Boundary layer transition in choked nozzles

In this study, we investigate the transition from laminar to turbulent flow in boundary layers within nozzles used as standard flow meters. Experiments are conducted to analyse the effects of surface roughness, the radius of curvature at the nozzle throat and the level of free stream turbulence. The results indicate that, for industrial nozzles with standard roughness levels, surface roughness does not significantly influence the transition process. Additionally, tests on three different nozzles reveal that a smaller throat radius corresponds to a higher Reynolds number at the transition point. To understand this behaviour, we develop a theoretical model where the laminar boundary layer profiles are derived using an analytical formulation that accounts for compressibility and favourable pressure gradients in these nozzles. The stability characteristics of this boundary layer are examined within the framework of linear stability theory, assuming parallel flow. Since Tollmien–Schlichting waves are stabilised by the favourable pressure gradient, a spatial transient growth analysis is employed to explore the role of bypass mechanisms. Similar to the flat-plate boundary layer case, the optimal perturbations are identified as streaks. Due to the nozzle wall’s convex curvature, the highest growth is observed at low but non-zero frequencies, leading to unsteady streak formation. A transition model, based on the N -factor of optimal unsteady streaks, is used to estimate the onset of transition. This model successfully reproduces the experimentally observed effects of curvature and can be used to optimise the design of mass-flow-meter nozzles. Finally, the critical roughness size required to trigger a roughness-induced transition is estimated theoretically and compared with experimental observations. The impact of distributed roughness on transition is examined in relation to stability theory, showing that the tested roughness levels are ineffective in triggering transient growth mechanisms.