# Why don't bypass ducts in jet engines narrow down the flow to accelerate it?

Since decreasing the flow area increases flow velocity, why don't turbofan bypass ducts narrow down to produce more thrust?

• How would accelerating the flow create more thrust? – GdD Aug 3 '20 at 15:16
• It is really hard to say from cutaways if the bypass duct narrow down. – Manu H Aug 3 '20 at 15:21
• It increases the velocity of the air @JZYL, but it doesn't create more energy. – GdD Aug 4 '20 at 7:35
• @GdD But it does create more thrust. See Asced's response below. – JZYL Aug 4 '20 at 11:11
• No, Asced says you get the same thrust either way @JZYL. 'there are two ways to produce the same thrust: strongly accelerate few air massflow or speed up a little bit a big amount of gas. Turbofans use the second strategy, mainly because it is more efficient.' – GdD Aug 4 '20 at 11:36

if you decrease the duct cross-section, you must apply work to accelerate the flow through the smaller duct. this means the fan driving the duct has to work harder (it must absorb more shaft horsepower) against that constriction in the flow and you derive no benefit- unless you mount the fan on a more powerful engine, in which case you are burning more fuel to drive the fan-and-duct system. So, there is no free lunch available here.

• Flow acceleration/deceleration is isoenergetic/isentropic. The increase in dynamic pressure (acceleration) is balanced out by the decrease in static pressure as total pressure remains constant because no work is done on the fluid. Thrust should remain the same because you are trading momentum thrust (m_dot * v) for pressure thrust (p_e - p_ambient)*A_nozzle, however pressure thrust is not as efficient as momentum thrust, so a good nozzle will have a 0 pressure difference at design operating conditions. – Stuart Buckingham Aug 6 '20 at 18:10

Mostly because there is no need to strongly accelerate the flow. In fact, thrust engine is given with the formula below:

$$F_N \approx \dot{m} \cdot \left(V_{out} - V_{in} \right)$$

Which means, there are two ways to produce the same thrust: strongly accelerate few air massflow or speed up a little bit a big amount of gas. Turbofans use the second strategy, mainly because it is more efficient.

Indeed, propulsion systems efficiency can be calculated as below, which highlights gains of creating thrust with small speed up and so huge massflow (bigger fan diameter, which is last decades tendency for civil aircrafts):

$$\eta_{p} = \frac{F_N\cdot V_{in}}{\Delta \dot{E}_k} \approx \frac{\dot{m} \cdot \left(V_{out} - V_{in} \right)\cdot V_{in}}{\tfrac{1}{2}\dot{m}\left(V_{out}^2-V_{in}^2 \right)} = \frac{2}{1+\tfrac{V_{out}}{V_{in}}}$$

Note that this formula doesn't give you the overall engine efficiency resulting to thrust specific fuel (TSFC) consumption ($$\eta_{thp}$$ = $$F_N$$$$V_{in}$$ / $$P_{fuel}$$$$\dot{m}_{fuel}$$).

• For a given engine, TSFC decrease if you add an extra duct in order to accelerate the flow, since more thrust is produced with same fuel. But, for a given thrust (fixed by aircraft flight mission) civil engine are globally more efficient with small acceleration.
• Furthermore, the relatively small excess of thrust may not worth it due to extra weight needed to extend duct nozzle.
• Turbofans use the second strategy, mainly because it is more efficient. - indeed, that's the point of building a high-bypass turbofan instead of a no-bypass turbojet. – Peter Cordes Aug 4 '20 at 0:03
• Yes, completely agree – Acsed. Aug 4 '20 at 7:01
• Yes, but “there are two ways to produce the same thrust” is perhaps a bit of a misleading way to phrase it. In fact, you always need to both have mass flow and accelerate it, the tradeoff decision is in how much of each you do. – leftaroundabout Aug 4 '20 at 12:58
• @leftaroundabout: I thought it was clear with the next sentence. But I got your point, I could edit to avoid confusion – Acsed. Aug 4 '20 at 13:19
• "For a given engine, TSFC decrease if you add an extra duct in order to accelerate the flow, since more thrust is produced with same fuel.", If this is the case then you would make the aircraft more efficient. With more thrust, you could reduce the fuel flow back to the required level and end up with a better engine. – ROIMaison Aug 5 '20 at 11:52

The simple answer is that the pressure ratio across fan is generally small, in order to maximize the propulsive efficiency, as outlined in @Asced's answer.

If you have a flow that has high total pressure (compared to inlet total pressure), then you have the real-estate to accelerate it further isentropically until the nozzle pressure reaches the ambient pressure, to maximize thrust.

