THE NETMIX REACTOR: 3D CFD MODELLING AND PRESSURE DROP MEASUREMENTS

14 th European Conference on Mixing Warszawa, 10-13 September 2012 THE NETMIX REACTOR: 3D CFD MODELLING AND PRESSURE DROP MEASUREMENTS Carlos M. Fonte, M. Enis Leblebici, Madalena M. Dias, José Carlos B. Lopes Laboratory of Separation and Reaction Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal lopes@fe.up.pt Abstract. Three NETmix prototypes with different geometry were used to obtain experimental data of pressure drop and a model for predicting pressure drop in NETmix reactors was developed. This model incorporates a single adjustable parameter and it is only dependent on the geometric configuration of the network. The dynamic measurement of pressure drop was used to evaluate the mixing dynamics in the NETmix chambers and, above the critical Reynolds number, the natural oscillation frequency was quantified. Furthermore, a three-dimensional Computational Fluid Dynamic (CFD) transport model was also developed and validated. The energy performance of the three NETmix prototypes was quantified and shown to be competitive with the compared existing static mixers by evaluating the power number and Z factor. The new 3D CFD transport model allows the computation of transport properties and overcomes the need of obtaining experimental data each time a new NETmix configuration is designed. Keywords: NETmix reactor, pressure drop, power number, Z factor, CFD. 1. INTRODUCTION The NETmix Reactor is a new technology [1] consisting of a network of mixing chambers interconnected by transport s (Figure 1a). Networks are generated by the repetition of unit cells where each unit cell consists of one chamber and two inlet and two outlet s oriented at a 45º angle from the main flow direction and can either be constructed from cylindrical chambers and rectangular cross section area s (2D unit cell, Figure 1b) or from spherical chambers and cylindrical s (3D unit cell, Figure 1c). (a) (b) (c) Figure 1. a) Representation of the NETmix network; b) 2D unit cell; c) 3D unit cell. Above a critical Reynolds number, the flow inside the mixing chambers evolves to a self-sustained oscillatory laminar flow regime inducing local strong laminar mixing. This occurs due to the geometric characteristics of NETmix network. A network model was developed to describe and predict the behaviour and performance of NETmix [2]. From the point of view of modelling, it was shown that chambers can be assumed to behave as 107

perfectly mixing zones and the s as plug flow perfect segregation zones. The NETmix Reactor can therefore be understood, along the main flow direction, as a plug flow reactor with local maximum mixing. The mixing degree was defined and quantified [2, 3] showing that mixing can be controlled effectively and efficiently making it particularly suited for complex and fast kinetics reactions. However, the performance of the NETmix reactor, in terms of energy requirements, was yet to be studied and compared with others mixers. The main goal of this work was the development of a model that describes the pressure drop along NETmix reactors and its validation with experimental data and CFD simulations. From this pressure drop model, it is possible to evaluate the performance of any NETmix reactor topology by defining two benchmarking properties, the power number and Z factor, for comparison with other type of mixers. 2. PRESSURE DROP MODELLING 2.1 Pressure drop model The total pressure drop of each unit cell, Δ puc, was modelled using an analogy with an equivalent pure resistive electric circuit [4], where the flow rate through the s corresponds to the current across the resistance branches and the pressure drop between chambers corresponds to the voltage between nodes and is expressed by Δ puc = Rq where R is the total hydraulic resistance from the inlet to the outlet of the unit cell and q is the flow rate through the. This hydrodynamic model assumes the flow to be isothermal, incompressible and steady and the hydraulic resistance to be the sum of three F LF NLF F LF terms, R = R + R + R where R is the friction resistance in the s, and R and NLF R are hydraulic resistances related to the contractions and expansions in the chambers. The friction resistance in laminar regime is given by 2 2 ( ) μ ( ) R F = 12fρl o q d A = 32 l o d A (1) h h where f is the friction factor, ρ is the fluid density, l o is the length, d h is the hydraulic diameter, A is the cross sectional area. The linear flow resistance, LF R, in the chamber was defined by Koplik [5] as ( h ) = 32μ (2) LF * 2 R l d A * where l = 2d h π for this kind of geometry. This resistance exists whenever an unbounded jet flow is to be considered. When the fluid leaves the, the canonical friction term cannot model the energy transfer in the chamber as the flow is not bounded by the walls. Instead, the fluid s solid is replaced with a viscous surrounding as long as the NLF jet keeps its form. The nonlinear flow hydraulic resistance, R, that takes into account the energy dissipation due to accelerations/decelerations in the mixing chambers is modelled as NLF R = 12ρKq A (3) 2 where K is a coefficient analogous to the coefficients for sudden contractions and expansions generally used in the calculation of pressure drop in pipe systems. The value of K only depends on the geometrical characteristics of NETmix and can be determined from CFD simulations or experimental data. The total pressure drop in the system, Δ pnetmix, can then be determined by the sum of the pressure drop for the total number of rows in the flow direction. 108

