Vacuum Engines

[JEB'S DESTINY]

I have always been wondering, why do vacuum engines have a bigger bell proportionally to other sea level engines or atmospheric engines? Is it more efficient that way, or some other reason?

Vacuum Engine

Atmospheric Engine

[Mad Rocket Scientist]

Yes. Basically, the faster the exhaust, the higher the specific impulse, and the more efficient the engine is. And to get speed, you first need to make the area the flow is going through smaller, trading pressure for speed like a garden hose nozzle. But at supersonic speeds, that no longer works and you have to start expanding the area. The shape of this is called a de Laval nozzle, and looks like this:

When the exhaust comes out of a rocket engine, it has very little pressure, and a lot of speed. When the pressure drops below the ambient pressure, it stops working very well, and can even destroy the engine, so atmospheric engine are designed to expand the exhaust to around sea level pressure, and vacuum engines designed to expand the exhaust to as low a pressure as possible, before the weight of the bell exceeds the benefit of higher specific impulse.

[sevenperforce]

Expansion ratio.

A larger nozzle allows the exhaust gases more opportunity to expand against the nozzle to produce thrust. More thrust for a given amount of propellant = more efficient.

So, the question is: why don't all engines have ginormous nozzles?

The first reason is pressure. The more the exhaust gases expand, the lower their pressure drops. If an engine is firing inside the atmosphere, and its exhaust gas drops below atmospheric pressure, then air pressure is going to start to flow into the nozzle around the lip. This decreases thrust and efficiency and can even cause catastrophic damage if the exhaust flow becomes too uneven and exerts asymmetric pressure on the nozzle.

The other reason is weight. Making your exhaust nozzle twice as big may only increase your thrust and efficiency by a few percent. It's worth it for an upper-stage engine, where weight isn't as much of an issue and efficiency is vital, but for atmospheric engines you don't want the engine to be too large or too heavy because you need high thrust and low weight to get off the ground quickly.

[Bill Phil]

Your engine is more efficient when the pressure of the exhaust equals the pressure of the environment you're in. The longer the engine bell the lower the pressure, and in space there's very little pressure. An ideal engine would be infinitely long, but that's not possible, and eventually you'll start hurting your mass ratio as you add length.

[Northstar1989]

The explanations given here about Expansion Ratios do an excellent job of summarizing why vacuum rockets have larger nozzles, but I would just like to expand the discussion a step further...

The mass-effectiveness of an engine nozzle is determined not only by ambient pressure but also, in large part, the [Combustion] Chamber Pressure and [Combustion] Chamber Temperature of the rocket...

The hotter and more pressurized the exhaust is before it reaches the throat of the rocket nozzle, the more additional Thrust you can obtain by expanding the exhaust flow further.  This is because what a rocket nozzle essentially does is convert thermal energy and pressure into kinetic energy- which is why the degree to which the exhaust cools and decreases in pressure is directly related to how much it increases in velocity.

As a result of this, advances in the Chamber Pressures of current rocket designs make it worthwhile to have a larger nozzle than in past eras.  For instance the SpaceX Merlin engine set new records for Chamber Pressure for conventional rocket engines- and its vacuum version thus derives relatively more benefit from the Expansion Ratio of its nozzle than an engine with a lower Chamber Pressure and the same nozzle would...

Note that Chamber Pressure is tied up with Mass Flow Rate, but the two are not the same- an engine with a higher Chamber Pressure will often tend to have a higher Mass Flow Rate than an engine with a lower Chamber Pressure and, but if its Expansion Ratio is higher, it will also tend to have a higher ISP...

[NSEP]

 

[sevenperforce]

13 hours ago, Northstar1989 said:

The mass-effectiveness of an engine nozzle is determined not only by ambient pressure but also, in large part, the [Combustion] Chamber Pressure and [Combustion] Chamber Temperature of the rocket...

The hotter and more pressurized the exhaust is before it reaches the throat of the rocket nozzle, the more additional Thrust you can obtain by expanding the exhaust flow further.  This is because what a rocket nozzle essentially does is convert thermal energy and pressure into kinetic energy- which is why the degree to which the exhaust cools and decreases in pressure is directly related to how much it increases in velocity.

As a result of this, advances in the Chamber Pressures of current rocket designs make it worthwhile to have a larger nozzle than in past eras.  For instance the SpaceX Merlin engine set new records for Chamber Pressure for conventional rocket engines- and its vacuum version thus derives relatively more benefit from the Expansion Ratio of its nozzle than an engine with a lower Chamber Pressure and the same nozzle would...

