Abstract
During the last years considerable improvement of the derivation of turbulence power spectrum from Laser Doppler Anemometry (LDA) has been achieved. The irregularly sampled LDA data is proposed to approximate by several methods e.g. Lomb-Scargle method, which estimates amplitude and phase of spectral lines from missing data, methods based on the reconstruction of the auto-correlation function (referred to as cor- relation slotting technique), methods based on the reconstruction of the time series using interpolation between the uneven sampling and subsequent resampling etc. These different methods were used on the LDA data mea- sured in an agitated vessel and the results of the power spectrum calculations were compared. The measurements were performed in the mixing vessel with flat bottom. The vessel was equipped with four baffles and agitated with a six-blade pitched blade impeller. Three values of the impeller speed (Reynolds number) were tested. Long time series of the axial velocity component were measured in selected points. In each point the time series were analyzed and evaluated in a form of power spectrum.
Highlights
The mixing operation is commonly used phenomenon in several industries namely chemical and process engineering
The irregularly sampled Laser Doppler Anemometry (LDA) data is proposed to approximate by several methods e.g. Lomb-Scargle method, which estimates amplitude and phase of spectral lines from missing data, methods based on the reconstruction of the auto-correlation function, methods based on the reconstruction of the time series using interpolation between the uneven sampling and subsequent resampling etc
For the flow field measurements LDA (Laser Doppler Anemometry) was used and the time ensemble averaged mean velocities were obtained, the time series of the local velocities enabled the analysis of turbulence spectra as well as correlation functions.Subsequently the turbulence spectra and correlation functions can be used to derive time and length scales and dissipation rate
Summary
The mixing operation is commonly used phenomenon in several industries namely chemical and process engineering. The design of a big industrial agitated vessels is developed through modeling of the particular processes in small-scale conditions. In that case most processes are designed and controlled through the values of the power input per unit mass, the turbulence and the dissipation rate seems to have an essential role in that modeling, at least for high Reynolds number. The LDA data is unevenly sampled so the spectral analysis requires nonstandard processing. – a slotting technique and a cosine transform; One possibility is to use as a direct transform the LombScargle method instead of common Fourier transform to performed spectral analysis on unevenly sampled data described e.g. in [2]. The slotting technique used Tummers & Passchier [7], Nobach [8] who used and improved the reconstruction method and established the web page: http://ldvproc.nambis.de for LDA signal and data processing, which contains program source codes
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