Monitors

A Monitor is a tool for capturing data from the solver about the model.

Data (such as volume fraction, pressure, velocity, etc.) for a given monitor region is written to a CSV file while the solver is running. To define monitors, the following inputs must be preceded by “mfix.”:

Description

Type

Default

monitors

Names of the monitors to be computed

String

None

monitors.[monitor]

Monitor type

String

None

mfix.monitors = my_monitor0  my_monitor1

mfix.monitors.my_monitor0 = Eulerian::VolumeIntegral::MassWeightedIntegral
mfix.monitors.my_monitor1 = Lagrangian::Average::VolumeWeightedAverage

Region Selection

To define a monitor, there must be a region already defined in the regions inputs. A Monitor region is a single point, plane, or volume. Multiple regions cannot be combined for a monitor. The following inputs must be preceded by “mfix.monitors.”:

Description

Type

Default

[monitor].region

Define the region in which the monitor will be computed

String

None

# regionA and regionB to be defined in the "regions" inputs section
mfix.monitors.my_monitor0.region = regionA
mfix.monitors.my_monitor1.region = regionB

Monitor Output

The monitor data will be output to a file with name given by the input “plot_file”, and the extension .csv is automatically added. The monitor output file is in Comma Separated Value (CSV) format. The first line of the file provides header information. The following inputs must be preceded by “mfix.monitors.”:

Description

Type

Default

[monitor].plot_file

Define the name of the plotfile where monitor output will be saved

String

None

[monitor].plot_int

Define the timestep frequency for saving monitored data to file

Int

-1

[monitor].plot_per_approx

Define the approximated simulation time at which saving monitored data

Real

0

[monitor].output.openmode

Sets the open mode for the monitor output file. Admissible values are:

  • “app” for appending to the file if it already exists

  • “trunc” for overwriting the output file if it exists

String

“app”

[monitor].output.setw

Sets the field width to be used on output file

Int

0

[monitor].output.setfill

Sets the filling character for the output file

Char

‘’

[monitor].output.setprecision

Sets the decimal precision to be used to format floating-point values in the output file

Int

0

[monitor].output.format

Sets the format flags. Admissible values are:

  • “defaultfloat”

  • “fixed”

  • “scientific”

String

“”

mfix.monitors.my_monitor0.plot_file = monitor0_output
mfix.monitors.my_monitor0.plot_int = 10

mfix.monitors.my_monitor1.plot_file = monitor1_output
mfix.monitors.my_monitor1.plot_per_approx = 0.01

Monitor Variables

The variables to be monitored can be specified in the inputs by including the following input preceded by the “mfix.monitors.”:

Description

Type

Default

[monitor].variables

Define which variables are to be monitored by this monitor

String

None

mfix.monitors.my_monitor0.variables = T_g  vel_g  p_g  gp_y  X_gk

mfix.monitors.my_monitor1.variables = density  drag_y  T_s  txfr_vel_x

Eulerian Monitors

There are different types of monitors available. A monitor type applies an operator (for example a sum, an area integral or a volume integral) to the variable. The dimensionality of the region determines which operators can be applied.

The table below summarizes the nomenclature used to describe the monitor operators:

Symbol

Description

\(\phi_{ijk}\)

Variable value at indexed cell

\(\varepsilon_{ijk}\)

Phase volume fraction at indexed cell

\(\rho_{ijk}\)

Phase density at indexed cell

\(\vec{v}_{ijk}\)

Phase velocity at indexed cell

\(A_{ijk}\)

Cross-sectional area of cell

\(V_{ijk}\)

Volume of indexed cell

The following table lists all the fluid phase variables that can be monitored:

Description

ones

values of \(phi\) is set to 1.

ep_g

fluid volume fraction

p_g

fluid pressure

ro_g

fluid density

trac

tracer

vel_g

fluid velocity (all the three components of the velocity)

vel_g_[x/y/z]

x, y, or z component of the fluid velocity

gp

fluid pressure gradient (all the three components of the gradient)

gp_[x/y/z]

x, y, or z component of the fluid pressure gradient

T_g

fluid temperature

h_g

fluid enthalpy

X_gk

fluid species mass fractions (monitor all the fluid species)

