[mkhm]

Hi experts in fluid mechanics,

The case that I have to consider is a supersonic reactive flow.

The nozzle is designed such that the desired Mach number at the nozzle outlet is obtained in a non-reactive case. However, when the reactions are added, there is a significant amount of heat release and due to that the desired Mach number at the nozzle outlet is not reached anymore. The question is how to optimize/modify the geometry such that the cooling by expansion compensate the heat release by reactions ?

Thanks in advance,
Mary

[LuckyTran]

In a properly designed system, most of the combustion takes place (~98% of the heat release) in the entry run before the acceleration occurs in the nozzle throat. So you can just set your inlet boundary condition to be the post-combustion products and ignore the heat release. You might still want to consider chemical reactions due to various concentrations of species present and getting the right thermophysical properties, but it's typical to not have a combustion/flame model.

[mkhm]

Originally Posted by LuckyTran

In a properly designed system, most of the combustion takes place (~98% of the heat release) in the entry run before the acceleration occurs in the nozzle throat. So you can just set your inlet boundary condition to be the post-combustion products and ignore the heat release. You might still want to consider chemical reactions due to various concentrations of species present and getting the right thermophysical properties, but it's typical to not have a combustion/flame model.

LuckyTran, thanks for your answer. My question is not related to simulation settings. It's more a fundamental question. I don't have a combustion case but that would not change the nature of problem. We have some reactions in the nozzle (not before, just within the nozzle). Due to that, the specific heat ratio is changing which results in the fact that the Mach number/temperature/pressure profiles are not similar to the case without reactions. I know there are different techniques to change the geometry with respect to the heat release such that the flow field profiles are not impacted and would similar to the case without reactions. My question is which is the best method to consider ?

[LuckyTran]

Then it's not important whether or not there are any reactions. Even without reactions, the specific heat and properties would be changing anyway. Are you asking how to design a nozzle with variable thermophysical properties in general? That's the same procedure as a non-reacting case which you have already designed. Or did you already optimize the nozzle assuming constant specific heat. Then maybe you have an issue. And then I'll have to ask what exactly did you optimize for to begin with (because there's more than 1 way to design a nozzle).

[mkhm]

Originally Posted by LuckyTran

Then it's not important whether or not there are any reactions. Even without reactions, the specific heat and properties would be changing anyway. Are you asking how to design a nozzle with variable thermophysical properties in general? That's the same procedure as a non-reacting case which you have already designed. Or did you already optimize the nozzle assuming constant specific heat. Then maybe you have an issue. And then I'll have to ask what exactly did you optimize for to begin with (because there's more than 1 way to design a nozzle).

you are right when you say that even in non-reactive case, gamma can change and the question persists independently from the fact that there are reactions or not. Agree. But, lets say that the impact of heat release on the gamma is much more significant than the expansion itself. I am rather looking for a design with some kind of feedback loops where we start with a design and then we measure the heat release. Based on the amount of heat release, we change again the design and we measure again the heat release. So we keep repeating this procedure till the heat release by reactions does not change the flow fields profiles.

[LuckyTran]

The impact of the heat release is to change the temperature. If you have designed the nozzle with variable (temperature dependent) gamma then you can design a nozzle with heat release by marching from inlet to end the same way. The only contribution from CFD is it gives you the heat release and temperature field. Consider that I prescribe the heat release using some hypothetical analytical function and give you this function, you won't even need CFD anymore. It's the same procedure.

Consider also that I prescribe a Mach number profile, you can select the nozzle contour that gives this Mach number profile. The magical Mach number profile that is being targeted is the one from your non-reacting case.


Another way to think of it is to consider Instead of measuring the heat release, measure the gamma.

[aerosayan]

Originally Posted by mkhm

Hi experts in fluid mechanics,

The case that I have to consider is a supersonic reactive flow.

The nozzle is designed such that the desired Mach number at the nozzle outlet is obtained in a non-reactive case. However, when the reactions are added, there is a significant amount of heat release and due to that the desired Mach number at the nozzle outlet is not reached anymore. The question is how to optimize/modify the geometry such that the cooling by expansion compensate the heat release by reactions ?

Thanks in advance,
Mary

Disclaimer : Not an expert.


- Ensure that your mach no. at the nozzle throat is reaching 1.

- Ensure that most of the combustion happens before the nozzle throat, in the high pressure region of the combustion chamber.

[mkhm]

Originally Posted by LuckyTran

The impact of the heat release is to change the temperature. If you have designed the nozzle with variable (temperature dependent) gamma then you can design a nozzle with heat release by marching from inlet to end the same way. The only contribution from CFD is it gives you the heat release and temperature field. Consider that I prescribe the heat release using some hypothetical analytical function and give you this function, you won't even need CFD anymore. It's the same procedure.

Consider also that I prescribe a Mach number profile, you can select the nozzle contour that gives this Mach number profile. The magical Mach number profile that is being targeted is the one from your non-reacting case.


Another way to think of it is to consider Instead of measuring the heat release, measure the gamma.

Thanks for your reply.
To sum up:
First step, it would be to design the nozzle depending on the gamma parameter. The only example in my mind (if you have another example, please mention it) it is through the method of characteristics and considering the gamma variable. Something like this work:
https://pdfs.semanticscholar.org/7a4...487.1612796166
In this work, that geometry is designed bases on equation number 4.49. In this case, sigma (equation 4.23) is 0D chemistry production/consumption rates, is not it ? because otherwise with CFD calculations the Mach profile would not be the one designed by moc as it is impacted already by the heat release.

[mkhm]

Originally Posted by aerosayan

Disclaimer : Not an expert.


- Ensure that your mach no. at the nozzle throat is reaching 1.

- Ensure that most of the combustion happens before the nozzle throat, in the high pressure region of the combustion chamber.

My case is not combustion related chemistry and the chemical reactions must occur within the nozzle.