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Accepted Manuscript High-efficiency mixing process in secondary rotating stream Dong-guang Wang, Yu-hua Wang, Zhen-yu Sun, Rong-tao Zhou, Bai-Kang Zhu, Ren-Kun Zhang PII: DOI: Reference:
S1385-8947(16)31792-2 http://dx.doi.org/10.1016/j.cej.2016.12.040 CEJ 16234
Received Date: Revised Date: Accepted Date:
31 July 2016 8 December 2016 10 December 2016
Please cite this article as: High-efficiency mixing process in secondary rotating stream, Chemical Engineering Journal (2016), doi: http://dx.doi.org/10.1016/j.cej.2016.12.040
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High-efficiency mixing process in secondary rotating stream
Dong-guang Wanga,*, Yu-hua Wang a, Zhen-yu Sunb, Rong-tao Zhouc, Bai-Kang Zhua, Ren-Kun Zhang a, a
Petrochemical &Energy Engineering School, Zhejiang Ocean University, 1 Haida
South Road, Lincheng New District, Zhoushan 316022, Zhejiang, P.R. China. b
State Key Laboratory of Organic–Inorganic Composites, Beijing University of
Chemical Technology, 15 Third Ring Road, Chaoyang District, Beijing 100029, P.R. China. c
State Key Laboratory of Multiphase Complex Systems, Institute of Process
Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, P.R. China.
1
Abstract Primary rotating flow (PRF) and secondary rotating stream (SRS) are two basic rotating flow patterns. We compared their mixing performances via the iodine transfer process from CCl4 to water. When the mixing power consumptions of the SRS mixer and PRF blender were approximated, the maximum value of KαSRS exceeded 71.7 s-1. Kα SRS was higher than Kα PRF 3 orders of magnitude, but the total energy
consumption of the SRS mixer was lower than that of the PRF blender 2 orders of magnitude. It was also found that Kα SRS increased sharply with the decrease of τ, which is consistent with the typical characteristics of Higee technology. Furthermore, computational fluid dynamics (CFD) was applied to simulate the pressure and flow field distributions of SRS. Based on the analysis of the velocity distribution mappings, it is concluded that SRS spontaneously generates intensive convection and vigorous shear stress under the reversing high-gravity field. The curve of KαSRS versus semi-circle channels is composed of a peak line and a wave line. In theory, we systematically illustrated the reasons for the high efficiency of SRS from four perspectives: time mixing, thermodynamics, momentum and mass transfers, opposite energy flows. Having many advantages and potentials, SRS will be widely explored and applied in chemical engineering field.
Keywords: Secondary rotating stream; Reversing high-gravity field; Multiscale mixings; Mass transfer; Computational fluid dynamics (CFD); Process intensification;
2
1. Introduction Mixing operation is an important component of modern industry engineering. Especially in chemical reaction engineering, ideal multiscale-mixing is benefit to fast reaction process by controllable intrinsic kinetics. Therefore, the development of green and clean chemical industry [1] urgently needs to go forward to exploring an ideal fast reactor with the following excellent performances [2, 3]: such as continuous operation, ultrafast multiscale mixings without back-mixing, small volume with high yield, the lowest energy consumption, uniform feeding distribution, excellent maneuverability, good tightness and machinability, easy cleaning, simulating, and scale-up. The same as those available mixing technologies [4-10], the ideal fast reactor firstly must be able to generate intensive convection and vigorous shear stress. Compared with impinging forced convection [11], rotating forced convection is characterized by smaller energy dissipation and larger scale mixings. PRF always has serious back-mixing and inertial spin. During inertial spin, the shear stress between flow layers is extremely low. The whirl style of SRS not only inhibits back-mixing and large-scale inertial spin, but also reverses the direction of centrifugal force field every 180° rotation. High-gravity is derived from centrifugal force, which is much higher than normal gravity. Conventional high-gravity (Higee) technology, being carried out in a rotating packed bed (RPB), has exhibited prominent process intensification characteristics including vigorous shear stress, rapid surface renewal, ultrafast mass transfer and micro-mixing, miniaturization, high efficiency, high-quality product and easy scale-up [12-15], etc. Dynamic high-gravity reactor 3
