The Number Density Calculation feature computes the number density of particles in each mesh element of the selected domains. Optionally, it also computes the average velocity of particles in each mesh element.
The definition of the number density changes depending on which option is selected from the Particle release specification list in the physics interface
Particle Release and Propagation section.
If Specify release times (the default) is selected, then the number density of particles
Nd,p is defined as
The number multiplication factor of the ith particle
nn,i can be specified in the settings for the
Number Density Calculation node.
If the Compute average velocity check box is selected, then additional variables for the average velocity components
va (SI unit: m/s) are defined in each mesh element:
where vi (SI unit: m/s) is the particle velocity.
If Specify current is selected from the
Particle release specification list, then the particle number density is computed by integrating over time,
If the Compute average velocity check box is selected, then additional variables for the total velocity normalized by mesh element volume
vt (SI unit: 1/(m
2·s) or 1/(m·s) depending on space dimension) are defined in each mesh element:
Then the average velocity va is found by dividing by the number density,
The implicit assumption with the Specify current option is that the total flux of particles through the system is constant over time, with each model particle representing some number of real particles per unit time. Incidentally, this is why the mesh element area or volume can be included on the right-hand side of the previous equations; if the mesh elements were deforming over time, then this assumption of constant particle flux would be violated.