underexpanded and overexpanded / emergency

[cjl]

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

That's exactly what my graphs above show. Fixed expansion ratio, varying altitude.

 

[abap]

lets look at your equation;
Ve = sqrt((2*k/(k-1))*(R*Tc/M).*(1-(Pe./Pc).^((k-1)/k)));

here, Pe is not changing if your area ratio is fixed right? because if chamber pressure is fixed and all the other parameters are fixed, nozzle exit pressure doesnt change.

so , only parameter here is, pressure diffrence,
F = q*Ve+(Pe-Pa).*Ae;

and if we are getting closer to space, the increasing ratio should be increased like mines.
where is the error ?

 

[cjl]

Correct - only the pressure thrust term should change. Ve is unchanging, and so is momentum thrust, so total thrust should scale exclusively as the nozzle area multiplied by the change in ambient pressure.

 

[abap]

Ok thanks, now i have your same graph.
Well, thank you so much, when i need help, i will post here =) i have to write some more codes,
Thank you

 

[jsdemar]

Abap: where are you located? What university do you attend?

 

[abap]

hey,
i am in Turkey, Istanbul Technical University, metallurgy and Material engineering.
My grad project is, carbon-carbon composite based rocket nozzle design.
that software is out of this topic, but i am triing to present some more things.
My codes were correct exept some bugs and some english translation problems .

We are triing to make thermal barriers on nozzle throat (like ZrC coating ) for al2o3 abrasivve effect and triing to see the affects "what happens if we make 3D c-c composite, 4D c-c composite on throat", and what will be the quality if we use izophase and mezophase. Mainly focused on material.

 

[jsdemar]

hey,
i am in Turkey, Istanbul Technical University, metallurgy and Material engineering.
My grad project is, carbon-carbon composite based rocket nozzle design.
that software is out of this topic, but i am triing to present some more things.
My codes were correct exept some bugs and some english translation problems .

We are triing to make thermal barriers on nozzle throat (like ZrC coating ) for al2o3 abrasivve effect and triing to see the affects "what happens if we make 3D c-c composite, 4D c-c composite on throat", and what will be the quality if we use izophase and mezophase. Mainly focused on material.

I have good friends from Turkey. My graduate degree advisor was from there, and I've taught students from Turkey. All are smart and fun people!

Is it possible to find a partner for your project at your engineering school? Someone who is an aero major or computer science major? Otherwise, I think it would be best to concentrate on the materials & processes and not on the performance of the nozzle.

 

[luke strawwalker]

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?

I'm not a PhD, but I'll try to explain, in layman's terms...

The gases expand as they come out of the throat of the combustion chamber and into the nozzle. The nozzle has to be sized for the amount of expansion to maximize efficiency in turning the expansion of the gas into useable thrust (power). Problem is, the rate of expansion of the gas is not a constant-- it varies with the outside atmospheric pressure, which acts to limit the gas's expansion. Of course, this effect varies with altitude-- at sea level, atmospheric pressure is at it's highest, and limits expansion the most. As the rocket ascends through the atmosphere toward space, the atmospheric pressure falls off rather quickly, then at a lower rate until the rocket is in the 'vaccuum' of space (which near earth is not a true deep vaccuum, BTW, but above the sensible atmosphere for sake of this discussion can be called a vaccuum for all intents and purposes).

Now, if the nozzle is sized "too small" (underexpanded) then the gases don't get a chance to expand to the maximum amount they can, which means the rocket engine is not extracting all the thrust and power it can from the exhaust stream, hence wasting energy (and thus lowering ISP, which is essentially "fuel economy" or work produced per unit of fuel).

If the nozzle is "too big" (overexpanded) the gases are free to expand as much as they want; in fact, TOO MUCH at sea level, where the atmospheric pressure is trying to contain the exhaust plume. The gases "overexpand" and the pressure inside the nozzle gets too low, and the atmosphere ends up pushing up into the nozzle, since the fast moving gas inside the nozzle exerts less pressure on the nozzle than the static atmospheric pressure outside, which leads to flow seperation, where the hot gases 'detach' from the nozzle face and mix with air, creating turbulence and vortices and wasting energy, and other bad stuff like that. As the rocket rises, the external atmospheric pressure becomes less and less, so the plume's expansion is more smooth and eventually flow seperation and things like that will go away as the expansion ratio "becomes right" as the engine ascends on the rocket into the vaccuum. BUT in the meantime, a lot of energy (and thus fuel) has been wasted.

