Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy


Mechanical and Materials Engineering


Khayat, Roger E


The laminar axisymmetric flow and heat transfer of a circular impinging jet and hydraulic jump on a solid surface is analyzed theoretically using boundary-layer and thin-film approaches. Liquid jet impingement features many applications such as jet rinsing, jet cooling, liquid atomization and chemical reactors. The associated hydraulic jump dramatically affects the performance of the heat and mass transfer in such applications. In the current thesis, the effects of inertia, surface tension, surface rotation, gravity and heat transfer are comprehensively explored for impinging jet flow and the formation of hydraulic jump.

The boundary-layer heights and film thickness are found to diminish with inertia. The wall shear stress is found to decrease with radial distance for on a stationary impingement surface but can increase for a rotary surface for large rotation speeds. When the surface is in rotation, a maximum liquid thickness occurs, reflecting the competition between inertia and rotation effects. The location of the hydraulic jump is determined for both low- and high-viscosity liquids. For low-viscosity liquid, the location of the jump is determined subject to the thickness near the trailing edge under static condition, reflecting the importance of surface tension. For high-viscosity liquids, the jump coincides with a singularity caused by gravity in the thin-film equation when surface tension is neglected. Downstream of the hydraulic jump, the recent finding of a constant ‘jump Froude number’ is also justified.

The heat transfer analysis of impinging jet flow involves a two-way coupling due to the temperature-dependent viscosity and surface tension. To consider this non-linear coupling which is largely missing in the existing theoretical approaches, we develop a simple and iteration-free model, making exploring the influence of heat transfer on the flow field and the hydraulic jump feasible theoretically. Both the hydrodynamic and thermal boundary layers are found to decrease with a higher heat input at the solid surface. Enhanced heating is also found to push the hydraulic jump in the downstream direction. The Marangoni stress causes the hydraulic jump to occur earlier. The hydraulic jump leads to shock-type drops in the Nusselt number, confirming previous findings in the literature.

Summary for Lay Audience

The current thesis presents a theoretical analysis on the flow and heat transfer of a column of liquid impacting a solid surface which is known as the impinging jet flow. Impinging flow is encountered in many applications such as jet rinsing, industrial cooling, combustion engine cooling, liquid atomization and chemical reactors. For impinging jet flow, the hydraulic jump is an abrupt increase in the depth of the liquid layer which can be daily observed at the bottom of a kitchen sink in tap water flow. The hydraulic jump can significantly affect the performance of the associated applications. It is not surprising that hydraulic jump moves further away from the impingement point for a larger speed of the incoming jet. But the quantitative dependence of jump location on the flow rate, including the heat transfer character, is still not completely settled due to complexity of fluid flow. For low-viscosity liquid, we find that surface tension is important on the location of the jump. But for a high-viscosity liquid, it turns out that gravity is more dominant on the hydraulic jump. It is also found that rotation of the solid surface can push the hydraulic jump further away from the impingement point. In the heat transfer analysis of impinging jet flow in cooling applications, the viscosity of a liquid depends on the temperature. However, this dependence is largely neglected in existing theoretical analyses due to the mathematical difficulty. In this regard, we develop a simple and efficient model that can incorporate this dependence so that heat transfer and flow field can be more accurately calculated. The current results show that a higher heat input from the solid surface can push the hydraulic jump further away. In addition to the hydraulic jump, the important features of the flow field and heat transfer are comprehensively presented in the thesis. For validation, our quantitative predictions are compared with existing measurements and good agreements are achieved.

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