The DPM concentration is defined as:

DPM concentration = (Avg. particle mass in cell * Part resi. Time * Strength of particle) / Cell volume ...1

Strength of particle = number in parcel / dt_flow ...2a

= total particle flow rate / mass of single particle in the stream ....2b

From equation 1 and equation 2b,

DPM conc. = (Avg. particle mass in cell * Part resi. Time * Total particle flow rate) / (mass of single particle in stream * cell volume) .....3

Example:

Consider the following example to make things more clear.

a. A simple channel flow with constant velocity of 1m/s is used.

b. The top and bottom surface are defined as symmetry to ensure the plug flow condition.

c. The particles with total mass of 0.1 Kg/s and velocity of 1m/s are injected as single injection at the center of inlet.

d. This ensures that DPM concentration is non-zero only at the center line and is zero everywhere else.

A single stream of particle is modelled, hence,

Average particle mass in cell = Average mass of particles in particle stream ...4

From equations 3 and 4,

DPM conc. = Part resi. Time * Total particle flow rate / Cell volume

For the test case, Part resi. Time = 0.002 s, Total particle flow rate = 0.1 Kg/s, Cell volume = 2.08e-6 m3

DPM conc. = 0.002 * 0.1 / 2.081 e-6 = 95 Kg / m3