Influence of wall roughness on discharge coefficient of sonic nozzles

• Standard k–e model in core region and wall functions in the boundary layer region.
• The relations between discharge coefficients and relative roughness were obtained.
• Simulation results were analyzed and verified theoretically.
• Relative roughness should be used in ISO 9300 rather than absolute roughness.
• Relative roughness of sonic nozzle should be provided in the further research.

To research the influence of roughness on discharge coefficient of axisymmetric sonic nozzles systematically, a turbulence model was established, and standard k–ε model was used in the turbulent core region while Wall Functions was carried out in the boundary layer region. A series of numerical simulations were conducted to research discharge coefficients of 6 critical flow Venturi nozzles with throat diameter ranging from 0.5 to 100 mm when Reynolds numbers ranges from 104 to 109 and relative roughness from 10−2 to 10−6. The validity of the simulation model was confirmed by both the experimental data of Stewart and ISO 9300 empirical equation. According to the simulation results and theoretical analysis, the relations between discharge coefficient and relative roughness were obtained. It is recommended that the dimensionless parameter relative roughness should be used in ISO 9300 rather than absolute roughness. Additionally, when the machining of nozzle cannot satisfy the ISO 9300 requirement or the Reynolds numbers exceed the upper limits of the ISO 9300 equation, the effect of roughness should be considered, and the relative roughness of sonic nozzle should be provided clearly in the further experiment of discharge coefficient.