Post by deskjetser on Dec 7, 2016 11:39:23 GMT
This thread is dedicated to discussing in detail, the intra-actions and inner workings of both chemical combustion rockets and nuclear thermal rockets.
This is intended to be a resource for use by everyone; And I will be updating this as often as I can with my findings from tests and data gathered in CDE.
If you have any questions or queries, feel free to reply to this thread or PM me. Especially if you feel something is missing!
Quick information access library:
CDE Propulsion Table
Material study
Chemical combustion rockets: Material study data
All engines tested on flourine hydrogen. Controlled variables are: CCR @ 25, NER @ 733 & NEA @ 10. All engines optimised using same technique to the same level of precision.
Nuclear thermal rockets: Material study data
DATA COMING SOON; In the meantime the data on chemical rockets is vaguely sufficient
Nozzle design
Chemical combustion rockets: Ideal nozzle angle for a given exhaust velocity
Find your desired PEV, 99% of PEV with fluorine hydrogen is 5.1km/s exhaust velocity; Then find the lowest cost angle for your target PEV and increase expansion ratio until target PEV is achieved.
Verified on fluorine hydrogen and fluorine methane; Alternate fuels accuracy not yet tested. A higher angle is more desireable as it decreases nozzle dimensions.
Nuclear thermal rockets: Ideal nozzle angle for a given exhaust velocity
DATA COMING SOON; In the meantime the data on chemical rockets is vaguely sufficient (Higher PEV requirements = lower angle trend). The trend is slightly moved a little though.
Current resource library:
Decane NTR synopsis
I've put an unprecedented amount of time and effort into finding the limits of Decane cooled nuclear thermal rockets, and my efforts have been rewarded with these three beauties. (See below.)
I do hope someone finds something useful in my synopsis, and since this is my first thread pls be nice! ◕ω◕ Feedback is appreciated!
Caution, wall of text incoming!
Ultimate Construction Factors
There are a few key factors to achieving the very best thrust to mass ratio and exhaust velocity, which are the two most important factors in rocket engine design.
Factor 1: Injector composition
The turbo pump material is a critical part of making a light pump. It must have a yield strength sufficient for the operational stresses, be of an acceptably low density to reduce pump mass and be as inexpensive as possible.
Since the turbo pump machinery makes up, when designed optimally, the second or first most massive component of the entire rocket; It is preferable to select an excessively low density material rather than a material of higher yield strength.
For the purposes of this synopsis, this leaves us with two candidates. Lithium and potassium.
Barring real life limitations; These materials have extremely low densities, adequate yield strengths and are hugely inexpensive.
Factor 2: Injector dimensions
In CDE increasing the rotational speed of the turbo pump, increases its mass; I won't go into this as I can only speculate as to the reasons.
Factor 1 and 2 are eminently linked here, as my ventures have shown. It is endlessly preferable, discounting overall rocket size requirements, to have an excessively large and slow rotating turbo pump.
From my experiments; For a turbo pump to move a set amount of coolant, a smaller faster rotating turbo pump requires a material of higher yield strength, and as such almost exclusively denser. Compounded with the fact that a faster rotating pump increases in mass linearly, there is a clear cutoff point for acceptable pump rotational speed per the pump dimensions.
You can have a small, heavy pump. Alternatively, you can have a large, light pump. Compromise how you will, but this thread is about performance barring size.
Factor 3: Chamber composition
Boron has its limits; I have reached them. However, I have found from my tests that upto ~304MN boron is still the best option. (All three engines below use chambers composed of boron.)
Alternative materials have only been the subject of a very small amount of scrutiny in my endeavours, since I was always able to overcome the thermal expansion stress limitations; As such I won't cover any details on alternative materials.
Overcoming the limits of boron is the core of the next factor.
Factor 4: Chamber and nozzle dimensions
I will cover the most desirable attributes of a chamber design, and what limits it:
- Small throat radius; Since a smaller radius reduces the overall size, and thus mass, of the engine. This is limited by the thermal expansion stress and internal chamber pressure.
To overcome the thermal expansion stress which starts to really hamper boron around the 300MN mark, an increased throat radius is necessary to reduce this expansion stress. Increasing this radius also adds the benefit of needing less thick chamber walls to contain the pressure, while at the same doubly reducing the thermal stress when compounded with an increased throat radius; Since thinner walls reduce expansion stress too.
- Thinner chamber walls; This should be pretty self explanatory, since thinner walls offer overall less mass. Walls that are too thick increase thermal expansion stress, have increased difficulty dissipating thermal energy and massively increase the mass of your engine. How thin the walls can be made is limited by internal pressure and by extension the throat radius as well as chamber contraction ratio.
- Between 3 and 5 chamber contraction ratio; There is an ideal ratio for each engine. Increasing this ratio increases thrust, mass, reactor dimensions and marginally increases exhaust velocity. Decreasing has the inverse result. Increasing this ratio also increases the internal pressure experienced by the chamber, while decreasing this ratio increases thermal expansion stress. Upper and lower limits for this ratio are down to internal pressure and as such, wall thickness and thermal expansion stress.
- Higher expansion ratio nozzle; A higher expansion ratio allows for the exhaust gasses to accelerate to greater velocities, increasing exhaust velocity. Really there are no limiting factors, other than gimballing speed and willingness to compromise thrust to mass ratio. Increasing this ratio increases mass at a rather linear rate, and has diminishing returns for increasing exhaust velocity; As such the cutoff point at which the compromise between increased exhaust velocity and increased mass, is down to personal preference and design requirements.
