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I'm asking this question since I can't intuitively understand how the acceleration of mass flow and therefore the increase of its momentum can actually mechanically act on the combustion chamber walls and nozzle walls to induce momentum thrust.

For example, when it comes to pressure thrust induced by pressure recovery at various diffuser sections within a propulsion system, it is easy to understand that the parallel component of the force (parallel to the axis of total thrust vector) acting on the diffuser walls of the inlet, compressor diffuser, compressor stator blades, etc will induce an asymmetric load and therefore result in forward thrust. It is also intuitively understandable how the propeller/fan/compressor of gas turbine engines will induce thrust, since it is mechanically altering the mass flow, giving it more momentum and as a result of conservation of momentum, an opposing momentum, i.e. momentum thrust will occur on the individual propeller/fan/compressor blade.

Though, how does the reaction force actually act on combustion chamber/afterburner or nozzle walls? For example, from what I understand the combustion chamber and the afterburner of the gas turbine engine is a constant pressure device so it's not an increase in pressure load acting on the engine compartment that is resulting in thrust when it comes to combustion chambers of gas turbines. The way I understand combustion is that it adds heat energy to the mass flow, and subsequently some of that energy will do work and get converted into kinetic energy resulting in increased mass flow velocity. I can understand that somehow, the expanded gas would be interacting with the chamber wall mechanically resulting in increase of momentum and reactionary force, but it's just not intuitive enough and I'd like to have some better explanation to it.

As for the nozzle, according to NASA's beginner's guide to aeronautics nozzle is not doing any thermodynamic work and there's no pressure change throughout the nozzle. Though this seems a bit counterintuitive to me since my understanding is that a nozzle decreases the pressure of mass flow and increases its velocity. For such reason it is also not understandable to me how the nozzle exit speed greatly influences total thrust when there is no thermodynamic work involved (i.e. conversion of thermal energy into kinetic work, increasing momentum); it must mean that I'm not understanding some basic fundamentals correctly.

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  • $\begingroup$ Welcome to Aviation.SE. Interesting question, and something that I didn't realize I don't have an explanation for, until I see it asked like that. Nicely done! $\endgroup$
    – Ralph J
    Commented Jul 29, 2023 at 23:15
  • $\begingroup$ @RalphJ Thank you. I've been searching for the answer of this question but came to no avail through quite a few literatures. It is somewhat counterintuitive to me so hopefully I can get some answers! $\endgroup$
    – MK.s
    Commented Jul 30, 2023 at 2:21
  • $\begingroup$ Related: On which point(s) in a jet engine does the reaction force act? $\endgroup$
    – mins
    Commented Jul 30, 2023 at 11:05
  • $\begingroup$ @sophit Yes, thank you, this is exactly the answer I was looking for. So would it be correct if I think of shear force (action) induced thrust (reaction) interacting with combustion chamber rigid body in the same way how a boundary layer induces drag through shear, but reveresed? $\endgroup$
    – MK.s
    Commented Jul 30, 2023 at 15:21

3 Answers 3

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It all comes down to where you draw your control volume.

At one extreme you can draw your control volume as a simple rectangle box 'around' the engine, but with a good bit of space between the boundary of the volume and the engine. The 'top' and 'bottom' boundaries of the control volume are streamlines -- no mass flows through them. The 'front' of the control volume is the inflow -- it is far enough ahead of the engine that flow entering the control volume has freestream properties. The 'back' of the control volume is the outflow. It has two portions -- the flow that went around the engine (the boundary is far enough away that this again has freestream properties) -- and the flow that went through the engine.

With this control volume, all of the control volume boundaries have equal pressure on both sides, so there is no pressure contribution to thrust. However, the flow that goes through the engine has a change in momentum, which leaves us with $T=\dot{m}\,\left(V_j-V_\inf\right)$.

Where $V_j$ is the jet velocity, $T$ is thrust, $\dot{m}$ is the mass flow through the engine.

At another extreme, you could shrink the control volume down such that it coincides with all of the surfaces of the engine. In this case, the only mass flow that crosses the boundary is the fuel flow coming in from the injectors. If they point aft, they will contribute some thrust, but they could also be arranged to contribute nothing to thrust. To obtain the thrust, you need to perform a detailed integration of all shear and pressure forces on the boundary on every surface. These surfaces point in complex directions, so to do this integral, you have to be really careful.

Both of these approaches (and any in-between) will give the same answer. Every action has an equal and opposite reaction. Things that happen entirely 'inside' the control volume can be ignored -- they cancel themselves out such that all we need to worry about is what happens to the control volume boundary.

In practice, it is much simpler to draw the control volume far away. It makes all the math & bookkeeping much easier. It gets us the overall answer -- but without a ton of details (what is the force on an individual compressor blade).

What matters is consistency. You can't draw your control volume one place -- and then try to reconcile that part of the boundary with something that happens on the interior of the control volume.

This also works in the opposite manner. Instead of a control volume, you can think about a control mass -- a small chunk of fluid moving through an engine. We can think of it as a tiny cube. It starts off with freestream properties. The only forces that act on this control mass are pressures and shear on the six faces. The control mass will accelerate due to these forces. The energy of the control mass can change due to heat transfer in or out of each face. If the control mass is up against a boundary, then the pressure on that face will equal the pressure on the boundary.

The acceleration of the flow is intimately tied to the pressures in the flow and on the surfaces that interact with the flow.

In a simple model of a rocket, the combustion chamber is at constant pressure, but that is certainly not true in the nozzle. The nozzle expands the flow and accelerates it. Fundamentally the nozzle converts the thermodynamic energy from combustion into kinetic energy of the exhaust gas. As it does this, the gasses expand from high pressure in the combustion chamber to ambient pressure at the nozzle exit. A jet engine adds a turbine between the combustor and nozzle in order to extract work to drive the compressor (and anything else). But the turbine is also a flow expander (like the nozzle).

