Compressible flow in nozzles is one of the most exciting topics in fluid mechanics and aerospace engineering! When fast-moving gases zoom through a changing tube shape, amazing things happen that engineers must understand to build rockets and jet engines. First of all, nozzle flow behaves very differently from regular water flowing through pipes because gases can squish together when they move really fast. Additionally, the gas velocity can suddenly jump from below the speed of sound to supersonic flow inside specially shaped converging-diverging nozzles. Moreover, these special tubes can turn ordinary pressure into incredible pushing force that sends rockets to space! Furthermore, the Mach number (which tells us how fast the gas moves compared to sound) changes dramatically as the gas travels through narrow and wide sections of the nozzle. Most importantly, correctly modeling this compressible flow helps us build better jet engines, rocket motors, and even medical devices that use fast-moving gases! Understanding how shock waves form inside these tubes and how the flow physics change throughout the nozzle geometry is absolutely essential for modern propulsion systems that power everything from tiny model rockets to massive space launch vehicles that carry satellites and astronauts to orbit.

Figure 1: Compressible flow in nozzle– aerospace engineering application

Simulation Process

Having split from the midplane, the Axisymmetric approach is applied to solve flow equations in a cylindrical framework. Consequently, only 13530 cells established a structured grid. The ideal gas density model describes how a gas’s density changes with pressure, temperature, and composition. It is commonly used to predict gases’ behavior under different conditions. The supersonic flow in the interior zone increases the expectation of a high Mach number of regions.

Figure 1: Structured grid on half-modeled nozzle region

Post-processing

The Mach number pattern shows us something even more exciting – air breaking the sound barrier! When air enters the nozzle on the left side, it moves pretty slowly with a Mach number of just 0.05 (5% of sound speed). But then, something magical happens! Our analysis shows the air speeds up dramatically to Mach 2.93 at the exit – that’s almost three times faster than sound! Additionally, notice how the air reaches exactly Mach 1.0 (sound speed) precisely at the narrowest point of the nozzle. This perfect match with theory is called “choked flow” and it’s super important for rocket design! Most importantly, the smooth increase in speed after the throat means we’ve created perfect supersonic flow without any harmful shock waves that could waste energy. This ideal flow pattern is exactly what engineers look for when designing rocket engines and high-speed wind tunnels!

Figure 3: Mach number distribution showing flow acceleration from subsonic (M=0.05) at the inlet to supersonic (M=2.93) at the outlet

The temperature changes in our nozzle tell an amazing story about how fast-moving air cools down! As air rushes through the converging-diverging nozzle, it starts hot on the left side at 300 Kelvin (about room temperature) but gets super cold on the right side at only 111 Kelvin (that’s colder than frozen carbon dioxide!). Our simulation captured this massive temperature drop of 189 Kelvin, which happens because the air expands and uses up its heat energy to move faster. Also, notice how the temperature drops most quickly right after the middle squeeze point! Furthermore, this cooling effect is exactly why rockets and jet engines need special heat-resistant materials only in certain areas. Most importantly, this perfect temperature pattern proves that our compressible flow model correctly captures the physics of high-speed air movement through changing pipe shapes!

Figure 4: Static temperature distribution in the converging-diverging nozzle