From the dynamic measurement of pressure drop it is also possible to evaluate the mixing dynamics in the NETmix. Above a certain Reynolds number in the, known as the critical Reynolds number, the flow inside the mixing chambers evolves to a self-sustained oscillatory flow regime inducing local strong laminar mixing. These oscillations are intrinsic to the nature of the flow and not determined by external factors [6]. The natural frequency of these oscillations, f osc, in NETmix mixing chambers was proposed to be related to the residence time inside the chambers [6] and is expressed as ( ) fosc = 1τ = Vchamber μ dh Aρ Re (4) where τ is the residence time, V chamber is the volume of the chamber, and Re is the Reynolds number defined as Re = ρdhυ μ where υ is the average velocity at the. 2.2 Assessment of different mixers A common approach in the analysis of the power consumption in stirred tanks is to plot the power curve, that is the relationship between the dimensionless power number and the Reynolds number. The dimensionless power number, N p, is defined as the ratio between the total amount of energy supplied to the system and the energy that is needed to cause the fluid motion necessary for mixing. For the NETmix system operating in laminar regime, the power number can be expressed as o ( ) ( π ) ( ) ( ) NP =Δpmixer Δpmixer Δ pfriction = 1+ l + 2dh dhk 64 Re (5) where Δ pmixer is the mixer s pressure drop and Δ pfriction is the pressure drop due to friction. Another common way of interpreting the pressure drop for static mixers is by the Z factor. It is defined as the ratio between the pressure drop through the static mixer, Δ pstatic mixer, and the pressure drop through an empty tube of equal length and diameter, Δ pempty tube. For the NETmix geometry, the Z factor for laminar regime is expressed as o 0 0 ( h ) h ( ) Z =Δpstatic mixer Δ pempty tube = l + 2d π L + d K 64L Re (6) As can be seen in Equations 9 and 10, for the same Reynolds number, both the power number and the Z factor, are not dependent on the fluid properties, and are only dependent on the geometrical configuration of the NETmix reactor. 2.3 Experimental setup For these studies, three different NETmix geometries, built for different purposes, were used: one geometry with spherical chambers and cylindrical s and two geometries with cylindrical chambers and rectangular cross section area s. The geometrical characteristics of the three prototypes are summarized in Table 1. Water and glycerol solutions of 10%, 20% and 60% in mass were used in the measurements and the studies were carried out at room temperature. The differential pressure drop was measured with a pressure transducer at the inlet and outlet of each NETmix prototype at the reactor s inlet and outlet. Furthermore, the Lab-scale NETmix 2D front cover was also drilled at 2/3 in height to measure the pressure difference along the time at two outlet s from the same chamber. The pressure sensor was calibrated for each set of experiments so the voltage signal acquired could be converted to differential pressure. The pressure sensor sends voltage data to the computer via a data acquisition board. 109

Table 1. NETmix prototypes geometrical characteristics. Geometry Lab-scale Multi-inlet NETmix 3D NETmix 2D NETmix 2D Number of rows, n x 29 49 65 Number of columns, n y 8 15 16 Chamber diameter, D (mm) 6.5 7 8.75 Channel diameter, d (mm) 1 1.5 1.5 Geometry depth, ω (mm) 3 5.9 Channel length, l o (mm) 2 3 5.4 Total volume, V (ml) 23 140 1500 3. CFD MODEL Due to computer memory limitations, it is not possible to simulate, with the necessary grid refinement, the whole NETmix flow domain. Since the geometry and the expected pattern of the flow have a periodically repetitive nature, it is possible to simulate a larger system by modeling a small part that is far from its edge. The model s 3D geometry consists of a portion of the lab-scale NETmix 2D reactor prototype with 5 rows and 3 columns. The chambers of the first and third columns are half chambers and to their outer limits, a periodic boundary condition was applied as can be seen in Figure 2. At the chamber and walls a no-slip condition was assumed. A uniform velocity profile was applied to the network inlet s and a constant and uniform pressure value was set at the network outlet s. The fluid used in the simulation was water with constant physical properties at room temperature. The flow field simulation is achieved by numerical integration of the continuity and Navier-Stokes equations. The 3D simulations were performed in an Intel Xeon 3GHz 8-core machine running the finite-volume commercial CFD software ANSYS Fluent 13.0. A refined computational grid with 1.33 million elements was used. As an initial condition for the transient simulations, steady state simulations were performed. Non-friction walls were placed in the middle of the chamber to keep the flow segregated. The transient simulations were performed for a total flow time of 15τ. Outlets Periodic surfaces Periodic surfaces Inlets 4. RESULTS AND DISCUSSION Figure 2. Boundary conditions 4.1 Pressure drop experimental results An averaged value of the dynamic measurement of the signal received from the pressure transducer was converted to differential pressure. Figure 3 summarizes the pressure drop measurement results obtained for the three NETmix prototypes and the respective model fitting. To find the value of K, the experimental data was fitted to the model by the least squares method and the model was considered to fit well the experimental data with maximum deviations of 15%. The flow oscillations may be characterized by studying their frequency using power spectral analysis. The power spectral analysis was performed to the fluctuation of the signal 110

