Injection Option

Overview

Both the number and the location of particles must be considered when adding massless tracers, inertial particles, or DEM particles to the system. The number of particles added to the system is defined by an injection rate and an injection duration.

When adding particles to a system, there are two factors to consider: (1) the number of particles entering the system, and (2) the location of the particles entering the system. The number of particles entering the system is defined by an injection rate and an injection duration. The location of the particle injection is typically defined using children geometry, an inlet boundary condition, or a background injection. Physically speaking, injection along or within a child geometry injection represents a bolus type addition, whereas a background injection represents an initial loading condition. Defining the injection rate along an inlet boundary condition typically represents a particle injection process. This may be used for residence time analysis or particle accumulation studies.

These parameters can be defined by the following options.

Dump

A single impulse addition of particles into the injection geometry. The dump defines the total number of particles added to the system at a single user-defined time.

In the example below, 10,000 particles are dumped instantaneously into the child geometry. This dump occurs at 1 second. The total number of particles added to the system will be equal to the dump value.

Download Sample File: Dump

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family.

Child surface

Particles are injected along the surface of the child geometry of the particle family.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Dump Value UDF

unitless | This UDF defines the number of particles to be dumped into the injection location at the dump time. This is a System UDF.

Dump Time UDF

s | This UDF defines the time at which particles are dumped into the injection location. This is a System UDF.

Feed

Continuously feed particles into the injection geometry at a user-defined number flow rate over a user-defined period. The feed rate can vary per user-defined expression. The total number of particles added to the system during the feed period can be calculated from the time interval of the feed rate:

\[N_T = \int_{t_{\text{start}}}^{t_{\text{stop}}} \dot{n}_f \, dt\]

where \(N_T\) is the total number of particles added to the system via the feed, and \(\dot{n}_f\) is the time evolution of the feed rate. The limits on the integral represent the feed start and stop time.

In the example below, particles are continuously fed into the child geometry at a rate of 5,000 particles beginning at 1 second and ending at 4 seconds. Per the above integral, the injection adds 15,000 particles to the system.

Download Sample File: Feed

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family. A child geometry must be added in order to inject in a child volume.

Child surface

Particles are injected along the surface of the child geometry of the particle family. A child geometry must be added in order to inject in a child surface.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Feed Rate UDF

#/s | This UDF defines the particle feed rate into the injection location. This is a System UDF.

Download Sample File: Feed Rate UDF

Injection Ramp Time

s | Time over which the injection rate increases from 0 to the resolved feed rate. The ramp is modeled as a quarter sine wave. Physically speaking, the ramp is analogous to the time required to open a value and actuate a blower/pump. Ramp time typically ranges from 0.5–2.0 seconds.

Start Time

s | The time at which the feed injection begins.

Stop Time Option

s | The time at which the feed injection stops.

End of Simulation

The injection stops at the end of the simulation.

Specified

The injection stops at a user-specified time.

Stop Time

s | The time particles are stopped. Only used for Feed-type particles. A value of -1 indicates the end of the simulation.

Volume Feed

Continuously feed particles into the injection geometry at a user-defined volume flow rate for a user-defined period. The total number of particles added to the system during the volume feed period can be calculated from the time interval of the feed rate and the associated diameter:

\[N_T = \int_{t_{\text{start}}}^{t_{\text{stop}}} \frac{\dot{V}_f}{\langle V \rangle} \, dt\]

where \(N_T\) is the total number of particles added to the system via the feed, \(\dot{V}_f\) is the time evolution of the volume feed rate, and \(\langle V \rangle\) is the average volume of the particles added to the system. The limits on the integral represent the feed start and stop time.

In the example below, 1-mm diameter particles are continuously fed into the child geometry at a rate of 0.157 L/min. The feed rate begins at 1 second and ends at 4 seconds. Over the 3-second addition window, a total solids volume of 7.85 mL is added to the system. This feed process adds a total of 15,000 particles to the system (as expected given the 1-mm diameter particle size).

Note

The user should make sure that the number of particles added to the system is reasonable, given the GPU memory.

Download Sample File: Volume Feed

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family.

Child surface

Particles are injected along the surface of the child geometry of the particle family.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Volume Feed Rate UDF

L/min | This UDF defines the particle addition feed rate. The particle volume is calculated from the particle diameter. This is a System UDF.

Download Sample File: Volume Feed Rate UDF

Specified Feed Rate

#/s | Read only.

Injection Ramp Time

s | Time over which the injection rate increases from 0 to the resolved feed rate. The ramp is modeled as a quarter sine wave. Physically speaking, the ramp is analogous to the time required to open a value and actuate a blower/pump. Ramp time typically ranges from 0.5–2.0 seconds.

Start Time

s | The time at which the volume feed begins.

Stop Time Option

s | The time at which the volume feed stops.

End of Simulation

The volume feed stops at the end of the simulation.

Specified

The volume feed stops at a user-specified time.

Stop Time

s | The time particles are stopped. Only used for Feed-type particles. A value of -1 indicates the end of the simulation.

Note

When mass transfer and/or reactions are present, consider the relationship between the volumetric and molar injection rate.

The volumetric injection rate is linked to the molar injection rate via the particle density. For solid particles, where the molar density can be treated as a constant, the user-set volumetric injection rate (e.g., m³/s) is directly proportional to the mass injection rate (e.g., moles/s) via the solid particle molar density.

