On the evaluation of power density models for oscillatory baffled reactors using CFD

https://doi.org/10.1016/j.cep.2018.11.002Get rights and content

Highlights

  • CFD validation of power density estimation models in oscillatory baffled devices is for the first time investigated.

  • We have updated the orifice discharge coefficient and the dependency on the number-of-baffles term for the Quasi-steady model.

  • We have updated the dependency on the number of baffles & proposed empirical model to estimate mixing length for the Eddy enhancement model.

  • Both models are validated for a much wider application range than originally stated and for both batch and continuous.

  • Both revised models can be used interchangeably with high confidence.

Abstract

While continuous oscillatory baffled reactors (COBR) have been proven a viable alternative to traditional batch reactors for organic synthesis and crystallization, research into the estimation of power density for this type of device has largely been stagnated for the past 25 years. This work reports, for the first time, detailed analysis and examination of the applicability, capability and deficiencies of two existing models using CFD methodology. The “quasi-steady” model (QSM) over-estimates power dissipation rates due to the inaccurate formulation of two of its geometric parameters for modern COBRs. By using a revised power law dependency on the number-of-baffles term (nx) and an appropriate orifice discharge coefficient (CD), we demonstrate that the updated QSM can not only be used for a much wider application range than previously outlined, but also for both batch and continuous operations. The “eddy enhancement” model (EEM) generally provides better predictions of power density for the conditions tested; however, its accuracy can substantially be enhanced by applying the aforementioned power law dependency on n and an empirical correlation proposed in this work to estimate EEM’s “mixing length”. After full validation, both models give very similar power density estimations and can be used interchangeably with high confidence.

Introduction

While stirred tank reactors have been the workhorse in chemical industry, tubular plug flow reactors, such as continuous oscillatory baffled reactors (COBR), have emerged as a viable alternative. Significant process and economic benefits were reported in the utilization of COBR in a broad range of processes, e.g. crystallization [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]], reactions [[18], [19], [20]], heterogeneous catalysis [[21], [22], [23]] and fermentation processes [24,25]. However, in terms of evaluation of power dissipation rate for this type of reactors, research has largely been stagnated for the past 25 years [26]. Essentially two published models have been used in the field of COBR and OBR (oscillatory baffled reactors): the “quasi-steady” model (QSM) from the work of Jealous and Johnson [27] and the “eddy enhancement” model (EEM) by Baird and Stonestreet [28,29]. The origin of both models was stemmed from the evaluation of pressure drop over oscillatory devices; while the equations were empirical, research has neither been carried out on the validation of the above models nor on how these models could be used in continuous operation where there is a net flow. In this paper, we report, for the first time, a detailed analysis and examination of the applicability, the capability and the deficiencies of the two models using a CFD methodology.

Section snippets

Background for power dissipation models

In order to predict power density (εv) due to pulse generation in pulsed columns, Jealous and Johnson in 1955 developed the QSM from pressure drop, which accounted for inertial and frictional effects of the flow, as well as pressure drop due to a static head that was present on their experimental setup [27]. QSM power density equation for oscillatory baffled reactors was then derived from the work of Jealous and Johnson as [28,29]:εv=2nρωxo31/α213πCD2L

Due to the constriction of an orifice

Validation approach

The targeted device is a NiTech DN15 COBR reactor (DN15 for short) with the design details provided by the manufacturer, Alconbury Weston Ltd (http://www.a-w-l.co.uk/); Fig. 1 shows the geometric dimensions of the DN15, the overall length is 752 mm containing 32 baffled cells.

Table 1 lists the conditions for our parametric CFD study covering a wide range of both geometric and operational parameters such as baffle hole diameter (Db), baffle spacing (Lb), volumetric flow rate (Q), oscillation

Mesh

Table 2 shows the mesh characteristics used for the simulations.

Numerical model

The ANSYS® Fluent 16.0 CFD package was used for all the numerical simulations of this work. Three-dimensional incompressible time-dependent Navier-Stokes equations were solved:u=0ρ(ut+uu)=p+μ2u

All the simulations were performed using the pressure-based segregated solver together with the SIMPLE pressure-velocity coupling algorithm. A second order upwind scheme was utilized for the spatial discretization of the

Results

In previous CFD simulations of OBR and COBR [49], a quasi-steady state, indicating the flow was fully developed and cycle-repeatable, was achieved in 5–7 cycles of oscillation. Applying the same methodology, Fig. 4 (left) shows the change of the volume-weighted averaged strain rate with time; a quasi-steady state is seen after cycle 5. Being conservative, all the data presented on this study were taken from the cycle 7 (included) onwards. Furthermore, Fig. 4 (right) plots Δp(t) at different

Conclusions

In this work, we have, for the first time, provided CFD validations to the two existing models for the estimation of power density in oscillatory baffled devices. The existing QSM over-estimates power dissipation rates due to the inappropriate formulation of two of its geometric parameters for modern OBRs/COBRs. By using a revised power law dependency on the number-of-baffles term (nx) and an appropriate CD, the QSM was subsequently validated for a much wider application range than previously

Acknowledgements

The authors wish to thank the EPSRC and Heriot-Watt University for the financial support provided for this project and the Doctoral Training Centre in Continuous Manufacturing and Crystallization EPSRC (EP/K503289/1). We also thank the EPSRC funded ARCHIE-WeSt High Performance Computer (EP/K000586/1).

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