### 16.3.2. Particle Field Variables

Particle field variables are particle variables that are defined at the vertices of the fluid calculation. In contrast to track variables, these variables can be used in the same way as “standard” Eulerian variables. This means that particle field variables are available for use in CEL expressions and User Fortran, they can be monitored during a simulation, and are available for general post-processing in CFD-Post. Additionally, particle field variables can be used in the same way as particle track variables as input to particle User Fortran and for coloring tracks. When used for coloring tracks, the field variables have to be interpolated onto the tracks, and so this operation will be slower than coloring with a track variable.

The following particle variables are available as field variables:

#### 16.3.2.1. Particle Sources into the Coupled Fluid Phase

For fully-coupled particle simulations involving energy, momentum and mass transfer to the fluid phase, the following variables are written to the results file:

Long Variable Name | Short Variable Name | Units | Availability
--- | --- | --- | ---
Particle Energy Source | ptenysrc | [W m^-3] | 2 A, C, M, P, R
Particle Energy Source Coefficient | ptenysrcc | [W m^-3 K^-1] | 2 A, C, M, P, R
Particle Momentum Source | ptmomsrc | [kg m^-2 s^-2] | 2 A, C, M, P, R
Particle Momentum Source Coefficient | ptmomsrcc | [kg m^-3 s^-1] | 2 A, C, M, P, R
Total Particle Mass Source | ptmassrctot | [kg s^-1 m^-3] | 2 A, C, M, P, R
Total Particle Mass Source Coefficient | ptmassrcctot | [kg s^-1 m^-3] | 2 A, C, M, P, R
For multi-component mass transfer, the following Additional Variables are available [a]:
Particle Mass Source | ptmassrc | [kg s^-1 m^-3] | 2 A, C, M, P, R
Particle Mass Source Coefficient | ptmassrcc | [kg s^-1 m^-3] | 2 A, C, M, P, R
[a] The variables for multi-component take the following form: <Particle Type>.<Particle Component>.<Variable Name>

Particle source terms are accumulated along the path of a particle through a control volume and stored at the corresponding vertex. A smoothing procedure can be applied to the particle source terms, which may help with convergence or grid independence. For details, see Particle Source Smoothing in the CFX-Solver Modeling Guide.

#### 16.3.2.2. Particle Radiation Variables

Long Variable Name | Short Variable Name | Units | Availability
--- | --- | --- | ---
Particle Radiative Emission | ptremiss | [W m^-3] | 2 A, C, M, P, R
Particle Absorption Coefficient | ptabscoef | [m^-1] | 2 A, C, M, P, R

Particles can also interact with the radiation field and either emit or absorb radiation.

#### 16.3.2.3. Particle Vertex Variables

By default, particle vertex variables are not written to the results file, except for the `Averaged Volume Fraction`. The other vertex variables can be written to the results file if they are selected from the Extra Output Variables List in the Output Control section of CFX-Pre or if they are used in a monitor point, CEL expression or in (Particle) User Fortran.

The following particle variables are available:

Long Variable Name | Short Variable Name | Units | Availability
--- | --- | --- | ---
Averaged Velocity | averaged vel | [m s^-1] | 1 A, C, M, P, PR, R
Averaged Volume Fraction | vfpt | [ ] | 1 A, C, M, P, PR, R
Averaged Temperature | averaged temperature | [K] | 1 A, C, M, P, PR, R
Averaged Mass Fraction [a] | averaged mf | [ ] | 1 A, C, M, P, PR, R
Averaged Particle Time | averaged pttime | [s] | 2 A, C, M, P, PR, R
Averaged Mean Particle Diameter (D43) | averaged mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Arithmetic Mean Particle Diameter (D10) | averaged arithmetic mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Surface Mean Particle Diameter (D20) | averaged surface mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Volume Mean Particle Diameter (D30) | averaged volume mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Sauter Mean Particle Diameter (D32) | averaged sauter mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Mass Mean Particle Diameter (D43) | averaged mass mean particle diameter | [m] | 2 A, C, M, P, PR, R
Averaged Particle Number Rate | averaged particle number rate | [s^-1] | 2 A, C, M, P, PR, R
For simulations with the particle wall film model activated, the following additional vertex variables are available:
Averaged Volume Fraction Wall | vfptw | [ ] | 1 A, C, M, P, PR, R
Averaged Film Temperature | averaged film temperature | [K] | 1 A, C, M, P, PR, R
[a] This variable takes the following form: <Particle Type>.<Particle Component>.<Variable Name>