- Lower nozzle expansion angle; A lower expansion angle effectively elongates the nozzle having a similar effect to increasing the expansion ratio. The effects of decreasing this angle are largely similar to increasing the expansion ratio, however with an extreme increase in mass. As with the expansion ratio, the compromise is largely down to preference and design requirements.
- Lower percentage of regenerative cooling; While it may seem counter intuitive, increasing this percentage also increases thermal expansion stress because it increases the delta-t across the chamber. Ideally a balance between cooling and expansion stress should be achieved. If a situation where no balance can be found, ie; the engine is either not dissipating enough heat, or is experiencing too much thermal expansion stress. Then the chamber is incorrectly sized for the workload, and the throat radius should be increased as well as decreasing the wall thickness until a balance can be found.
- Minimum Reactor core height; This should be adjusted to a minimum after everything else. Note that there is an ideal ratio between throat radius and core height, which differs with each engine.
Factor 5: Reactor fuel and control
I cannot speak as to the viability of anything other than Uranium 235 Dioxide and Uranium 233 Dioxide, since I have not experimented with any other fissile material. Generally speaking of the two though, isotope 235 is the better performing but more costly fuel. Whereas isotope 233 is a much cheaper but less well performing alternative. Typically in trails an engine fuelled with U233 was 78.18% less costly, and yielded decreases of only 0.1887% in exhaust velocity, 1.6% in thrust and 5.231% in thrust to mass ratio.
Note that using U233 requires more massive control rods, which increases the dimensions and weight of the reactor. These losses could be minimised through further experimentation, thus increasing further the appeal of isotope 233. However, for pure performance U235 was used as the fuel of choice in my endeavours.
Average neutron flux is desired to be at the absolute maximum without causing the reactor to loose criticality before its operational lifetime; With this you are extracting the most amount of energy possible from your fuel mass, allowing more coolant to be passed over the reactor, increasing thrust.
For all tests boron nitride has been used for control rods, since it is cheap and effective at controlling the fission process.
Factor 6: Gimballing and reaction wheel composition
To Yield the highest thrust to mass ratio, the smallest possible gimbal inner radius must be used down to the nearest thousandth of a meter. A smaller radius decreases the supporting structure mass, which as far as I can tell is made of aluminium; And since aluminium is exceedingly dense compared with what the engine is made of, it is desirable to minimise its use to the limit of possibility.
Momentum wheels should be comprised of the lightest possible material which can gimbal the engine faster than 3RPM. This is because the size of the wheel is determined by the gimbal inner radius, which in turn is determined by the turbo pump, which is rather large if designed optimally. As such, using the least dense material for this that can withstand the stresses needed to rotate the engine faster than 3RPM, is crucial.
This leaves us with the same material options as the injector along with some extras. Lithium, potassium polyethylene and ultra high molecular weight polyethylene or UHMWPE for short; These are again for the purpose of this synopsis only, since larger engines will require stronger materials.
Armour for peak performance should be graphite aerogel simply for its extremely low density. If an armoured engine is required, this is the wrong synopsis for you; Only thorough bred glass cannons here!
Factor 7: General component scaling
These are more of a general rule of thumb for engine design. These apply to most if not all the previous factors.
- There is an ideal dimension; You can have a small, powerful but exceedingly heavy rocket. You can have a large, powerful and exceedingly light rocket. Anything else is a compromise, and there is no interchanging benefits between these two philosophies. There is however an equilibrium; Making something like the chamber too small, will mean there is less area for the same internal forces to act upon. Constricting 300MN to a small package will require increased build strength, and thus mass. Find the ideal dimension for your thrust requirements.
- Smaller is better; This applies to everything but injectors, expansion ratios and chamber dimensions. Smaller means less mass and less material costs, its that simple.
Balance these two systems of design to find the goldilocks zone.
Scaling Possibilities
My experimentation has shown that surprisingly linear scaling can be achieved with minimal effort, at least between the ranges of 12 and 300MN.
The system I have developed allows for scaling only to be effected by increasing material strength requirements, such as; Momentum wheels and injectors. Everything else scales rather linearly. There is however a sharp drop off in TMR somewhere around the ~200MN mark, as can probably be evident from just observing the three engines below.
The largest factors affecting larger engines TMR, is the gimbal inner radius and boron thermal expansion stress limitations. This is the reason I stopped marching forward at 300MN after observing the sharp drop off in linearity.
I welcome criticism and challenges to this statement. Although from what I have recognised, scaling is near linear and as to be expected. So there are no excuses for heavy powerful engines, unless specifically designed that way, anymore!
Limits
In theory then, as engine size increases beyond 300MN so will material strength requirements; One should be able then with great effort to plot the mass, TMR and cost increases. My prediction would be to see a first linear increase, then tapering off ever so gradually until finally a plateau of engine performance scaling is reached. One half of a parabola, if you will.
Since I do not have unlimited time to create all the engines upto this plateau, I am left with this mere theory.
Summary
I hope if you read through all this, that you managed to gleam some useful scraps of information from it. My hope is for this to point people in the right direction, and for people to have a greater understanding of the intra-actions of the NTR designer.