only create static high-gravity field, but static SRS mixer [16] generates dynamic high-frequency-reversing high-gravity field. The reverse frequency is much higher than that of hand shaking a cuvette. Nth rotating stream (N>2) is derived from SRS. At the same angular velocity of rotation, Nth rotating stream has higher reverse frequency than SRS. In our recent work [17], SRS and large-scale feeding distribution were combined together to achieve fast multiscale mixings. As a result, well-defined Fe3O4/MnOOH nanocomposites with 12.5 % of optimal coating ratio were continuously rapid synthesized in 0.2 s. The film-coating time was shorter than that of traditional method [18] 3~4 orders of magnitude. This feeding mode of SRS has enormous potentials for large-scaled and low-cost production of complicated materials. Furthermore, SRS and its derivatives may prove high-efficient multiscale mixing in many actual or potential industry processes, such as ionic liquid catalysis, nanoparticle fluidized catalysis, supercritical extraction, hydrothermal synthesis, polymerization, and precipitation, etc. In these processes, the transfer steps will be significantly accelerated by the reversing high-gravity field. Here we first quantitatively compared the differences of mixing performances between SRS mixer and PRF blender by unitary mass transfer process. The purpose is looking forward to realize fast ionic liquid catalytic reaction by using SRS reactor instead of stirred autoclave. The pressure and flow field distributions of SRS were simulated and discussed. Finally, we proposed the concept of mechanical energy circulation system. 4
2. Experimental The iodine transfer process from CCl4 phase to H2O phase was selected as the model system. During the mixing experiments, the volumes or flow rates of the two phases were basically equal. 2.1 Equipment 2.1.1. PRF blender The PRF blender was composed of a 250mL reagent bottle, a magnetic paddle with 25 mm-length and 10 mm-thickness, and a magnetism mixer (85-2 Model; Mei-Xiang Co., Shanghai, China). The liquid holdup of the rotating magnetic paddle was 3.0 ml. The stirring power was kept at the maximum value (20 W), as the maximum stirring speed at 2600 rpm. 2.1.2. SRS mixer As shown in Fig. 1(A), the SRS mixer had two inlets and five outlets. The impinging angle between the two feeding streams was 120°. The secondary rotating channel was composed of three parts in series (I, II, and III). Each part comprised 24 semi-circle channels with a total volume (VR) of 2.072 ml. All the semi-circle channels had the same inner diameter (10 mm) and the same cross section with 1.0 mm width and 5.0 mm depth. The 1.0 mm of hydraulic width reduced the consumption of CCl4 reagent, and is the minimum size of macro-channel. The 5.0 mm depth will increase the heat exchange area. P0 was the entrance pressure. Every exit could discharge liquid or connect with a pressure meter. For example, Exit 2 was used to measure pressure, see Fig. 1(B-D). In order to minimize the impact of the branch 5
channel on the pressure drop, a 1 mm diameter of stainless steel rod was filed and then inserted into the fork of the branch channel. When Exit 2 was used to discharge emulsion, the uniformity rod and 1mm thickness of silicone rubber were inserted into the main channel. 