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Thesis Format

Integrated Article

Degree

Doctor of Philosophy

Program

Mechanical and Materials Engineering

Supervisor

Khayat, Roger E.

Abstract

The steady laminar incompressible flow of an axisymmetric impinging jet of either a Newtonian fluid or a viscoplastic fluid of the Heschel-Bulkley type and the hydraulic jump of either a circular or polygonal shape on a solid disk is analyzed. The polygonal jump is induced by azimuthal dependence edge conditions: a non-circular disk or a circular disk with a variable edge film thickness. The thin-film and Kármán–Pohlhausen approaches are utilized as theoretical tools.

To cross the jump smoothly, a composite mean-field thin-film approach is proposed. The stress singularity for a film freely draining at the disk edge is found to be equivalent to an infinite film slope. The flow in the supercritical region is insensitive to the gravity strength, but is greatly affected by the viscosity. The existence of the jump is not necessarily commensurate with the presence of recirculation.

The disk size is found to can affect the film thickness in the subcritical region, vortex size and jump length significantly. The jump is relatively steeper with a stronger recirculation zone for a higher obstacle. Scaling laws for the jump properties, such as the jump radius and length, and edge film thickness, are proposed. The surface scaling separating the regions of existence/non-existence of the recirculation is found through numerical results.

The non-circular jump originated from the disk non-circularity or periodic edge film thickness is found. The balance of mass and momentum is established in the radial and azimuthal directions. The geometry of a non-circular disk has little influence on the jump shape. A small azimuthal variation in the edge thickness for a circular disk leads to a significant loss of axial symmetry. An increase in the number of peaks and valleys appears as the disk radius decreases.

The viscoplastic jump is found to occur closer to impingement, with growing height, as the yield stress increases; the subcritical region becomes invaded by the pseudo-plug layer. The viscosity does not influence sensibly the jump location and height except for small yield stress; only the yielded layer is found to remain sensitive to the power-law rheology for any yield stress.

Summary for Lay Audience

The impinging jet and hydraulic jump is a phenomenon that can be observed in the kitchen sink daily. When opening the tap, a column of water from the faucet impacts the bottom of the sink, spreading radially outward, and a water film rises abruptly at a critical radial location, a hydraulic jump forms. Although it is simple at first glance, the impinging jet and hydraulic jump have a complex flow structure and extensive industrial applications, such as rinsing, cleaning, cooling and coating. The appearance of a hydraulic jump can significantly influence the characteristics of flow, and the performance of related applications. In industrial applications, the fluid employed may not be a common fluid such as water or oil, but a complex fluid such as mud, pastes and concentrated suspensions. The current thesis presents a theoretical investigation of the circular impinging jet of common and complex fluids, and the hydraulic jump of either a circular or polygonal shape on a solid disk. The polygonal jump is induced by azimuthally dependent edge conditions: a non-circular disk or a circular disk with a variable edge film thickness. To investigate the flow features at the jump level, a composite model for a continuous jump is proposed. The momentum balance equations are established in both the radial and azimuthal directions for a polygonal jump. The model that takes the rheology of complex fluid into account is also presented. It is found that a larger flow rate, smaller viscosity, and lower gravity level lead to a larger jump radius. The existence of the jump is not necessarily commensurate with the presence of recirculation. The geometry of a non-circular disk has little influence on the jump shape. A small azimuthal variation in the edge thickness for a circular disk leads to a significant loss of axial symmetry. The complex fluid jump is found to occur closer to impingement, with growing height compared with the common fluid.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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