If you have any comments, suggestions or questions please feel free to ask! If you could also let me know in the poll whether you found this helpful, that would be awesome too!
Thanks for reading, and happy designing!
*Edit* For reference Simien uses 20kg of U235 dioxide, Blackburn 200kg and Bona uses 500kg.
Nozzle design theory
After a long battle with spreadsheets and analysing data, I feel I have enough coherent findings to present.
Please note though, I am kicking this out the door incomplete. I have been battling with this for a while now, and this is just what I have to show for now. It will get better!
What is the expansion ratio and angle?
Please forgive me for glossing over this, I just want to clarify the basics for new players.
Expansion ratio
The expansion ratio of the rocket nozzle is the simple ratio betwen the area of the throat size and final nozzle area. For example; A ratio of 100 on an engine with a throat radius of 5mm, will yield a final nozzle diameter of 10cm.
This is because the area of the 5mm throat is 78.54mm², and with an expansion ratio of 100, the final nozzle will have 100 times that area with 7853mm² and a radius of 50mm.
This can be calculated as follows:
Expansion angle
The expansion angle of the nozzle is the final angle at which the nozzle curve ends, also known as the nozzle wall exit angle. Since in CDE all nozzles are based upon a bell nozzle design, and there are no more inputs for nozzle dimensions; This angle solely determines the overall length of the nozzle.
Below is a basic diagram to help illustrate the above ratio and angle explanation.
How does expansion ratio and angle influence engine parameters?
The job of a rocket nozzle is to convert high pressure high temperature slow moving gas, into low pressure low temperature fast moving gas. To facilitate this process, nozzles use Bernoulli's principle to effectively increase the potential amount of energy released from a reaction.
In an ideal world, a nozzle in a vacuum would harness the reaction mass long enough for it to completely diffuse to the same levels as the environment around it. However in reality, having a nozzle long enough for the reaction mass to completely diffuse to a vacuum, is not viable. The nozzle needed would be excessively huge and cumbersome.
Just elongating the nozzle, to increase the time the reaction mass has to diffuse, does not net all possible gains however. If a long low expansion ratio nozzle is used, the reaction mass may still be under considerable pressure by the end; This is due to the insufficient volume allowed for expansion at the end of the nozzle. Therefore a combination of volume increase and expansion angle must be used to net all possible gains from a reaction mass under pressure.
Nozzle efficiency
Efficiency is determined by the nozzles ability to do two things; Provide adequate volume for the pressurised reaction mass to expand, and doing so at a rate suited to the propellant. This means allowing enough of an expansion ratio, and making sure the angle is at a rate which suits the rate of expansion of the combustion products.
Engine factors
When one begins to factor in the rest of the engine design, further work must be done to find an acceptable ground of compromise. Other factors such as engine mass, cost, thrust to mass ratio and overall thrust must be considered. A nozzle can only be optimised for four parameters however; Thrust to mass ratio, exhaust velocity, mass and size.
An engine nozzle with the best possible thrust to mass ratio will inherently have poor exhaust velocity, but will be small and of low weight.
An engine nozzle with the best possible exhaust velocity will inherently have poor thrust to mass ratio, and will be large, heavy.
There are sweet spots though, and a compromise can yield acceptable parameters with relative ease.
'Sweet spots' of design
From my experiments conducted, there have shown to be preferable combinations of expansion ratio and angle; This differs from chemical rockets and nuclear thermal rockets unfortunately, and I didn't discover this until late in testing. However, the rules of design still apply; The data here is just not directly applicable to NTRs.
Testing was carried out on a mockup flourine hydrogen chemical rocket, specifically designed small to make observations as accurate as possible. This is since larger engines in CDE loose some parameter resolution; ie, the same number of decimal places are kept in the display, but the order of magnitude increases.
The below graph, to the best of my abilities , is showing relative parameter effects on exhaust velocity, TMR, thrust and cost. Note that cost is directly proportional to mass, and was used instead of mass as it graphs easier with the other values.
A graph showing: Expansion ratio on the x axis. Exhaust velocity on the y axis. Thrust, TMR and cost (directly relative to mass) on the y2 axis. Line opacity decreases as angle increases (10° most opaque, 16 degrees least opaque).
You can view the data more accurately for yourself here.
Note that for some reason the google spreadsheet may not have updated to show the most recent version.
This graph does nicely illustrate a few things though; Adding a nozzle to the combustion chamber initially raises TMR, then plateaus before falling. The crossing point for cost and TMR, at least in these tests, has always been around similar TMR levels before a nozzle was added. Concurrently this is also a rather good place for the nozzle design, since it nets respectable exhaust velocity along with acceptable TMR.
Personally, this is where I would try to position my future nozzle designs for optimal balance.
Also note that with higher expansion angles, the TMR downward trend after peak is elongated. This strongly indicates that a higher expansion angle is preferable when a high TMR is needed, as the cost and thus mass, rises much more gradually with an angle of 16° than with an angle of 10°.
Angle for a given expansion ratio
The tests were conducted on 4 different angles of expansion in what I have deemed myself to be an ideal zone of construction; 10°, 12°, 14°, and 16°. I will be adding to this and increasing the resolution of my data as time goes on, as well as conducting the same tests on NTRs.
