convergingdiverging

Convergingdiverging refers to a geometry that first narrows and then widens, a configuration most commonly associated with converging-diverging nozzles. These nozzles, also called de Laval nozzles, are used to control compressible flow and achieve high exhaust speeds.

In a convergingdiverging nozzle, the flow passes through a throat, the narrowest section. Subsonic gas accelerates as it approaches the throat and reaches Mach 1 at that point. In the subsequent diverging section, the flow becomes supersonic and continues to accelerate even as the cross-sectional area increases. Throughout this process, the static pressure and temperature drop while the total (stagnation) conditions remain constant along a frictionless streamline.

Key concepts include mass flow continuity, which requires rho V A to remain constant. At the throat, flow can become choked, meaning the mass flow rate is at its maximum for the given stagnation conditions. The critical pressure ratio, P0/P, for choked flow depends on the gas’s specific heat ratio γ, with P0/Pc = (2/(γ+1))^(γ/(γ−1)) in idealized terms. The exit conditions depend on ambient pressure: if the exit pressure matches ambient, the nozzle is perfectly expanded; if not, the jet is underexpanded or overexpanded, affecting thrust and efficiency.

History and applications: the design traces to the work of Gustaf de Laval in the late 19th century and was later perfected for rocket propulsion and jet engines. Convergingdiverging nozzles are essential in propulsion systems to generate high-velocity exhaust and thrust, and are also used in high-speed wind tunnels and various research instruments that study compressible flow. The concept emphasizes how area variation governs flow speed and pressure in gases.