# Residence Time Distribution¶

Goal: Predict residence time distribution and minimum time of flight

Simulation Particulars

4.7 m tall x 2.4 m diameter air filled tank

Single 0.33 m inlet on side

Single 0.25 m outlet on top

5 m/s inlet velocity

1 atm outlet pressure

Modeling Approach

Inject tracer particles into the inlet stream beginning at simulation time 10.0 seconds and ending at simulation time 10.1 seconds. We wait 10 seconds before injection to ensure that this system has reached steady state. The 0.1 second duration is small compared to the system time scale, such that the injection represents a tracer spike.

System resolution: 100 lattice points (dx=0.024 m)

Inlet ramp time: 2 seconds

Particle diameter/specific gravity: 0/0 (to make scalar particles)

DataOutputInterval and SliceOutputInterval: 0.01 s and 0.1 s

Data Collection

The solver automatically generates exitAgeList.dat files upon particles exiting the outlet. This file is a cumulative list of the particleID, particle age, and originID of each particle that exits the tank; this is all the data required to calculate RTD and minimum time-of-flight.

Data Analysis/Results

The minimum time of flight is represented by the first particle to exit the system—the particle in the exitAgeList with the lowest age. The residence time distribution is defined as the histogram of all the exit ages, which can be calculated in Excel or Matlab. For this system, the minimum time of flight is 1.61 s. Until 35 seconds, the effects of plug flow and fluid bypassing are prevalent. After this time period, the reactor behaves as an ideal stirred tank with a mean residence time of 34.5 s. This configuration is suboptimal; 45% of the injected chemistry exits before becoming well stirred.