Improved Prediction of the Flow in Cylindrical Critical Flow Venturi Nozzles Using a Transitional Model

Critical flow Venturi nozzles (CFVNs) are a state-of-the-art secondary standard widely used for gas flow measurements with high precision. The flow rate correlates with the type and thickness of the boundary layer (BL) inside the nozzle throat. In the cylindrical type—one of the two standard designs of CFVNs—the nozzle throat encompasses a defined axial length in which the BL develops. This numerical study is concerned with the BL effects in a cylindrical CFVN by means of two turbulence models. Compared to experimental data, the k- \(\omega\) $\omega$ SST model predicts the discharge coefficient well for high and low Reynolds numbers, but not in the intermediate regime. The \(\gamma\) $\gamma$ - \(Re_{\theta }\) $R{e}_{\theta }$ model, on the contrary, agrees well with experimental data in the entire flow range. Relevant quantities and profiles of the BL are separately investigated in the laminar, turbulent, and transitional region. The calculated laminar and turbulent BL thicknesses correspond to predictions based on integral methods for solving the BL equations. Simple representations are proposed for the Zagarola-Smits scaled laminar and turbulent deficit BL profiles removing the effects of axial position, Reynolds number, and pressure gradient. Furthermore, the shape factor is investigated as a characteristic parameter for determining the transitional region.