Hydrodynamics and mixing in continuous oscillatory flow reactors—Part II: Characterisation methods
Introduction
In Part I of this series [1], time-resolved laminar CFD simulations have been performed to study the flow generated in five oscillatory baffled reactor (OBR) designs, three of which are novel compared with the single orifice baffles or disc-and-donut baffles that have been traditionally used for this type of device. The flow generated by these designs has been assessed by examining instantaneous velocity fields, shear strain rate fields and pressure drop.
This study highlighted the complex flow behavior and the formation of vortices in the reactor due to both flow blockage by the baffle design and flow reversal. Indeed, depending on the baffle geometry, there is more or less fluid recirculation, dominant axial flow and shear strain rate variation. The disc-and-donut baffles generate multiple vortices and the helical blade designs create a complex 3D flow with a significant transverse component. In terms of shear strain rates, which are of interest for multiphase applications, the disc-and-donut baffles and the helical blade baffles provide the highest values, which are more than two times greater than those generated by the single orifice design. It is interesting to note however that the maximum strain rates are localised and occupy relatively small volumes in the reactor; only the disc-and-donut baffles provide substantial spatial variation of shear strain rate. This means that only a small amount of fluid passing through the reactor may experience high shear stress. The work also showed that the baffle design has a huge impact on pressure drop, which is as expected. The disc-and-donut design causes the highest pressure drop, which is greater by about a factor of five than that with the single orifice baffles. The pressure drop generated by helical baffles is approximately half that of the disc-and-donut design. Indeed, although the ensemble of the results provide knowledge on the flow mechanisms and operating characteristics of OBRs, it is clearly difficult to conclude on the impact of baffle design on the performance of the reactor with velocity and shear strain rates alone.
As previously reported in the introduction of Part I, the majority of the studies in the literature describe the flow generated in OBRs in a qualitative manner using planar velocity fields and velocity profiles [2], [3], [4], [5] or shear strain rate fields [6]. A significant number of studies have also evaluated the performance of OBRs in terms of axial dispersion via the analysis of residence time distributions [7], [8], [9], [10], [11], [12], [13]. The general observation of these studies is that for oscillatory Reynolds numbers (ReO) greater than approximately 200, the axial dispersion coefficient increases linearly when with increasing ReO, being proportional to the product A.f. For ReO < 200, however, a decrease in ReO also causes an increase in the axial dispersion coefficient such that there is a minimum axial dispersion as a function of ReO. Smith and Mackley [9] explain the minimum in the axial dispersion coefficient due to the interaction of net flow and oscillatory flow whereby significant radial mixing is generated without excessive axial mixing. They have also shown that an increase of the net Reynolds number (Renet) also causes an increase in the axial dispersion coefficient.
The main objective of this paper is to develop alternative methods that allow OBRs to be characterised and assessed in terms of different performance criteria: radial and axial fluid stretching and mixing, and shear strain rate history. The performance of these methods is then demonstrated using the five different reactor geometries presented in Part 1. A Lagrangian particle tracking method has also been used to carry out an analysis of the residence time distribution, which completes various studies in the literature [9], [10], [11], [12], [14], [15].
Section snippets
Flow computation and particle tracking
The methodology used to perform the flow simulations was described fully in Part 1 of this paper [1]. In addition to the usual analysis of the flow field variables we also performed Lagrangian particle tracking to provide additional information. We used particles having the same density as the fluid and a diameter of 1 micron which have a Stokes numbers of O(10−5) and therefore follow the fluid faithfully. With this method there is no interaction between particles and no physical and little
Radial and axial fluid stretching
This technique follows the radial and axial distances separating two initially adjacent particles as a function of time. It is used to quantify radial and axial mixing separately. Fluid elements that experience significant stretch in the radial direction are in zones of good radial mixing, whereas fluid elements with very little stretching experience poor radial mixing. Small stretching distances in the axial direction, however, highlight near plug-flow behavior. On the other hand high amounts
Verification of characterisation methods
In addition to verifying that the solution is mesh independent, which was shown in Part I of this study [1]. the independency of the performance characteristics (determined by particle tracking techniques) on mesh size and the number of tracking particles used was also checked. The effect of these parameters, as well as the reactor length and the injection position of the tracer particles, on fluid stretching, the axial dispersion coefficient and the strain rate history were investigated.
Radial and axial fluid stretching
Fig. 5 shows the average stretching normalised by the tube diameter, and , of each fluid element over 50 s as a function of the initial normalised radial position in the OBR with single orifice baffles. For good mixing, the OBR geometry should promote stretching in the radial direction but minimize axial stretching, such that plug-flow behavior is achieved. It can be seen from Fig. 5 that in general the axial stretching is more than 100 times greater than the radial stretching for the
Conclusions
In this work three analysis methods for characterising the flow generated in oscillatory baffled reactors have been developed. These methods analyse axial and radial stretching (and mixing) capacity, shear strain rate history and residence time distribution using data obtained using CFD. Axial and radial stretching is useful to evaluate spatial mixing and the presence of chaotic flow, if required; shear strain rate is useful for applications that are shear-dependent, such as droplet break up,
Acknowledgements
This work was part of the AGRIBTP project on bio-products for building and public works funded by the European Union, région Midi-Pyrénées and the French Government. D.F.F. gratefully acknowledges funding from INP Toulouse.
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