Analysis of flow structures and energy spectra in chemical process equipment

Abstract

Studies have been carried out to extract relevant information on flow structures, their break-up distribution and the associated local turbulence phenomena using the 1D and 2D energy spectra. The 1D analysis uses the hot film anemometry (HFA) and large eddy simulation (LES) data sets, while the 2D analysis uses the PIV results. The chemical process equipment considered for the study are jet loop reactor (JLR), channel flow (CHA) and bubble column reactor (BCR). The work involves relative comparison of spectral methods, namely, fast Fourier transform (FFT), discrete wavelet transform (DWT), continuous wavelet transform (CWT), eddy isolation methodology (EIM) and proper orthogonal decomposition (POD) in evaluating the 1D and 2D spectra for the three equipment. FFT studies are used to identify the dominant frequencies, but they do not reveal the time dependent changes in the flow structure. This limitation is overcome by using the EIM, DWT and CWT and methodologies for identification of flow structures are discussed. Using DWT, a novel intermittency-based quantifier, namely, the scale relative local intermittency measure (SRLIM) is found to be particularly useful for identification of intermittent flow structures. For example, it has been used to track the intermittent bursts in the CHA, the vortex tube related intermittencies in the JLR and the bubble induced eddies in the BCR. The advantages of CWT for obtaining the eddy time-scale and length-scale distribution from the velocity time series is shown. The evaluation of distributions has been carried out using wavelet transform modulus maxima (WTMM) along with a symbolic analysis of the loci of the maxima lines. The structure break-up distribution and the energy break-up distribution that are obtained show a generalization to the known L and P models for intermittencies. The turbulence parameters, i.e., local turbulent kinetic energy, energy dissipation rate and turbulent viscosity, have been calculated and compared using the results obtained from the FFT, DWT, CWT and EIM. For the different approaches these parameters lie in reasonable ranges.

Keywords:

• flow structures
• spectral analysis
• wavelet transform
• intermittency
• eddy size break-up
• turbulence
• energy dissipation rate

Acknowledgment

VRK gratefully acknowledges the Department of Science and Technology, New Delhi, India for funding the project SR/S3/CE/054/2003-SERC-Engg and the Center of Excellence in Scientific Computing (CoE-SC) at NCL for providing computational facilities. The authors gratefully acknowledge the help rendered in coding the WTMM methodology for eddy identification by Neha Walani and Shalini Tripathi. SSD and MVT acknowledge university grant commission for the financial support during this work.