Now, how does this all fit together practically?? Well, the rocket is the heaviest it will ever be at liftoff, because it has it's maximum fuel load at that moment. It's also in the densest part of the atmosphere it is going to encounter. SO, to extract the maximum thrust (which is necessary to get the rocket from a standstill up and moving, while it's at/near it's maximum weight) the nozzle has to be carefully sized for the rocket so that it has the best expansion ratio for sea level atmospheric pressure, or close to it. These are called "sea level optimized" nozzles. The rocket will produce maximum thrust and efficiency at liftoff, but as the rocket ascends into the outer atmosphere (remember that roughly 90% of earth's atmosphere is below 20 miles high!) the efficiency will fall off, because the engine nozzle is actually UNDEREXPANDED at those altitudes, so energy (hence fuel) is being wasted because the exhaust flow can't expand enough to extract the maximum amount of energy from the rocket exhaust. This is usually OK though because the rocket usually stages within a few minutes of liftoff, while still in the "upper atmosphere". Sometimes, depending on the particular thrust capabilities, fuel choice, engine design, gross liftoff weight, etc. the nozzle is actually designed to be optimized to a 'midpoint' somewhere above sea level-- so the nozzle is actually slightly overexpanded at liftoff, goes through the "perfect" expansion ratio somewhere during the flight, and ends up "underexpanded" near the end of the burn, but LESS UNDEREXPANDED than if the nozzle were optimized perfectly for sea level. This increases efficiency (thrust and ISP) later in the burn where it can be more important to performance than just maximizing the gross maximum liftoff thrust.

Now, for an upperstage engine, which will be ignited somewhere above 20 miles in altitude, on up to 40, 50, even 60 or more miles up, the nozzle can be optimized for the full expansion ratio capabilities of the engine's exhaust gas flow, because the engine will be operating, at most, in only the top 10% of Earth's atmosphere. SO, usually the nozzle has a MUCH higher expansion ratio, to extract the maximum ISP from the exhaust flow, meaning that performance is maximized by being able to deliver the biggest amount of cargo for the fuel load the rocket is capable of carrying, dependent upon the other design factors involved (engine cycle and design, chosen fuel, structure optimization of the upperstage, etc.) These are typically called "vaccuum optimized" nozzles. Actually, depending on the design tradeoffs, the upperstage engine nozzle(s) can end up being slightly overexpanded if the rocket stages early (lower in the atmosphere) and is truly optimized for vaccuum operations, or if the rocket is rather heavy and gravity losses are more of an issue than underexpansion, the nozzle may actually be optimized for greatest efficiency and thrust at staging, and end up slightly underexpanded in vaccuum, which lowers the vaccuum ISP. Note too that most engines, if you check them out on astronautix or other sites, will have TWO ISP figures-- one for vaccuum and one for S.L. or sea level. That is, of course, with the standard nozzle fitted, not optimized either way. Vaccuum ISP is closest to the 'theoretical maximum' ISP the engine is capable of extracting from it's fuel and oxidizer, and the design (engine cycle predominantly) choices of the engine in question.

Now, certain engines fall into certain 'gray areas'... For instance, the Space Shuttle Main Engines (SSME's) are ignited on the launch pad, and burn all the way almost to orbit. How does one design the nozzle for an engine like that?? Well, it's all about tradeoffs. If you optimize the nozzle for sea level liftoff conditions to extract maximum thrust and energy from the exhaust at liftoff (sea level) the engine is going to be HORRIBLY underexpanded and inefficient in vaccuum. If you optimize the engine for pure vaccuum performance, the engine will be extremely OVEREXPANDED at sea level and will likely suffer flow seperation and other such stuff, and be terribly inefficient and underpowered when you need the most raw thrust to get the heavy rocket off the pad and accelerating through the dense atmosphere. Neither situation is ideal. SO, the designers must choose a "mid-point" where the engine is balanced between being SOMEWHAT overexpanded at sea level and somewhat underexpanded in vaccuum. Both lower the maximum ISP attainable, but are necessary tradeoffs to construct such an engine, and those inefficiencies can be partially dealt with in other ways (like using high-energy fuel/oxidizer like LOX/LH2, and using a more sophisticated and complex engine design combustion cycle). In the case of the SSME, most of the liftoff thrust to physically get the vehicle moving is coming from the SRB's, so the SSME's can be pushed closer to vaccuum optimization, so long as they aren't overexpanded to the point of flow seperation and other problems like that. Actually, the shuttle needs to extract the most energy from it's hydrogen/oxygen fuel/oxidizer once it's above the sensible atmosphere and accelerating to orbital velocity, and ISP is very important at that point, really moreso than thrust (so long as thrust is high enough to prevent objectionable gravity losses, which trajectory can play into as well).