A common point of confusion: increasing the chamber pressure does not increase specific impulse without limitation; otherwise you could get ridiculously high isp just by amping up pressure. Rather, it increases the specific impulse for a given expansion ratio.

Chemical propellants have a certain amount of chemical potential energy. Igniting them in the combustion chamber converts this chemical energy into thermal energy with very high efficiency. However, converting that thermal energy into controlled thrust (kinetic energy) is the hard part. The more your exhaust flow expands, the more of its thermal energy is converted into kinetic energy. 

An engine with a chamber pressure of 2 atmospheres can have 50% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. An engine with a chamber pressure of 10 atmospheres can have 90% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. The SpaceX Raptor engine has a chamber pressure of 247 atmospheres, so it can have 99.6% of its thermal energy converted to thrust by expanding to 1 atmosphere.

Of course there are always other efficiency losses; these percentages are the theoretical maximum. But it means overall that for a generally higher chamber pressure, you can utilize more of the total energy at sea level, and you can use more of the total energy with a smaller engine nozzle.

[KG3]

16 hours ago, sevenperforce said:

 

An engine with a chamber pressure of 2 atmospheres can have 50% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. An engine with a chamber pressure of 10 atmospheres can have 90% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. The SpaceX Raptor engine has a chamber pressure of 247 atmospheres, so it can have 99.6% of its thermal energy converted to thrust by expanding to 1 atmosphere.

Of course there are always other efficiency losses; these percentages are the theoretical maximum. But it means overall that for a generally higher chamber pressure, you can utilize more of the total energy at sea level, and you can use more of the total energy with a smaller engine nozzle.

How are jet engines related to rocket engines in regards to chamber pressures and exhaust velocity?  (I'm asking about the type of jet engines with an after burner)  They are basically an air breathing rocket but don't use a de Laval type nozzle, right?  They are by definition designed to operate in an atmosphere although at different altitudes and air pressures.  

[PB666]

17 minutes ago, KG3 said:

How are jet engines related to rocket engines in regards to chamber pressures and exhaust velocity?  (I'm asking about the type of jet engines with an after burner)  They are basically an air breathing rocket but don't use a de Laval type nozzle, right?  They are by definition designed to operate in an atmosphere although at different altitudes and air pressures.  

Jet engines (.i.e modern efficient turbofans) have bypass flow, a jet engine works in two part process. the first part is that air goes into a turbine, were it reacts with gas to create work on the blades of the turbine, this is used to force air around the turbine to the back were both are mixed, the heat from the gas mixes with the forces air creating more work (the colder the incoming air temperature the higher the expansion ratio, the more pressure at the back of the engine). The outflow of the turbine and the impelling of air around the turbine create a larger gas flow.

That is less important than what the jet does. A propellar on a plane creates work, but the tips of the propeller are forces to work against Mach forces when the blade travels fast enough, propellers cannot compress air well in the direction orthogonal to motion and make the air go faster (jet) than a certain speed. A jet compresses the air inward toward the axis of forward motion, in doing this it accelerates the air without needing for impeller blades to match that pesky Mach speed. So for aircraft that fly about one-half Mach or lower a propellar (or turboprop) is an appropriate propulsion. Once the craft exceeds 170 m/s in speed than Mach but below Mach speed a jet engine is more appropriate.

Note (wikipedia-United Airlines 777 N797UA LAX.jpg) that the front of this Rolls Royce Trent Engine is about 2 workman in height, the back is about is a small fraction. So that if the Air comes in a laminar flow at say 250m/s (something that may occur close to Mach speed) then if the area at the back is say 1/2th the area then its exiting at  500 m/s. 

Note: wikipedia - File:Turbofan3_Labelled.gif Note that as one is closer to the axis of rotation the blue arrows move faster. Inside the turbine (yellow) they move the fastest. This engine converts some of the work done on gas in turbine (slowing it down, into work done on the bypass air (speeding it up).

If we remember the equation F = 2 * eff * E/t / exhaust velocity.  A jet engine (modern tubofan) does not expell gas at 3500 m/s, it more like 300 meters per second, so it can use the energy to create magnitudes more force, or in the case of a jet engine versus rocket 10 times the Force for the same amount of power input. For a low velocity turbofan it can do this magnitudes more force per gram of fuel. But that defeats the purpose, because the atmosphere is 1/5th as thick at 13 km as MSL and because jet engines work better when the bypass air is closer to 0K, you can not take advantage of high altitude flight if your jet engine is at its coffin's corner at 7 km. So that jet engines are designed to fly generally at a certain altitude, forgoing some thrust by having some higher exhaust velocity so that they can travel at sub-mach speed higher, the higher the flight the more efficient the system works.

