \alpha \, dV,\]

where \(𝛼\) is the local volume fraction and \(Ω\) is the simulation domain.

The Volume LB and Fluid Volume LB quantities account for lattice-Boltzmann density weighting, providing a corrected measure of effective fluid volume. These metrics are useful for tracking mass conservation and phase distribution in multiphase systems.

Conversion Metrics

The conversion quantities (e.g., Fluid to Particle Volume Conversion Rate, Particle to Fluid Volume Conversion Rate) describe the rate at which material transitions between Eulerian fluid and Lagrangian particle representations.

These are typically computed as volumetric or number-based rates,

\[\mathbf{V}_{f \to p}, \, \mathbf{V}_{p \to f}.\]

These terms are critical for ensuring consistency between fluid and particle mass balances and for interpreting phase-change or coupling processes.

Energy Metrics

The energy quantities (e.g., Kinetic Energy, Potential Energy) describe the total energy content of the fluid.

Kinetic energy is computed as

\[E_k = \frac{1}{2} \int_\Omega \rho \, |\mathbf{u}|^2 \, dV.\]

Potential energy is computed relative to a reference state,

\[E_p = \int_\Omega \rho g z \, dV.\]

These metrics are useful for understanding flow intensity, energy input, and gravitational effects.

Flow and Kinematic Metrics

Flow quantities (e.g., Mean Velocity, Max Velocity, Mean Strain Rate, Mean Vorticity) describe the motion and deformation of the fluid.

Spatial means are computed as volume-weighted averages,

\[\langle \phi \rangle = \frac{1}{V} \int_\Omega \phi \, dV.\]

These metrics provide insight into overall flow behavior, mixing intensity, and rotational structures.

Turbulence and Dissipation Metrics

Turbulence quantities (e.g., Mean Energy Dissipation Rate, Mean Sub-Grid Turbulent Viscosity, Mean Turbulent Kinetic Energy) characterize both resolved and modeled turbulence.

The energy dissipation rate represents the rate at which kinetic energy is converted into heat through viscous effects:

\[\varepsilon = \text{resolved} + \text{sub-grid contributions}\]

These metrics are critical for understanding mixing, scale-up behavior, and turbulence intensity.

Thermodynamic and Material Properties

Quantities such as Mean Pressure and Mean Fluid Viscosity describe the average thermodynamic and transport properties of the fluid.

These are computed as volume-weighted averages and provide context for interpreting flow behavior and material response.

Extrema and Stability Metrics

The extrema quantities (e.g., Max Velocity, LB Density Max, LB Density Min) provide indicators of flow intensity and numerical stability.

Large velocity magnitudes may indicate strong flow regions, while bounds on lattice-Boltzmann density are important for maintaining numerical stability.

Time-Averaged Metrics

Time-averaged quantities (e.g., Time-Avg Mean Velocity, Mean Time-Avg Pressure, Mean Time-Avg Energy Dissipation Rate) represent running averages over time. These values are computed according to the user-defined time-averaging scheme.