An experimental investigation on the performance of conical nozzles for argon cluster formation in supersonic jets

This work intends to get a better understanding of cluster formation in supersonic nozzles of different geometries. The throat diameters d are within 0.26 mm < or = d < or = 0.62 mm, the half-opening-angle alpha within 4.2 degrees < or = alpha < or = 11.3 degrees, and the length L of the conical section is 17.5 mm (eight nozzles) or 12 mm (two nozzles). Thus the so-called "equivalent sonic-nozzle diameter d(eq)" for these conical nozzle geometries, defined by d(eq)=0.74 d/tan alpha (for monatomic gases), is in the range of 1.59 mm < or = d(eq) < or = 5.21 mm. Source temperature for the clustering experiments was T(0)=298 K, and the backing pressure P(0) was between 0.5 and 30 bars. The (average) cluster sizes observed for these conical nozzles deviate from the predictions of the simple stream-tube-model. These deviations are accounted for by introducing the so-called "effective equivalent sonic-nozzle diameter d(eq)*," defined as the product of the equivalent sonic-nozzle diameter d(eq) and a new parameter delta, d(eq)*=deltad(eq). The parameter delta serves to modify the equivalent diameters d(eq) of the conical nozzles, which are applied in the idealized cases where the gas flows are suggested to be formed through free jet expansion. Then, delta represents the deviation of the performance in cluster formation of the practical conical nozzles from those predicted based on the idealized picture. The experimental results show that the values of delta can be described by an empirical formula, depending on the gas backing pressure P(0) and the parameter d(eq) of the conical nozzles. The degradation of the performance of the present conical nozzles was found with the increase in P(0) and the larger d(eq). It was revealed that delta is inversely proportional to a fractional power (approximately 0.5-0.6) of the molecular density n(mol) in the gas flows under the present experimental conditions. The boundary layers effects are considered to be mainly responsible for the restriction of the performance of the conical nozzles in cluster formation.