So jet engines are not designed to create the most amount of Forced air per unit of fuel, but designed to have an exhaust velocity at high altitude that allows optimal system efficiency in a zone between 25,000 and 45,000 feet.
(The reason they are not designed to work at a higher altitude which they could, wing loading, the craft would need a larger wing area, ozone levels increase above 45,000, the engines would be larger an bulkier to increase inlet pressure . . . .unless you are flying above Mach 1 at 45,000 feet . . . .the designs are not really beneficial). 

[Green Baron]

27 minutes ago, PB666 said:

Note (wikipedia-United Airlines 777 N797UA LAX.jpg) that the front of this Rolls Royce Trent Engine is about 2 workman in height, the back is about is a small fraction. So that if the Air comes in a laminar flow at say 250m/s (something that may occur close to Mach speed) then if the area at the back is say 1/2th the area then its exiting at  500 m/s.

Remains to add that the exhaust gases from the turbine contribute less than the fan in modern day high bipass turbofans. The (smaller) exhaust part is heated inside and so expands (before it was compressed), so the area alone doesn't describe all of the process.

The bypass air isn't supersonic, that'll make hell of a noise. It encloses the center stream, which may be close to/around sound speed, thus silencing the whole engine. For this, the two flows are designed to not mix and produce as little shear as possible (immediately after the engine).

Source: Wikipedia :-)

 

2 hours ago, KG3 said:

How are jet engines related to rocket engines in regards to chamber pressures and exhaust velocity?  (I'm asking about the type of jet engines with an after burner)  They are basically an air breathing rocket but don't use a de Laval type nozzle, right?  They are by definition designed to operate in an atmosphere although at different altitudes and air pressures.  

I am not sure if the two principles can be compared. On the one hand you have the suction, compression, combustion and exhaust (and maybe a mechanical part to turn like a fan or a propeller), on the other mixing of a combustible and oxidizer (or just some boom stuff) and directed exhaust. The first ones are designed to last 10,000s of hours, the latter ones minutes.

But i am ready to be corrected :-)

[KG3]

6 hours ago, Green Baron said:

I am not sure if the two principles can be compared. On the one hand you have the suction, compression, combustion and exhaust (and maybe a mechanical part to turn like a fan or a propeller), on the other mixing of a combustible and oxidizer (or just some boom stuff) and directed exhaust. The first ones are designed to last 10,000s of hours, the latter ones minutes.

But i am ready to be corrected :-)

I guess I was interested in the old fashion afterburner jet engine (not the high bypass turbofan type) and how they are similar and different from a rocket engine.  They are similar in that both combine fuel and oxidizer to create a fast expanding exhaust and thrust.  However the rocket exhaust exits via a bell shaped nozzle and the afterburner exhaust exits basically via a tube.  Maybe the jet engine has to accommodate the %80 or so of the stuff in the air that isn't oxygen as well as the exhaust?     

[sevenperforce]

12 minutes ago, KG3 said:

I guess I was interested in the old fashion afterburner jet engine (not the high bypass turbofan type) and how they are similar and different from a rocket engine.  They are similar in that both combine fuel and oxidizer to create a fast expanding exhaust and thrust.  However the rocket exhaust exits via a bell shaped nozzle and the afterburner exhaust exits basically via a tube.  Maybe the jet engine has to accommodate the %80 or so of the stuff in the air that isn't oxygen as well as the exhaust?     

Actually, an afterburning jet engine does accelerate exhaust gases beyond the speed of sound, so it has a converging-diverging de Laval nozzle like a rocket. The problem, though, is that the same nozzle also needs to work in "dry" mode with the afterburner off, when the exhaust gases are moving slower than Mach 1. So most afterburning turbofans have a complex tulip-like nozzle that can change shape, from converging in dry mode to converging-diverging in wet mode. The outside still looks generally like a tube, though:

Spoiler

 

[Northstar1989]

On 3/9/2018 at 3:20 PM, sevenperforce said:

A common point of confusion: increasing the chamber pressure does not increase specific impulse without limitation; otherwise you could get ridiculously high isp just by amping up pressure. Rather, it increases the specific impulse for a given expansion ratio.