X_gk_[species]

fluid “species” mass fraction (only species “species” is monitored)

vort

fluid vorticity (all the three components of the vorticity)

vort[x/y/z]

x, y, or z component of the fluid vorticity

txfr_velocity

interphase velocity transferred to the fluid (all the three components of the velocity)

txfr_vel_[x/y/z]

x, y, or z component of the interphase velocity transferred to the fluid

txfr_beta

drag coefficient

txfr_gammaTp

convection coefficient multiplied by the solids temperature

txfr_gamma

convection coefficient

chem_txfr_X_gk

rate of mass transferred to the fluid phase due to heterogeneous chemical reactions (monitor all the fluid species)

chem_txfr_X_gk_[species]

fluid “species” rate of mass transferred due to heterogeneous chemical reactions (only species “species” is monitored)

chem_txfr_velocity

rate of velocity transferred to the fluid phase due to heterogeneous chemical reactions (all the three components of the velocity)

chem_txfr_vel_[x/y/z]

x, y, or z component of the rate of velocity transferred due to heterogeneous reactions

chem_txfr_h

rate of enthalpy transferred to the fluid phase due to heterogeneous chemical reactions

divtau

divergence of the viscous stress tensor (all the three components)

divtau_[x/y/z]

x, y, or z component of the divergence of the viscous stress tensor

Uniform Scalar Field

The following table lists all the fluid phase space-uniform variables that can be monitored:

Description

thermo_p_g

fluid thermodynamic pressure

For a uniform scalar field, the monitor data value is simply the value of the variable at current time:

Value

Eulerian::UniformScalarField::Value

Returns the value of the field quantity in the selected region.

\[\phi_{ijk}\]

Point Region

For a point region, the monitor data value is simply the value of the variable at that point:

Value

Eulerian::PointRegion::Value

Returns the value of the field quantity in the selected region.

\[\phi_{ijk}\]

Area or Volume Region

The following monitor types are valid for area and volume regions:

Sum

Eulerian::AreaRegion::Sum

Eulerian::VolumeRegion::Sum

The sum is computed by summing all values of the field quantity in the selected region.

\[\sum_{ijk}\phi_{ijk}\]
Min

Eulerian::AreaRegion::Min

Eulerian::VolumeRegion::Min

Minimum value of the field quantity in the selected region.

\[\min_{ijk} \phi_{ijk}\]
Max

Eulerian::AreaRegion::Max

Eulerian::VolumeRegion::Max

Maximum value of the field quantity in the selected region.

\[\max_{ijk} \phi_{ijk}\]
Average

Eulerian::AreaRegion::Average

Eulerian::VolumeRegion::Average

Average value of the field quantity in the selected region where \(N\) is the total number of observations (cells) in the selected region.

\[\phi_0 = \frac{\sum_{ijk} \phi_{ijk}}{N}\]
Standard Deviation

Eulerian::AreaRegion::StandardDeviation

Eulerian::VolumeRegion::StandardDeviation

The standard deviation of the field quantity in the selected region where \(\phi_0\) is the average of the variable in the selected region.

\[\sigma_{\phi} = \sqrt{\frac{ \sum_{ijk} (\phi_{ijk}-\phi_{0})^2 }{N}}\]

Surface Integrals

The following types are only valid for area regions:

Area

Eulerian::SurfaceIntegral::Area

Area of selected region is computed by summing the areas of the facets that define the surface.

\[\int dA = \sum_{ijk} \lvert A_{ijk} \rvert\]
Area-Weighted Average

Eulerian::SurfaceIntegral::AreaWeightedAverage

The area-weighted average is computed by dividing the summation of the product of the selected variable and facet area by the total area of the region.

\[\frac{\int\phi dA}{A} = \frac{\sum_{ijk}{\phi_{ijk} \lvert A_{ijk} \rvert}}{\sum_{ijk}{\lvert A_{ijk} \rvert}}\]
Flow Rate

Eulerian::SurfaceIntegral::FlowRate

The flow rate of a field variable through a surface is computed by summing the product of the phase volume fraction, density, the selected field variable, phase velocity normal to the facet \(v_n\), and the facet area.

\[\int\varepsilon\rho\phi{v_n}dA = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert\]
Mass Flow Rate

Eulerian::SurfaceIntegral::MassFlowRate

The mass flow rate through a surface is computed by summing the product of the phase volume fraction, density, phase velocity normal to the facet \(v_n\), and the facet area.

\[\int\varepsilon\rho{v_n} dA = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}{v}_{n,ijk} \lvert A_{ijk} \rvert\]
Mass-Weighted Average

Eulerian::SurfaceIntegral::MassWeightedAverage

The mass flow rate through a surface is computed by summing the product of the phase volume fraction, density, phase velocity normal to the facet, and the facet area.

