What is a CD nozzle simulator?
A converging-diverging nozzle is a duct that narrows to a throat and then widens again. It is the classic way to turn stored pressure into a fast jet, and it is the shape behind steam turbines, jet exhausts and rocket engines.
This simulator lets you set two numbers: the inlet total pressure P₀ and the back pressure Pᵦ. From those two values it works out whether the throat is choked, where a shock stands, and what Mach number the flow reaches at the exit.
Why look inside?
From the outside it is just a tube. Showing the flow field and the Mach number chart reveals the two features that make the nozzle interesting: the throat reaching Mach 1 and a normal shock standing inside the divergent section.
Two ideas matter most: once the throat chokes the mass flow stops rising, and the exit Mach number is set by the pressure ratio, not by how hard you push.
1. Set the driving pressures
Inlet total pressure P₀ is the energy the air carries as it enters. Back pressure Pᵦ is the pressure the exit sees. Together they set the pressure ratio Pᵦ / P₀ that decides everything downstream.
2. The throat chokes
As the duct narrows, the air speeds up and its static pressure falls. Once the pressure ratio drops below about 0.53 the throat reaches Mach 1, and from then on adding more inlet pressure cannot raise the mass flow any further.
3. The divergent section speeds it up
Past the throat the area grows. In supersonic flow a larger area means faster flow, so the same mass of air keeps accelerating and the Mach number climbs toward the exit.
4. A normal shock can stand inside
If the back pressure is higher than the supersonic exit can match, the nozzle forces a normal shock into the divergent section. Across that thin sheet the flow jumps from supersonic to subsonic and the pressure rises sharply.
5. The exit Mach number settles
With no shock the flow leaves at the fully supersonic Mach number fixed by the nozzle area ratio. With a shock inside, the exit flow is subsonic and the exit Mach number is lower still, exactly as the chart shows.
What does a converging-diverging nozzle do?
It converts pressure into speed. The duct narrows to a throat and then widens, so subsonic air accelerates through the throat and keeps speeding up in the divergent section until it is supersonic.
What does choked mean?
Below a back-to-inlet pressure ratio of about 0.53 the throat reaches Mach 1. Adding more inlet pressure then cannot raise the mass flow any further, so the nozzle is said to be choked.
Why does a shock appear inside the nozzle?
If the back pressure is too high for the supersonic exit to match, the nozzle forces a normal shock into the divergent section. Across the shock the flow drops sharply from supersonic to subsonic.
What sets the exit Mach number?
It is set by the ratio of back pressure to inlet pressure. For a fully supersonic exit the Mach number is fixed by the area ratio; a higher back pressure moves a shock into the duct and lowers the exit Mach number.
What do the shaded colours mean?
Blue marks subsonic flow and orange marks supersonic flow. Watching the two colours shows where the nozzle reaches Mach 1 and where a shock flips the flow back to subsonic.
Why does the chart jump at the shock?
A normal shock is a sudden change, not a gradual one. The Mach number curve drops almost vertically at the shock station and then continues subsonic toward the exit.