Modal Analysis And Analytical Modeling Of Tornado-Like Vortices
Abstract
Regardless of the type of vortex chamber, many tornado simulators generate flows that reveal similar flow patterns and a general agreement on the variations of the flow structures with swirl ratio (the ratio of tangential velocity to radial velocity) was achieved. However, very little is known about the underlying physics of the flow, mostly of the fluctuating one, as the previous studies have mainly focused on qualitative flow visualization and the quantitative description of the mean flow.
Herein, coherent structures in tornado-like vortices are extracted using modal decomposition techniques. Modal analysis helps us to better understand the complex vortex dynamics including vortex wandering, vortex breakdown and sub-vortex dynamics. Proper orthogonal decomposition (POD) is applied on the fluctuating velocity field to investigate the prominent mechanisms for a range of swirl ratios (0.22≤S≤0.96). Moreover, another technique dynamic POD is used to provide the time evolutions of coherent structures. Based on the results of the fluctuating velocity field, the three-dimensional vortex structure is revealed.
Despite the accepted measurement techniques for surface pressure, the choice of processing tools for interpretation of the data is challenging. Here, a comparison between some common statistical techniques and modal analysis is provided. Since POD method sometimes results in non-physical modes, another technique, called independent component analysis (ICA), is used. Based on the results of surface pressure fluctuations, statistical properties of coherent structures in tornado-like vortices, including their spectral characteristics, are provided. The discussions of modal analysis presented here is applicable to a large class of swirling flows, regardless of the reference to tornado-like vortices.
By identifying a reduced number of modes representative of tornado-like turbulent velocity field, one can construct simplified but physically meaningful analytical models. Here, both mean and, for the first time, the fluctuating flow fields are analytically modeled. The mean flow field is modeled using a combination of Burgers-Rott model and stagnation flow. The fluctuations attributed to random motion of the vortex (wandering phenomenon) are modeled by solving deconvolution integral through assuming a Gaussian PDF for wandering motions, and the fluctuations attributed to sub-vortex dynamics are modeled using POD.