Abstract

This work presents the study of the flow in a jet-driven vortex chamber over a wide range of Reynolds numbers, contraction ratios, inlet angles, area and aspect ratios. Dimensional analysis furnishes the general functional relationships between the fundamental dimensionless quantities. Application of the integral equations of continuity and energy over the control volume, along with the minimum-pressure-drop or maximum flow rate postulate, provide the required analytical means to relate the predominant non-dimensional parameters such as the chamber geometry, the core size, pressure drop, Reynolds number, and viscous losses. Both the n = 2 vortex model, with reverse and non-reverse flow, and the free vortex model have been used at the vortex chamber exit plane. The theoretical results are found to successfully capture most of the salient properties of the flow. The influence of vortex chamber geometry, such as contraction ratio, inlet angle, area ratio, aspect ratio, and Reynolds number, on the flow field has been analyzed and compared with the present experimental data. A parametric study explores how the pressure coefficient and the core size vary with the different dimensionless properties. The observations show the pressure drop to decrease with the length. At first this appears to be counterintuitive since one habitually expects the pressure drop to be larger for longer pipes. A closer examination however, reveals that in addition to the radial-axial plane flow there is also a substantial centrifugal force, which decays with the length, thus shaping the development of the overall flow-field. The pressure drop across the vortex chamber differs from that in pipe flow, due to the mechanism of swirl flow. It depends mainly on intensity of tangential velocity. If the chamber length is increased, the vortex decay factor decreases, which leads to less pressure drop. The current theory confirms that the previous published models are only applicable for high Reynolds numbers where the inertia dominates the viscous forces. Based on the present theory, a new approach to determine the tangential velocity and radial pressure profiles inside the vortex chamber is developed and compared with the available experimental data. The n = 2 vortex model with reverse flow gives better results for strongly swirling flow.