Experimental and numerical analysis of three-dimensional free-surface turbulent vortex flows with strong circulation

Abstract

Strong free-surface vortex flows are widely employed in various civil engineering and industrial applications. However, a review of the state-of-the-art suggests that a number of areas surrounding the underlying flow mechanics in these systems requires additional attention and are therefore explored in this study. The research focuses on experimental and numerical analysis as well as analytical investigations of the flow problem. Experimental modelling was performed in two phases: investigation into the effects of the approach flow geometry and an exploration of the mean three-dimensional velocity fields and secondary flow processes. Twelve geometries of a typical scroll type vortex chamber were constructed and independently tested in a customised hydraulic test rig. Model discharges were monitored using a magnetic flow meter and the approach flow depths and water surface profiles were monitored using a depth gauge apparatus. The horizontal velocity field in the far- to mid-field was measured using a 2D particle tracking velocimetry system. Particle streak velocimetry was employed to determine the near-field tangential and axial velocity fields. The results highlighted an explicit dependence of the circulation number NΓ and the discharge number NQ on the approach flow conditions. Two empirical auxiliary parameters ���� and ���� were proposed and further modelled to yield an alternative depth-discharge equation. The model was validated using a scaled model and a prototype. Scale effects in the physical models were found to be negligible. The investigation of the primary flow field indicated that the tangential velocity field was independent of the sub-surface depth away from the tank boundaries. Using the available velocity data and laser-induced fluorescence images, the radial velocity was observed to be confined at the vessel floor and free-surface. The axial velocity appeared to be concentrated in a downward direction in the core region as well as in a newly observed upward direction at the tank periphery. Further analysis showed that the ideal irrotational tangential velocity model agrees with the experimental data in the far-field. However, large discrepancies were observed in the near-field close to the vortex core. Based on analytical and numerical analysis, it was proposed that the discrepancy was as a result of the axial velocity gradient in the core region which was not accounted for in the original assumptions of the model. As a result, an alternative tangential velocity profile was devised based on a correction multiplier containing the inverse of the circulation number and the empirical exponent ��. The model relieves the discrepancy of the ideal model by reducing it in areas of strong axial flow to within reasonable levels. iii Three-dimensional numerical modelling of the strong free-surface vortex was performed using an Eulerian-Eulerian homogeneous multiphase flow model in the ANSYS CFX computational fluid dynamics code. The experimental data was used as a benchmark to compare the solutions of the numerical model for various test cases in a single model. The comparison showed that the maximum solution accuracy was obtained using a radially structured mesh and a solution independent mesh density was presented. The model was strongly dependent on the type of turbulence model used. Standard Reynolds averaged Navier-Stokes equations appeared to be highly dissipative and overestimated the generation of turbulence in the core region which generated significant errors in the solution. The modified shear stress transport with curvature correction as well as the Reynolds stress models delivered the greatest model accuracy. It was also found that transient modelling was necessary to resolve the unsteady features of the flow field, namely that of free-surface oscillations and the radial flow field. However, the final comparison using the Reynold Stress models nonetheless rendered a significant error in under predicting the free-surface and over predicting the tangential velocity distribution by approximately 12 and 22 % respectively. It was concluded that further refinement of the mesh at the free-surface and in the drop shaft region was required to further improve the numerical solution. In a final contribution, based on the experimental and numerical observations of the primary and secondary flow fields, an alternative description of the flow mechanics in a strong free-surface vortex was made based on the concept of a newly defined ‘virtual Taylor-Couette’ flow system. Based on this flow representation, a hypothetical description highlighting the likely stages of stability based on various states of the ‘Taylor-like’ vortices which occur in the secondary flow field was proposed. The overall description serves to provide a universal scientific understanding of both ‘weak’ and ‘strong’ free-surface vortices as well as the transitional dissipative state at a depth coinciding with the critical submergence.