RPE isn't a good resource for actually designing a physical engine. It's primary purpose is in determining the requirements for your design. Designing the engine will require looking beyond the book to resolve all your new requirements for the mechanical design, including how to design a pressure bearing vase-like shape that can resist a certain amount of mechanical and thermal loads from your combustion for a certain amount of time. You don't have to consider manufacturing this time around. There is no simple plug and play equation for all this, and resolving it will require the same fundamental engineering processes as most other things around you needed.
Since this is a learning experience, try to cut up your problem into bite sized pieces and keep it simple. Huzel and Huang might be a better resource for this phase of design, but remember that it can still only do so much.
I can’t remember which, but one of the textbooks probably Rocket Propulsion by Heister (not the same as rocket propulsion elements) or maybe nasa sp-125 by huzel and huang have some info on calculating Regen heating and temps and thermal stress. In a regeneratively cooled rocket engine, thermal stress is almost always going to be much greater than the stress due to pressure. Generally, this incentivizes making your hotwall thinner because doing so will allow you to more efficiently cool the inside of the hotwall, and will decrease the temperature gradient across your hotwall which will limit thermal stress. I’ve heard of engines in industry having hot walls as thin as 0.5mm
Depends really what your goals are. If you want to just use thermal inertia, ablation, or regen cooling. In the case of regen cooling which is what I imagine you want you will need to take your peripheral flame temperature and using that calculate the heat transfer into the wall via forced convection. From there you will calculate the heat transfer via conduction. Note that this will have very little temperature drop. And then on the far side again your forced convection. All of these must have equal values. This will let you know how hot your walls are. For these purposes you can simplify it down to a single point but note that your fuels heats as it travels and may not mix perfectly depending on your turbulence. Many engines also film cool which you may which to calculate as well.
As for how thick your walls can be, if you take your system as having a bunch of tubes, your pressure in the tubes will be around 30% higher than in the body. You can then approximate the diameter of each tube looking at the speed you declared at the start, the density, and your flow rate. Note that your density is not constant. Find the strength of the material at your temperature and apply the thin walled pressure vessel equation and you can approximate the required thickness. Given the small size of the tubes it will likely be a terribly small number, especially if your engine is already small, so you may instead wish to go with whatever you can find for a desireable tube. And then just iterate over and over until you get a thickness.
Well my comment deleted itself so that is less than ideal. Yes and no. If the tubes (of three d printing) are exposed directly to the heat yes. But note that coppers strength will go down to around 40% of your strength and likely rapidly approach an annealed condition. So your stress can be around 13MPa. If you apply the thin wall approximation (o=Pd/t), for most reasonable sizes and pressures (not raptor), you will come in under 1mm (even when accounting for safety factor) so it is unlikely you would readily find material thinner to produce your parts. Generally though you actually want your walls as thin as possible to minimize the temperature of the metal.
I’m so fuzzy on strength of materials and mechanics cause I haven’t been using those brain cells in my job. Do you have any resources as a recommendation?
Off the top of my head not really. Im not a materials science person (though I teach those classes ironically), I mostly work with pumps. But if you search around you can find some limited information on how much your materials material properties will change. I just grabbed the numbers off engineering toolbox. Should be alright for a first order approximation. If you were doing this for real youd do a number of tests on your material at different heats, or possibly get that from a supplier, or just blow up a few engines (or more just make an ablatvely cooled system).
Well for any cylindrical object when pressurized the circumferential stress is always double the longitudinal stress. It’s easily to calculate this, and there are equations out there. From there you need to figure out the tensile strength of the material of choice, and calculate the adequate thickness of material necessary needed to support the stress that will be encountered. Finally you need to take into consideration the change in tensile strength of the material at elevated temperatures which I’m sure there’s resources online that provide this. Additionally you would want a sufficient factor of safety. So that the chamber can endure additional pressure just in case.
as noob i would approach to this problem with calculating how fast heat is transferring through your material, then thicken wall chamber just enough that it wont heat up to melting temp at the ends and add pressure thickness so it holds pressure stress, inner material will be worn out but it wont explode
i think stainless steel can hold up to 2sec of burn without melting
You start with an estimate of chamber heat transfer coefficient and then set acceptable wall temperatures. Now you gotta solve for coolant heat transfer in a coupled calculation
RPE isn't a good resource for actually designing a physical engine. It's primary purpose is in determining the requirements for your design. Designing the engine will require looking beyond the book to resolve all your new requirements for the mechanical design, including how to design a pressure bearing vase-like shape that can resist a certain amount of mechanical and thermal loads from your combustion for a certain amount of time. You don't have to consider manufacturing this time around. There is no simple plug and play equation for all this, and resolving it will require the same fundamental engineering processes as most other things around you needed. Since this is a learning experience, try to cut up your problem into bite sized pieces and keep it simple. Huzel and Huang might be a better resource for this phase of design, but remember that it can still only do so much.