Then there are "plug nozzle" or aerospike engines-- they have a 'cone' for a nozzle and the combustion chamber is a toroid (donut) shaped chamber surrounding the base of the inverted cone. The fuel and oxidizer are burned and the combustion gases expelled from the ring across the face of the inverted cone, which acts as a nozzle. Aerospike engines are considered to be "naturally optimized" since the surrounding atmospheric pressure contains the exhaust gases and limits their expansion naturally, which means no tradeoffs between underexpansion and overexpansion are necessary, since the exhaust plume will expand in direct proportion to the reducing atmospheric pressure surrounding the engine as it ascends through the atmosphere. However, the aerospike "inverted cone" nozzle is somewhat less efficient at extracting power from the exhaust stream than a bell nozzle is, which tends to hurt ISP and thrust.

Hope this helps! OL JR

 

[luke strawwalker]

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.

Two reasons--

First, the SRB's purpose is to lift the heavy shuttle vehicle and fully loaded external tank from the standing start off the pad at sea level. The higher atmospheric pressure at sea level requires a lower expansion ratio be chosen to prevent overexpanding the exhaust gases and reducing raw thrust, which the SRB's are intended to deliver (maximum raw thrust, that is).

Second, solid fuels by their very nature tend to be much lower ISP than most liquid fuels. BUT, they are very good at delivering massive, raw thrust. That is their purpose on the shuttle, and their nozzles are optimized for that, at the expense of maximum efficiency in ISP, especially at altitude. Once the shuttle gets near SRB sep, over half the fuel/oxidizer in the External Tanks is already gone, so the underexpanded losses of the smaller AER nozzles aren't as important (and the ISP losses aren't that important either or they'd have chosen a higher ISP fuel). Maximum liftoff thrust is what counts, and that's what they're designed for.

Now, that said, there ARE "vaccuum optimized" solid rocket motor nozzles-- many satellite kick stages use solid propellants and their nozzles are more vaccuum optimized. The other readily available example is the Delta II/III rockets that use airstarted SRM's... 6 of the 9 solid rocket motors are lit on the pad for additional liftoff thrust. When they burn out, they're seperated, and 3 more SRM's are airlit and deliver more additional thrust for a period of time in the flight, when the rocket is already high in the atmosphere. If you look at these versions of the Delta, you'll notice that the 3 airlit SRM's have SIGNIFICANTLY larger nozzles than the adjoining 6 that are ground lit. The ground lit nozzles need a lower expansion ratio for operation in the dense lower atmosphere (sea level optimized) and the airlit nozzles need a higher expansion ratio to extract the highest efficiency from the SRM exhaust when in the upper atmosphere (vaccuum optimized).

Hope this helps! OL JR

 

[luke strawwalker]

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 :=)

Yes, combustion chamber exhaust pressure is important, because usually the higher the combustion chamber pressure (to a point) the more efficient the engine is (higher ISP). That is why the SSME gets such phenomenal ISP and also why it was such a difficult and expensive engine to design and construct-- it's chamber pressure is VERY high.

That is also the reason why pump-fed engines are SO superior to pressure-fed engines-- pump fed engines can operate at far higher combustion chamber pressures than a pressure fed engine. The pumps have to be designed to boost the fuel/oxidizer pressures sufficiently to overcome the high pressures in the combustion chamber and inject them into the combustion chamber, but that is far easier to accomplish with a pump than a pressure fed system, where the tank pressure must be higher than the combustion chamber pressure for fuel to flow into the combustion chamber. When you figure in the difficulties with building a tank that must be lightweight enough to fly, yet still capable of holding sufficient pressure to force the fuel into the highly compressed combustion chamber without rupturing, pressure fed engines VERY RAPIDLY run into a brick wall in regards to both tank size and maximum combustion chamber pressure attainable.

Back to the original question, as I understand it, when the exhaust gases come out of the combustion chamber and begin to expand, if they expand too much (overexpanded) the pressure in the exhaust flow can drop too rapidly and actually drop below the ambient atmospheric pressure. Of course, the surrounding atmosphere doesn't like that (ever suck on a straw until it collapses flat?) and it's pressure pushes inward on the exhaust flow attempting to equalize the pressure difference. This can result in flow seperation of the exhaust flow from the nozzle surface, which creates all kinds of bad problems, not the least of which is turbulence in the flow that robs efficiency and lowers ISP, etc.

Hope this helps! OL JR

 

[luke strawwalker]

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.

