Measurements of Diesel Spray Droplet Size with Ultra-Small Angle X-Ray Scattering

The strong scattering of visible light by spray droplets has severely impeded the ability of optical diagnostics to probe dense sprays. X-rays interact more weakly with spray droplets than visible light; as such, multiple scattering effects are rarely important in the x-ray regime. As such, x-ray radiography (which relies on absorption) and x-ray phase-contrast imaging (which relies on subtle refractive and diffractive effects at phase boundaries) have provided unique insights regarding the breakup of dense sprays. The current study extends these measurements to study the droplet size in the near-nozzle region of diesel sprays using ultra-small angle x-ray scattering (USAXS). Though USAXS has been used to study particle size in many systems, this is the first attempt to use it to study high-speed sprays. The principles underlying the USAXS measurements will be described, and initial measurements of a diesel spray from a single-hole nozzle will be shown over a range of conditions. * Corresponding Author Introduction Diesel spray behavior is well-known to have a strong impact on diesel engine performance and emissions. Diesel sprays are used to quickly disperse fuel and mix it with the cylinder gases. Small nozzle holes and high injection pressures are used to create a fine mist of spray droplets, which can then rapidly evaporate in the hot cylinder gases. While many measurements of diesel sprays have been performed, knowledge of the spray droplet size in the near-nozzle region is still relatively sparse. The near-nozzle region of diesel sprays is optically dense, which severely hampers optical diagnostics of these sprays. Nevertheless, some studies of diesel spray droplet size have been performed, using PDPA [1,2], light extinction [3,4], and scattering [5], though generally in the spray farfield. While these studies have provided valuable validation information for spray models, a better understanding of spray breakup requires droplet size measurements closer to the site of primary breakup. X-ray techniques have distinct advantages over optical diagnostics in optically-dense sprays. The dominant interaction of x-rays with hydrocarbons at moderate x-ray photon energy is absorption. Scattering is weak, and as such multiple scattering effects can be largely ignored. Monochromatic x-ray radiography has been used to quantitatively measure the fuel density field in various diesel sprays [6]. X-ray phase contrast imaging has been used to study the morphology of sprays [7]. These past x-ray measurements, however, have not directly measured droplet size in sprays. Smallangle x-ray scattering (SAXS) is a well-established technique for studying nanoscale particles [8]. Its use for studying aerosols and sprays is less common. Lin et al. have used SAXS to study droplet size in a supercritical ethylene jet [9]. Wyslouzil, et al. have used SAXS to study aerosol formation in supersonic flows [10]. In both of these flows, droplets formed by homogeneous nucleation, and as such were much less than 1 μm in diameter. To the authors’ knowledge, SAXS has not previously been used to study droplet size in a more conventional spray, where droplets are sheared from a bulk liquid structure into smaller droplets. This study will describe a set of proof-of-concept measurements of droplet size in diesel sprays using ultra-small-angle X-ray scattering (USAXS). The theoretical basis of these measurements will be described, as well as the experimental setup. The initial results of these measurements and their implications will be detailed. Finally, the prospect for future measurements and limitations of the technique will be described. SAXS Theory A brief overview of the relevant theory for SAXS will be given here; more detail can be found in other references [8,11]. SAXS is based on the principle of interference of scattered waves from electrons in materials. Unlike absorption, which is mainly due to interactions with core shell electrons, all electrons in a material contribute to SAXS. For particulate matter, the scattering pattern is related to the particle shape and size. If particles are assumed to be spherical, scattering patterns can be used to quantitatively determine particle size. SAXS data are presented in terms of a scattering vector q. If one assumes that the particles are randomly oriented, the scattering is axisymmetric, and only the magnitude of q matters. The scattering vector is related to the scattering angle and the x-ray wavelength by: