Quasi-steady deformation and drag of uncontaminated liquid drops

Abstract

Over 3000 fully resolved numerical simulations have been performed of axisymmetric liquid drops in a uniform gaseous stream. By applying a body force, the drops were held at a fixed velocity relative to the gas in order to determine their quasi-steady deformation response. The solutions were obtained using a new two-fluid spectral/hp finite element method which, as determined by validation tests, is accurate to within 1% for the conditions studied. Liquid-to-gas density ratios between 5 and 500, viscosity ratios between 5 and 15, Weber numbers between 0.1 and 50, and Ohnesorge numbers between 10 −4 and 10 were studied, enabling us to better understand the droplet behavior. Three distinct drop shapes (prolate, oblate, and dimpled) were observed, and the conditions that cause the appearance of these shapes were determined. This allowed a correlation to be developed for predicting the drop shape as a function of the dimensionless parameters governing the system. In addition, a simple criterion predicting the onset of a three-dimensional instability associated with a tumbling motion of the drops was determined. In investigating the drag force on the drops, we found that the current correlations for estimating the effect of internal circulation on the drag for spherical drops were inaccurate and therefore proposed a new correlation. Using this and the deformation correlation, we created a drag model for deforming liquid drops. This model predicts the correct trends in all cases and is usually within 5% of the numerical results. Near break-up, the error becomes larger due to the large deformations in drop shape.