Spatial averages
The following inputs must be preceded by “mfix.” and control whether to compute spatial averages, and how often to output the results. n is the number of spatial averages implicitly defined by the size of avg_region_x_w.
Description |
Type |
Default |
|
|---|---|---|---|
avg_int |
Interval, in number of CFD dt’s, to write output |
Int |
-1 |
avg_file |
Base file name which is appended with the data type (vel_p, p_g, ep_g or vel_g), the number of this type of averaging, and the .csv file extension |
String |
avg_region |
avg_ep_g |
Average and save fluid-phase volume fraction (if 1) |
n*Int |
0 |
avg_p_g |
Average and save fluid-phase pressure (if 1) |
n*Int |
0 |
avg_vel_g |
Average and save fluid-phase velocity (if 1) |
n*Int |
0 |
avg_T_g |
Average and save fluid-phase temperature (if 1) |
n*Int |
0 |
avg_ro_p |
Average and save particle density (if 1) |
n*Int |
0 |
avg_vel_p |
Average and save particle velocity (if 1) |
n*Int |
0 |
avg_T_p |
Average and save particle temperature (if 1) |
n*Int |
0 |
avg_region_x_w |
Lower bound of averaging region in x-direction |
n*Real |
None |
avg_region_x_e |
Upper bound of averaging region in x-direction |
n*Real |
None |
avg_region_y_s |
Lower bound of averaging region in y-direction |
n*Real |
None |
avg_region_y_n |
Upper bound of averaging region in y-direction |
n*Real |
None |
avg_region_z_b |
Lower bound of averaging region in z-direction |
n*Real |
None |
avg_region_z_t |
Upper bound of averaging region in z-direction |
n*Real |
None |
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:
|
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:
|
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 |
|
|---|---|
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 |
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.
\[\sum_p w_p \phi_p\]- 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, preceeded 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, \(\Gamma\).
\[\sum_{p \in \Gamma}\phi_p w_p V_p \frac{v_p}{\left| v_p \right|}\]