Maximum pressure for a combustion chamber

Greetings All!

I am not sure if this is the correct place to post this, but I think that since rocket fuel is considered a chemical reaction, this sections seems appropriate. Right, to the topic. Me and my team from the spaceflight society are looking forward to building a hybrid rocket fuelled by paraffin wax. I was tasked with making equations for safe dimensions for the combustion chamber and specially finding the maximum pressure our combustion chamber can withstand. I have searched through articles, journals, documents and I barely found something that explains how the pressure of the nozzle is calculated, but no go with the chamber. I have found some equations for pressurised vessels, but I really think those equations are not the ones I am looking for, so I really don't even know where to start :S

Any help is appreciated, and if someone has a link to a journal or document that explains how to actually build a combustion chamber, it would be heaven-sent.
 

berkeman

Mentor
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Greetings All!

I am not sure if this is the correct place to post this, but I think that since rocket fuel is considered a chemical reaction, this sections seems appropriate. Right, to the topic. Me and my team from the spaceflight society are looking forward to building a hybrid rocket fuelled by paraffin wax. I was tasked with making equations for safe dimensions for the combustion chamber and specially finding the maximum pressure our combustion chamber can withstand. I have searched through articles, journals, documents and I barely found something that explains how the pressure of the nozzle is calculated, but no go with the chamber. I have found some equations for pressurised vessels, but I really think those equations are not the ones I am looking for, so I really don't even know where to start :S

Any help is appreciated, and if someone has a link to a journal or document that explains how to actually build a combustion chamber, it would be heaven-sent.
Welcome to the PF.

Can you post links to what you have found so far? What do you know so far about the yield stress of different metals and alloys?
 
Welcome to the PF.

Can you post links to what you have found so far? What do you know so far about the yield stress of different metals and alloys?
Sure :)

https://physics.stackexchange.com/questions/35238/how-thick-does-steel-have-to-be-to-be-able-to-withstand-300-bar-sphere
I found this quite useful, however, it relates to a sphere, not a cylinder. Also the "If you plan to use this information in any real life project, be extremely careful with what you do" really makes me think twice about using this method, since we only get one shot at this each year.

https://www.slideshare.net/KJSavaliya/design-of-pressure-vessel
It gives designs, but im not looking for complex designs, but equations that work on my design.

https://link.springer.com/chapter/10.1007/978-94-017-2774-7_41
I understood this chapter gave insight to how can a pressure vessel fail either by yielding or cracking, however no mention of melting due to the heat.

https://physics.stackexchange.com/questions/196789/how-do-i-calculate-the-maximum-pressure-a-container-can-withhold
This seemed to be the closest I could get to an answer, but I only understood half of it and this answer does not account for fracture.

Fundamentals of Hybrid Rocket Combustion and Propulsion. A book I managed to read online through my University. Sadly, it is too complex and I cant find something related to finding the maximum pressure of a combustion chamber based on its dimensions. The book in many sections already assumes we know the pressure. I also read Design and Test Planning for a 250 KLBF Thrust Hybrid Rocket Motor, but this paper also assumes that the maximum pressure its already known. eg. Page 5. "... the motor pressure ramps smoothly up to a maximum pressure of 950 psig"

In my knowledge, yield stress is the maximum amount of stress a material can take before turning plastic, meaning, before it ruptures and it is unable to go back to its original shape. It also means that it is the stress in which the relationship between the stress and the strain stops being linear. The yield stress is different in every material due to Young's Modulus.

Back to the topic, my main concern is that there are multiple sources that talk about a similar procedure (a chamber that has fuel on it), but I cant figure out which one to use or how to even use it (its frustrating!). There are so many methods and all I want is equation that yields the maximum pressure that it would theoretically sustain based on the material of the container (steel in our case) the thickness of it and its dimensions. I know that Young's modulus will help with the material, but so far I have not found an equation that uses it.
 
Welcome to the PF.

Can you post links to what you have found so far? What do you know so far about the yield stress of different metals and alloys?
Also, thank you for the warm welcome and for your aid! :D
 

Tom.G

Science Advisor
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You realize what you are trying to do is extremely dangerous and that it would be irresponsible for us to try to help you with this.
 

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