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  • $\begingroup$ Thank you for a thorough answer regarding the methodology. In answering my question I think setting a control volume that has boundaries that matches exactly with engine surfaces, as you've suggested, would be most helpful. Also, you greatly helped by suggesting that I should look into shear; I've considered that shear in this case would probably only contribute to the rearward thrust for some reason, although I'm probably wrong with that assumption. $\endgroup$
    – MK.s
    Commented Jul 30, 2023 at 6:27
  • $\begingroup$ I'm glad I've reminded you about shear -- but it isn't a significant player in propulsion. In fact, it will almost always amount to a loss (source of inefficiency). Most propulsion analysis can be done in terms of quasi 1D flow -- where there is only one component of velocity (x), but the cross sectional area can change (A). When doing Quasi 1D analysis by hand, we usually work from station to station -- engine inlet, compressor face/exit, burner inlet/exit, turbine inlet/exit, engine nozzle, etc. By hand, we don't pay close attention to the details of the area change between stations. $\endgroup$ Commented Jul 30, 2023 at 18:43
  • $\begingroup$ However, Quasi 1D can also be applied in much more detail, breaking each engine component into many steps and then subjected to numerical methods. In either case, F=P dA. Force is pressure acting on the change in area. The force on the air is equal and opposite the force on the walls of the tube. $\endgroup$ Commented Jul 30, 2023 at 18:51
  • $\begingroup$ Oh, so does that mean you could disregard of mass flow itself and just calculate using given pressure and rate of area change subject to pressure at any given part of the engince? Also, what you've described about shear is how I've also initially understood, that shear caused at boundary layer at the surface of each engine components would lead to surface drag. Though after reading your post and comment from Sophit above, I've thought that maybe shear is how momentum thrust is derived, especially in isobaric process where there is no area change. Am I understanding this wrongly? $\endgroup$
    – MK.s
    Commented Jul 30, 2023 at 19:43
  • $\begingroup$ If you knew the pressure everywhere in an engine, you could calculate thrust by integrating pressures (and you would need to know the fuel flow rate to the injectors). This is the idea of the 'shrunk down' control volume approach. The shears are there, but they are a viscous effect that always act against motion - they are not essential to making thrust. With the shrunken control volume, there is no fluid in the control volume -- so there is no air to accelerate. We ignore it. With the big control volume, there are no surfaces for pressure to act on, so we ignore them. $\endgroup$ Commented Jul 31, 2023 at 0:05
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how does the reaction force actually act on combustion chamber/afterburner or nozzle walls?

Let's first clarify what the reaction force is: It is the force which accelerates a mass of burning fuel-air mixture while it passes through the combustion chamber.

What causes this acceleration? In Newtonian physics, a force is needed to accelerate a mass. Here, acceleration happens due to the isobaric heating which expands the burning fuel-air mixture. In an isochoric process (volume stays constant), no acceleration occurs but pressure rises. Here, the burner can is open at both ends and surrounded by colder air, so the volume of the burning fuel-air mixture is free to expand in all directions. However, there is high-pressure air flowing in from the diffusor which blocks the expansion in forward direction and to the sides. However, downstream expansion is still possible, so that is where the gas expands to, accelerating in the process.

In one sentence, the force which accelerates the gas in the combustion chamber is the pressure force of the air flowing in from the compressor and diffusor.

To be precise: The flow in the combustion chamber can best be approximated as a subsonic Rayleigh flow, so a small pressure loss can be observed along the flow direction as the burning fuel-air mixture heats up and its stagnation pressure drops along the way. Also, friction will cause another pressure loss.

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  • $\begingroup$ Thank you so much. I've realized talking with another person that I was too focused in the word "constant pressure" (or as you point out that combustion in a constant diameter combustion chamber is isobaric) and ignored the fact that pressure drop at turbine inlet nozzle would naturally induce the mass flow to a rearward direction. As for the other part of the question, I think Sophit and Rob gave me the answer, that shear forces could act as an action force that results in forward acceleration of engine rigid body from reaction force. These two clarifications answer the question I've asked. $\endgroup$
    – MK.s
    Commented Jul 30, 2023 at 15:27
  • $\begingroup$ @MK.s I wouldn't put so much importance on shear. Pressure is the dominant source of the propulsive force. By far. $\endgroup$ Commented Jul 31, 2023 at 9:52
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From a fluid dynamics point of view, forces can be transmitted either through pressure or viscosity (aka friction aka shear).

The pressure contribution is by far the biggest one and can be simply understood by looking at the following picture (taken from this answer):

pressure distribution in combustion chamber

This picture is about the combustion chamber of a rocket, but the basic idea is the same: the horizontal force is given by the pressure acting on all the vertical areas of the chamber. As pointed out in another answer, the combustion in a turbojet/turbofan happens at more or less constant pressure so that the biggest contribution come from the vertical end of the combustion chamber and of the nozzle.

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  • $\begingroup$ Thanks for the answer, though my question would then be how an afterburner works. As you'd know the afterburner fuel injector/flamholder is separated from the turbine exit diffuser cone and afterburners also "doesn't apply additional pressure forward of the fuel injector". Shouldn't that mean there is no "plane that is normal to the nozzle axis" where the thermodynamic work of the afterburner can act on? Or is it that, although there is no pressure increase within the afterburner chamber, additional force is still being transmitted to the diffuser cone? $\endgroup$
    – MK.s
    Commented Jul 31, 2023 at 18:25

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