Calculation of Ignition Delay Time

[Vaibhav Singh]

Hi,
I am calculating the Ignition Delay time using two approach -
1. using max gradient of Temperature (dT/dt)

2. using max gradient of OH species (dOH/dt)

When I am simulating the results, I am not getting the same result from both the methods. I believe that the IDT from both the methods should be same. I am used different mechanism to validate the IDT, but every time I am getting different IDT curve for both the methods.

I want to ask whether my assumption of same IDT is correct or not? If yes, than why I am getting different result ? 
Can anyone help in this?

Thanks

[Steven DeCaluwe]

Hi Vaibhav,

No, I would not assume that the two methods give the same IDT.   The max temperature gradient is a function of the enthalpy of reaction times the rate of progress for each reaction at a given time and the average specific heat at that time.  The OH species formation is just one of many species being formed (though it is a key intermediate in the combustion mechanism).  There is no guarantee that the two gradients will be maximized at the exact same time. 

This is slightly outside my field, but my memory is that there are yet other metrics for IDT, which may be more standard.  Happy to hear from others on this, but the short answer is definitely “No, I would not expect them to be the same.”

Best regards,

Steven

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[Vaibhav Singh]

Thanks for the reply Steven. 

Can you please share any paper or example in which the IDT values differ for the two cases? 

Best Regards,

Vaibhav

[Richard West]

Hi,

Even the IDT derived from tracking OH can be different from that derived from tracking excited OH* - as presented just yesterday at the combustion symposium:

https://doi.org/10.1016/j.proci.2024.105286

But certainly the IDT derived from pressure rise or temperature rise could well be different from that derived from OH or OH*. 

And the differences can be fuel- and condition-dependent. 

Best,

Richard

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[Steven DeCaluwe]

Hi Vaibhav,

You can likely look at some of the seminal work in this field for this information (I have a vague sense that Ron Hansen’s group at Stanford has some nice work here that shows what you are looking for). Beyond that, I regretfully must decline your request -- combustion is not my field and I don’t have time to dive into the literature on it.

But I don’t know why one would expect them to be the same.  They are two separate events, both correlated with the speed of ignition.  It’s like if someone at the olympics this month wanted to measure a runner’s 100 meter dash speed, and compared the time at which their right knee crossed the finish line vs. when their right foot crossed.  Separate events, both tightly coupled via the runner’s speed, but separate nonetheless.  The IDT is perhaps more complex that there is no definitive “correct” metric (vs the 100m dash).

The theory (i.e. the simulation) backs this up, as my reply yesterday explains. Off the top of my head, the equations can be written as:

1. Rate of temp change  dT/dt = sum(qdot_i*delta_h_i)/(C_p*rho). Where qdot_i is the rate of progress for reaction i (mol-rxn/m3/s), delta_h_i is enthalpy change of reaction (kJ/mol-rxn), and C_p is the (composition- and temperature-dependent) specific heat (kJ/kg-K) and rho the mass density (kg/m3) at time t.

2. Rate of OH concentration change d(OH)/dt = sum(qdot_i*nu_OH_i) Where nu_OH_i is the net stoichiometric coefficient for OH for reaction i. 

Both generally scale with the speed of reactions qdot_i, but there is nothing in the theory that would suggest the two would be maximized at exactly the same time, unless either the qdot or the delta_h for the OH producing reactions are sufficiently large to dominate over those from all other reactions (or I suppose if Cp of OH was much lower than the average Cp at other times during the reaction).

Best regards,

Steven

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[Bryan Weber]

Hi Vaibhav,

I feel I have to weigh in here, as a former expert in this field :) Like Steven and Richard, I question why you are assuming that these should give you the same result and I'd challenge you to provide literature sources that show they should be the same. From my recollection of about 10 years ago, there were at least 5 separate methods of measuring IDT, depending on the experiment that was used to validate the model:

1. Maximum pressure gradient (dP/dt)

2. Maximum temperature gradient (dT/dt)

3. Maximum OH gradient (d[OH]/dt)

4. Maximum excited OH gradient (d[OH*]/dt)

5. Extrapolate the maximum OH or OH* gradient back to the baseline

In particular, the chemistry of OH* is usually not included in models, but OH* is used for experimental measurements, so there's already an assumption when validating models that OH and OH* are peaking at the same time, which as Richard pointed out may not be correct.

Relatedly, I wonder by how much are these times differing, as a percentage? For example, you can subtract the two values and divide the difference by the smaller of the two. If that is less than (just a guess) say 10% or 5% you are probably well within the uncertainty you'd expect from the uncertainty in the kinetics parameters for OH production, depending on which mechanism you're using and which fuel you're using. By the way, this method of calculating the % difference (linearly) should be fine for small differences but if the differences are larger (order of 50-100%) you may be better off using a logarithmic ratio since IDT varies logarithmically.

Finally, there is also the possibility that you've made a mistake in your calculation, but you did not provide a script or other information to know how you're doing the calculation. If you provide that, perhaps someone could provide some feedback on your methodology.

Best,

Bryan

[Vaibhav Singh]

Thanks, Richard, for this insight. I will look into this.

Regards,

Vaibhav

[Vaibhav Singh]

Thank you, Steven, for the explanation. Also, I will conduct a more thorough literature review on this.

 Regards,

Vaibhav

[Vaibhav Singh]

Hi Bryan,

Thank you for weighing in with your insights. Your points are very well taken, and I appreciate your detailed breakdown of the different methods for measuring ignition delay time (IDT). The differences you mentioned in measurement methods are indeed crucial and can significantly impact the results.

To address your queries and suggestions:

1. Literature Reference: I understand the need for a solid reference to support my approach. There is a relevant point mentioned in the paper Predicting ignition delay times of C1-C3 alkanes/hydrogen blends at gas engine conditions by Kalyan Kuppa, Andreas Goldmann, and Friedrich Dinkelacker. The paper states: "The definition of ignition delay depends on the criteria defined. The criteria could be the maximum temperature gradient, maximum concentration (OH, CH), or maximum total heat release rate. The ignition delay provided by most criteria are almost identical" .

2. Percentage Difference: I agree that calculating the percentage difference between the IDT values could provide valuable insight into the extent of the discrepancy. I will calculate the difference and see if it falls within the expected uncertainty range.

3. Calculation Methodology: I am sharing the python script and methodology used for the calculation to ensure there are no errors and to receive feedback on improving it. I am using the "gri30" mechanism for the faster simulation.

Your suggestion about using a logarithmic ratio for larger differences is also noted and seems like a sound approach.

Thank you once again for your valuable input. I will incorporate these considerations and share the results for further feedback.

Best regards, 

Vaibhav