\[\frac{\int\varepsilon\rho\phi{v_n}dA}{\int\varepsilon\rho{v_n}dA} = \frac{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert}{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert}\]
Volume Flow Rate

Eulerian::SurfaceIntegral::VolumeFlowRate

The volume flow rate through a surface is computed by summing the product of the phase volume fraction, phase velocity normal to the facet \(v_n\), and the facet area.

\[\int\varepsilon{v_n}dA = \sum_{ijk}\varepsilon_{ijk}{v}_{n,ijk} \lvert A_{ijk} \rvert\]

Volume Integrals

The following types are only valid for volume regions:

Volume

Eulerian::VolumeIntegral::Volume

The volume is computed by summing all of the cell volumes in the selected region.

\[\int dV = \sum_{ijk}{ \lvert V_{ijk}} \rvert\]
Volume Integral

Eulerian::VolumeIntegral::VolumeIntegral

The volume integral is computed by summing the product of the selected field variable and the cell volume.

\[\int \phi dV = \sum_{ijk}{\phi_{ijk} \lvert V_{ijk}} \rvert\]
Volume-Weighted Average

Eulerian::VolumeIntegral::VolumeWeightedAverage

The volume-weighted average is computed by dividing the summation of the product of the selected field variable and cell volume by the sum of the cell volumes.

\[\frac{\int\phi dV}{V} = \frac{\sum_{ijk}{\phi_{ijk} \lvert V_{ijk} \rvert}}{\sum_{ijk}{\lvert V_{ijk} \rvert}}\]
Mass-Weighted Integral

Eulerian::VolumeIntegral::MassWeightedIntegral

The mass-weighted integral is computed by summing the product of phase volume fraction, density, selected field variable, and cell volume.

\[\int \varepsilon\rho\phi dV = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} \lvert V_{ijk}\rvert\]
Mass-Weighted Average

Eulerian::VolumeIntegral::MassWeightedAverage

The mass-weighted average is computed by dividing the sum of the product of phase volume fraction, density, selected field variable, and cell volume by the summation of the product of the phase volume fraction, density, and cell volume.

\[\frac{\int\phi\rho\varepsilon dV}{\int\rho\varepsilon dV} = \frac{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} \lvert V_{ijk}\rvert}{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk} \lvert V_{ijk}\rvert}\]

Lagrangian Monitors

There are different types of monitors available. A monitor type applies an operator (for example a sum, an area integral or a volume integral) to the variable. The dimensionality of the region determines which operators can be applied.

The table below summarizes the nomenclature used to describe the monitor operators:

Symbol

Description

\(\phi_p\)

Variable value of the indexed particle

\(m_p\)

Mass of the indexed particle

\(V_p\)

Volume of the indexed particle

\(\mathcal{w}_p\)

Statistical weight of the indexed particle [1]

The following table lists all the solids phase variables that can be monitored:

Description

position

particles position (all the three components)

pos_[x/y/z]

x, y, or z component of the particles position

id

particles id

cpu

particles cpu

radius

particles radius

volume

particles volume

mass

particles mass

density

particles density

oneOverI

particles inverse of momentum of inertia

velocity

particles velocity (all the three components)

vel_[x/y/z]

x, y, or z component of the particles velocity

omega

particles angular velocity (all the three components)

omega_[x/y/z]

x, y, or z component of the particles angular velocity

statwt

particles statistical weight

dragcoeff

particles drag coefficient

drag

particles drag (all the three components)

drag_[x/y/z]

x, y, or z component of the particles drag

cp_s

particles specific heat coefficient

T_s

particles temperature

convection

particles convective heat transfer

phase

particles phase

state

particles state

X_sn

particles species mass fractions (for all the solids species)

X_sn_[species]

solids “species” mass fraction (only species “species” is monitored)

txfr_velocity

rate of velocity transferred to the fluid phase due to heterogeneous chemical reactions (all the three components)

txfr_vel_[x/y/z]

x, y, or z components of the transferred velocity due to heterogeneous reactions

txfr_h

rate of enthalpy transferred due to heterogeneous chemical reactions

txfr_X_sn

rate of mass transferred due to heterogeneous chemical reactions (for all the species)

txfr_X_sn_[species]

solids “species” rate of transfer due to heterogeneous reactions (only species “species” is monitored)

General particle properties

General particle properties can be obtained from area (plane) and volume regions. For area regions, all particles in Eulerian cells that intersect the plane are used in evaluating the average.

