underexpanded and overexpanded / emergency

[abap]

hi all, i have a graduation project in university, which is carbon-carbon based rocket nozzle design.
I have a question about bell-shaped nozzles.
Well, on books it writes that, "bell-shaped nozzles are efficient on an optimum altitude". Well according to formula,
F=m.̇v2+(p2-p3 ).A2
if the atmospheric pressure is lower than the nozzle exit pressure, performance increases. Thrust increases, specific impusle increases. So where is my error ? How can "bell-shaped nozzle is efficient on an optimum altitude" be possible?

 

[jsdemar]

The simplest way to look at it is: you want all the mass to accelerate straight down with the highest velocity. If the nozzle is underexpanded or overexpanded, there is sideways vector component to the exhaust gases.

The best expansion ratio will depend on the propellant gas products, the chamber pressure, and the ambient atmospheric pressure. See bottom graph:
https://thrustgear.com/docs/nozzle_optimization.html

Since the rocket will not be at any one pressure (altitude) for the whole burn, the expansion ratio is a compromise.

The bell shape vs. a straight cone is about 2 or 3% more efficient.

-John

 

[abap]

thanks,
we can say this right?
"if altitude incrases, the specific impulse,thrust increases"
because atm. pressure is decreasing.
all my calculations are based on book, "rocket propulsion elements".
but this, "bell-shaped nozzles works efficiently on a specific altitude"
so we have to use, very small area expension ratios right ?
because if the exit pressure decreases, the performance will decrease,
and nasa's solid rocket boosters which has 600 tons of weight has an AER of 7.
i will get crazy, on book it writes, "for higher altitues, high AER's are used"
but when we look to the solid rocket boosters, they are smal as 7
how come???
i will get crazy about this.
calculations say that AER must be small. but book say diffrent.

 

[FredA]

Nozzle design is your grad project and you are asking this?
Really?
What part of the project is original research?

 

[abap]

no, i am writing an analyz program, calculations are correct, many companies said ok about results.
i am talking about theories and practical things.
well, according to my result, optimuum Area expension ratio is 7 for an solid rocket booster, and nasa used, 6.97 or something.
But books write different things.

My project is carbon carbon composite based rocket nozzle design. material based project but i am adding some softwares in it. some simulation :=).
well, i coulnd find anyone answer correctly to this questions.
every links you gave accept that "p2=p3", eheh all of them are perfect rockets,
i am not asking this.
ok?
did u get what i say ?

 

[abap]

read this,
from an article
"Mainly for sea level operating engines, the rocket
motor performance is also governed by another
physical parameter: the pressure of the gases exit
plane of the nozzle. This pressure must be as near
as possible to outside pressure, which depends on
altitude"

did you see?
so why not we always choose small area expension ratios ? because nozzle exit pressure will be higher.
my question is this :=)

 

[dave carver]

This is why rocket engine design is now going in the direction of Aerospike technology. Something you might look into..

Another thing I thought of(well, maybe this is my idea ). Have you ever seen a collapseable drinking glass? They are made with tapered rings that when expanded out seal against the next ring making a drinking cup. My idea is esentially the same but with rings dropping down to increase the nozzle expansion area at the proper time.

So a launch sequence would go like: at ignition slightly overexpanded through optimum to slightly underexpanded, ring drop to slightly over expanded to optimum to slightly underexpanded. Process continuing until all rings are used.

 

[abap]

yes yes, aerospike's are forgotten after nasa's X-33 tests :=) but now, colombia university has some researches about it. well my subject is bell-shaped nozzle.
Thank you

 

[dave carver]

Then about the only thing you might be able to do is turkey tail exaust nozzles like on a jet fighter. This way you can constantly be increasing your nozzle diameter in your predetermined bell shape nozzle. It would be your problem finding a material that could handle the heat.

 

[abap]

"It is well known that a rocket engine develops max-
imum thrust when the pressure at the Laval’s nozzle
outlet is equal to the atmospheric pressure. As the
altitude varies with the rocket trajectory, the atmo-
spheric pressure varies and the engine loses part of its
thrust. To compensate such thrust loss it is necessary"

well, did you see? it is from article named, the optimization of rough surface supersonic nozzles
but when you calculate from equations, you find that, thrust increases as the rocket rises and atm. pressure decreases. i am crazy about this =). i wish you understood what i wanted to say.

 

[cjl]

1) You're a college student. Please try using fewer abbreviations, proper capitalization, and proper grammar. It makes everything much easier to read, and I would certainly hope you would be capable of it by this point.

