Three-dimensional fractal scaling of bursting events and their transition probability near the bed of vortex chamber

The structure of flow inside the vortex chamber is complicated and fully three-dimensional particularly near the bed of the chamber. The secondary currents inside the vortex chamber play the main role in sediment extraction. In this study, fractal dimension of 3-D bursting process was used to define the turbulent coherent structure of the flow at the bed of the vortex chamber. It is very important for the entrainment of sediment particles from the bed and moving them towards the flushing orifice. The 3-D bursting process were categorized into eight different cubic zones according to sign of 3-D velocity fluctuations. The turbulent data was measured at 48 points near the bed of chamber using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 300,000 time series data including time series of v′, u′, ω′, v′u′ and v′ω′ for each particular cubic zone. It was found that the fractal dimensions of 3-D velocity fluctuations and tangential and radial Reynolds shear stress for eight cubic zone of 3-D bursting process are very different. The fractal dimensions of Df(v′ω′) in cubic zone of 1, 2, 3, 4, 5, 6, 7 and 8 was found to be 1.639, 1.630, 1.609, 1.586, 1.636, 1.618, 1.623, and 1.641, respectively. With the application of 1st order Markov process, transition probabilities of 64 movements were found for the measured data along the radius and at the bed of the chamber. Additionally fractal dimension of the bursting events computed for eight particular stable organizations with the transition probability of the events. The mean fractal dimension of tangential velocity fluctuation u′ for eight movements was found to be 1.667, 1.704, 1.700, 1.695, 1.709, 1.693, 1.697 and 1.689, respectively.