with time obtained with the pressure transducer for the Lab-scale NETmix 2D prototype. The signal was obtained from two measuring points at two outlets of a single chamber located at a middle region of the NETmix reactor. For a given Reynolds number, the dominant peak indicates the natural frequency of oscillation inside the chambers and is shown in Figure 4. The frequency of oscillation is fitted by a universal model (Equation 4), with a maximum deviation of 10%, and is only dependent on inertial effects: the flow rate and reactor volume. (a) (b) (c) Figure 3. Pressure drop obtained experimentally and model fitting for a) Lab-scale NETmix 2D, b) NETmix 3D; c) Multi-Inlet NETmix 2D. 4.2 Benchmarking Power number results for the three NETmix prototypes are shown in Figure 5. These results are compared with power number data of stirred tank mixers with different impeller designs obtained in the literature [7]. Results show that the power number for NETmix decreases with increasing Reynolds number and becomes significantly lower than the corresponding values for stirred tanks. Figure 4. Frequency of oscillation as a function of the Reynolds number. Figure 5. Power Number plot for the NETmix prototypes and for several stirred tanks with different impellers [7]. Figure 6 shows the Z factor values for the NETmix prototypes as a function of the Reynolds number. In this range of Reynolds numbers, the three prototypes exhibit Z factor values one order of magnitude lower than the commercial static mixers data found in the literature [8] and therefore can be operated with smaller pressure drops and, consequently, with a reduced consumption of energy. 4.3 CFD Simulation Results The CFD simulation results were compared to the experimental data and to the model fitting for the Lab-scale NETmix 2D prototype (Figure 7). The experimental data and the CFD simulation results are in a good agreement with a maximum deviation of 15%. It can be concluded that CFD simulations can be used to evaluate the pressure drop through NETmix reactor and overcome the need of experimental data for new configurations. 111

Figure 6. Z factor for the NETmix prototypes as a function of Re. The gray area corresponds to a typical range of Z factors for some commercial statics mixers [8]. 5. Figure 7. Pressure drop as a function of the Reynolds number obtained experimentally and from CFD simulations. CONCLUSIONS Experimental data of pressure drop obtained from three different NETmix prototypes was used to develop a model for prediction of the pressure drop with a single adjustable parameter that is only dependent on the geometric configuration of the network. The dynamic pressure measurements were also used to assess mixing dynamics in NETmix reactor and to confirm and extend a previously proposed model for the frequency of oscillation in the chambers. NETmix s mixing efficiency was previously estimated. However from this work, its energy performance was quantified and shown to be competitive with existing mixers by evaluating N P and Z factor for the three NETmix prototypes. The new 3D CFD transport model allows the computation of transport properties and overcomes the need of experiments each time a new NETmix configuration is designed. ACKNOWLEDGMENTS This work is partially financed by FEDER Funding through COMPETE - Programa Operacional Factores de Competitividade, and by Portuguese National Funding through FCT - Fundação para a Ciência e a Tecnologia within the scope of project PEstC/EQB/LA0020/2011. Carlos M. Fonte gratefully acknowledges the PhD grant from FCT (SFRH/BD/39040/2007). 6. REFERENCES [1] Lopes J.C.B., Laranjeira P.E., Dias M.M., Martins A.A., "Network mixer and related mixing process". PCT/IB2005/000647, February 2005. European Patent EP172643 B1, October 2008. [2] Laranjeira P.E., Martins A.A., Lopes J.C.B., Dias M.M., 2009. "NETmix, a new type of static mixer: Modeling, simulation, macromixing, and micromixing characterization", AIChE Journal, 55, 2226-2243. [3] Gomes P.J., Fonte C.P., Santos R.J., Dias M.M., Lopes J.C.B., 2010. "Experimental and numerical characterization and quantification of mixing in a NETmix reactor", in: ECCE 7-7th European Congress of Chemical Engineering & CHISA 2010-19th internation Congress and Process Engineering, Process Engineerig Publisher, Prahe, Prague, Czech Republic. [4] Martins A.A., Laranjeira P.E., Lopes J.C.B., Dias M.M., 2007. "Network modeling of flow in a packed bed", AIChE Journal, 53, 91-107. [5] Koplik J., 1982. "Creeping flow in two-dimensional networks", Journal of Fluid Mechanics, 119, 219-247. [6] Laranjeira P.E., 2005. "NETmix Static Mixer Modelling, CFD Simulation and Experimental Characterisation", in: Departamento de Engenharia Química, Universidade do Porto, Porto. [7] Bates R.L., Fondy P.L., Corpstein R.R., 1963. "Examination of Some Geometric Parameters of Impeller Power", Industrial & Engineering Chemistry Process Design and Development, 2, 310-314. [8] Thakur R.K., Vial C., Nigam K.D.P., Nauman E.B., Djelveh G., 2003. "Static Mixers in the Process Industries A Review", Chemical Engineering Research and Design, 81, 787-826. 112