The situation is more complex for gas bubbles. As with solid particles, the user-set volumetric injection rate (e.g., m³/s) is directly proportional to the mass injection rate (e.g., moles/s) via the gas bubble density. The molar density of the gas bubbles added to the system, however, is a function of the pressure and temperature. The pressure and temperature used by the simulation to define the molar density of the gas bubbles entering the system are presented as part of the bubble property grid.

When comparing simulation predictions to experimental data, users should confirm that the molar injection rate realized in the simulation matches the molar injection rate applied in the experiment. This point is particularly relevant to bubble injections, where differences in the reference pressure/density can lead to differences in molar flow (even for the same volumetric flow rate).

Initial Mass Fraction

A single impulse addition of particles into the injection geometry at a user-defined fraction of the mass of the injection geometry.

In the example below, particles are added into the child geometry with a number density that realizes a mass fraction of 0.000654. This particle addition is a one-time event that occurs at 1 second. The solid mass fraction in the child geometry, \(\phi_m\), is defined from:

\[\phi_m = \frac{m_s}{m_s + m_f}\]

where \(m_s\) is the mass of the solid particles in the child geometry and \(m_f\) is the mass of the fluid in the child geometry. The total number of particles added to the system, \(N_T\), is then defined by:

\[N_T = {\left(\frac{\phi_m \rho_f}{\rho_s + \phi_m \rho_f + \phi_m \rho_s}\right) \left(\frac{V_c}{\langle V \rangle}\right)}{}\]

where \(\rho_f\) is the density of the fluid, \(\rho_s\) is the density of the solid particles, \(V_c\) is the volume of the child geometry, and \(\langle V \rangle\) is the average volume of the particles added to the system.

This example has a mean particle diameter of 1 mm, a particle density of 1000 kg/m³, a fluid density of 1000 kg/m³, and an initial mass fraction of 0.000654. The volume of the child geometry, as computed at run time, is 0.0106 m³. The system added 13,296 particles into the child geometry to achieve the target mass fraction of 0.000654.

Download Sample File: Initial Mass Fraction

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family.

Child surface

Particles are injected along the surface of the child geometry of the particle family.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Mass Fraction

Initial mass fraction dump value.

Start Time

s | The time at which the mass fraction injection begins.

Initial Volume Fraction

A single impulse addition of particles into the injection geometry at a user-defined fraction of the volume of the injection geometry.

In this example, particles are packed into the child geometry with an initial volume fraction of 0.000654. This particle addition is a one-time event that occurs at 1 second. The volume mass fraction in the child geometry, \(\phi_v\), is defined from:

\[\phi_v = \frac{V_s}{V_s + V_f}\]

where \(V_s\) is the volume of the solid particles in the child geometry and \(V_f\) is the volume of the fluid in the child geometry. The total number of particles added to the system, \(N_T\), is then defined by:

\[N_T = \phi_v \left(\frac{V_c}{\langle V \rangle}\right)\]

Where \(V_c\) is the volume of the child geometry and \(\langle V \rangle\) is the average volume of the particles added to the system.

This example has a mean particle diameter of 1 mm and an initial mass fraction of 0.000654. The volume of the child geometry, as computed at run time, is 0.0106 m³. The system added 13,296 particles into the child geometry to achieve the target volume fraction of 0.000654.

Download Sample File: Volume Fraction

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family.

Child surface

Particles are injected along the surface of the child geometry of the particle family.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Volume Fraction

Initial volume fraction dump value.

Start Time

s | The time at which the volume fraction injection begins.

Total Mass

A single impulse addition of particles into the injection geometry in which the mass informs the total number of particles added to the system.

In this example, particles are initially packed into the child geometry with a mass of 0.005236 kg. This particle addition is a one-time event that occurs at 1 second. The total number of particles added to the system, \(N_T\), is then defined by:

\[N_T = \frac{m_s}{\rho_s \cdot \langle V \rangle}\]

Where \(m_s\) is the mass of solids added to the child geometry, \(\rho_s\) is the density of the solids, and \(\langle V \rangle\) is the average volume of the particles added to the system.

This example has a mean particle diameter of 1 mm and a mass of 0.005236 kg. The system added 10,000 particles into the child geometry to achieve the target mass.

Download Sample File: Total Mass

Injection Location

This option describes where particles will enter the system.

Child volume

Particles are injected within the volume enclosed by the child geometry of the particle family.

Child surface

Particles are injected along the surface of the child geometry of the particle family.

Boundary Condition

Particles are injected at a user-defined boundary condition.

Injection Boundary Condition

This selection identifies which inlet will inject particles into the system.

Random Background

Particles are injected uniformly across the fluid domain. For free surface models, particles will not be added to the headspace.

Total Mass Value

kg | Total mass of particle dump.

Dump Time UDF

s | This UDF defines the time at which particles are dumped into the injection location. This is a System UDF.

No Injection

The particle feed rate is not directly controlled by the user. Instead, particles are dynamically generated across the system via free-surface Eularian-Lagrangian conversion, immiscible two fluid Eularian-Lagrangian conversion, or volumetric particle generation.

Important

With this option, the user must also select an Eularian-Lagrangian conversion or volumetric particle generation in order to introduce particles into the system.

Particles created during this eularian conversion process will assume the properties specified in the property grid. The example below shows a free-surface gas-to-particle conversion with an impeller.

Download Sample File: Eularian Conversion

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