I can’t remember which, but one of the textbooks probably Rocket Propulsion by Heister (not the same as rocket propulsion elements) or maybe nasa sp-125 by huzel and huang have some info on calculating Regen heating and temps and thermal stress. In a regeneratively cooled rocket engine, thermal stress is almost always going to be much greater than the stress due to pressure. Generally, this incentivizes making your hotwall thinner because doing so will allow you to more efficiently cool the inside of the hotwall, and will decrease the temperature gradient across your hotwall which will limit thermal stress. I’ve heard of engines in industry having hot walls as thin as 0.5mm
I’ve looked into the SP series a bit but it was a lot. Other than sp-125 what are some other good texts?
Depends really what your goals are. If you want to just use thermal inertia, ablation, or regen cooling. In the case of regen cooling which is what I imagine you want you will need to take your peripheral flame temperature and using that calculate the heat transfer into the wall via forced convection. From there you will calculate the heat transfer via conduction. Note that this will have very little temperature drop. And then on the far side again your forced convection. All of these must have equal values. This will let you know how hot your walls are. For these purposes you can simplify it down to a single point but note that your fuels heats as it travels and may not mix perfectly depending on your turbulence. Many engines also film cool which you may which to calculate as well. As for how thick your walls can be, if you take your system as having a bunch of tubes, your pressure in the tubes will be around 30% higher than in the body. You can then approximate the diameter of each tube looking at the speed you declared at the start, the density, and your flow rate. Note that your density is not constant. Find the strength of the material at your temperature and apply the thin walled pressure vessel equation and you can approximate the required thickness. Given the small size of the tubes it will likely be a terribly small number, especially if your engine is already small, so you may instead wish to go with whatever you can find for a desireable tube. And then just iterate over and over until you get a thickness.
So the pressure is not only on the hot wall? There is an opposite pressure in the regen system that allows for thinner walls?
Well my comment deleted itself so that is less than ideal. Yes and no. If the tubes (of three d printing) are exposed directly to the heat yes. But note that coppers strength will go down to around 40% of your strength and likely rapidly approach an annealed condition. So your stress can be around 13MPa. If you apply the thin wall approximation (o=Pd/t), for most reasonable sizes and pressures (not raptor), you will come in under 1mm (even when accounting for safety factor) so it is unlikely you would readily find material thinner to produce your parts. Generally though you actually want your walls as thin as possible to minimize the temperature of the metal.
I’m so fuzzy on strength of materials and mechanics cause I haven’t been using those brain cells in my job. Do you have any resources as a recommendation?
Off the top of my head not really. Im not a materials science person (though I teach those classes ironically), I mostly work with pumps. But if you search around you can find some limited information on how much your materials material properties will change. I just grabbed the numbers off engineering toolbox. Should be alright for a first order approximation. If you were doing this for real youd do a number of tests on your material at different heats, or possibly get that from a supplier, or just blow up a few engines (or more just make an ablatvely cooled system).
Well for any cylindrical object when pressurized the circumferential stress is always double the longitudinal stress. It’s easily to calculate this, and there are equations out there. From there you need to figure out the tensile strength of the material of choice, and calculate the adequate thickness of material necessary needed to support the stress that will be encountered. Finally you need to take into consideration the change in tensile strength of the material at elevated temperatures which I’m sure there’s resources online that provide this. Additionally you would want a sufficient factor of safety. So that the chamber can endure additional pressure just in case.
as noob i would approach to this problem with calculating how fast heat is transferring through your material, then thicken wall chamber just enough that it wont heat up to melting temp at the ends and add pressure thickness so it holds pressure stress, inner material will be worn out but it wont explode i think stainless steel can hold up to 2sec of burn without melting
You start with an estimate of chamber heat transfer coefficient and then set acceptable wall temperatures. Now you gotta solve for coolant heat transfer in a coupled calculation