Computational-fluid-dynamics study of a Kenics static mixer as a heat exchanger for supercritical carbon dioxide
Graphical abstract
Introduction
Static mixers are largely used in industry in a wide range of operations, such as liquid or gas homogenization under laminar or turbulent flow conditions, continuous co-current mixture of liquid–liquid or gas/liquid dispersions, and as heat exchangers and mass transfer contacting devices [1], [2], [3], [4]. The static mixer considered in the present study is the Kenics® KM mixer. This mixer design has been employed in the process industry since the mid-sixties, mainly for in-line blending of liquids under laminar flow conditions.
The Kenics® KM mixer is comprised of a series of mixing elements aligned at 90°, each element consisting of a short helix of one and a half pipe diameters in length. Each helix has a twist of 180° with right-hand and left-hand elements being arranged alternatively in the pipe. The helical mixing element directs the flow of material radially toward the pipe walls and back to the center. Additional velocity reversal and flow division result from combining the alternating right- and left-hand elements. The complex fluid flow in the mixer has propelled several studies on its pressure drop and Z-factor, mixing performance [5], [6], [7], heat transfer enhancement [8], [9], [10], and mass transfer rate [11], [12].
The use of static mixers in supercritical fluid extraction (SFE) processes has been proposed recently as alternative contacting devices [13], [14] and as heat exchangers [15]. SFE has proved effective in the extraction of oils and its derivatives for use in the food, cosmetics, and pharmaceutical industries [16], [17], [18]. Heat transfer plays an important role in the operation of SFE processes. For instance, heat exchangers are needed to pre-heat the supercritical fluid (SCF) stream before being fed to the high pressure vessel, or to change temperature conditions of the high pressure flow before separation of the solubilized solutes from the SCF solvent takes place [15].
We have recently demonstrated the utility of static mixers as heat transfer devices for supercritical carbon dioxide (scCO2) flow and compared its thermal efficiency against a conventional tube-in-tube heat exchanger under similar operating conditions [15]. The heat fluxes obtained with a Kenics static mixer were one order of magnitude higher than the ones observed with the tube-in-tube heat exchanger. The heat transfer enhancement was considered to be caused by the cross-sectional mixing of the fluid and to a lesser extent by conduction across the metallic mixing elements. The heat transfer in the static mixer was also affected by temperature-induced variation of physical properties, especially in the pseudo-critical region of the fluid (defined as the temperature where the isobaric specific heat of the fluid reaches a maximum for a given pressure), which impacts the heat transfer coefficient.
The unique characteristics exhibited by SCFs in the vicinity of the pseudo-critical temperature, where rapid variations of the physical properties takes place, make the optimization of heat exchangers in SFE plants a challenging task and calculations of heat transfer coefficients are, in general, inherently associated to measures with great uncertainty. The ability of computational fluid dynamics (CFD) to simulate numerically the flow and temperature distribution in a mixer can contribute significantly to the understanding of the mixing and heat transfer processes and to provide for better, faster, and cheaper design optimization.
Over the last years many studies have been done using CFD techniques to characterize and optimize the mixing efficiency and the design configuration of Kenics static mixers. Numerical studies using Eulerian and Lagrangian methods, by means of tracer and particle tracking techniques have been used to characterize the optimum insert twist angle in mixing performance, and to determine the residence time distribution and velocity profiles in the transition between elements. Hoobs et al. [19], [20] have produced a significant amount of work on the numerical characterization of a Kenics static mixer. They report that flow transitions at the entrance and exit of each element affect the velocity field over around 25% of the element length under creeping flow conditions. Particle tracking simulations were used to compute residence time distributions, striation evolution, and the coefficient of variation as a function of the number of mixer elements for low Reynolds number flows. Byrde and Sowley [21] studied the optimization of a Kenics static mixer for Reynolds numbers above the non-creeping flow regime. These authors used a Lagrangian approach to determine an optimum element twist angle in the mixing efficiency. Rauline et al. [22] compared numerically the Kenics static mixer and a Sulzer SMX mixer under different circumstances. They show that the SMX mixer can be roughly 3.3 times shorter than the Kenics static mixer and give the same amount of distributive mixing. Song and Han [23] proposed a general correlation for the pressure drop in a Kenics static mixer from CFD calculations. They used the standard k–ɛ turbulence model for high Reynolds numbers. Kumar et al. [24] studied the performance of a static mixer over a wide range of Reynolds number through CFD analysis. In their CFD model the turbulent flow was calculated using either the k–ɛ or the k–ω turbulence models. Rahmani et al. [25] studied numerically the thermal performance of a Kenics static mixer with an aspect ratio of 0.84. Two different boundary conditions for the mixer metal surface – adiabatic and constant temperature – were analyzed. These authors show that helical static mixers can decrease the temperature gradient in fluid elements and produce a more uniform temperature distribution within the fluid.
A few papers evaluated the performance of low Reynolds number turbulence models in predicting mixed convective heat transfer to SCFs, giving special attention to the features which enable these fluids to respond to changes in the turbulence field due to influence of flow acceleration and buoyancy [26], [27], [28]. CFD methods have been also applied to heat-exchanger processes with SCFs in a wide range of applications [29], [30], and are now being considered as an important tool in the design and optimization of high pressure equipment.
In this work, CFD is employed to study the thermal efficiency of a Kenics static mixer for pre-heating scCO2 and to analyze the flow and temperature patterns and heat transfer efficiency. The CFD model is validated by comparing the predicted numerical results against experimental thermal data reported in the literature for heating fluids under low and high pressure conditions. Three turbulent models are employed to model the flow and heat transfer under high pressure conditions, with large variations of the physical properties.
Section snippets
Numerical simulation
The numerical computations were carried out using the commercial CFD package Fluent 6.3.26 (Fluent Inc., Lebanon, NH, USA). This solver uses a control-volume formulation for solving the conservation equations of mass, momentum, and energy. To calculate the turbulent flow in the static mixer, the standard k–ɛ, the renormalization group (RNG) k–ɛ, and the k–ω turbulence models were employed [31], [32]. The simulations were performed in a symmetric multiprocessing UNIX workstation with 8 Gb RAM and
Results and discussion
The CFD model of the Kenics static mixer was validated by comparing the predicted results against experimental thermal data available in the literature for heating fluids under both low and high pressure conditions.
Experimental data for scCO2 heating in a Kenics static mixer was collected from the previous work of Simões et al. [15]. Experimental pressure drop and heat transfer data were gathered at pressures ranging from 8 to 21 MPa, static mixer wall temperatures from 313 to 353 K, and mass
Conclusions
The forced convective heat transfer in a Kenics type static mixer using supercritical CO2 was modeled using CFD. The main geometry and meshing of the static mixer was generated using Gambit software (Fluent Inc.) and the 3D simulations were carried out using the Fluent software. A mesh sensitivity test was performed and the CFD model validated by comparing the predicted results against experimental data available in the literature for fluids under low and high pressure conditions. Three
Acknowledgments
Financial support by Fundação para a Ciência e Tecnologia, under project grant number POCTI/EME/61713/2004 and PhD grant SFRH/BD/19243/2004 is gratefully acknowledged.
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