Effects of Molecular Complexity and Reservoir Conditions on the Discharge Coefficient of Adapted Planar Nozzles

The transonic flow at throat section of a convergent-divergent nozzle is studied in adapted conditions to assess the influence of the fluid molecular complexity and total thermodynamic state on the discharge coefficient. The standard Sauer method is applied to solve the transonic perturbation potential equation in the vicinity of the nozzle throat. An analytic expression is derived that allows one to compute the discharge coefficient in terms of the nozzle curvature at the throat section and of the value of the fundamental derivative of gasdynamics at sonic conditions, which depends on the fluid molecular complexity and on the thermodynamic state in the reservoir. A linear dependence of the discharge coefficient on the sonic value of the fundamental derivative of gasdynamics is exposed.