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?
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?
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.
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.