We determine the size of argon clusters generated with a planar nozzle, based on the optical measurements in conjunction with theoretical modelling. Using a quasi-one dimensional model for the moments of the cluster size distribution, we determine the influence of critical physical assumptions. These refer to the surface tension depending on the presence of thermal equilibrium, the mass density of clusters, and different methods to model the growth rate of the cluster radius. We show that, despite strong variation in the predicted cluster size, 〈N〉, the liquid mass ratio, g, can be determined with high trustworthiness, because g is predicted as being almost independent of the specific model assumptions. Exploiting this observation, we use the calculated value for g to retrieve the cluster size from optical measurements, i.e., calibrated Rayleigh scattering and interferometry. Based on the measurements of the cluster size vs. the nozzle stagnation pressure, we provide a new power law for the prediction of the cluster size in experiments with higher values of the Hagena parameter (Γ*>104). This range is of relevance for experiments on high-intensity laser matter interactions.

We consider condensing flow with droplets that nucleate and grow, but do not slip with respect to the surrounding gas phase. To compute the local droplet size distribution, one could solve the general dynamic equation and the fluid dynamics equations simultaneously. To reduce the overall computational effort of this procedure by roughly an order of magnitude, we propose an alternative procedure, in which the general dynamic equation is initially replaced by moment equations complemented with a closure assumption. The key notion is that the flow field obtained from this so-called method of moments, i.e., solving the moment equations and the fluid dynamics equations simultaneously, approximately accommodates the thermodynamic effects of condensation. Instead of estimating the droplet size distribution from the obtained moments by making assumptions about its shape, we subsequently solve the exact general dynamic equation along a number of selected fluid trajectories, keeping the flow field fixed. This alternative procedure leads to fairly accurate size distribution estimates at low cost, and it eliminates the need for assumptions on the distribution shape. Furthermore, it leads to the exact size distribution whenever the closure of the moment equations is exact.

The kinetic equation ͑KE͒ and its first-and second-order approximations, the general dynamic equation ͑GDE͒, and the Fokker-Planck equation ͑FPE͒, respectively, have been evaluated based on ͑a͒ their equilibrium distributions, ͑b͒ a nucleation pulse experiment, and ͑c͒ an expanding nozzle flow. Large differences are observed between the equilibrium distributions of the FPE and KE, whereas the GDE does not have an equilibrium distribution at all. For the nucleation pulse experiment, good agreement is found between the KE, FPE, and GDE due to quasisteady nucleation. For the condensing nozzle flow, the difference between the GDE and the KE distributions is large, although the relevant flow variables show fair agreement. A sensitivity study of the KE solution with respect to uncertainties in ͑a͒ the surface tension model, ͑b͒ the sticking probability, and ͑c͒ the equilibrium distribution revealed that both the sticking probability and the equilibrium distribution have a significant influence on the predicted condensation onset. Furthermore, it is found that the proposed Wölk and Strey-corrected Courtney equilibrium distribution yields the best agreement with the reported measurements.

No abstract

No abstract