- Condition 1; Close to the maximum possible exhaust velocity for the propellant in use; In the case of the test, flourine hydrogen has a maximum attainable velocity of 5.15km/s.
Attaining ~95% of this (4.9km/s) favours a slightly lower expansion angle nozzle, with lower mass and higher thrust to mass ratio than its comparisons. For the tests when trying to achieve ~95% of the maximum possible exhaust velocity, an angle of 12° was superior to the other angles in respects to the above mentioned parameters.
- Condition 2; Around 91% of the maximum attainable exhaust velocity (4.72km/s); This condition favours a higher expansion angle, as tests revealed 16° was superior to the other angles in respects to mass and thrust to mass ratio.
4.9km/s Analysis
In my tests, each angle had data recorded for every 0.01km/s change in exhaust velocity once past an expansion ratio of ~16. This was continued until 95% of the maximum theoretical exhaust velocity was achieved, at 4.9km/s. Since each angle has its data cut off at this point, it clearly illustrates on the graph the comparison of cost/mass and TMR between the four angles at the data cutoff points; The graph below has highlighted these points, where an angle of 12° shows superior cost/mass and TMR to the other angles.
Circled on the data end point trend lines, are the cost/mass and TMR of the 12° data @ 95% of max exhaust velocity.
Further extrapolation
Using the above analysis on cost/mass data end points, the data can be further simplified and expanded to show the ideal angle for a given exhaust velocity; This will show visually the 'pits' of lowest cost/mass, allowing the nozzle designer to pick the best angle suited to their application.
By far the most important factor of nozzle design is achieving the lowest possible mass for the application. Since cost and mass are directly proportional to each other, this graph illustrates the ideal zones of lowest cost for a given exhaust velocity target in 1% increments. Note that generally when no cost/mass difference is shown between two angles, the higher of the two angles is preferable; This is because a greater angle will shorten the nozzle, making it easier to gimbal and more compact.
Data end point lines for 1% exhaust velocity increments, showing relative cost/mass increases.
Examples, using the above graph:
- Using a flourine hydrogen rocket where ~5km/s exhaust velocity is required (97% of max possible); The lowest point on the graph for the yellow 97% line is at 10 degrees. This will be the best angle for the application.
- Using a flourine hydrogen rocket where ~5.1km/s exhaust velocity is required (98% of max possible); The lowest points on the graph for the red 98% line are at 10 and 8 degrees. The best angle will be between these two, however an angle closer to 10 will be preferable.
- Using a flourine methane rocket where ~3.85km/s exhaust velocity is required (95% of max possible); The lowest points on the graph for the purple 95% line are at 12 and 14 degrees. The best angle will be between these two, however an angle closer to 14 will be preferable.
Conclusion
Henceforth the tests determine that as requirements for higher exhaust velocities increase, the ideal expansion angle decreases. As requirements for exhaust velocities decrease however, the ideal expansion angle increases.
The data
The data I have gathered can be directly applied to chemical rockets, and has been verified on both flourine hydrogen and flourine methane engines.
To use this data, find the % of how much exhaust velocity you would like from your combustion reaction within the usable data; Then compare the cost or mass with the other angles to find the least massive. That will be the appropriate angle. Note that to directly apply this data, you must ignore expansion ratio; Just set your angle to the chart showing the least mass for your velocity requirement, and increase your expansion angle until you achieve this exhaust velocity requirement.
Its finicky, I know I am sorry. This is the best I could manage. If you do need help further explaining this, feel free to PM me and ill be happy to do my best to make it clearer!
Stay tuned, I will be adding NTR data soon!
This is intended to be a resource for use by everyone; And I will be updating this as often as I can with my findings from tests and data gathered in CDE.
If you have any questions or queries, feel free to reply to this thread or PM me. Especially if you feel something is missing!
Quick information access library:
CDE Propulsion Table
Please read this post before using: childrenofadeadearth.boards.net/post/23508
docs.google.com/spreadsheets/d/1o8ggi5-HgEHX7ql4oAJVVCK7MiySgCs44I8TnBhh7sM/edit?usp=sharing
docs.google.com/spreadsheets/d/1o8ggi5-HgEHX7ql4oAJVVCK7MiySgCs44I8TnBhh7sM/edit?usp=sharing
Material study
Chemical combustion rockets: Material study data
All engines tested on flourine hydrogen. Controlled variables are: CCR @ 25, NER @ 733 & NEA @ 10. All engines optimised using same technique to the same level of precision.