2) Yes, a given nozzle will produce more thrust at high altitude than at sea level. Momentum thrust will remain constant for a given nozzle, but as the external pressure decreases, the pressure thrust will increase. What you don't seem to understand (which is rather shocking considering that this is your grad project) is that at a given altitude, the optimum performance is achieved with all of the thrust as momentum thrust (in other words, Pexit = Patm). If you have a nozzle that is optimally expanded at sea level, and you take it up to 50,000 feet, it will have greater thrust at 50,000 feet than at sea level. It will have less thrust though than a nozzle that is optimally expanded at 50,000 feet, because the optimally expanded nozzle will have a higher exhaust velocity. This higher exhaust velocity causes a greater increase in thrust than the pressure effect that you are considering does, which is why optimal expansion is so desirable.

This is also why most launch vehicles take off with overexpanded engines - as the rocket climbs, it will spend the greatest possible time at something near the ideal expansion ratio.

This is an excellent webpage that talks about this in much more detail, including mathematics:
https://www.braeunig.us/space/sup1.htm

 

[rocketguy101]

This is why rocket engine design is now going in the direction of Aerospike technology. Something you might look into..

Another thing I thought of(well, maybe this is my idea ). Have you ever seen a collapseable drinking glass? They are made with tapered rings that when expanded out seal against the next ring making a drinking cup. My idea is esentially the same but with rings dropping down to increase the nozzle expansion area at the proper time.

So a launch sequence would go like: at ignition slightly overexpanded through optimum to slightly underexpanded, ring drop to slightly over expanded to optimum to slightly underexpanded. Process continuing until all rings are used.

you mean like this on the RL-10B-2

 

[dave carver]

Yup, that's pretty much it.

 

[abap]

2) Yes, a given nozzle will produce more thrust at high altitude than at sea level. Momentum thrust will remain constant for a given nozzle, but as the external pressure decreases, the pressure thrust will increase. What you don't seem to understand (which is rather shocking considering that this is your grad project) is that at a given altitude, the optimum performance is achieved with all of the thrust as momentum thrust (in other words, Pexit = Patm). If you have a nozzle that is optimally expanded at sea level, and you take it up to 50,000 feet, it will have greater thrust at 50,000 feet than at sea level. It will have less thrust though than a nozzle that is optimally expanded at 50,000 feet, because the optimally expanded nozzle will have a higher exhaust velocity. This higher exhaust velocity causes a greater increase in thrust than the pressure effect that you are considering does, which is why optimal expansion is so desirable.

This is also why most launch vehicles take off with overexpanded engines - as the rocket climbs, it will spend the greatest possible time at something near the ideal expansion ratio.

This is an excellent webpage that talks about this in much more detail, including mathematics:
https://www.braeunig.us/space/sup1.htm

thank you .
just one question; on rocket details, i read "thrust on vacuum", which is higher than the normal thrust value.
Well, according to this detail, if the rocket aproaches to the space, the thrust increases, because ambient pressure aproaches to zero, right?
so we have to have a grap like x=y, but on this page https://www.braeunig.us/space/sup1.htm , we see a curve, (but here there are 3 diffrent nozzle exit areas), i have one.
my main objective is finding "what changes if the area expansion ratio change". just this.
thx.

 

[cjl]

Yes, vacuum thrust is highest for any rocket motor. That plot on the page that I linked to doesn't show thrust vs atmospheric pressure though. It shows thrust vs exit pressure at a constant atmospheric pressure.

If the expansion ratio changes, the thrust changes, but in which direction depends on where you are on the curve plotted on that page. If you are already optimally expanded, moving the expansion ratio either way will result in reduced thrust. If you are underexpanded, increasing the expansion ratio will increase thrust, and if you are overexpanded, decreasing the expansion ratio will increase thrust. This is separate from the issue of changing ambient pressure - as the ambient pressure changes, the optimum expansion ratio changes, and for a given expansion ratio, the thrust changes as well.

 

[abap]

Yes, vacuum thrust is highest for any rocket motor. That plot on the page that I linked to doesn't show thrust vs atmospheric pressure though. It shows thrust vs exit pressure at a constant atmospheric pressure.

If the expansion ratio changes, the thrust changes, but in which direction depends on where you are on the curve plotted on that page. If you are already optimally expanded, moving the expansion ratio either way will result in reduced thrust. If you are underexpanded, increasing the expansion ratio will increase thrust, and if you are overexpanded, decreasing the expansion ratio will increase thrust. This is separate from the issue of changing ambient pressure - as the ambient pressure changes, the optimum expansion ratio changes, and for a given expansion ratio, the thrust changes as well.