However, if your total pressure behind the fan is not much higher than that of the inlet, then the available flow to accelerate via a convergent duct will be small. Depending on the pressure ratio, you can add a small ratio convergent duct, but you will need to trade off against viscous losses and added weight.

• The physics are correct but the engines don't work this way, unfortunately. Most fans operate at axial Mach numbers around 0.5 (slowed down by the intake) -- if you were exhausting the bypass jet at M=0.5, you'd actually slow down the aircraft. The bypass nozzle does accelerate the flow, all the way to the speed of sound when the fan delivers enough pressure (which it does most of the time). I've put some pictures in my answer to show what that looks like. – Zak Aug 7 '20 at 12:06

They do. It's just not by very much. Typical high bypass engine like a GE90 might narrow down the exit area by a few percent. Small enough that you probably don't even notice it when looking at it. But the air can feel it.

Lots of turbofans have convergent nozzle fan ducts although the convergence is mild. This is the Cf-34, which has a small but noticeable convergence. On a lot of engines it's barely discernible. It's because the designers are only after a small increase in velocity of the fan discharge.

• The convergence is a consequence of the increase in diameter. The cross section area shouldn't change as much (but it does narrow down a bit; that much is correct). – Peter Kämpf Aug 4 '20 at 17:18
• Just a bit of taper in the 1st 3rd just after the compressor inlet. Interesting thing about the CF-34. The annular compressor inlet in the earlier -3s was intended to be FOD resistant (a vestige of the A-10) and sees only a small ram effect and that plus the load from the hydraulic pump means these engines don't windmill very well and could core lock after a flameout if speed wasn't maintained. Later -#s raised the rear of the inlet lip to create a stronger ram effect into the compressor and partially unload the hydraulic pump so these engines will windmill right down to minimum flying speed. – John K Aug 4 '20 at 17:42
• Ok I get your point about the diameter. There may be no effective choke at all. If I was still working I could probably find out what the net cross sectional change is directly from GE. – John K Aug 4 '20 at 17:46

Thrust is not the whole story. Pure jets produce a very high velocity exhaust which may be suitable for a high speed aircraft such as a fighter, but airliners need to produce the required thrust at reasonable efficiency. Thrust is linearly proportional to momentum change of the air stream (linearly proportional to velocity change), but energy change is proportional to the square of the velocity change. What this means is that it is more energy efficient to make a small velocity change to a large mass of air than to make a large velocity change to a smaller mass of air. Processing large amounts of air can bring efficiency issues also, so a final design is an exercise in optimization trading off between numerous factors driven by the specific application (airliner, fighter, etc.).

You are of course correct in that higher exhaust velocity (for the same massflow) would produce more thrust. You may have overlooked that current turbofan engines do have a convergent bypass duct/nozzle. The axial Mach number at the fan is typically somewhere around Mach 0.5 to 0.6, and at the exhaust it's much higher than that (because the airplane is flying faster than that, and you get no jet if your exhaust is slower than you're flying...). Also: If the bypass flow acelerates more, the power to accelerate it needs to come from somewhere...

Assuming subsonic flow (i.e. the flow stays below the speed of sound everywhere)

There is a certain ambient static pressure around the bypass exhaust nozzle*. That unfortunately already determines the static pressure at the exit, and the bypass flow can only accelerate until it reaches that pressure. If you made the nozzle any smaller than that, you'd just get less massflow at the same exit velocity. In other words: The pressure ratio which the fan produces (minus intake and duct losses...) determines which velocity the bypass flow can reach when it exits the nozzle, and the amount of air you want to move through the duct determines the nozzle area. Now you could of course keep your nozzle area constant and make the fan bigger instead, but that would just mean you get slower flow through the fan, and a bigger, heavier fan. Which means more work for the intake to slow the flow down, a bigger engine, and not enough fan efficiency gained to make it worthwile.

In transonic, compressible flow (i.e. what real passenger aircraft do these days)

Except for a few conditions (engines idle, taxi, partially during take-off), the pressure ratio of the fan is usually large enough to accelerate the flow to supersonic. Now as you may be aware, the cross-section of an accelerating streamtube contracts only until it reaches the speed of sound, and expands afterwards. The theoretical ideal nozzle for this sort of thing is a convergent/divergent deNaval nozzle, and the massflow through such a nozzle is determined by the temperature, density and cross-section area at the narrowest point. This means that for a given desired massflow and a given operating condition (incoming flow, fan pressure ratio), the nozzle area is fixed, unless you want to change the mass-flow, but then you need to also change the fan pressure ratio to keep thrust constant, and now you've built a different engine.

