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I am reading the book Mechanics and Thermodynamics of Propulsion, by Hill and Peterson. I found out this image while reading the chapter 5, "Thermodynamics of Aircraft Engines":

Turbofan and Turboprop

Why would there be a gearbox in the turboprop but not on the turbofan? Was this just a result of a simple, quick, representative sketch? Or did authors forget to add the gearbox to the turbofan?

Later in the text, it says:

The gearbox is necessary so that both propeller and core engine can operate at optimum rotational speed.

There it says "optimum rotational speed". Is that the speed of the compressor? The speed of the fan? Or maybe an intermediate, flight-airspeed-dependant speed? How does the gearbox know which is that "optimum speed"?

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    $\begingroup$ Note that "hot flow" and "cold flow" in the fan engine drawing need to be swapped to make it correct. The missing gearbox is not a mistake, however. $\endgroup$ – Peter Kämpf Apr 5 '15 at 14:14
  • $\begingroup$ True @PeterKämpf, I didn't even notice it. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 19:35
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    $\begingroup$ Please don't use images for content that is purely textual without even any formatting. Images are inaccessible to the partially sighted and to search engines. I've edited to replace it with text. $\endgroup$ – David Richerby Apr 5 '15 at 22:43
  • $\begingroup$ Great. Thinking about it, it would have been much easier using quotes. Thanks for the edit and for the tuit. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 22:46
  • $\begingroup$ In the past, the fan is small and rotates fast, for simplicity the designers simply increased the size of low pressure turbine to accommodate it and it worked reasonable well. New generation of high bypass turbofans requires the fans be much too large hence require too much torque/too low an RPM to drive, and if the turbines were again enlarged to accommodate this, it would sacrifice too much efficiency. This is why newer generation of high bypass turbofans are indeed geared (hand has much smaller low-pressure turbines than previous generations). $\endgroup$ – user3528438 May 1 '17 at 5:08
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The bigger the diameter, the lower the optimum speed. Generally, fan and propeller blades should run at a high dynamic pressure, but still at subsonic speeds to avoid the higher losses involved with supersonic flow. Since the tip will be the part with the highest speed, and propellers have bigger diameters than fans, propellers run at lower speeds.

The high pressure compressor and turbines of an airliner engine will run at above ten thousand RPM, while the propeller wants to run at about 1800 to 2200 RPM. The propellers on the Tu-95 even run at only 750 RPM. Both the fan and the propeller are powered by separate low pressure turbines which also have an optimum speed, and the faster the turbine runs, the more torque it will produce for a given size. For that reason, the low pressure turbine and the shaft of a big airliner engine run at between 2500 and 4000 RPM, and the turbine of the PT-6, a classical turboprop engine, at 30.000 RPM. Since power is torque times RPM, a faster running shaft will be lighter than one running at low speed, so the speed is only reduced directly at the propeller mount.

A fan's optimum speed is between that of the compressor and the propeller and would ideally also need a gearbox, but here the transmitted power is so high that a compact gearbox will be hard to design. Even if it runs at 98% efficiency, it will produce waste heat in the order of several hundred kilowatts in case of a big airliner engine. Some small engines with just a single turbine use gearboxes already (e.g. the Lycoming ALF507), and now the next generation of efficient fan engines are also introducing gearboxes. But so far, most engine designs have preferred to run the fan faster than what would be ideal. Note that the tip speed of a modern, ungeared fan is already well above Mach 1.

Their bigger diameter makes propellers more efficient. The more air mass is involved in thrust creation, the higher the propulsive efficiency will be. Fans need to be smaller precisely because they will run with the speed of the low pressure turbine, and to convert the available power into thrust, they need a much higher solidity ratio, which translates into a higher wetted surface, which increases friction losses.

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    $\begingroup$ Changed my mind, I will accept this answer since you made it too well editing it hours ago. A lot of rich, useful information can be extracted from your answer. This is a great contribution to this forum, thanks. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 19:24
  • $\begingroup$ Even if it runs at 98% efficiency, it will produce waste heat in the order of several hundred kilowatts in case of a big airliner engine. Just curious, but since this is a jet engine, can't it simply be air-cooled? :) $\endgroup$ – DrZ214 May 1 '17 at 4:37
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    $\begingroup$ @DrZ214: The engine is operating in rather thin air, and the gearbox needs to be very compact. There is simply not enough surface, even with lots of cooling fins. You will need to run oil through the gearbox and cool this in an external radiator - this is what has prevented the use of geared fans on larger engines so far. $\endgroup$ – Peter Kämpf May 1 '17 at 4:50
  • $\begingroup$ Apologies if this has already been covered, but I RT the last paragraph of the original post I'm not sure if it's been explained the point of the gearbox is the different sides of it can rotate at different speeds, not just one speed being selected for both sides. I get the impression that most of these gearboxes are engineered with a specific fixed ratio for that particular engine and they're not adjustable right? $\endgroup$ – StarWeaver Feb 18 '18 at 9:09
  • $\begingroup$ @StarWeaver: Yes, those gearboxes have a fixed ratio between turbine and fan speed. The running speeds of gas turbines do not differ much between idle and full thrust. $\endgroup$ – Peter Kämpf Feb 18 '18 at 21:43
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There it says "optimum rotational speed". Is that the speed of the compressor? The speed of the fan?

Both. Each has its own optimal speed (that is not the same) and the gear allows them to work at that speed. Defining what "optimal" is, is part of the engineers job; usually "optimal" is what gives the maximum efficiency, but depending on the design restrictions a different speed might be selected.

How does the gearbox know which is that "optimum speed"?

