Quantifying flow structure in vortex chamber using fractal dimension

Abstract

The flow in a vortex chamber consists of a series of vortices with a variety of different length scales. In the present study, an effort was made to scale and quantify flow structure inside the vortex chamber. To understand the structure of flow in a vortex chamber, three dimensions of flow velocity were measured using acoustic Doppler velocity meter (ADV). The velocity of the flow was measured in a fine grid from the bed to the water surface at sections 45°, 90°, 135° and 180° in the radius of the chamber. To scale the eddies of the flow, a fractal interpolation function algorithm was used to compute fractal dimension of tangential velocity, vertical velocity and Reynolds shear stress. The variation of the fractal dimension for tangential velocity, vertical velocity and Reynolds shear stress at the depth of flow and at the distance from the center of the chamber is investigated in this study. The results indicated that no significant variation for the fractal dimension of vertical velocity fluctuation and Reynolds shear stress was found for the depth in all sections. However, the fractal dimension of tangential velocity fluctuates significantly over the depth and in the distance from the center. As a result, the averaged value of fractal dimension for tangential velocity is lower than the value of fractal dimension for vertical velocity and Reynolds shear stress. The average fractal dimensions of tangential velocity are 1.63, 1.64, 1.64 and 1.63 for the sections of 45°, 90°, 135° and 180°, respectively.