This is already done on the RL10-B-2 engines... they have an extendable carbon/carbon nozzle extension that drops into place shortly before the engine is ignited (the RL10 family are AMAZING engines-- going back to the dawn of the space age, first (IIRC) mass produced LH2 engine, EXTREMELY efficient (and getting better!) and VERY simple and cheap to produce. PWR thinks they could produce them for about the same price as helicopter engines if the production rate was high enough! The only problem is they are small engines and you have to cluster a bunch of them to get high thrust. Using them for smaller payloads isn't a problem, or even larger payloads in orbit or deep space, but putting them on an upperstage which ignites much sooner in the flight of a rocket, especially a large, heavy rocket, can lead to VERY bad gravity losses from insufficient thrust, and tweaking the trajectory can help with that only SO much... That's one reason why the J-2 was SO good-- as much thrust as nearly 10 RL10's... but then again, that's why we should have finished the RL60-- only need about 4 of them to equal a J-2!)

Of course that's a neat idea, "drop down" nozzle extensions IN FLIGHT UNDER POWER, but designing something to actually do it safely and reliably, that would be a challenge!

Later! OL JR

 

[luke strawwalker]

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

Ok... I'm late to the party...

I'm also out of my depth, so I'll defer! Over to you guys!

(When the math starts I run for the door! LOL

"A man's got to know his limitations"... Clint Eastwood.

later! OL JR

 

[abap]

You are the guy man.
Thank you so so much and all the other guys that helpmed me alot. Well, you are practically in the job, not just theory.
I fixed my analyz software, and got answers why solid rocket booster has, lower AER's and sea level optimized.
Now i can see differece from my anaylzy software.

Well this graph show the diffrence, per altitude.
same exit pressure, different area exp ratios. (Thrust in Newtons, Altitudes in Meters)

As we see, the smaller one is, efficnt on lower altitudes, and lower on higher altitudes.
That is why solid rocket boosters need smaller AER's on sea levels.

Than your , very thank youi, so much thank you, i dont know anyword reamins to highligt the thanks =)).

last question is,

rl10 nozzles are c-c based ?

i was playing with black powder rockets 6 years ago =) , and i heard no one like me making his own fuel and rocket in Turkey. I was at apcforum.net, and was making high explosvies as well. Well, what a chance, i am nearly in same forums again =))). Destiny , huh ?

 

[luke strawwalker]

You are the guy man.
Thank you so so much and all the other guys that helpmed me alot. Well, you are practically in the job, not just theory.
I fixed my analyz software, and got answers why solid rocket booster has, lower AER's and sea level optimized.
Now i can see differece from my anaylzy software.

Well this graph show the diffrence, per altitude.
same exit pressure, different area exp ratios. (Thrust in Newtons, Altitudes in Meters)

As we see, the smaller one is, efficnt on lower altitudes, and lower on higher altitudes.
That is why solid rocket boosters need smaller AER's on sea levels.

Than your , very thank youi, so much thank you, i dont know anyword reamins to highligt the thanks =)).

last question is,

rl10 nozzles are c-c based ?

i was playing with black powder rockets 6 years ago =) , and i heard no one like me making his own fuel and rocket in Turkey. I was at apcforum.net, and was making high explosvies as well. Well, what a chance, i am nearly in same forums again =))). Destiny , huh ?

Yes the nozzle extension is carbon/carbon (IIRC) but the combustion chamber and main nozzle are regeneratively cooled (again IIRC).

Later! OL JR

 

[cjl]

You are the guy man.
Thank you so so much and all the other guys that helpmed me alot. Well, you are practically in the job, not just theory.
I fixed my analyz software, and got answers why solid rocket booster has, lower AER's and sea level optimized.
Now i can see differece from my anaylzy software.

Well this graph show the diffrence, per altitude.
same exit pressure, different area exp ratios. (Thrust in Newtons, Altitudes in Meters)

As we see, the smaller one is, efficnt on lower altitudes, and lower on higher altitudes.
That is why solid rocket boosters need smaller AER's on sea levels.

Than your , very thank youi, so much thank you, i dont know anyword reamins to highligt the thanks =)).

last question is,

rl10 nozzles are c-c based ?

i was playing with black powder rockets 6 years ago =) , and i heard no one like me making his own fuel and rocket in Turkey. I was at apcforum.net, and was making high explosvies as well. Well, what a chance, i am nearly in same forums again =))). Destiny , huh ?

Looks perfect. You can see exactly the same curve shapes I was getting earlier (though I can nearly guarantee you that the exit pressure is different between those two motors).

 

[abap]

thank you ehehe,, i am relaxed now = ). thanks so much. now i will try to show as many data as i can =) and present after material properties. thank you =)

 

[abap]

9 years passed and my questions are still here wow. Thank you everyone for their help . I developed a simulation program which derives the performance result based on dimensions of rocket and outside variables. It was giving mathematical results and also drawing charts as well. I used C# to develop and project name was Macbeth. I am not sure how many of users still here but thanks again . Now i have a totally different job but for sure those helps really helped me a lot to graduate.