It does not "know", it is simply built so that everything will run smoothly. In this question it has been explained why there is not manual transmission on aircrafts: the gear ratio is fixed. This also answer your question, it is fixed and the gear ratio is selected during the design phase.

Why would there be a gearbox in the turboprop but not on the turbofan?

Because the propeller runs at much slower speeds. The fan can be connected directly to the low pressure turbine, while a propeller would rotate too fast.

The propeller rotates much slower than the fan because it operates on a different principle: the fan accelerates a smaller amount of air by a larger $\Delta V$ (it has to act also as a firts stage for the compressor) while the propeller accelerates an higher amount of air by a smaller $\Delta V$. This difference is noticeable also in other three aspects: the fan is ducted and has many more blades (remember, it's a first stage for the compressor), while the propeller has a few blades and is not ducted; additionally, as Peter mentions in his answer, the propeller generally has a larger diameter than a fan.

Please also have a look at this question where the differences between turbofan and turboprop are discussed

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  • $\begingroup$ I gather most turboprop propellers rotate at around 1000-1500 RPM compared to like 4000 RPM for turbofans. $\endgroup$ – Thunderstrike Apr 5 '15 at 12:00
  • $\begingroup$ Where did you read that, @MikeFoxtrot? @Federico, to my question "Why would there be a gearbox in the turboprop but not on the turbofan?" you answered "Because the propeller runs at much slower speeds". How does that answer my question? Good overall answer anyway, I only need that question to be solved. Thanks. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 12:04
  • $\begingroup$ @JoseLopez quick google search seems to suggest numbers in that region. I think that (normally at least) the turbofan has two separate shafts for both the compressor and fan, hence more control of ideal speeds than a turboprop where the prop is connected to the compressor shaft and necessitating the need for a gearbox to control the speed. $\endgroup$ – Thunderstrike Apr 5 '15 at 12:09
  • $\begingroup$ @Federico on more thing before choosing this answer as the accepted answer. You don't give me a clear definition of what an optimal rotational speed is. What is considered optimal? Maybe you could edit your answer to make it even clearer. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 13:40
  • $\begingroup$ @Federico alright, I figured out optimal had to be somewhat closely related to the word efficiency. Thanks. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 14:05
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Turbofan engines would benefit from a gearbox between the LP turbine and the fan, just like turboprops do. The problem is twofold:

Own photo

  1. The scale of the gearbox. A B777 delivers over 100,000 hp of power (torque at the fan times rotational speed). The largest geared turbofan presently in production and installed on aircraft in regular service, the PW1000G, produces 30,000 hp.
  2. The environment that the gearbox is exposed to. Manoeuvres, gusts, landing bumps, air turbulence create big problems for keeping the geared fan rotating within tight tolerances with the nacelle.

Rolls Royce is currently developing and testing the Ultrafan and has successfully tested at 70,000 hp. The current Trent 1000 has the LP turbine running at the same RPM as the fan, and this results in the LP turbine running relatively slowly. The problem is partially solved by expanding the radius of the LP turbine, so that the linear turbine blade velocities are higher.

Own photo

Expanding the LP turbine further is not an option, due to the higher drag and weight penalties that would involve. A gearbox would speed up the LP turbine and would allow for a smaller LP diameter, with associated lower weight.

Source: a discussion with a Rolls Royce engineer at the Singapore Airshow.

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Turboprop engines are (generally) powered by centrifugal or axial/centrifugal flow engines. These are smaller (again, generally) than an axial flow engine. This small size allows components to rotate at really, really, really ridiculous speeds, up to 50,000 rpm (maybe more). Spinning a propeller at even 5000 rpm is very inefficient for the few seconds the blades would stay together. The gearbox reduces the rpm to speeds slow enough to design a propeller around.

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    $\begingroup$ I feel like this answer has absolutely nothing to do with the questions I made. Anyway, thank you for reminding us what a gearbox is. $\endgroup$ – Jose Lopez Garcia Apr 5 '15 at 19:32
  • $\begingroup$ You are correct. I left too much out. My apologies. $\endgroup$ – The Jimmest Apr 7 '15 at 17:02
  • $\begingroup$ Some of the newer generation of turbofans do indeed have a gearbox between the N1 compressor and the bypass fan assembly. The P & W Purepower is an example. $\endgroup$ – The Jimmest Apr 7 '15 at 17:38
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A propeller has a bigger diameter than a fan, and because of that, the structure of the blade on a propeller sustain more 'g' (more centrifuge force if you will) so the blade of a propeller will eventually explode if it rotates to fast, because there is more mass away from the center of rotation, it 'pulls' everything outside. It's rotational inertia. (and you need a big propeller diameter because it needs to provide enough push for the airplane to fly).

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Efficiency dictates the optimun rotational speed of propellers and turbines so a gearbox will keep both of them at their best.

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    $\begingroup$ Welcome to aviation.se. while this seems to be correct, could you specify what are you adding to the already provided answers? in its current state this seems only to repeat informations that have already been posted. $\endgroup$ – Federico Apr 20 '16 at 8:25
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As others have said the optimum speeds of the (smaller) turbine and the prop of a turboprop are wholly incompatible, with the turbine needing to move several times faster, whereas in turbofans while they are not optimum they are typically close enough to their optimum speed that the increased weight, cost, complexity and potential for failure of a gearbox to transmit the huge amount of power that goes to the fan is not worthwhile, so a direct shaft is used.

Some smaller turbofans are geared which allows a faster, more efficient turbine and a slower, quieter fan but it is only recently that a geared turbofan big enough for an A320 has been produced, so I expect they're a while off yet for widebodies.

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