Interplay of Forces in Impinging Jet Flow and Circular Hydraulic Jump
Abstract
The circular liquid jet impingement with subsequent hydraulic jump formation is studied theoretically using boundary-layer and thin-film approaches. Three different scenarios are tackled, namely, an accelerated Newtonian jet impinging on a stationary disk, a steady Newtonian jet impinging on a rotating disk, and a steady viscoelastic liquid jet impinging on a stationary disk. Accordingly, the effects of jet acceleration, gravity, centrifugal forces, and fluid elasticity on the flow behaviour and the jump are examined. The results are validated against numerical simulation and existing measurements. The findings show that the thickness of the boundary layer developing near impingement diminishes with jet acceleration but remains unaffected by centrifugal forces, aligning with previous findings in rotating boundary-layer flows. On the other hand, the film thickness increases with jet acceleration and disk rotation but decreases with fluid elasticity. For a jet velocity that increases linearly with time, the jump radius and conjugate depths increase over time, but their evolution is predominantly linear only at later times. The flow responds to the jet acceleration quasi-steadily near impingement but exhibits a long-term transient behaviour near the jump after the acceleration is halted. In the case of a rotating disk, two flow regimes are identified. The first regime corresponds to weak disk rotation characterized by the formation of a jump, and the second regime corresponds to dominant disk rotation characterized by the formation of a hump. In the jump regime, the flow transitions from predominantly azimuthal near the disk to predominantly radial towards the free surface, while in the hump regime, the flow maintains an azimuthal character around the hump. The vortex associated with the jump is found to diminish with increasing rotation, indicating a potential occurrence of a type 0 jump on a rotating disk. For the viscoelastic case, the radial flow across the jump is faster compared with the Newtonian case. In addition, the fluid elasticity yields an increase in the jump height and a decrease in its radius, resulting in the jump occurring in closer proximity to the impingement point.