2.2. Experimental procedure We firstly prepared CCl4 solution containing 1000 mg/L I2, deionized water, 1g/L of KI solution, and standard iodine solution containing 7.30 mg/L I2 and 1.0 g/L KI. The used reagents (Sinopharm) were of analytical grade. In each PRF blender experiment, 100 ml CCl4 solution and 100 ml deionized water were added to the reagent bottle in order, and the bottle was sealed by a lid. Subsequently, the magnetism mixer was opened to the maximum and timed. When a mixing operation was stopped, the liquid stood for 30 min. Subsequently, 5 mL clear aqueous solution was transferred into a 100 mL volumetric flask and immediately diluted with the KI solution to volume. Finally, the sample was prepared. CCl4 solution and deionized water were separately poured into the two tanks, as shown in Fig. 1. High pressure air of 0.8 MPa was introduced into the two tanks to drive the two streams flow into the SRS mixer. The two flow rates were regulated to a pre-set equal flux by two liquid flow meters. Subsequently, we collected 200 mL of the discharged emulsion into a measuring cylinder. The collected volume and time were recorded to calculate the total flux. The emulsion shortly separated into aqueous layer and CCl4 layer in the cylinder. The actual volumes of the two layers were also recorded. The volume difference between the two layers must be less than 5 mL. 6
Otherwise, we had to repeat the operation until the requirement was met. Then, the aqueous layer was poured into a reagent bottle. After the reagent bottle stood for 30 min, a sample was prepared as described above. A series of standard solutions were prepared by diluting the standard iodine solution to 5%, 10%, 15%, 20%, and 25% with the KI solution. Thereafter, a visible spectrophotometer (Model- 722G; Shanghai Jingke Co., China) was used to measure the absorbance values of the standard solutions and the samples at the maximum absorption wavelength of 370 nm. The validity of the standard solutions and samples was limited in 24 h. The sample concentrations were eventually calculated from the standard curve. 3. Results and discussion The iodine transfer processes from CCl4 phase to H2O phase is described as dC = K α ⋅ ∆C dt
(1)
During the data processing, since the iodine distribution coefficient between two phases is more than 50, ΔC was treated as the concentration gradient between the equilibrium bulk concentration (C∞ ) and the bulk concentration (C) in the aqueous phase. Pc is the volumetric mixing power consumption, W/ml or MPa/s. PcPRF was always kept at 0.10 MPa/s. PcSRS was expressed by
PcSRS =
∆P
τ
≈
P0 ⋅ V0 VR
(2)
3.1. PRF blender The experimental results are shown in Table 1. During the mixing process, the 7
emulsion layer was formed only when the bottom of the aqueous layer fully touched the magnetic paddle, as shown in Fig. 3. The formation of emulsion layer significantly increased the mass transfer area between the two phases. If Kα PRF does not change with time, then Eq. (1) is integrated to t =
1
Kα PRF
C∞ ⋅ I n . C∞ − C
(3)
Fig. 4(A) shows the regression curve of sample concentration versus operation time. This curve was determined by Kα PRF, whose variation was synchronous with that of the momentum transfer. At the beginning, the momentum transfer instantaneously reached the maximum because the velocity gradient between the PRF and the magnetic paddle was the largest. With the decrease of velocity gradient, the PRF gradually entered inertia spin state. According to this trend, the sample points at the inertia spin state were regressed to a smooth curve based on Eq. (3). C∞ and the minimum of KαPRF were derived from the curve. Subsequently, the points at the second stage were regressed along the above regression curve based on the fact that the decline of KαPRF slowed down as time progresses. Fig. 4(B) shows the variation curve of KαPRF with time. The variation of KαPRF involved three stages: first, it rose to the maximum (t<5 s); then, it monotonically reduced to the lowest level (t<400 s); finally, it stayed at the lowest level (t>400 s). The maximum of KαPRF was roughly 30 times higher than the minimum. 3.2. SRS mixer The experimental results are shown in Table 2. During data processing, the SRS mixer was approximated as a plug flow reactor because secondary flow made the 8
residence times of all fluid elements tend to be equal. The two fluxes were approximately equal to half of V0. The basic equation of the mixing process was expressed as τ =
VR
V0
=
1 Kα SRS
C∞ ⋅ I n C∞ − C .