Chemical propellants have a certain amount of chemical potential energy. Igniting them in the combustion chamber converts this chemical energy into thermal energy with very high efficiency. However, converting that thermal energy into controlled thrust (kinetic energy) is the hard part. The more your exhaust flow expands, the more of its thermal energy is converted into kinetic energy. 

An engine with a chamber pressure of 2 atmospheres can have 50% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. An engine with a chamber pressure of 10 atmospheres can have 90% of its thermal energy converted by expanding to 1 atmosphere or 100% converted by expanding to vacuum. The SpaceX Raptor engine has a chamber pressure of 247 atmospheres, so it can have 99.6% of its thermal energy converted to thrust by expanding to 1 atmosphere.

Of course there are always other efficiency losses; these percentages are the theoretical maximum. But it means overall that for a generally higher chamber pressure, you can utilize more of the total energy at sea level, and you can use more of the total energy with a smaller engine nozzle.

Well said.  I hope you don't think I was saying anything differently than that.

Just to be clear, you can *always* increase ISP by increasing chamber pressure or expansion-ratio (keeping one the same and increasing the other), it's just that, as you said, those improvements become progressively smaller and smaller as you approach a mathematical limit.

Your math is off, though.  It's not nearly as simple as dividing the chamber pressure by the final exhaust pressure to find the percentage of thermal energy you harness.  A rocket that expands its exhaust from 100 atmospheres to 1 atmosphere is *a lot* less than 99% efficient.  The math involved actually really hard- as in beyond my mathematical abilities hard (my abilities are just advanced single-variable calculus, basic statistics, and very limited amounts of multivariable calculus)- although there are simpler equations that exist that give a reasonable first approximation of the efficiency...

[Northstar1989]

15 hours ago, KG3 said:

How are jet engines related to rocket engines in regards to chamber pressures and exhaust velocity?  (I'm asking about the type of jet engines with an after burner)  They are basically an air breathing rocket but don't use a de Laval type nozzle, right?  They are by definition designed to operate in an atmosphere although at different altitudes and air pressures.  

Most afterburning jet engines *do* expand their exhaust to some degree at certain altitudes and speeds.  Just because it's not as obvious as with a rocket doesn't mean it's not happening.

In fact, let me clarify something- rocket engines *ARE* jet engines.  Rockets are actually just a subtype of jet engine that relies on internal propellant.

Don't just take my word for it, though- It's literally in the first paragraph of the Wikipedia page on jet engines:

"A jet engine is a reaction engine discharging a fast-moving jet that generates thrust by jet propulsion. This broad definition includes airbreathing jet engines (turbojets, turbofans, ramjets, and pulse jets) and non-airbreathing jet engines (such as rocket engines). In general, jet engines are combustion engines."

https://en.m.wikipedia.org/wiki/Jet_engine

Internal Combustion Airbreathing Jet Engines (what most people think of when they use the term "jet engine") and rockets can actually be understood with many of the same equations, and share many of the same design-principles...

Both generally include a narrow throat (much narrower than the rest of the engine) that compresses the exhaust stream to the speed of sound (Mach 1), and most high-performance jet engines that are designed to operate at supersonic speeds (i.e. most afterburning jets in things like fighter aircraft, but NOT the jets you see on large subsonic passenger aircraft) then expand the exhaust- because that is the only way to accelerate the exhaust beyond Mach 1 (you also got more Thrust that way- right up until you expand the exhaust to ambient atmospheric pressure...)

---

So, it's the same principle in an internal combustion airbreathing jet engine designed to fly at supersonic speeds as in a rocket nozzle, really.  Compress the exhaust from a combustion chamber until its velocity reaches Mach 1, then expand it to accelerate it further (ideally, enough to equal ambient pressure).  The nozzle may look a bit different, but the working principles are largely the same.

One of the biggest differences that DOES exist, however, is that many high-performance jets have variable-geometry "petals" that determine the final aperture the exhaust passes through- allowing the jet to produce exhaust at different pressures depending on the altitude as well as throttle/afterburner setting (increasing the throttle or igniting the afterburner increases the Mass Flow Rate through the engine- resulting in higher exhaust pressure unless you increase the expansion-ratio...), such as to better match the ambient pressure.  Ideally, the petals should be opened wider at higher altitudes, higher throttle settings, and when using the afterburner...