Large engine 5000kg/s | ||||
---|---|---|---|---|
Boron | Diamond | Reinforced CC | Amorphous C | |
Mass t | 81.4 | 241 | 621 | 291 |
Cost Mc | 1.41 | 5.26 | 47.2 | 6.5 |
Throat Radius cm | 48 | 43.4 | 98.8 | 43.6 |
Chamber wall mm | 12.3 | 26.4 | 26.4 | 52.9 |
% Mass increase over boron | 196.1 | 662.9 | 257.5 | |
% Cost increase over boron | 273 | 3247.5 | 361 |
Medium engine 500kg/s | ||||
---|---|---|---|---|
Boron | Diamond | Reinforced CC | Amorphous C | |
Mass t | 2.01 | 4.81 | 12.2 | 10.5 |
Cost kc | 34.5 | 104 | 922 | 235 |
Throat Radius cm | 11.7 | 8.48 | 19.1 | 15.7 |
Chamber wall mm | 5.04 | 13.7 | 13.8 | 14.7 |
% Mass increase over boron | 139.3 | 507 | 422.4 | |
% Cost increase over boron | 201.4 | 2572.5 | 581.2 |
Small engine 50kg/s | ||||
---|---|---|---|---|
Boron | Diamond | Reinforced CC | Amorphous C | |
Mass kg | 61.5 | 139 | 321 | 261 |
Cost kc | 0.999 | 2.93 | 24 | 5.75 |
Throat Radius cm | 3.32 | 2.36 | 4.98 | 3.82 |
Chamber wall mm | 1.78 | 4.93 | 5.28 | 6.06 |
% Mass increase over boron | 126 | 422 | 324.4 | |
% Cost increase over boron | 193.3 | 2302.4 | 475.6 |
Tiny engine 50g/s | ||||
---|---|---|---|---|
Boron | Diamond | Reinforced CC | Amorphous C | |
Mass g | 29.2 | 32.2 | 34.9 | 33.3 |
Cost c | 0.162 | 0.24 | 0.77 | 0.27 |
Throat Radius mm | 1 | 1 | 1.3 | 1 |
Chamber wall mm | 0.1 | 0.116 | 0.204 | 0.233 |
% Mass increase over boron | 10.3 | 19.5 | 14 | |
% Cost increase over boron | 48.1 | 375.3 | 66.7 |
Nuclear thermal rockets: Material study data
DATA COMING SOON; In the meantime the data on chemical rockets is vaguely sufficient
Nozzle design
Chemical combustion rockets: Ideal nozzle angle for a given exhaust velocity
Find your desired PEV, 99% of PEV with fluorine hydrogen is 5.1km/s exhaust velocity; Then find the lowest cost angle for your target PEV and increase expansion ratio until target PEV is achieved.
Verified on fluorine hydrogen and fluorine methane; Alternate fuels accuracy not yet tested. A higher angle is more desireable as it decreases nozzle dimensions.
(Possible Exhaust Velocity Target) Cost & relative mass | 6 Degrees | 8 Degrees | 10 Degrees | 12 Degrees | 14 Degrees | 16 Degrees | 18 Degrees | 20 Degrees | 22 Degrees |
(99% PEV) Cost c | 7.94 | 7.58 | 8.55 | ||||||
(98% PEV) Cost c | 3.44 | 3.06 | 3.06 | 3.45 | |||||
(97% PEV) Cost c | 1.73 | 1.5 | 1.42 | 1.46 | 1.61 | ||||
(96% PEV) Cost c | 0.992 | 0.921 | 0.909 | 0.949 | 1.05 | ||||
(95% PEV) Cost c | 0.731 | 0.683 | 0.663 | 0.663 | 0.698 | 0.773 | |||
(94% PEV) Cost c | 0.539 | 0.518 | 0.515 | 0.526 | 0.559 | ||||
(93% PEV) Cost c | 0.462 | 0.442 | 0.436 | 0.437 | 0.45 | ||||
(92% PEV) Cost c | 0.388 | 0.378 | 0.377 | 0.384 | 0.396 | ||||
(91% PEV) Cost c | 0.351 | 0.344 | 0.342 | 0.343 | 0.35 | ||||
(90% PEV) Cost c | 0.326 | 0.32 | 0.318 | 0.318 | 0.321 | 0.327 |
Nuclear thermal rockets: Ideal nozzle angle for a given exhaust velocity
DATA COMING SOON; In the meantime the data on chemical rockets is vaguely sufficient (Higher PEV requirements = lower angle trend). The trend is slightly moved a little though.
Current resource library:
Decane NTR synopsis
I've put an unprecedented amount of time and effort into finding the limits of Decane cooled nuclear thermal rockets, and my efforts have been rewarded with these three beauties. (See below.)
I do hope someone finds something useful in my synopsis, and since this is my first thread pls be nice! ◕ω◕ Feedback is appreciated!
Caution, wall of text incoming!
Ultimate Construction Factors
There are a few key factors to achieving the very best thrust to mass ratio and exhaust velocity, which are the two most important factors in rocket engine design.
Factor 1: Injector composition
The turbo pump material is a critical part of making a light pump. It must have a yield strength sufficient for the operational stresses, be of an acceptably low density to reduce pump mass and be as inexpensive as possible.
Since the turbo pump machinery makes up, when designed optimally, the second or first most massive component of the entire rocket; It is preferable to select an excessively low density material rather than a material of higher yield strength.
For the purposes of this synopsis, this leaves us with two candidates. Lithium and potassium.
Barring real life limitations; These materials have extremely low densities, adequate yield strengths and are hugely inexpensive.
Factor 2: Injector dimensions
In CDE increasing the rotational speed of the turbo pump, increases its mass; I won't go into this as I can only speculate as to the reasons.
Factor 1 and 2 are eminently linked here, as my ventures have shown. It is endlessly preferable, discounting overall rocket size requirements, to have an excessively large and slow rotating turbo pump.
From my experiments; For a turbo pump to move a set amount of coolant, a smaller faster rotating turbo pump requires a material of higher yield strength, and as such almost exclusively denser. Compounded with the fact that a faster rotating pump increases in mass linearly, there is a clear cutoff point for acceptable pump rotational speed per the pump dimensions.
