Pressure on the Walls of a Rocket Motor Bell Nozzle

[Islam Hassan]

Is the pressure due to the hot gas exhaust stream on the inside walls of a rocket motor bell nozzle positive or negative?

Does the rocket exhaust exert a outward pressure on the nozzle walls due to the sheer volume of the exhaust gases or is the pressure a negative one due to the exhaust stream following a trajectory which is quasi-parallel to the nozzle walls?

It would seem in any case that at very high altitudes and low air densities, the pressure is positive since the exhaust stream fans out very broadly on its exist from the nozzle. What is the case at sea level however?IH

 

[Chestermiller]

Can you please provide a diagram.

 

[cjl]

The pressure inside the nozzle is very high near the throat, and decreasing as you approach the exit plane. For a nozzle operating in its design condition (neither over nor underexpanded), the pressure will reach ambient at the exit plane of the nozzle, so it is higher than ambient at all points inside the nozzle. This is desirable since everywhere inside the nozzle where pressure is above ambient, there is a thrust contribution due to the angle of the nozzle walls. If a nozzle is overexpanded (extended beyond this point where the pressure inside the nozzle is equal to the ambient pressure), all further regions of the nozzle will actually cause a net negative thrust, as the internal pressure pushing these wall segments forward will be lower than the external pressure pushing them backwards.

Most nozzles used for space vehicles are designed to be slightly overexpanded at sea level, with pressure at the exit plane slightly below ambient (so if you look carefully at rocket plumes, you tend to see a bit of flow contraction after the flow leaves the nozzle). This is because the slight loss of thrust and efficiency at ignition and liftoff is made up for by an increase in performance later in flight after the ambient pressure has decreased. As I alluded to before however, the optimum thrust and efficiency occurs when the pressure at the exit plane is exactly equal to the ambient pressure around the rocket, which will cause the exhaust to come out straight and parallel with no flow expansion or contraction after exiting the nozzle.

 

[Islam Hassan]

The pressure inside the nozzle is very high near the throat, and decreasing as you approach the exit plane. For a nozzle operating in its design condition (neither over nor underexpanded), the pressure will reach ambient at the exit plane of the nozzle, so it is higher than ambient at all points inside the nozzle. This is desirable since everywhere inside the nozzle where pressure is above ambient, there is a thrust contribution due to the angle of the nozzle walls. If a nozzle is overexpanded (extended beyond this point where the pressure inside the nozzle is equal to the ambient pressure), all further regions of the nozzle will actually cause a net negative thrust, as the internal pressure pushing these wall segments forward will be lower than the external pressure pushing them backwards.

Most nozzles used for space vehicles are designed to be slightly overexpanded at sea level, with pressure at the exit plane slightly below ambient (so if you look carefully at rocket plumes, you tend to see a bit of flow contraction after the flow leaves the nozzle). This is because the slight loss of thrust and efficiency at ignition and liftoff is made up for by an increase in performance later in flight after the ambient pressure has decreased. As I alluded to before however, the optimum thrust and efficiency occurs when the pressure at the exit plane is exactly equal to the ambient pressure around the rocket, which will cause the exhaust to come out straight and parallel with no flow expansion or contraction after exiting the nozzle.

So would it be correct to say that the nozzle contributes positive pressure and hence thrust due to the angle of the nozzle walls only in an accessory capacity? And that the bulk of the thrust load is applied at the face of the injector?IH

 

[cjl]

I'm not sure I would go that far. It's been a while since I ran the numbers, but I'd expect the nozzle to contribute quite substantially to the overall thrust, though you could check on this if you knew the nozzle throat area and the combustion chamber pressure, as the nozzleless contribution could then be approximated (somewhat accurately) as just being the chamber pressure multiplied by the nozzle throat area. Compare that value to the actual thrust and you have some idea of what the nozzle contribution actually is.