(4)
Eqs. (3) and (4) are basically same except for Kα SRS and τ. Figure 5(A) shows the concentrations versus τ of all the samples. At the same initial and terminal concentrations, the τ in the SRS mixer was usually 2–4 orders of magnitude shorter than the operation time in the PRF blender. Thus, Kα SRS of every sample was calculated according to Eq. (4). The results are shown in Fig. 5(B). The five curves corresponded to five groups of samples separately obtained from the five exits. One curve corresponded to a group of samples obtained at the approximate flux of 18.7 ml s-1. Their actual fluxes are shown in Fig. 5(D). Strikingly, the maximum of Kα SRS reached 71.7 s-1. From Fig. 5(B), it was concluded that Kα SRS increased with τ
being shortened. Two aspects were relevant. When V0 was constant but VR was increased, Kα SRS reduced from 71.7 s-1 to 9.13 s-1. This tendency was similar to the curve of KαPRF versus operation time. This suggests that small-scale inertia spin still occurred in SRS and derived from secondary flow [19], because the spin direction of secondary flow was unvaried in the flow field of SRS. When VR was unchanged but V0 was elevated, Kα SRS increased sharply with the decrease of τ. Fig. 5(C) indicates the reversing high-gravity field versus τ. The unit of high-gravity level is g, the acceleration of normal gravity field. The two intensities of the reversing high-gravity field also increased sharply with the decrease of τ. The synchronism demonstrated that 9
the reversing high-gravity field significantly improved Kα SRS . This is the typical characteristic of Higee technology. Thus, SRS comprises two opposite actions: small-scale inertia spin versus reversing high-gravity field. Fig. 5(D) shows the pressure distributions in the SRS mixer. The distribution of pressure drop in the three parts of the secondary rotating channels was relatively uniform, but that in the first part was obviously different. 3.3. Comparison of mixing performances To compare the mixing performances of the two mixers, we separately selected two samples. One was collected from the Exit 3 of the SRS mixer when V0 was 18.94 mL/s. The other was obtained after being agitated for 300 s in the PRF blender. Both had the same terminal concentration of 15.2 mg/L. The comparison results are shown in Table 3. Surprisingly, PcSRS was only 27.4 times higher than PcPRF, but Kα SRS was 2700 times higher than Kα PRF . This growth mode was completely nonlinear. Moreover, the total energy consumption and mixing time of the PRF blender were separately 100 times and 28.4 times higher than those of the SRS mixer. In the PRF blender, all the emulsion drops were generated from the rotating paddle. Table 3 indicates that the liquid holdup, rotary diameter and mixing power consumption of the paddle were close to those of the 24 semi-circle channels. The most difference between them was that the liquid did not repeat into the SRS mixer, but always repeated into the paddle. This led to a significant difference in the driving force of mass transfer (ΔC) between them. The driving force in the SRS mixer always maintained at the highest level, yet that in the PRF kept at the lowest level. Therefore, 10
the weak back-mixing is the first reason for the high-efficiency of SRS. During the above experiments, the waste CCl4 solution containing slightly less than 1 g/L of iodine was collected and decolorized by Na2S2O3 solution. According to the stoichiometric formula, 1 g of I2 consumes 1.246 g of Na2S2O3. When 100 mL of the waste liquid was treated by 100 mL, 1.25 g/L of Na2S2O3 solution in the PRF blender, the decolorization time lasted about 90 s～120 s. This process was accomplished readily in the SRS mixer (see Video). It was observed that when the total flux was higher than 23.1 mL s-1 and the outlet position was Exit 3, the collected CCl4 phase was colorless. The decolorization time in the SRS mixer was three orders of magnitude shorter than that in the PRF blender. 4. CFD simulation 4.1. Procedure We simulated the flow pattern of SRS in the first three representative semi-circle channels of the SRS mixer. The swept hexahedral meshes were used to discretize the domain for the computational efficiency and accuracy, as shown in Fig. 2(A). Both the axial and cross-sectional meshes were constructed to provide accurate resolution of the flow field throughout the domain, see Fig. 2(B-C). The total amount of the meshes was 735,060. The operating conditions and physical properties are shown in Table 4. The model involves two immiscible liquids, and the basic equations in the simulation are conservation of mass, momentum, and energy. The two-phase mixture model was used to simulate the 3D two-phase flow by using FLUENT package. 11
