A nozzle and Experiments



A nozzle (from the nose, meaning ‘small spout’) is a tube of varying cross-sectional area (usually
axisymmetric) aiming at increasing the speed of an outflow and controlling its direction and shape.
Nozzle flow always generates forces associated to the change in flow momentum, as we can feel by handholding
a hose and opening the tap. In the simplest case of a rocket nozzle, relative motion is created by
ejecting mass from a chamber backwards through the nozzle, with the reaction forces acting mainly on
the opposite chamber wall, with a small contribution from nozzle walls. As important as the propeller is
to shaft-engine propulsions, so it is the nozzle to jet propulsion, since it is in the nozzle that thermal
energy (or any other kind of high-pressure energy source) transforms into kinetic energy of the exhaust,
and its associated linear momentum producing thrust.
The flow in a nozzle is very rapid (and thus adiabatic to a first approximation), and with very little
frictional loses (because the flow is nearly one-dimensional, with a favorable pressure gradient except if
shock waves form, and nozzles are relatively short), so that the isentropic model all along the nozzle is
good enough for preliminary design. The nozzle is said to begin where the chamber diameter begins to
decrease (by the way, we assume the nozzle is axisymmetric, i.e. with circular cross-sections, in spite that
rectangular cross-sections, said two-dimensional nozzles, are sometimes used, particularly for their ease

of directionability). The meridian nozzle shape is irrelevant with the 1D isentropic model; the flow is only


dependent on cross-section area ratios.
Real nozzle flow departs from ideal (isentropic) flow on two aspects:
• Non-adiabatic effects. There is a kind of heat addition by non-equilibrium radical-species
recombination, and a heat removal by cooling the walls to keep the strength of materials in longduration
rockets (e.g. operating temperature of cryogenic SR-25 rockets used in Space Shuttle is
3250 K, above steel vaporization temperature of 3100 K, not just melting, at 1700 K). Shortduration
rockets (e.g. solid rockets) are not actively cooled but rely on ablation; however, the
nozzle-throat diameter cannot let widen too much, and reinforced materials (e.g. carbon, silica) are
used in the throat region.
Nozzles 2
• There is viscous dissipation within the boundary layer, and erosion of the walls, what can be
critical if the erosion widens the throat cross-section, greatly reducing exit-area ratio and
consequently thrust.
• Axial exit speed is lower than calculated with the one-dimensional exit speed, when radial outflow
is accounted for.
We do not consider too small nozzles, say with chamber size <10 mm and neck size <1 mm, where the
effect of boundary layers become predominant.


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