 

[Islam Hassan]

I'm not sure I would go that far. It's been a while since I ran the numbers, but I'd expect the nozzle to contribute quite substantially to the overall thrust, though you could check on this if you knew the nozzle throat area and the combustion chamber pressure, as the nozzleless contribution could then be approximated (somewhat accurately) as just being the chamber pressure multiplied by the nozzle throat area. Compare that value to the actual thrust and you have some idea of what the nozzle contribution actually is.

I'll try to work it out. The thought came to me because when one looks at the thinness and intricacy of nozzle walls what with their integral cooling ducts and all, it is hard to imagine that they are designed to bear significant structural loadings...and that at a heinously high thermal gradient too...IH

 

[sophiecentaur]

And that the bulk of the thrust load is applied at the face of the injector?

The thrust will be due to the pressure over the whole of the nozzle. it varies over the nozzle so you would need to Integrate the Pressure times the infinitesimal areas over the nozzle. The thrust will be the rearwards component of this force and the nozzle has to be strong enough to support this and the lateral forces. A pretty high stressed device in several respects.

 

[cjl]

The thrust will be due to the pressure over the whole of the nozzle. it varies over the nozzle so you would need to Integrate the Pressure times the infinitesimal areas over the nozzle. The thrust will be the rearwards component of this force and the nozzle has to be strong enough to support this and the lateral forces. A pretty high stressed device in several respects.

To be fair, some of the thrust does come from pressure on the injector face as well. If you sawed off the nozzle at the throat, the thrust would come from the area difference between the injector face and the back of the combustion chamber, since the rear has a hole in it (there would also be a pressure difference, especially around the hole, but I'm neglecting that for simplicity right now). Adding the nozzle does add the component you reference here though, and as I speculated before, I'd expect the nozzle contribution to be very significant to the overall thrust of the rocket engine.

 

[sophiecentaur]

To be fair, some of the thrust does come from pressure on the injector face as well

That makes sense.

I'd expect the nozzle contribution to be very significant to the overall thrust of the rocket engine.

I looked at Images of "rocket nozzle" and there seems to be a bigger range of ratios of injector diameter to nozzle diameter, for different designs, than I expected. But your comment puts the nozzle contribution into perspective; sometimes it seems as if the nozzle contribution would only be about the same as from the injector.

 

[Islam Hassan]

That makes sense.

I looked at Images of "rocket nozzle" and there seems to be a bigger range of ratios of injector diameter to nozzle diameter, for different designs, than I expected. But your comment puts the nozzle contribution into perspective; sometimes it seems as if the nozzle contribution would only be about the same as from the injector.

Yes that would be my impression too. Doubtless the nozzle does contribute to thrust —and perhaps more at higher altitudes than at sea level— but I doubt that such contribution would be more than, say, 50% at most.

I am still intrigued by the thinness of nozzle walls though. To my mind they would have to be tremendously strong to contain the exhaust pressures. Especially that they are not homogenous but are criss-crossed by super-cooled fuel/oxidiser ducts and are therefore also operating at mind-boggling temperature gradients. Does anyone know of what material and how nozzle walls are made?IH

 

[sophiecentaur]

To my mind they would have to be tremendously strong to contain the exhaust pressures.

It must rely on the symmetry of the forces - as in a balloon.

 

[A.T.]

Doubtless the nozzle does contribute to thrust —and perhaps more at higher altitudes than at sea level— but I doubt that such contribution would be more than, say, 50% at most.

The parameter you are looking for is called "thrust coefficient" (total_thurst / chamber_thurst):

https://www.nakka-rocketry.net/th_thrst.html

I found values of up to 1.8, so the nozzle indeed provides less than 50% of total thrust.

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680010365.pdf

But you might look for more data, to confirm this.

 

[Islam Hassan]

The parameter you are looking for is called "thrust coefficient" (total_thurst / chamber_thurst):

https://www.nakka-rocketry.net/th_thrst.html

I found values of up to 1.8, so the nozzle indeed provides less than 50% of total thrust.

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680010365.pdf

But you might look for more data, to confirm this.

Thanx A.T...much obliged...IH