Purdue University Graduate School


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posted on 2022-07-27, 20:17 authored by Weixiao ShangWeixiao Shang

The impinging jets atomizer is widely used in engineering applications. As two liquid jetsimpinging to each other, a liquid sheet is first formed and then breaks up into small dropletsto comply the atomization. The features such as size, shape, velocity, thickness, etc., of thesheet/droplet are controlled by various impingement parameters such as impinging angle,jet velocity, and physical properties of the liquid. Since the sheet generation is prior to thedroplet, the modeling of the sheet is the premise of the droplet modeling. Therefore, to studythe atomization of the impinging jet atomizer, it is important to pay effort on the research ofimpinging sheet both experimentally and theoretically. In this research, the characterizationof the impinging sheet formed by two jets is given in two specific aspects, the thicknessand the velocity. A non-intrusive measurement technique, partial coherent interferometry(PCI) is developed and applied to measure the thickness of the impinging sheet dynamically.The PCI unitizes the calibrated linear relationship between the optical path difference andthe degree of coherence to measure the impinging sheet thickness. By placing the sheet inone of the two branches of the designed interferometer, the optical path is altered basedon the sheet thickness and shown as the change of the degree of coherence of interferencepattern recorded by the camera. With a calibration process, the thickness of the sheet is thencan be measured via a designed interferometer. The velocity measurement of the impingingsheet is implemented via particle tracking velocimetry (PTV) adopted with the shadowgraphtechnique. To implement the particle tracking velocimetry, seeding particles are added intothe fluid and with the aid of an imaging acquiring system and the post-processing algorithm,the locations of those particles in different frames are identified. Thus, the velocity of the fluidis estimated as the velocity of the particles calculated from the recorded images. However,while applying the PTV to investigate the impinging sheet studied in this research, theparticles can be recorded at a large field of view with insufficient magnification. This is ownedto the so-called "particle induced lens effect" found when applying the small particles to athin liquid sheet. When the seeding particles move to the region where the sheet thicknesshas a similar scale as the particle, the fluid will wrap around the particle and act as a positivelens. For shadowgraph imaging, the collimated light forms an enlarged shadow at the image plane by passing through such lens. Experimentally, the thickness measurements via PCIare implied to the impinging sheet generated under a range of Reynolds number between 269to 370 and velocity measurements via PTV are implied to the ones under Reynolds numberof 362 to 430. The measured results for both thickness and velocity are different from thetheoretical model of the impinging sheet which implies the need for a review of sheet model.Therefore, in this research, the author proposed a revised impinging sheet model considerthe friction effect due to the air over the sheet. A theoretical analysis is made base on theboundary layer equation under the cylindrical coordinate with unique boundary conditionsassumed for the impinging sheet. By introducing the unique similarity variable found byauthor, the equation could be transformed to an ordinary differential equation and solvednumerically. The revised model first predict the air boundary layer profile over the sheet,then, estimate the sheet velocity profile as a function of the distance to the impinging pointand the azimuth angle. As a parameter of the revised sheet model, the jet velocity profilebefore the impingement is also assumed as a free jet gradually developed from a Posieuilleflow and estimated in advance. The revised model is compared with the experimental resultsand some key parameters are identified empirically.

Other than the thickness and velocity, this research is also interested in measuring thegeometry of the sheet and the detached droplets. Thus, a multi-view digital inline holography(DIH) technique is developed to capture the three-dimensional shape of the impinging sheetand the locations of the droplets. The DIH determines the shape and location of the targetin a detection volume base on the recorded hologram. The MvDIH, as the name suggested,combines the DIH results from multiple orientations to reconstruct the shape and the locationof the target. Two reconstruction ideologies, cross-section based one and the outline basedone, are proposed. The former estimates the target by finding the intersection of the recordedcross-sections of the target from different views. The latter estimates the target geometryby combining the outlines determined by DIH at different views. To evaluate the feasibilityof such technique, a test model which imitates the droplet and liquid ligament structure isapplied to the measurement in this research. Yet, the application on a real impinging sheetis not implemented.


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Jun Chen

Additional Committee Member 2

Paul E. Sojka

Additional Committee Member 3

Terrence R. Meyer

Additional Committee Member 4

Li Qiao

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