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
