Three‐dimensional wall jets: Axial flow in a stirred tank

Bittorf, Kevin J.; Kresta, Suzanne M.

doi:10.1002/aic.690470605

Cited by 32 publications

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“…On the bottom the fluid diverges, changing its direction, and then travels upward along the vessel wall. Bittorf and Kresta (2001) showed that axial impellers drive four wall jets that propagate upward along the four baffles in the tank. The wall jets penetrate the bulk of the tank, involving two thirds of the tank volume in active circulation (Bittorf and Kresta, 2000).…”

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confidence: 98%

Resonant geometries for circulation pattern macroinstabilities in a stirred tank

Roussinova

Kresta

Weetman³

2004

AIChE Journal

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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...

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confidence: 98%

Resonant geometries for circulation pattern macroinstabilities in a stirred tank

Roussinova

Kresta

Weetman³

2004

AIChE Journal

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“…These velocities are similar in magnitude to the tip core velocities reported for axial impellers, which range from Ž . 0.210V to 0.326V Bittorf and Kresta, 2001 .…”

Section: U Mmentioning

confidence: 98%

“…impellers, which decays as 1rz Bittorf and Kresta, 2001 . In addition, the Rushton turbine is often placed at C sTr2, so the annular jet typically traverses only 0.5T, rather than the full height of the tank, as is the case for down pumping axial impellers.…”

Section: T T T Tmentioning

confidence: 99%

“…driven by axial impellers Bittorf and Kresta, 2001 , where the jet originates from a point source from 0.07T to 0.12T below the bottom of the tank, and spreads at an angle of 20Њ, exactly twice as fast as the spread of the annular jet:…”

Section: T T T Tmentioning

confidence: 99%

“…flow is driven by axial impellers. Bittorf and Kresta 2001 show that the 3-D jets behave as one-quarter of a round jet, Correspondence concerning this article should be addressed to S. M. Kresta. concentrated at the upstream side of each baffle and decaying with U A1rz and bA z. Description of the flow in the m bulk of the tank in terms of wall jets allows reduction of a whole set of velocity profiles to a few key characteristics of the jet which apply over a large region of the tank.…”

Section: Introductionmentioning

confidence: 99%

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Internal annular wall jets: Radial flow in a stirred tank

Kresta¹,

Bittorf²,

Wilson³

2001

AIChE Journal

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CFD Simulations of Three‐dimensional Wall Jets in a Stirred Tank

Bhattacharya

Kresta

2002

Can J Chem Eng

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1C omputational fluid dynamics (CFD) is increasingly being used for the simulation of stirred tanks due to recent advances in computer speed and efficiency of numerical schemes. While simulations involving both steady state (Kresta and Wood, 1991;Fokema et al., 1994;Harvey et al., 1995; Ranade and Dommetti, 1996 and others) and time varying (Perng and Murthy, 1992; Derksen and Van den Akker, 1999) methods have been reported in the literature, emphasis has mainly been on the quantitative validation of flow close to the impeller. The main objective of this study is to extend the existing protocols for simulating time-averaged velocity fields to flow near the tank wall and in the bulk of the tank.Studies with axial impellers show that wall jets form in the region between the baffles and the tank wall and drive the bulk flow, imposing a single characteristic velocity scale on both the upflow at the wall and the recirculation in the center of the tank. Accuracy in prediction of the mean flow characteristics of the wall jets and the simulation of the bulk flow in the tank are therefore intimately linked. Moreover, Bittorf (2000) has shown that the velocities in the three-dimensional wall jets, in balance with the settling velocities of the solids, determine the cloud height of suspended solids at high solids concentration. The cloud height of the suspended solids along with the just suspended speed (N js ) of the impeller determines the uniformity of solids distribution in a stirred tank. While explicit relations between N js and the fluid/particle properties and the impeller type are available, the cloud height model proposed by Bittorf (2000) requires an accurate description of the effect of size, off-bottom clearance and speed of the impeller on the core velocity or source velocity of the jet. This study aims to address these issues by developing a low-cost CFD protocol which can be used to obtain geometry dependent parameters to the degree of accuracy required, without having to resort to scale model experiments.While a detailed description of the wall jets is available in Bittorf and Kresta (2001), the key results are restated here to facilitate comparison with CFD simulations in later sections. Figure 1a shows one of the wall jets formed between the baffle and the tank wall. The expansion of the jet and the decay of axial velocity in a vertical plane close to the baffle are shown for different axial positions in the tank. At any axial location, the axial velocity (U ) increases rapidly from the no slip condition at the wall to its maximum value (U m ), and then decreases with a smaller gradient. At y~ 1.7b, the axial velocity reverses direction due to recirculation and asymptotically approaches the recirculating velocity (U R ). The The flow near the tank wall in a stirred tank driven by a 45°pitched-blade turbine is simulated with Multiple Reference Frames, the k-e turbulence model and standard wall functions. The results are compared to the three-dimensional wall jet identified in a previous paper. The self-...

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Three‐dimensional wall jets: Axial flow in a stirred tank

Cited by 32 publications

References 18 publications

Resonant geometries for circulation pattern macroinstabilities in a stirred tank

Resonant geometries for circulation pattern macroinstabilities in a stirred tank

Internal annular wall jets: Radial flow in a stirred tank

CFD Simulations of Three‐dimensional Wall Jets in a Stirred Tank

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