In real life, most turbofans use a simple convergent nozzle to accelerate the flow from fan Mach number (M=0.5 to 0.6) to the speed of sound (M=1), or a convergent nozzle with a "flare" at the end. Here's a picture from this (unfortunately paywalled) paper of what the flow looks like: You can nicely see how the bypass duct and nozzle are contracting and the flow is accelerating towards the exit, all the way to Mach 1, and how it continues to expand further and reach about Mach 1.3. (That's not a finished design, and the shock waves are stronger than they need to be. The paper goes on to explain how to reduce them but that's another topic).

The reasons why there's no convergent/divergent nozzle is that in slow flight (e.g. at take-off), the incoming air has fairly little dynamic pressure and the fan can't push the total pressure to supercritical by itself. Here's a picture (with a slightly different exhaust) at Mach 0.17: An overexpanded nozzle at this condition would incur bigger losses than an underexpanded one would in cruise, and take-off and early climb are critical design points for the engine. This, and not wanting to build a longer nozzle with a bigger exit radius are the reasons why turbofan engines (on civil airliners) don't usually have convergent/divergent nozzles.

Anyway: The point is that bypass ducts on modern turbofan engines do contract, and do accelerate the bypass flow, all the way to the speed of sound as long as the fan delivers enough pressure increase to allow that.

smal aside on bypass nozzle design

One reason why underexpanding nozzles are not as bad as overexpanding ones is that the flow has more pressure than needed to get to Mach 1, and since supersonic flow expands, that's what it does as soon as it clears the nozzle (see the first picture). As a result, the streamlines in the back of the engine nacelle expand, and the jet takes up more space than if it was just nicely flowing out straight. That creates an "obstacle" for the oustide flow which further increases static pressure on the exhaust system and also on the rear of the nacelle. This additional pressure pushes the aircraft forward. All in all, there's very little thrust lost, as long as the bypass jet is only a little faster than the speed of sound (as in this case). If it had enough pressure to get to Mach 2.0 or above, that would be a very different matter.

(*) to be more precise: The ambient static pressure around the nozzle is usually a bit above the farfield pressure. So the bypass jet does not accelerate all the way immediately but stays is a little slower on the rear of the engine and only quite gets to its final velocity a little behind the engine. You can see that nicely in the second picture, for the core jet which doesn't get to it's final Mach number until it passes the tip of the cone.

• Exit pressure is not limited to the same as ambient - it is dictated by the flow through the engine. A well designed nozzle will have an exit pressure equal to ambient because pressure thrust is less efficient than momentum thrust. However, an aircraft operates through a variety of throttle settings and altitude, so it is expected that there will be pressure thrust and pressure drag at certain points of the flight envelope. – Stuart Buckingham Aug 6 '20 at 17:43
• Also high bypass turbofans never have nozzles that are designed to go critical (M = 1). A convergent nozzle would generate shocks in the exhaust which would waste so much energy as well as destroying the hearing of anyone near the airport. Narcelles and inlets are designed to slow the incoming airflow so it always remains subsonic. even Concorde and SR-71 had mechanisms to ensure engine flow was always subsonic. Unless you have a fuel that combusts instantly, engine cores,and therefore bypasses must remain subsonic. – Stuart Buckingham Aug 6 '20 at 17:48
• The actual pressure at the nozzle exit in flight is the same as around the nozzle exit. There's no way to avoid that. You might design your nozzle for some particular exit pressure, but get a different one in flight, but that just means that the actual velocity and massflow (and pressure produced by the fan) will adapt to the new counterpressure they're seeing. As I mentioned in the answer, underexpanded flow will expand outside of the nozzle and thus affect the exit pressure somewhat. Virtually all turbofans on airliners in service today are underexpanding in cruise. – Zak Aug 7 '20 at 9:42
• The fan of course operates in subsonic axial flow. In the bypass duct itself, you'd try to keep the flow as slow as possible to minimize friction losses, but the nozzle contracts to accelerate the flow (because if you don't convert the pressure increase from the fan to jet velocity, why even have a fan?). Most turbofan engines (A320, not SR71!) don't have a divergent section, and the flow expands outside of the nozzle. Search for "underexpanded nozzle" to see pictures, but keep in mind that the bypass jet doesn't expand to Mach 3 but just ~1.3 – Zak Aug 7 '20 at 10:35
• I've looked for open-source pictures but the best thing I find is figure 3a on this paper (page 3): mafiadoc.com/… -- The "separate flow" configuration is what most recently-designed civil turbofans are using, and the figure shows some shock patterns on the oustide. However, those are pretty weak oblique shocks, and they're confined to the jet (of course). It shows the bypass jet expanding a little, too. – Zak Aug 7 '20 at 10:36