Resonant geometries for circulation pattern macroinstabilities in a stirred tank

Abstract

Published online in Wiley InterScience (www.interscience.wiley.com). Circulation pattern macroinstabilities and precessing vortices are known to exist in stirred tanks, but until recently they have eluded a full quantitative analysis. In this article, frequency analysis of the axial velocity reveals a resonant frequency and geometry for the 45°pitched-blade turbine (PBT) in a flat-bottom cylindrical tank. Unlike other axial impellers, such as the hydrofoils A310 and HE3, the PBT produces a large-scale circulation macroinstability at the scale of the vessel diameter. The macroinstability is superimposed on the turbulent random fluctuations with a timescale that is very long compared to the blade passage frequency and the inertial convective range of the turbulent cascade. In this article it is shown that the circulation pattern macroinstabilities generated by the 45°PBT are coherent and propagate throughout the tank only under very specific conditions (D ϭ T/2 and C/D ϭ 0.50). The normalized frequency of the coherent macroinstability, or Strouhal number, is f MI /N ϭ 0.186. This corresponds to a period of roughly five rotations of the impeller, or 20 individual blade passages. The laser Doppler velocimeter data used in this work are unevenly spaced because they are collected in burst detection mode. This severely complicates spectral or frequency analysis. Standard algorithms such as the fast Fourier transform, autocorrelation methods, and wavelet analysis all require evenly spaced data. The Lomb periodogram was successfully used to extract the low-frequency content of the unevenly spaced data with a higher accuracy than is possible with other methods. The Lomb method also eliminates a short time-averaging step that was required in earlier work. © 2004 American Institute ofChemical Engineers AIChE J, 50: 2986AIChE J, 50: -3005, 2004 IntroductionIn the cylindrical stirred tank used throughout the chemical process industries, macroinstabilites in the gross circulation pattern can cause strong vibrations, unsteady loading, and even mechanical damage to tank internals. The vibrations are a significant problem in plant operations. When these vibrations are large, tanks may have to be shut down until the problem can be resolved.Three ranges of frequencies are present in the tank and different flows are associated with each frequency range. First, at any instant the velocity field contains a whole spectrum of high frequencies arising from turbulent eddies and vortices. Second, there are trailing vortices close to the tip of the impeller blades. If the blade width is D/5, where D is the impeller diameter, then the trailing vortices are approximately D/10 in diameter. These trailing vortices are present only in the region surrounding the impeller. They do not extend out to the R. Weetman is currently at rjweetman.com (e-mail: ron@rjweetman.com). Correspondence concerning this article should be addressed to S. M. Kresta at suzanne.kresta@ualberta.ca. © 2004 American Institute of Chemical Engineers FLUID MECHANICS AND TRA...

Ekman pumping and intermittent particle resuspension in a stirred tank reactor

“…at the end of the simulation, the jet returns to be confined within 2L r thus, closing a cycle. This behaviour is consistent with the results of Roussinova et al (2004) who observed a low frequency, high-amplitude variation of the axial velocity in correspondence to both the impeller stream and the wall due to the presence of what they call a "circulation pattern" macro-instability. The radial jet extension is associated with a shift of the core of the two toroidal vortices toward the jet.…”

Flow structure and the effect of macro-instabilities in a pitched-blade stirred tank

“…For PBT's, Roussinova et al (2004) reported that circulation pattern instability has one major peak at a frequency f/N =0.186 (N is the impeller rotational speed expressed in revolutions per second). Montes et al (1997) and Hasal et al (2000) obtained f/N= 0.057 for a precessional vortex instability inside a PBT tank at Re= 75,000.…”

“…Nikiforaki et al (2003) showed that a long enough sampling time is required to identify clear peaks of MI oscillations from the energy spectrum obtained using an FFT. Roussinova et al (2004) used a wavelet analysis of the time signal to identify the range of frequencies within which MI oscillations occurred. Ducci et al (2008) decomposed MI flow structures for a Rushton impeller STR using POD of the velocity signal to study interaction between MI's of high and low frequencies.…”

Flow Instabilities in Mechanically Agitated Stirred Vessels

“…We well denote such flow instabilities as jet impingement instabilities (JMIs). In a later investigation Roussinova et al (2004) extended the analysis to different axial impellers. In such work the authors used the LSP method for the spectral analysis.…”

“…Ducci & Yianneskis, 2007, Roussinova et al, 2004 showed that different kinds of macro-instabilities may be present simultaneously in stirred vessels. For instance Galletti et al (2005b) studied simultaneously with 2-point LDA the combined effect of precessional MIs and flow instabilities stemming from impeller clearance variations (CIs) in different regions of a vessel stirred with a RT.…”