You can have a small, heavy pump. Alternatively, you can have a large, light pump. Compromise how you will, but this thread is about performance barring size.
Factor 3: Chamber composition
Boron has its limits; I have reached them. However, I have found from my tests that upto ~304MN boron is still the best option. (All three engines below use chambers composed of boron.)
Alternative materials have only been the subject of a very small amount of scrutiny in my endeavours, since I was always able to overcome the thermal expansion stress limitations; As such I won't cover any details on alternative materials.
Overcoming the limits of boron is the core of the next factor.
Factor 4: Chamber and nozzle dimensions
I will cover the most desirable attributes of a chamber design, and what limits it:
- Small throat radius; Since a smaller radius reduces the overall size, and thus mass, of the engine. This is limited by the thermal expansion stress and internal chamber pressure.
To overcome the thermal expansion stress which starts to really hamper boron around the 300MN mark, an increased throat radius is necessary to reduce this expansion stress. Increasing this radius also adds the benefit of needing less thick chamber walls to contain the pressure, while at the same doubly reducing the thermal stress when compounded with an increased throat radius; Since thinner walls reduce expansion stress too.
- Thinner chamber walls; This should be pretty self explanatory, since thinner walls offer overall less mass. Walls that are too thick increase thermal expansion stress, have increased difficulty dissipating thermal energy and massively increase the mass of your engine. How thin the walls can be made is limited by internal pressure and by extension the throat radius as well as chamber contraction ratio.
- Between 3 and 5 chamber contraction ratio; There is an ideal ratio for each engine. Increasing this ratio increases thrust, mass, reactor dimensions and marginally increases exhaust velocity. Decreasing has the inverse result. Increasing this ratio also increases the internal pressure experienced by the chamber, while decreasing this ratio increases thermal expansion stress. Upper and lower limits for this ratio are down to internal pressure and as such, wall thickness and thermal expansion stress.
- Higher expansion ratio nozzle; A higher expansion ratio allows for the exhaust gasses to accelerate to greater velocities, increasing exhaust velocity. Really there are no limiting factors, other than gimballing speed and willingness to compromise thrust to mass ratio. Increasing this ratio increases mass at a rather linear rate, and has diminishing returns for increasing exhaust velocity; As such the cutoff point at which the compromise between increased exhaust velocity and increased mass, is down to personal preference and design requirements.
- Lower nozzle expansion angle; A lower expansion angle effectively elongates the nozzle having a similar effect to increasing the expansion ratio. The effects of decreasing this angle are largely similar to increasing the expansion ratio, however with an extreme increase in mass. As with the expansion ratio, the compromise is largely down to preference and design requirements.
- Lower percentage of regenerative cooling; While it may seem counter intuitive, increasing this percentage also increases thermal expansion stress because it increases the delta-t across the chamber. Ideally a balance between cooling and expansion stress should be achieved. If a situation where no balance can be found, ie; the engine is either not dissipating enough heat, or is experiencing too much thermal expansion stress. Then the chamber is incorrectly sized for the workload, and the throat radius should be increased as well as decreasing the wall thickness until a balance can be found.
- Minimum Reactor core height; This should be adjusted to a minimum after everything else. Note that there is an ideal ratio between throat radius and core height, which differs with each engine.
Factor 5: Reactor fuel and control
I cannot speak as to the viability of anything other than Uranium 235 Dioxide and Uranium 233 Dioxide, since I have not experimented with any other fissile material. Generally speaking of the two though, isotope 235 is the better performing but more costly fuel. Whereas isotope 233 is a much cheaper but less well performing alternative. Typically in trails an engine fuelled with U233 was 78.18% less costly, and yielded decreases of only 0.1887% in exhaust velocity, 1.6% in thrust and 5.231% in thrust to mass ratio.
Note that using U233 requires more massive control rods, which increases the dimensions and weight of the reactor. These losses could be minimised through further experimentation, thus increasing further the appeal of isotope 233. However, for pure performance U235 was used as the fuel of choice in my endeavours.
Average neutron flux is desired to be at the absolute maximum without causing the reactor to loose criticality before its operational lifetime; With this you are extracting the most amount of energy possible from your fuel mass, allowing more coolant to be passed over the reactor, increasing thrust.
For all tests boron nitride has been used for control rods, since it is cheap and effective at controlling the fission process.
Factor 6: Gimballing and reaction wheel composition
To Yield the highest thrust to mass ratio, the smallest possible gimbal inner radius must be used down to the nearest thousandth of a meter. A smaller radius decreases the supporting structure mass, which as far as I can tell is made of aluminium; And since aluminium is exceedingly dense compared with what the engine is made of, it is desirable to minimise its use to the limit of possibility.
Momentum wheels should be comprised of the lightest possible material which can gimbal the engine faster than 3RPM. This is because the size of the wheel is determined by the gimbal inner radius, which in turn is determined by the turbo pump, which is rather large if designed optimally. As such, using the least dense material for this that can withstand the stresses needed to rotate the engine faster than 3RPM, is crucial.
This leaves us with the same material options as the injector along with some extras. Lithium, potassium polyethylene and ultra high molecular weight polyethylene or UHMWPE for short; These are again for the purpose of this synopsis only, since larger engines will require stronger materials.
Armour for peak performance should be graphite aerogel simply for its extremely low density. If an armoured engine is required, this is the wrong synopsis for you; Only thorough bred glass cannons here!
