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University of California at Berkeley, USA

  1. The results shown in Figure 9 and 10 and discussed in the text of the article indicate that both spray generation and initiation length for both turbulent free jets and turbulent wall jets have the same dependence on the Weber Number with just the constant of proportionality differing between the two cases. What is the physical significance of this? Does this imply that in your experiments the presence of a boundary layer has little fundamental effect on the spray dynamics?

  2. In the analysis linking turbulent eddy size to droplet generation, an implicit assumption was made that the flow is homogeneous and isotropic. In our experiments at Berkeley (at much lower Reynolds numbers) we find that the droplet size is strongly influenced by instabilities that develop due to the flow geometry. In your paper there is some indication that “the roughness elements become surprisingly long as ligaments protruding from the samples.” Do you see any indication of this comparing droplet sizes from experiments with different sizes or locations of trip wires or, possibly, between the two geometries?

  3. In the paper empirical models are presented for droplet generation at extremely high Reynolds Number, which are reasonable for full scale ships. What do the authors think are the next steps needed to (a) understand the fundamental physics of the flow and (b) provide input to numerical simulations or numerical design tools?


Our replies are numbered to correspond to Professor Liepmann's discussion:

  1. The presence of a developing turbulent boundary layer along the surface of the wall jets is fundamentally important because the surface only becomes roughened (which is a prerequisite for turbulent primary breakup) when the outer edge of this boundary layer reaches the surface. Beyond this, however, properties at the onset of turbulent primary drop breakup are similar for both free and wall jets because they only depend on properties of turbulence spectra that are the same for both flows. Greater differences between the two flows are possible for the variation of drop properties after turbulent primary drop breakup as a function of distance along the surface but this remains to be seen.

  2. The only assumptions made about the properties of the turbulence were that breakup was caused by eddies in the inertial range of the spectrum and that eddy sizes and velocities are related by equation (11); this does not entail an implicit assumption of homogeneous and isotropic turbulence. Without considering the details of Professor Liepmann's experiments, it is difficult to comment about his observations of drops sizes after primary breakup except to note that smaller inertial ranges of the turbulence spectrum at low Reynolds numbers would make large-scale features more important and that initial disturbances of wall jets can dominate the turbulent wall boundary layer phenomena emphasized during the present paper for some experimental configurations. Finally, effects of trip wire and flow properties on drop sizes for the present experiments were explained reasonably well by the phenomenological theories discussed here.

  3. There are a number of issues that should be better understood in order to provide the technology base needed to address these flows, including the evolution of drop size/velocity distributions and the rate of production of dispersed liquid due to turbulent primary breakup as a function of distance along the surface. The mean and turbulent structure of the liquid wall jet, the drag and ligament properties at the gas/liquid interface and the structure of the dispersed multiphase flow region adjacent to the liquid wall jet, among others.

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