Thx, and other question.
Well, acording to my calculation, best area expansion ratio is 9 for sea level, for the temperature 15 celcius, and 0,1013 atm pressure.
If we use AER 9 for a rocket, we will have a thrust, which is getting bigger from ground the air. right ?
So why not 8, why not 6 ? where is the base limit ?
https://www.astronautix.com/engines/srb.htm
Check out here, there are the details of a SRB and it has a AER of 7 .
According to this, there is no point using an AER of 10 or bigger .
But how to calculate base limit ? Nasa used 7, why not 6 ?

 

[cjl]

You can't just say that the best expansion ratio is 9 - not without knowing things like chamber pressure and temperature, and specific heat ratio of the exhaust gas.

Ignoring that for the moment though, and taking your scenario at face value, yes, a rocket with an optimal expansion ratio at liftoff will have a certain thrust at liftoff, which will increase as the rocket climbs. A rocket which is in all other respects identical, but has a higher expansion ratio at liftoff (I.E. overexpanded) will liftoff with less thrust than the optimally expanded nozzle, but the thrust will climb faster with altitude than the optimally expanded one does, until at some altitude above sea level, the thrust of the initially overexpanded motor will pass that of the initially optimum motor. At all altitudes above this altitude, the initially overexpanded motor will have greater thrust.

If you were to decrease the expansion ratio of the initially optimum nozzle, you would decrease its performance at all altitudes. Yes, its performance would climb as the rocket climbed, but in all cases it would be lower than the performance of the larger nozzle for that altitude.

I'll write a quick program to show what I mean - I'll post the graphs in a bit.

 

[daveyfire]

What Chris said. Note also that you're also using ideal rocket calculations to solve the flow parameters. This analysis is for a solid, no? Solids tend to have a lot of non-gas material in the nozzle, and long solids have nowhere near stagnation conditions feeding the nozzle, so a lot of the assumptions and parameters you solve using simple 1D isentropic relations need to be modified to figure out more realistic numbers.

Modern rocket nozzle sizing is a series of tradeoffs between performance, size, weight, and (perhaps most importantly) cooling capabilities. Booster nozzles usually aren't optimized for extreme altitude performance, but rather for performance at lower altitudes where the vehicle needs to get going as high as possible, as fast as possible, since large nozzles get heavy quickly and tend to be hard to cool. If you derive the coefficient of variation of overall delivered deltaV as a function of first stage Isp and first stage inert mass for a TSTO vehicle, you'll see that mass dominates the performance calculation (more than twice the effect).

Aerospikes seem to come and go in a cyclical fashion (1960s, 1980s, returning again soon... like other cutting edge technologies, e.g., hypersonics, plaid shirts), as people pull the drawings off the shelf, dust them off, say "Wow neat!", build a test article, and then realize that the trade in weight for performance isn't really useful except in SSTO flights where the same engine must work for long durations in both atmosphere and vacuum, and you'll really get bit by low Isp values.

The slight benefit of an aerospike nozzle on the first stage of a TSTO is far outweighed by the cooling and weight problems presented by the solid plug nozzle. And as for SSTO performance... well, we'll worry about that when someone flies a viable SSTO vehicle

 

[cjl]

OK, here's the output of a quick program I wrote that will hopefully better explain what I'm trying to say. You can see that while all of the engines climb in performance with altitude, there is still a definite benefit to the larger expansion ratios, especially at high altitude. For this particular graph, the exit pressures were as follows:

Underexpanded: 400 kPa
Optimally expanded: 101.325 kPa
Overexpanded: 25kPa

(I can post the code if anyone wants it - it's a fairly basic matlab routine)

 

[cjl]

OK, here's the code (it was requested that I post it)

Both files need to be put into the same folder for it to work, and it should be pretty self explanatory. It's kind of rough because I just threw it together, but if anyone has questions, feel free to ask.

View attachment rocket analysis.zip

 

[abap]

I think with these 2 equations, i can find exit velocity without finding the molecular mass of the gases in solid prop. rockets.
After exit velocity,
I can find thrust and Isp.
How is my logic, now help please ;
First i will calculate an optimum AER for an altitude. On that altitude, pe = pa, and pe is fixed in all altitudes for this aer and nozzle. For every 1000 meter till 80km, i will calculate, Isp, Thrust and nozzle exit temperature and all the other things. I will do this for many AER and compare their values.
my nozzle throat diameter is fixed, only exit diameter will change. mass flow rate is 4000kg/second. k=1.2, burn time = 124 seconds.

How is that ?

 

[jsdemar]

The example given by CJL shows you the compromise of choosing an expansion ratio. My original post shows you how to find the expansion ratio for a desired altitude and the propellant's specific heat ratio. Everything else you need to know is in "Rocket Propulsion Elements".

For a simulation vs altitude, use the thrust coefficient (Cf) as a factor applied to the nozzleless optimal rocket equations. A real-world case will also have an efficiency factor applied to the thrust due to thermal/friction/shock losses in the nozzle and due to combustion inefficiency.