The following are the formulae for particle vertex fields' size distributions:

Arithmetic Mean Diameter |
Surface Mean Diameter |
Volume Mean Diameter |
Sauter Mean Diameter |
Mass Mean Diameter |

##### 16.3.2.3.1. Variable Calculations

Particle vertex variables are calculated using the following averaging procedure:

| (16–1)

With:

- : Sum over all particles and time steps in a control volume

- : Particle integration time step

- : Particle number rate

- : Particle mass

- : Particle quantity

Slightly different averaging procedures apply to particle temperature and particle mass fractions:

Averaged Particle Temperature

| (16–2)

With:

Averaged Mass Fraction

- : Particle specific heat capacity

- : Particle temperature

| (16–3)

With:

- : Mass of species `c` in the particle

Due to the discrete nature of particles, vertex variables may show an unsmooth spatial distribution, which may lead to robustness problems. To reduce possible problems a smoothing option is available. For details, see Vertex Variable Smoothing in the CFX-Solver Modeling Guide.

#### 16.3.2.4. Particle Boundary Vertex Variables

Particle-boundary vertex variables are particle variables that are defined on the vertices of domain boundaries. They are normalized with the face area of the corresponding boundary control volume.

You can use these variables to color boundaries and to compute average or integrated values of the corresponding particle quantities.

You cannot use these variables in CEL expressions or User Fortran, and you cannot monitor them during a simulation.

Long Variable Name | Units | Availability
--- | --- | ---
Available at inlet, outlet, openings and interfaces:
Mass Flow Density | [kg m^-2 s^-1] | 2 B, R
Momentum Flow Density | [kg m^-1 s^-2] | 2 B, R
Energy Flow Density | [kg s^-3] | 2 B, R
Available at walls only:
Wall Stress | [kg m^-1 s^-2] | 2 B, R
Wall Energy Flow Density | [kg s^-3] | 2 B, R
Wall Mass Flow Density | [kg m^-2 s^-1] | 2 B, R
Erosion Rate Density | [kg m^-2 s^-1] | 2 B, R
Available in transient runs:
Time Integrated Mass Flow Density | [kg m^-2] | 2 B, R
Time Integrated Momentum Flow Density | [kg m^-1 s^-1] |
Time Integrated Energy Flow Density | [kg s^-2] | 2 B, R
Time Integrated Wall Energy Flow Density | [kg s^-2] | 2 B, R
Time Integrated Wall Mass Flow Density | [kg m^-2] | 2 B, R
Time Integrated Erosion Rate Density | [kg m^-2] | 2 B, R

#### 16.3.2.5. Particle RMS Variables

For some applications, it may be necessary to not only provide the mean values of particle quantities, but also their standard deviation in the form of particle RMS variables. Similar to particle vertex variables, these variables are also defined at the vertices of the fluid calculation. Particle RMS variables are available for use in CEL expressions and User Fortran; they can be monitored during a simulation, and are available for general postprocessing in CFD-Post. Additionally, particle RMS variables can be used in the same way as particle track variables as input to particle User Fortran and for coloring tracks.

By default, particle RMS variables are not written to the results file; unless, they have been explicitly requested by you (selected from the Extra Output Variables List in the Output Control section of CFX-Pre, usage in a CEL expression or in User Fortran) or if the stochastic particle collision model is used in a simulation.

The following particle variables are available as field variables, particularly useful for simulations that use the stochastic particle collision model:

Long Variable Name | Short Variable Name | Units | Availability
--- | --- | --- | ---
RMS Velocity | rms velocity | [m s^-1] | 1 A, C, M, P, PR, R
RMS Temperature | rms temperature | [K] | 1 A, C, M, P, PR, R
RMS Mean Particle Diameter | rms mean particle diameter | [m] | 3 A, C, M, P, PR, R
RMS Particle Number Rate | rms particle number rate | [s^-1] | 3 A, C, M, P, PR, R

##### 16.3.2.5.1. Variable Calculations

Particle RMS variables are calculated using the following procedure:

| (16–4)

With:

- : Instantaneous particle quantity

- : Average particle quantity

- : Fluctuating particle quantity

- : Average of square of particle quantity

- : Square of average of particle quantity

A smoothing option, as available for particle vertex variables, is available for particle RMS variables. For details, see Vertex Variable Smoothing in the CFX-Solver Modeling Guide.

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