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  1. My understanding is that the exhaust gas gains velocity as its heat converts to kinetic energy, regardless of the geometry of the nozzle, and the reason we have a convergent-divergent (CD) nozzle is to further accelerate the exhaust gas, as implied by the relation between $dv$ and $dA$ that depends on Mach number (https://www.grc.nasa.gov/WWW/K-12/rocket/nozzle.html#:~:text=A%20nozzle%20is%20a%20relatively,divergent%2C%20or%20CD%2C%20nozzle). So I view them as two separate effects, which means that if we have a nozzle that diverges first and then converges, the velocity of the gas will not necessarily decrease in the diverging part as implied by the relation between $dv$ and $dA$. Otherwise, where does the heat go if it does not go to increasing kinetic energy?

  2. The derivation of the relation between $dv$ and $dA$ cited above depends on conservation of mass. I read that this is not the case in real life and am wondering how mass is lost as the exhaust gas flows through the rocket nozzle. Is there an equation calculating the loss of mass and how do we account for it if there is not one? Would the relation between $dv$ and $dA$ still hold without the assumption that mass flow rate is conserved?

Peter Nazarenko
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Xi Liu
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    Does CD = compress/decompress? Does "What if we have a DC nozzle..." mean a decompress, then compress nozzle? Here's how I imagine what's happening. In the combustion chamber high temperature means molecules are moving at high speed in random directions. The average velocity squared $<v^2>$ about the center of mass of a small volume of gas is high, but the average velocity $$ is almost zero since it moves very slowly out the back. The magic of the decompression is that while it lowers $<v^2>$ (cools) a volume element, it converts all that conserved kinetic energy to center of mass motion. – uhoh Oct 17 '20 at 22:33
  • and converts it to a huge $$ pointed backwards. The nozzle's job is to harness that random molecular motion and turn it into a single direction out the back. Of course it's more complicated than this because there are heat transfer effects and chemical reactions are still happening, but that final D is really important. – uhoh Oct 17 '20 at 22:35
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    "Convergent/Divergent", not compress/decompress. – Russell Borogove Oct 17 '20 at 22:47
  • Mass is always conserved, as are momentum and energy. What do you mean “this is not the case in real life...”? The area mach relationship is based on isentropic flow assumptions. Perhaps that is what you’re referring to as “not the case in real life”? – Paul Oct 17 '20 at 23:05
  • "the velocity of the gas will not necessarily decrease in the diverging part": the gas accelerates in the diverging part of a rocket nozzle, as it is supersonic. It transitions from subsonic to supersonic at the throat. – Christopher James Huff Oct 17 '20 at 23:26
  • @RussellBorogove Oh I see; CD = Convergent/Divergent describe the shape of the nozzle, and that it serves to Compress/Decompress and that those also begin with CD is just a coincidence. I suppose that next you're going to tell me that that's not thrust shooing out of the nozzle? (humor) – uhoh Oct 17 '20 at 23:32
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    Folks why not consider being welcoming and instead of down voting and closing a new user's first question that begins "My understanding is that..." why not post a short answer and help them out? Voting to leave open so that someone will have an opportunity to answer. There's no need to insta-block potential answers. – uhoh Oct 17 '20 at 23:34
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    @uhoh I think linguistically it's more than coincidental, but yeah. – Russell Borogove Oct 18 '20 at 00:06
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    Thanks for your answers! My bad. I should have clarified that "C" means converging and "D" means diverging. What I do not understand is that, if we have a nozzle that diverges first, would the velocity of the exhaust increase or decrease in the diverging part? On the one hand, the Mach number is less than 1 in this part, so velocity should decrease as surface area increases; on the other hand, the heat of the gas is being converted to the kinetic energy of the gas, so it should keep being accelerated. Is there anything wrong with my thinking? – Xi Liu Oct 18 '20 at 00:54
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    A divergent passage accelerates a supersonic flow; it decelerates a subsonic flow.https://space.stackexchange.com/q/18904/6944 – Organic Marble Oct 18 '20 at 01:07

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To have something actually posted in answer form

The principle governing the shape of rocket nozzles is in its most reduced form the following:

  • A narrowing passage accelerates subsonic gasses, and decelerates supersonic gasses.
  • A widening passage decelerates subsonic gasses, and accelerates supersonic gasses.

It follows that we want the nozzle to become increasingly narrow while the flow is still subsonic, and once it has reached the speed of sound, we want the passage to become wider again to further speed up the flow.

The shape is therefore first converging, and then diverging. A "CD" nozzle.

CD nozzle

A "DC" nozzle would not be very practical. If the diverging part comes first, the subsonic flow is not accelerated. When it reaches the converging part, still subsonic, it may be able to accelerate some, barely reaching the speed of sound, which is too slow and not an efficient use of our rocket fuel.

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