Why does the diffuser section generate thrust in a jet engine?

Question

I am studying the thrust distribution of jet engines. But I'm now a bit confused.

In Rolls-Royce's "The Jet Engine" book, http://aeromodelbasic.blogspot.com/2012/05/thrust-distribution-distribution-of.html

At the start of the cycle, air is induced into the engine and is compressed. The rearward accelera- tions through the compressor stages and the resultant pressure rise produces a large reactive force in a forward direction. On the next stage of its journey the air passes through the diffuser where it exerts a small reactive force, also in a forward direction

I understand the first part of the paragraph that the compressor is providing forward thrust, as it is pushing (so compressing) air rearward. But why is the diffuser also providing forward thrust? And also why the nozzle is providing rearward thrust?

The similar conculsion is also shown here: http://www.pulse-jets.com/phpbb3/viewtopic.php?t=2183, that the diffuser is providing positive thrust by calculating the pressure force.

From my understanding of basic fluid mechanics, shouldn't a nozzle be providing forward thrust, like the sprinkler in the garden or a fire hose? And shouldn't a diffuser be providing rearward thrust, as the outlet speed is slower than the inlet speed, and so m dot X (v - u) is negative?

What's wrong with my understanding?

Answer 1

But why is the diffuser also providing forward thrust?

The diffuser slows down the flow to ease fuel-air mixing and combustion a bit later. If you only focus on entry and exit speeds, there would be no thrust.

However, if you look at the pressures on the diffuser walls, a different result emerges. Slower flow means higher static pressure, and the total pressure right at the compressor exit is already the highest within the whole engine. The pressure on those widening diffusor walls does indeed push the engine forward because of the forward slant of the pressure vector (which acts perpendicularly to the diffusor walls). Your linked pulse jet page explains this quite well.

Of course, no thrust would result if the flow were not heated and thus accelerated further downstream. So the diffuser all by itself will not create thrust; this happens only when it is placed inside a working jet engine.

And also why the nozzle is providing rearward thrust?

This is not always the case, but here the nozzle has a converging shape which helps to accelerate the subsonic flow and converts the remaining pressure to speed. The walls now have a backward-facing slant, so the pressure vector on them will contribute a backward-facing component. In addition, the high flow speed along the large nozzle walls causes some friction, which needs to be considered, too.

For a comparison, look at the cone behind the turbine wheels. Its thrust contribution only stems from the forward-facing pressure acting on it.

Answer 2

And shouldn't a diffuser be providing rearward thrust, as the outlet speed is slower than the inlet speed, and so $\dot{m}\times(v - u)$ is negative?

Conservation laws in physics are an excellent tool. They let you calculate a lot without looking at the minutiae details of the actual process. And this is great example: you can trivially calculate thrust of the whole engine from the change of momentum of the working fluid. But that won't tell you how the force is actually applied, only the sum of the forces on the entire engine.

The thrust break-down is the minutiae details of the process. And at that level, the only way to create a force is by pressure of the fluid, and since pressure always acts perpendicular to the surface, only the aft-facing surfaces can have forward thrust act on them, while any forward-facing surfaces have negative thrust act on them.

And it's no different in the sprinkler. The pressure inside is acting on all the walls, but there is a bit missing in the nozzle where the water flows out, so the force on the opposite wall prevails.