A method for measuring planar Sauter mean diameter of multi-component fuel spray based on the combined statistical extinction tomography and particle imaging velocimetry

This study proposed a new method for measuring planar Sauter Mean Diameter (SMD) of multi-component fuel spray using a SETScan optical patternator, a particle imaging velocimetry (PIV) and a previously validated evaporation model. Malvern experiments were conducted to obtain line-of-sight SMD, which could be considered as a reference value to compare with the planar SMD due to spray symmetry. The SETScan patternator provided the planar local surface area densities at two axial cross-sections of the spray (250 mm and 400 mm below the nozzle), and the total surface area was calculated by integrating local surface area density over the concerned cross-section area. The PIV was used to measure droplet velocities at the same cross-sections, so that the time for the droplets passing through the laser sheet of the patternator (concerned cross-sections) could be determined. The total droplet volume captured within the laser sheet was then calculated by multiplying the time and the initial flow rate. The planar SMD at the cross-section is the quotient of the total volume divided by the total surface area. However, there existed a noticeable discrepancy between the Malvern SMD and planar SMD at the lower cross-section due to the evaporation being ignored. Therefore, an evaporation model was adopted to correct the total droplet volume at the lower cross-section. In particular, the evaporation model based on the droplet heat and mass transfer incorporates the non-ideality consideration for multi-component fuel evaporation by determining the activity coefficients of fuel components. It turned out that the Malvern SMD was close to the proposed planar SMD at the upper cross-section (250 mm) for all the test fuels without evaporation consideration. For lower cross-section (400 mm), the proposed planar SMD modified by incorporating an evaporation model, fit the line-of-sight SMD value better than the planar SMD without evaporation correction. The planar SMD method provides relatively complete information on a planar basis and can be used for characterizing non-symmetry sprays as well.