Accurate theoretical calculation of the discharge coefficient for sonic nozzle using geometric parameter measurements in Re=(7.33×104–1.26×106)

Abstract

In order to improve the measurement accuracy and efficiency of sonic nozzles (SNs) in laminar boundary layer, a correlation model for theoretical discharge coefficient of sonic nozzle taking into account the viscous effects on the boundary layer along the nozzle wall (Cd,th,1), and the multi-dimensional characteristic effect of the core region (Cd,th,2) was proposed. The theoretical discharge coefficient is related to the measurement of geometric parameters, such as the throat diameter, d, and curvature radius, Rc. The detailed geometric measurements of sonic nozzle by 3D coordinate measuring machine were conducted. Then, the evaluation procedures of parameters d and Rc including roundness and waviness profile for designed SNs of d = 7.453 mm and d = 1.919 mm were presented in detail. The effect of waviness profile on the discharge coefficient and boundary layer transient was investigated. It indicated that waviness effect is quite complex. Finally, the validation of the theoretical calculation model of discharge coefficient was verified by the experimental data of National Institute of Metrology (NIM) and National Metrology Institute of Japan (NMIJ) based on the accurate measurements of the geometric parameters. The result showed that the consistency between the Cd,exp and the Cd,th is better than 0.11% when the effect of the heat transfer was considered within the range of Re= (7.33 × 104–1.26 × 106).