---

I also have a sneaking suspicion you don't fully understand how Expansion Ratio is defined.  If you have a 1.25 meter combustion chamber and turbofan on a jet engine, then a 0.05 meter throat, then a variable-geometry nozzle that can be anywhere from 0.600 meters to 1.25 meters in diameter, the Expansion Ratio varies between 12 and 25, not between 0.5 and 1.  The Expansion Ratio is determined by the ratio of diameters of the throat to the end of the nozzle, *NOT* by the ratio of diameters of the nozzle-end to the combustion chamber or the rest of the engine.  The throat diameter and nozzle diameter are the *only* numbers that matter here, in fact you can increase the Expansion Ratio just by making the throat diameter smaller while keeping the final nozzle diameter the same, although this can create problems with turbulent flow or excessive chamber pressures (higher than the walls of the combustion chamber can handle) if you take this too far...

 

Edited March 11, 2018 by Northstar1989

[sevenperforce]

10 hours ago, Northstar1989 said:

Well said.  I hope you don't think I was saying anything differently than that.

No worries; I was adding, not correcting.

10 hours ago, Northstar1989 said:

Just to be clear, you can *always* increase ISP by increasing chamber pressure or expansion-ratio (keeping one the same and increasing the other), it's just that, as you said, those improvements become progressively smaller and smaller as you approach a mathematical limit.

Right. I just like to remind people that the limit you approach is the theoretical total chemical potential energy of the propellants. You cannot generate more impulse than the chemical potential of your propellant allows.

10 hours ago, Northstar1989 said:

Your math is off, though.  It's not nearly as simple as dividing the chamber pressure by the final exhaust pressure to find the percentage of thermal energy you harness.  A rocket that expands its exhaust from 100 atmospheres to 1 atmosphere is *a lot* less than 99% efficient.  The math involved actually really hard- as in beyond my mathematical abilities hard (my abilities are just advanced single-variable calculus, basic statistics, and very limited amounts of multivariable calculus)- although there are simpler equations that exist that give a reasonable first approximation of the efficiency...

Well, yes, that was oversimplified. The math isn't far off; technically, the square of the exhaust Mach number is proportional to a function of the ratio of chamber pressure to outlet pressure, for a given propellant, such that the isp scales with pressure drop for most propellant combinations, up to the theoretical maximum isp for that propellant. But I didn't mean to imply that this provides even a first-order approximation of actual thermodynamic efficiency, only that it represents the scaling function between pressure drop and isp. 

The larger the pressure drop between chamber and outlet, the more thrust and isp you can squeeze out of your exhaust flow at any given expansion ratio.

10 hours ago, Northstar1989 said:

I also have a sneaking suspicion you don't fully understand how Expansion Ratio is defined.  If you have a 1.25 meter combustion chamber and turbofan on a jet engine, then a 0.05 meter throat, then a variable-geometry nozzle that can be anywhere from 0.600 meters to 1.25 meters in diameter, the Expansion Ratio varies between 12 and 25, not between 0.5 and 1.  The Expansion Ratio is determined by the ratio of diameters of the throat to the end of the nozzle, *NOT* by the ratio of diameters of the nozzle-end to the combustion chamber or the rest of the engine.  The throat diameter and nozzle diameter are the *only* numbers that matter here, in fact you can increase the Expansion Ratio just by making the throat diameter smaller while keeping the final nozzle diameter the same, although this can create problems with turbulent flow or excessive chamber pressures (higher than the walls of the combustion chamber can handle) if you take this too far...

Another issue: the limiting factor for chamber pressure is less often the chamber wall burst pressure and more often the engine cycle. You have to be able to get your propellants inside the chamber, after all. If you use a pressure-fed engine, you have to have tanks which can handle a greater pressure than your chamber. If you use a turbopump, you need power to run that turbopump. A gas-generator turbopump is the most straightforward way of doing it, but if you run too much propellant through your turbopump, you have less available propellant to actually burn in your engine. An expander cycle is more efficient, but is constrained by the specific heat of your fuel and the surface area of your exhaust bell. Staged combustion is best for supplying both high turbopump power and high efficiency, but it is terribly hard to get right.

SpaceX's Merlin engine has successfully uprated its turbopump speed multiple times, permitting higher flow and higher power. This has boosted Merlin thrust and Merlin isp over the years.

[RandomKerbal]

Basically, stuffs expand in space, you probably know diffusion right?

So, since flame(thrust) also expands, we need a longer nozzle to keep them inline. KSP's "Terrier" LF vacuum engine is fake.

Edited July 25, 2020 by RandomKerbal