The equations show how all the factors affect the performance. You should understand all the equations and write some software to investigate them before making intuitive assumptions about the results.

If your field of study is engineering, you should have had experience with these methods. If your field of study is computer software, I can understand why you are having difficult understanding the concepts and methods.

-John

 

[rocketguy101]

OK, here's the code (it was requested that I post it)

Both files need to be put into the same folder for it to work, and it should be pretty self explanatory. It's kind of rough because I just threw it together, but if anyone has questions, feel free to ask.

Nice! I converted your m files to a "sci" file that will run with the free software "scilab" https://www.scilab.org/. I use matlab at work, and play with scilab at home.

I placed your nozzle function in the main code--for some reason scilab balked at converting the stand alone function.

**note the "sci" in the attached zip file name attached.

View attachment Rocket_nozzle_analysis_sci.zip

 

[abap]

Hi guys, me again.
Well sorry for missunderstanding many things, because english is not my native language.
well,
on the webpage
https://www.braeunig.us/space/sup1.htm
there is comparing of 3 nozzle flow types.
well, there is a given throat area, but why we calculate the other three nozzle exit areas?
if we are triing to find the thrust change per pa/pe, we have to have a fixed area expension ratio.
but we see here it always changes.

is it calculating the nozzle exit area that corresponds to flow ? for example, there is a nozzle have a nozzle exit are X, but when it is underexpanded, it is seen as 1.5X, and when it is overexpanded it is 0.5X,
this is because of that ?

I have AER on 20.000 meters, 29 for example. , so on 20.000 meters, pa = pe.
and lets assume that nozzle exit area is X.
When calculating thrust on 10.000 meters and 40.000 meters,
should i calculate nozzle exit area from Mach equation or just use the value X ?

edit : damn it wont be like above.
wait , i will make some calculations.
argh, it is simple as hell, but they are not clear on topics

 

[cjl]

Hi guys, me again.
Well sorry for missunderstanding many things, because english is not my native language.
well,
on the webpage
https://www.braeunig.us/space/sup1.htm
there is comparing of 3 nozzle flow types.
well, there is a given throat area, but why we calculate the other three nozzle exit areas?
if we are triing to find the thrust change per pa/pe, we have to have a fixed area expension ratio.
but we see here it always changes.

For a given chamber pressure and set of fluid properties, Pe is directly related to area expansion ratio. You can't just keep the expansion ratio fixed while changing the exit pressure.

is it calculating the nozzle exit area that corresponds to flow ? for example, there is a nozzle have a nozzle exit are X, but when it is underexpanded, it is seen as 1.5X, and when it is overexpanded it is 0.5X,
this is because of that ?

I have AER on 20.000 meters, 29 for example. , so on 20.000 meters, pa = pe.
and lets assume that nozzle exit area is X.
When calculating thrust on 10.000 meters and 40.000 meters,
should i calculate nozzle exit area from Mach equation or just use the value X ?

edit : damn it wont be like above.
wait , i will make some calculations.
argh, it is simple as hell, but they are not clear on topics

I don't see what you're trying to say here.

 

[abap]

For a given chamber pressure and set of fluid properties, Pe is directly related to area expansion ratio. You can't just keep the expansion ratio fixed while changing the exit pressure.

yes but, for example , area exp ratio 29 (lets assuma it is optimal at 10km)
will be underexpanded over 10 km and, overexpanded below 10 km right?
so will the thrust-altitude graph be like the
https://www.braeunig.us/space/pics/figS1-2.gif ?
because thrust from momentum and thrust from pressure change will be diffrent.

 

[cjl]

No. The thrust altitude graph will be what I posted above. That graph that I posted shows the effect of altitude on thrust for various expansion ratios. You can see for example on the curve labeled as "overexpanded" that it is initially overexpanded, reaches a point of optimal expansion on the way up (the point where it is tangent to the ideal black line), and is underexpanded above that.

The graph in the link shows the effect of expansion ratio on thrust for a constant Pa, not the effect of varying Pa while holding Pe constant (which is shown in my graph above).

 

[abap]

this is a thrust(N)-altimeter(meter) graph of a rocket for AER of 19, and Pa = Pe at 6000 meter for this rocket.
well, is that graph true ?
it is drawn with me software

 

[cjl]

It doesn't quite look right. It should have the same shape as my graph above, but yours appears to turn up slightly at the end.

 

[abap]

It doesn't quite look right. It should have the same shape as my graph above, but yours appears to turn up slightly at the end.

yes but you said that thrust increases as the rocket increases,
because thrust from pressure diffrence will increase.
this is a fixed area expansion ratio.
we are aproaching to the vacuum