PaSR

Partially Stirred Reactor using Cantera for validating mixing models.

1. Dependencies

cantera >= 2.5
mlpack, networkx
yaml, numpy, scipy, matplotlib

2. Usage

### Typical input file (this example is in "inputs/KerM01.yaml")
# Input parameters for PaSR simulation.
case: non-premixed
mech: "mech/h2_sandiego.yaml"
mixing model: "KerM"
sigma_k: 0.1
number of particles: 1000
temperature: 300.0
pressure: 1.0
equivalence ratio: 1.0
residence time: 2.e-3
mixing time: 0.7e-3
number of residence times: 5
fuel:
  H2: 1.0
  N2: 1.0
oxidizer:
  O2: 0.21
  N2: 0.79

### Run PaSR simulation
# specify input by `--input`, output by `--output`
python PaSR_main.py --input inputs/KerM01.yaml --output data/KerM01.npy --doplot
# which can be written in short as
python PaSR_main.py -i inputs/KerM01.yaml -p

• PaSR simulation results of H2/N2-Air mixture, with IEM, MC and EMST as mixing model.

  

• PaSR simulation results of H2/N2-Air mixture, with KerM as mixing model of different kernel sizes.

  

3. Implementation details

3.1 EMST variance decay

The mixing happens on the edges of EMST tree, with:

The parameter controls the variance decay rate. Denoting, then from time to , one has:

And by variance decay rule of micro-mixing model:

Thus, following the variance decay rule, we need to let satisfy the equation

In general, ,, . To get at least one real number solution, one need:

Once is selected, the mixing ratio is hence to be:

For multiple scalars, single could not lead to target variance decay for all scalars. So a root finding technique is employed to estimate best .

Typically, the root finding process converges in 2-3 loops.

4. References

• Mixing Model paper

  Z. Ren, S.B. Pope, An investigation of the performance of turbulent mixing models, Combust. Flame 136 (2004) 208-216.

• EMST paper

  S. Subramaniam, S.B. Pope, A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees, Combust. Flame 115 (1998) 487-514.

• EMST code

  https://tcg.mae.cornell.edu/emst/

• PaSR code

  https://github.com/SLACKHA/pyJac/blob/master/pyjac/functional_tester/partially_stirred_reactor.py