Numerical study of the influence of inlet turbulence intensity, wall roughness, and heat transfer in toroidal and cylindrical sonic nozzles

Sonic nozzles are widely used as a state-of-the-art secondary gas flow standard. During each calibration, different parameters, e.g. inlet turbulence intensity, wall roughness, and heat transfer influence the characteristics of the nozzle. These parameters are often not measured but can significantly affect the development of the boundary layer and thus the prediction of the mass flow rate. This numerical study investigates the influence of different inlet turbulence intensities, relative roughness values, and wall temperatures in toroidal and cylindrical sonic nozzles. For increasing turbulence intensities, transition occurs at lower Reynolds numbers. For higher roughness values, the discharge coefficient decreases in the turbulent region. The wall heat transfer primarily affects the flow in the laminar region, where the flow rate is the highest for colder walls. Altogether, this numerical work provides a deeper understanding of how relevant parameters of nozzle calibration affect the mass flow rate and transitional behaviour in sonic nozzles.