Nozzle Dynamics - Converging Nozzles
The fundamental development that made modern propelling nozzles possible occurred in the late 19th century. Up until that point, all nozzles were simply converging in shape, meaning that they reduced the flow area down to a minimum diameter at the exit, as shown here. These nozzles were not very efficient, but they were the only option at the time.
Converging nozzles have existed for centuries, and required little scientific understanding to develop and use. Their primitive nature was sufficient for use in early gunpowder rockets, as well as for applications involving steam such as early locomotives and factory processes.
Converging nozzles have existed for centuries, and required little scientific understanding to develop and use. Their primitive nature was sufficient for use in early gunpowder rockets, as well as for applications involving steam such as early locomotives and factory processes.
JR
While the normal properties of pressure, temperature, and density are extremely important to the design of a nozzle, perhaps the most important feature of a nozzle is the area of the nozzle at different positions along the length. Within a converging nozzle, the area of the nozzle decreases along the length as seen above. When area is constricted, the velocity of a flow increases. If the area constricts enough to become a critical area (Mach number = 1.0), the exit jet becomes a sonic flow as it comes to equilibrium with the back pressure of the environment.
If this critical area appears, it is known as a choked flow at the throat of the nozzle, which is the point with the smallest area. The throat area can be found by solving the equation for mass flow (density times velocity times area) and is shown below.
\[\frac{A}{{{A_*}}} = \frac{1}{{Ma}}{[\frac{{(1 + .5(k - 1)M{a^2}}}{{.5(k + 1)}}]^{.5(k + 1)(k - 1)}}\]
If this critical area appears, it is known as a choked flow at the throat of the nozzle, which is the point with the smallest area. The throat area can be found by solving the equation for mass flow (density times velocity times area) and is shown below.
\[\frac{A}{{{A_*}}} = \frac{1}{{Ma}}{[\frac{{(1 + .5(k - 1)M{a^2}}}{{.5(k + 1)}}]^{.5(k + 1)(k - 1)}}\]
JL