Sum

Lagrangian::GeneralProperty::Sum

The sum of particle property, \(\phi_p\) in the selected region is calculated using the following expression.

\[\sum_p w_p \phi_p\]

Mass-Weighted Sum

Lagrangian::GeneralProperty::MassWeightedSum

The mass-weighted sum of particle property, \(\phi_p\) in the selected region is calculated using the following expression.

\[\sum_p w_p m_p \phi_p\]
Min

Lagrangian::GeneralProperty::Min

The minimum value of particle property \(\phi_p\) is the selected region is obtained using the following expression.

\[\min_p \phi_p\]
Max

Lagrangian::GeneralProperty::Max

The maximum value of particle property \(\phi_p\) is the selected region is obtained using the following expression.

\[\max_p \phi_p\]

Averaged particle properties

Particle properties can be averaged over area (plane) and volume regions. For area regions, all particles in Eulerian cells that intersect the plane are used in evaluating the average.

Average

Lagrangian::AveragedProperty::Average

The average value of particle property, \(\phi_p\) in the selected region is calculated using the following expression. For DEM simulations, the statistical weight of a particle, \(w_p\), is one such that the sum of the weights is the total number of observations in the selected region.

\[\bar{\phi} = \frac{\sum_p w_p \phi_p}{\sum_p w_p}\]
Standard Deviation

Lagrangian::AveragedProperty::StandardDeviation

The standard deviation of particle property, \(phi_p\) in the selected region is calculated using the following expression. \(\bar{\phi}\) is the averaged variable in the selected region.

\[\sigma_{\phi} = \sqrt{\frac{ \sum_p w_p (\phi_p-\bar{\phi})^2 }{\sum_p w_p}}\]
Mass-weighted average

Lagrangian::AveragedProperty::MassWeightedAverage

Mass-weighted average value of particle property, \(\phi_p\) in the selected region is calculated using the following expression.

\[\bar{\phi}_m = \frac{\sum_{p} w_p m_p \phi_p}{\sum_p w_p m_p }\]
Volume-weighted average

Lagrangian::AveragedProperty::VolumeWeightedAverage

Volume-weighted average value of particle property, \(\phi_p\) in the selected region is calculated using the following expression.

\[\bar{\phi}_v = \frac{\sum_{p} w_p V_p \phi_p}{\sum_p w_p V_p}\]

Flow rates

For Lagrangian monitors of type FlowRate, the flow plane must be specified in the inputs and it must be defined by one of the regions defined in the regions inputs. The following input for a monitor [monitor] of type FlowRate can be used, preceded by the “mfix.monitors” prefix.

Description

Type

Default

[monitor].plane

defines the plane through which the flow rate of the particles in the monitoring region [region] will be computed

String

None

Flow rate monitors for Lagrangian particles (DEM/PIC) are only valid for area (plane) regions. The set of particles crossing the flow plane, \(\Gamma\) is approximated using the height of the plane, \(h\), the position of the particle, \(x_p\), and the particle velocity normal to the plane, \(v_p\) such that

\[(v_p)\left(\frac{x_p - h}{\Delta t}\right) > 0\]

and

\[\left|v_p\right| \geq \left| \frac{x_p - h}{\Delta t} \right|\]
Flow rate

Lagrangian::FlowRate::FlowRate

The net flow rate of a general particle property \(\phi_p\) is computed by summing the properties of the set of particles projected to have crossed the flow plane, \(\Gamma\).

\[\sum_{p \in \Gamma} w_p \phi_p \frac{v_p}{\left| v_p \right|}\]
Mass-weighted flow rate

Lagrangian::FlowRate::MassWeightedFlowRate

The net mass-weighted flow rate is the sum of the general particle property \(\phi_p\) multiplied by the particle mass, \(m_p\) of the set of particles projected to have crossed the flow plane, \(\Gamma\).

\[\sum_{p \in \Gamma} w_p m_p \phi_p \frac{v_p}{\left| v_p \right|}\]
Volume-weighted flow rate

Lagrangian::FlowRate::VolumeWeightedFlowRate

The net volume-weighted flow rate is the sum of the general particle property \(\phi_p\) multiplied by the particle volume, \(V_p\) of the set of particles projected to have crossed the flow plane, \(\Gamma\).

\[\sum_{p \in \Gamma}\phi_p w_p V_p \frac{v_p}{\left| v_p \right|}\]