Factor 7: General component scaling
These are more of a general rule of thumb for engine design. These apply to most if not all the previous factors.
- There is an ideal dimension; You can have a small, powerful but exceedingly heavy rocket. You can have a large, powerful and exceedingly light rocket. Anything else is a compromise, and there is no interchanging benefits between these two philosophies. There is however an equilibrium; Making something like the chamber too small, will mean there is less area for the same internal forces to act upon. Constricting 300MN to a small package will require increased build strength, and thus mass. Find the ideal dimension for your thrust requirements.
- Smaller is better; This applies to everything but injectors, expansion ratios and chamber dimensions. Smaller means less mass and less material costs, its that simple.
Balance these two systems of design to find the goldilocks zone.
Scaling Possibilities
My experimentation has shown that surprisingly linear scaling can be achieved with minimal effort, at least between the ranges of 12 and 300MN.
The system I have developed allows for scaling only to be effected by increasing material strength requirements, such as; Momentum wheels and injectors. Everything else scales rather linearly. There is however a sharp drop off in TMR somewhere around the ~200MN mark, as can probably be evident from just observing the three engines below.
The largest factors affecting larger engines TMR, is the gimbal inner radius and boron thermal expansion stress limitations. This is the reason I stopped marching forward at 300MN after observing the sharp drop off in linearity.
I welcome criticism and challenges to this statement. Although from what I have recognised, scaling is near linear and as to be expected. So there are no excuses for heavy powerful engines, unless specifically designed that way, anymore!
Limits
In theory then, as engine size increases beyond 300MN so will material strength requirements; One should be able then with great effort to plot the mass, TMR and cost increases. My prediction would be to see a first linear increase, then tapering off ever so gradually until finally a plateau of engine performance scaling is reached. One half of a parabola, if you will.
Since I do not have unlimited time to create all the engines upto this plateau, I am left with this mere theory.
Summary
I hope if you read through all this, that you managed to gleam some useful scraps of information from it. My hope is for this to point people in the right direction, and for people to have a greater understanding of the intra-actions of the NTR designer.
If you have any comments, suggestions or questions please feel free to ask! If you could also let me know in the poll whether you found this helpful, that would be awesome too!
Thanks for reading, and happy designing!
*Edit* For reference Simien uses 20kg of U235 dioxide, Blackburn 200kg and Bona uses 500kg.
Nozzle design theory
After a long battle with spreadsheets and analysing data, I feel I have enough coherent findings to present.
Please note though, I am kicking this out the door incomplete. I have been battling with this for a while now, and this is just what I have to show for now. It will get better!
What is the expansion ratio and angle?
Please forgive me for glossing over this, I just want to clarify the basics for new players.
Expansion ratio
The expansion ratio of the rocket nozzle is the simple ratio betwen the area of the throat size and final nozzle area. For example; A ratio of 100 on an engine with a throat radius of 5mm, will yield a final nozzle diameter of 10cm.
This is because the area of the 5mm throat is 78.54mm², and with an expansion ratio of 100, the final nozzle will have 100 times that area with 7853mm² and a radius of 50mm.
This can be calculated as follows:
π·5²= 78.53mm²
78.53mm²·100= 7853mm²
√7853/π= ~50mm
78.53mm² throat area
7853mm² final nozzle area
~50mm final nozzle radius
Expansion angle
The expansion angle of the nozzle is the final angle at which the nozzle curve ends, also known as the nozzle wall exit angle. Since in CDE all nozzles are based upon a bell nozzle design, and there are no more inputs for nozzle dimensions; This angle solely determines the overall length of the nozzle.
Below is a basic diagram to help illustrate the above ratio and angle explanation.
How does expansion ratio and angle influence engine parameters?
The job of a rocket nozzle is to convert high pressure high temperature slow moving gas, into low pressure low temperature fast moving gas. To facilitate this process, nozzles use Bernoulli's principle to effectively increase the potential amount of energy released from a reaction.
In an ideal world, a nozzle in a vacuum would harness the reaction mass long enough for it to completely diffuse to the same levels as the environment around it. However in reality, having a nozzle long enough for the reaction mass to completely diffuse to a vacuum, is not viable. The nozzle needed would be excessively huge and cumbersome.
Just elongating the nozzle, to increase the time the reaction mass has to diffuse, does not net all possible gains however. If a long low expansion ratio nozzle is used, the reaction mass may still be under considerable pressure by the end; This is due to the insufficient volume allowed for expansion at the end of the nozzle. Therefore a combination of volume increase and expansion angle must be used to net all possible gains from a reaction mass under pressure.
Nozzle efficiency
Efficiency is determined by the nozzles ability to do two things; Provide adequate volume for the pressurised reaction mass to expand, and doing so at a rate suited to the propellant. This means allowing enough of an expansion ratio, and making sure the angle is at a rate which suits the rate of expansion of the combustion products.
Engine factors
When one begins to factor in the rest of the engine design, further work must be done to find an acceptable ground of compromise. Other factors such as engine mass, cost, thrust to mass ratio and overall thrust must be considered. A nozzle can only be optimised for four parameters however; Thrust to mass ratio, exhaust velocity, mass and size.
An engine nozzle with the best possible thrust to mass ratio will inherently have poor exhaust velocity, but will be small and of low weight.
