Publication Date


Document Type


First Advisor

Vaezi, Mahdi

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Solid-fluid interactions are commonly observed in natural transport phenomena and industrial applications such as sedimentation in rivers and pneumatic and hydraulic conveying of coarse particles. Here particle and fluid motion affect each other through force interactions, especially via drag force. To evaluate the magnitude of the drag force first the drag coefficient (CD) of the particle needs to be measured mostly experimentally. The CD depends on the particle’s geometry (i.e., shape, dimension, …) and the properties of the fluid medium. Since the solid particles commonly observed in nature or used in industrial setups come with irregular shapes, finding a relation between the measured CD of a disperse particle and the flow of a continuous phase characteristics is not a straightforward procedure. This difficulty is mainly due to the hardships in defining the irregularity type and amount of the solid particles. Using these various shape factors, several models have been developed to predict the CD of irregular shape particles, every model is specific to one or a series of similar shape(s) of the particle(s) within a particular range of the corresponding particle’s Reynolds number (Re). The goal of this work was to propose a general CD correlation based on a general shape factor that could be applied to a wide range of irregular shape and Reynolds Numbers (Re). To accomplish this, 60 reference model shapes were created in SolidWorks®, assuring the method's simplicity and reproducibility while achieving a wide range of irregularity from well-rounded to extremely angular and from spherical to prismoidal. Based on its capacity to discern the irregularity of the particle when compared to other shape factors, one was recommended as a general shape factor. Utilizing nonlinear regression analysis, a general CD correlation was generated using this general shape factor and 16 previously suggested CD correlations for the 60 reference model shapes spanning a range of Re from 0.001 to 300,000. When compared to the 16 previously proposed correlations, the correlation not only makes reasonable CD estimates, but it also addresses the limitations of those correlations, is more user-friendly, and can easily calculate the CD of a wide range of particles from spheres to highly irregular shapes with good accuracy. Finally, the 60 reference model shapes and 36 flat particles were 3D printed using additive manufacturing techniques, and their CD values were determined experimentally using video tracking techniques while dropping in a column of water. At 606 ≤ Re ≤ 2480, a comparison of empirically measured CDs with predicted values using the general correlation revealed a 35 percent average inaccuracy for flat and 43 for non-flat particles.


101 pages




Northern Illinois University

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