How to model ignition for constant volume combustion processes ??

[Aditya Karanam]

Dear All,

I need some help with a constant volume combustion simulation that I am trying to do. First of all, I am using Cantera 2.2.0 through the 'New-Python' interface. Here is the problem that I am trying to solve:

I have a constant volume vessel with adiabatic walls and filled with an initial mixture containing 10% H2, 20% O2 and 70% N2 (by mol) at initial temperature of 300K and initial pressure of 1atm. I want to ignite this mixture at t=to and study the transient major and minor species profiles as well as temperature and pressure variation. Obviously, at 300K and 1atm, the mixture will not self ignite and therefore an igniter is definitely required. I used the igniter given in one of the examples that comes with Cantera. Here is the script that I used:

###################################

import math

import csv

import cantera as ct

gas = ct.Solution('gri30.cti')

gas.TPX = 300.0, 101325, 'H2:0.1, O2:0.2, N2:0.7'

combustor = ct.IdealGasReactor(gas)

combustor.volume = 1.0

gas.TPX = 300.0, ct.one_atm, 'H:1.0'        #Pure H radicals used as an ignition source

igniter = ct.Reservoir(gas)

fwhm = 0.2                        #full width at half maximum for Gaussian pulse

amplitude = 0.1                 #amplitude of Gaussian pulse

t0 = 1.0

igniter_mdot = lambda t: amplitude * math.exp(-(t-t0)**2 * 4 * math.log(2) / fwhm**2)        #Taken from one of the examples that comes with Cantera

m3 = ct.MassFlowController(igniter, combustor, mdot=igniter_mdot)

sim = ct.ReactorNet([combustor])

tnow = 0.0

tfinal = 5.0

while tnow < tfinal:

tnow = sim.step(tfinal)

print tnow, combustor.T, combustor.thermo.P     

####################################

The problem that I am facing is that I am unable to get a solution which is independent of the igniter parameters. For example when amplitude=0.1 is used, the temperature and pressure does not raise at all; on the other hand when amplitude =0.5 is used, the temperature rises to >4000K which is also unrealistic. Same problem exists with the fwhm parameter also. 

How do I model the igniter which gives reliable solutions? Is the above mentioned the only way of modeling ignition in constant volume processes or is there a better and more robust way of doing this?

Any help on this will be highly appreciated.

Thanks in advance.  

[Nick Curtis]

There is no realistic way to model ignition in a zero-D system, where the concept of a 'spark' simply can't exist.
Sending in a radical H stream will influence the final state of the solution pretty much no matter what.

For a flow reactor, you can typically get good results by initializing the reactor to the HP equilibrium state of the mixture, but I'm not really aware of a good way to do that in a closed reactor.
Typically the ignition delays, etc. that people report for ConV simulations assume a starting temperature of 600+ K

Nick

[Alan Kong]

Hi Aditya

I did a similar simulation with the constant pressure vessel. What I observe is that you need to input enough radical to get the temperature to raise to the ignition temp of methane for it the ignite but the amount cannot be too much until it increase the temp too much.

Likewise, having a igniter of radical will change the chemistry of the system. Pathways, in the case of those involved with H may become activated by the higher concentration of H radical and you may get species that should not be present .

A usual guide is to compute your adiabatic temp and the final steady state temp should be near that. I am not sure about the adiabatic walls, if u have a constant volume and adiabatic wall and ignite the content, the Pressure should just keep rising since there is not heat loss.

If I were you, I will do a simulation case with 600K intiial temperature and let it autoignite and do another case with 300K initial temperature + igniter and try to compare the reaction path diagram at a choosing temp say 1000K-1200K where the ignition just started. You will definitely notice some difference in the reaction pathways but much of the major pathways are similar. 

Cheers

Alan

[Aditya Karanam]

Hi Alan/Nick, Thanks for your responses.

Alan, your suggestions have definitely provided a very good lead to me. If I understand correctly, I calculated the adiabatic flame temperature using the equilibrate('UV') function and obtained ~1340K. So now I have to tune my H radicals in the igniter (by some trial and error maybe...) so that the kinetics simulations end up with a steady-state temperature of ~1340K ? The only concern that I have is  with the underlying assumption that the steady state conditions are equivalent  to the equilibrium conditions (which theoretically happens only as t tends to infinity). Kindly suggest and correct me if I am mistaken.

Also could you please elaborate a little on the comparison of the reaction pathways between the self and forced ignition cases. I could not understand what you meant by ''compare the reaction path diagram at a choosing temp say 1000K-1200K where the ignition just started".

Can you send me a script that you used for the constant pressure case (if possible...). I will try to modify from that. This will be really helpful !

Thanks and best regards,

Aditya.