An engine nozzle with the best possible exhaust velocity will inherently have poor thrust to mass ratio, and will be large, heavy.
There are sweet spots though, and a compromise can yield acceptable parameters with relative ease.
'Sweet spots' of design
From my experiments conducted, there have shown to be preferable combinations of expansion ratio and angle; This differs from chemical rockets and nuclear thermal rockets unfortunately, and I didn't discover this until late in testing. However, the rules of design still apply; The data here is just not directly applicable to NTRs.
Testing was carried out on a mockup flourine hydrogen chemical rocket, specifically designed small to make observations as accurate as possible. This is since larger engines in CDE loose some parameter resolution; ie, the same number of decimal places are kept in the display, but the order of magnitude increases.
The below graph, to the best of my abilities , is showing relative parameter effects on exhaust velocity, TMR, thrust and cost. Note that cost is directly proportional to mass, and was used instead of mass as it graphs easier with the other values.
A graph showing: Expansion ratio on the x axis. Exhaust velocity on the y axis. Thrust, TMR and cost (directly relative to mass) on the y2 axis. Line opacity decreases as angle increases (10° most opaque, 16 degrees least opaque).
You can view the data more accurately for yourself here.
Note that for some reason the google spreadsheet may not have updated to show the most recent version.
This graph does nicely illustrate a few things though; Adding a nozzle to the combustion chamber initially raises TMR, then plateaus before falling. The crossing point for cost and TMR, at least in these tests, has always been around similar TMR levels before a nozzle was added. Concurrently this is also a rather good place for the nozzle design, since it nets respectable exhaust velocity along with acceptable TMR.
Personally, this is where I would try to position my future nozzle designs for optimal balance.
Also note that with higher expansion angles, the TMR downward trend after peak is elongated. This strongly indicates that a higher expansion angle is preferable when a high TMR is needed, as the cost and thus mass, rises much more gradually with an angle of 16° than with an angle of 10°.
Angle for a given expansion ratio
The tests were conducted on 4 different angles of expansion in what I have deemed myself to be an ideal zone of construction; 10°, 12°, 14°, and 16°. I will be adding to this and increasing the resolution of my data as time goes on, as well as conducting the same tests on NTRs.
- Condition 1; Close to the maximum possible exhaust velocity for the propellant in use; In the case of the test, flourine hydrogen has a maximum attainable velocity of 5.15km/s.
Attaining ~95% of this (4.9km/s) favours a slightly lower expansion angle nozzle, with lower mass and higher thrust to mass ratio than its comparisons. For the tests when trying to achieve ~95% of the maximum possible exhaust velocity, an angle of 12° was superior to the other angles in respects to the above mentioned parameters.
- Condition 2; Around 91% of the maximum attainable exhaust velocity (4.72km/s); This condition favours a higher expansion angle, as tests revealed 16° was superior to the other angles in respects to mass and thrust to mass ratio.
4.9km/s Analysis
In my tests, each angle had data recorded for every 0.01km/s change in exhaust velocity once past an expansion ratio of ~16. This was continued until 95% of the maximum theoretical exhaust velocity was achieved, at 4.9km/s. Since each angle has its data cut off at this point, it clearly illustrates on the graph the comparison of cost/mass and TMR between the four angles at the data cutoff points; The graph below has highlighted these points, where an angle of 12° shows superior cost/mass and TMR to the other angles.
Circled on the data end point trend lines, are the cost/mass and TMR of the 12° data @ 95% of max exhaust velocity.
Further extrapolation
Using the above analysis on cost/mass data end points, the data can be further simplified and expanded to show the ideal angle for a given exhaust velocity; This will show visually the 'pits' of lowest cost/mass, allowing the nozzle designer to pick the best angle suited to their application.
By far the most important factor of nozzle design is achieving the lowest possible mass for the application. Since cost and mass are directly proportional to each other, this graph illustrates the ideal zones of lowest cost for a given exhaust velocity target in 1% increments. Note that generally when no cost/mass difference is shown between two angles, the higher of the two angles is preferable; This is because a greater angle will shorten the nozzle, making it easier to gimbal and more compact.
Data end point lines for 1% exhaust velocity increments, showing relative cost/mass increases.
Examples, using the above graph:
- Using a flourine hydrogen rocket where ~5km/s exhaust velocity is required (97% of max possible); The lowest point on the graph for the yellow 97% line is at 10 degrees. This will be the best angle for the application.
- Using a flourine hydrogen rocket where ~5.1km/s exhaust velocity is required (98% of max possible); The lowest points on the graph for the red 98% line are at 10 and 8 degrees. The best angle will be between these two, however an angle closer to 10 will be preferable.
- Using a flourine methane rocket where ~3.85km/s exhaust velocity is required (95% of max possible); The lowest points on the graph for the purple 95% line are at 12 and 14 degrees. The best angle will be between these two, however an angle closer to 14 will be preferable.
Conclusion
Henceforth the tests determine that as requirements for higher exhaust velocities increase, the ideal expansion angle decreases. As requirements for exhaust velocities decrease however, the ideal expansion angle increases.
The data
The data I have gathered can be directly applied to chemical rockets, and has been verified on both flourine hydrogen and flourine methane engines.
Its finicky, I know I am sorry. This is the best I could manage.
Stay tuned, I will be adding NTR data soon!