H2/O2 explosion limit

[f.augus...@gmail.com]

Hi all,

I'm using Cantera 2.5.1 in Python on Windows 10.  

I'm trying to estimate the explosion limit for a stoichiometric H2-O2 mixture using GRI 3.0, as in the paper Explosion limits of H2/CH4/O2 mixtures: Analyticity and dominant kinetics by Liang et. al (2019) [1]. The goal is to obtain the Z-shape explosion limit containing all three explosion limits. The model used is a constant volume, adiabatic with radical destruction at the wall and the explosion criterion is a 50K temperature increment within 10 seconds. 

My problem lays on the addition of the radical destruction at the wall. In the literature, these reactions are usually expressed as R => wall destruction, where R is a radical such as H, OH, O, and so on. According to [2], in the gas phase, the wall reactions should impact the production rate of certain specie as a first order term written as k_R*[R]. How can I add these kind of reactions to the mechanism when they seem to not conserve matter? I think surface reactions might be the answer but I am not sure how the surface reactions affect the gas phase. 

I tried adding surface reaction, similar to the surf_pfr.py example (https://cantera.org/examples/python/reactors/surf_pfr.py.html). I added the reactions "H + Pt(s) => H(s)" and "HO2 + Pt(s) => HO2(s)" because the destruction of H and HO2 at the wall are the most important reactions for the explosion limit of hydrogen. However, I do know which Pt concentration or sites density I should consider. As I understand, the Pt concentration should not even have an effect on the production rate of H and HO2 as the wall reaction influence should just be k_OH*[OH] and k_HO2*[HO2]. 

I'd really appreciate any help. Thank you all

Kind regards,

Felipe

[1] Explosion limits of H2/CH4/O2 mixtures: Analyticity and dominant kinetics

[2] Explosion limits of hydrogen-oxygen mixtures from nonequilibrium critical points

[Bryan Weber]

Hi Felipe,

I don't think you need to use surface reactions here. If you have an Arrhenius rate for k, then you can create dummy species for the "adsorbed" gas phase species. I would copy-and-paste the definition of any relevant species and give them a new name, something like:

species:

- name: OH

  elements: {O: 1, H:1}

  ...

- name: OH-wall

  elements: {O:1 H:1}

  ...

Then you can add a reaction that converts OH -> OH-wall, and since there are no reactions that consume OH-wall, it will effectively be a sink for the radicals. Moreover, since the enthalpy of the two species will be the same, there won't be any energy released or absorbed by the reaction.

Best,

Bryan

[Felipe Gomes]

Hi Bryan,

Your suggestion worked perfectly! Thank you so much! I was able to replicated the results of the paper pretty much perfectly.

Kind regards,

Felipe

[nikhil verma]

Hello  Felipe and Bryan,

I have been trying to replicate the Z curve for Hydrogen Oxygen Mixture. As suggested by Bryan, I have included dummy species to serve as a sink for the radicals. I am facing issue with defining the reaction. The rate constant for the reaction is given by,

where,

In the above rate equation, v is only the function of Temperature. I have tried to rewrite the reaction as,

Then, I have defined the reaction in Cantera as,

R1 = ct.Reaction({"H": 1}, {"H_w": 1}, ct.ArrheniusRate(A1, 0.5, 0))
gas.add_reaction(R1)

Where, A1 is the first part of tern on the right hand side and b is taken as 0.5, and Activation energy is taken as 0. I am able to get the same trend qualitatively as given in the paper [1]. However, the graphs are elongated. I suspect the error, as how I have defined the reaction.

Can you please give me your valuable feedback, on how to define a reaction with non Arrhenius rate law. 

[1] Explosion limits of H2/CH4/O2 mixtures: Analyticity and dominant kinetics

Regards,

Nikhil 

[nikhil verma]

Any updates on this?

[Felipe Gomes]

Hi Nikhil,

Sorry for the late reply. 

First,  I'd recommend you to first try to replicate using the same mechanism, results will change for different mechanism as the paper shows. I'd recommend to replicate the GRI 3.0 results since GRI is a much lighter than AramcoMech 2.0. 

I believe that the equation of k_wall is wrong it should be k = 1/4*epsilon*v*S/V. 

Regarding some inconsistent results around the 1st explosion limit,  I think I had a similar problem at some point and it I remember solving  this by simply reducing the max_time_step of the ReactorNet object. I usually set the max_time_step as a fraction of the simulation 'endtime', something like:

endtime = 20 # [s]

r = ct.Reactor(gas)

sim = ct.ReactorNet([r])

sim.max_time_step = endtime/2000 # this ensures that the simulation takes at least 2000 times steps 

t = 0

while t < endtime:
     dt = sim.step() - t
      t += dt    

Hopefully this helps