Effect of reverse flow on performance of different types of a sonic nozzles

Sonic nozzles are used as precise standards for measuring gas flow because the flow rate becomes independent once the gas reaches the speed of sound at the throat. Studies have shown that toroidal nozzles consistently exhibit higher discharge coefficients than cylindrical nozzles, indicating their superior efficiency in measuring mass flow rates. In contrast, cylindrical nozzles with simpler geometries and cylindrical throats experience greater viscosity losses and higher flow separation. Previous studies have lacked the effects of reverse flow on different nozzle types, and its impact on the discharge coefficient, as analyzed through a combination of probability density function (PDF) analysis and velocity contour visualization. This study aims to fill this gap by providing numerical and experimental insights into the flow characteristics under various operating conditions. The study found that the toroidal nozzle exhibited almost the same discharge coefficient in both the exact and reverse directions, highlighting its reliability and making it a good option for applications in which the flow direction changes. However, the cylindrical nozzles exhibited more significant variations between the forward and reverse flow measurements at low inlet stagnation pressures. This was due to the sudden transition at the throat and the absence of a converging section, which caused turbulence and flow separation. For small throat diameters, experimental data showed that the discharge coefficient of the toroidal nozzle in the exact flow direction increased by 2.25% compared to the reverse flow performance at low inlet stagnation pressures and by 0.64% at high inlet stagnation pressures. The error between the experimental and numerical results for the exact direction was 0.43% and 0.21% for the low and high stagnation pressures, respectively. In addition, for a small throat diameter of 0.4064 mm at the exact and reverse positions, the boundary layer thickness almost matched the error between them by approximately 0.15%.