Turbulence is modeled by the standard k-ε mixture model. The schiller-naumann drag model is used to describe momentum exchange between phases. The first order upwind scheme is applied for the discretization of all the equations. SIMPLE method was adopted for the pressure-velocity coupling. 4.2. Results The simulation results of pressure and flow field distributions are displayed in Fig. 6. Fig. 6(A) indicates that the total pressure drop is 76.5 kPa, close to the measured values from 80 to 150 kPa. The simulated impingement between the two streams brings about 26.5 kPa of pressure drop. Although the impingement can greatly intensify micro-mixing [5], its instantaneous energy consumption is too high. Therefore, it is imagined that inelastic merging of two rotating flows will not only lower the feeding power consumption but also further accelerate the multi-scale mixings, as shown in Fig. 6(B). Furthermore, it can be seen from Fig. 6(A) that the axial distribution of the 50 kPa pressure drop is essentially uniform, and the radial distribution is reversed by the reversing high gravity. This suggests that the mechanical energy in the SRS is uniformly dissipated along the axial direction. In the 24 semi-circle channels, the energy dissipation time and distance were 0.109 s and 360 mm, respectively. However, the two values of the stirring paddle were just very low. The pressure drop curve of SRS was not far from that of an ideal reversible mixing process. According to the second law of thermodynamics, the ideal process has the highest mixing efficiency. Therefore, the energy efficiency of SRS was much higher than that of the stirring paddle. The uniform pressure drop distribution of SRS 12
is another reason for its high-efficiency. At the simulated conditions, the high-gravity level and reverse frequency are 287 g and 110 Hz, respectively. The two reversing fields of high gravity and static pressure generate the disturbed flow regions along axial direction, as shown in Fig. 6(C). It can be seen that there are obvious velocity boundary layers in SRS. Before SRS reaches to the center of a disturbed region, its boundary layer becomes thin. After it flows through the center, its boundary layer becomes thick. During this process, the shear stress has an obvious fluctuation, which makes KαSRS fluctuation above the static baseline. When ρ andμ of the emulsion are estimated to be 1400 kg/m3 and 1 mPa s, Re and D are calculated to be 5300 and 1700, according to the following two formulas: Re =
dv ρ
µ ,
d 2r
0. 5
D = Re
(5)
The two values are an order of magnitude higher than the two critical numbers of Dean vortices [20-22]. Fig. 6(D) shows the flow field distribution maps of five cross sections. It can be seen from Fig. 6(D) that secondary flow or its derivative Dean vortices are distributed in each cross section map. Astonishingly, the intensities of secondary flows in the 1-1 cross section are much stronger than those in the other four cross sections. In the five cross section maps, the intensities of secondary flows are arranged in the following order: 1-1≫2-2≈4-4>3-3≈5-5. In 1-1, the spontaneously high-speed rotating Dean vortexes are generated in less than 2.5 ms by the vigorous and balanced shear stress distribution, which also brings about the balanced KαSRS and concentration distributions. From 2-2 to 5-5, Dean 13
vortexes are difficult to be detected. The obvious uneven speed distributions of secondary flows suggest the uneven KαSRS and concentration distributions. The consequence of the two uneven distributions is very similar to that of back-mixing, i.e., the significant reduction of total KαSRS. Therefore, the Kα SRS of the first semi-circle channel is much higher than the average value of 71.7 s-1, and then a high peak line of KαSRS is formed. Therefore, we conjecture the model curve of KαSRS versus semi-circle channels, as shown in Fig.7. The peak line is fit for one-time feeding with ultrafast mixing, and the wave line is fit for continuous feeding with fast mixing. Since the Kα and concentration distributions are completely inhomogeneous in the PRF blender, this is the third reason for the high-efficiency of SRS. Obviously, the ideal reversible mixing process means that the wall friction is zero, and the reversing high gravity, reversing static pressure, as well as shear stress form the first dynamic balance. The second dynamic balance is formed between shear stress and surface tension, and the shear force distribution is completely uniform along the radial direction. Only ideal fast reactor can realize the ideal reversible mixing process. 5. PEF and NES From another perspective, a centrifugal pump and an SRS mixer can constitute a high-efficiency mechanical energy circulation system. In a split second, the former generates high positive energy flow (PEF) and the latter forms high negative energy stream (NES). Attraction, dependence, and transformation relations exist between PEF and NES. When sucked into the centrifugal pump, NES along axial direction is transformed into PEF along radial direction. The center of PEF is NES and both are 14
separated. Upon entering into the SRS mixer, a primary flow with high mechanical energy becomes SRS. SRS is NES along axial direction and develops Dean vortices along radial direction. Dean vortices belong to PEF during its development. The energy of PEF is derived from NES and both are completely integrated together. In the SRS mixer, PEF can directly absorb and largely transform the high pressure energy of NES into vigorous shear stress. In centrifugal pump, the existence time of PEF is extended with the intensity of high-gravity field being increased. If the two intensities of reversing high-gravity field in the SRS mixer are also increased, its PEF will also have longer existence time. 6. Conclusion SRS is a novel supplement of Higee technology. Many excellent performances of SRS reactor are close to those of ideal fast reactor. In this study, the mixing performances of SRS were quantitative analyzed and simulated. The mainly conclusions are as follows: 1. The mixing efficiency of the SRS mixer was not far from that of ideal fast reactor. Compared with the PRF blender, its mixing energy consumption lowered by 2 orders of magnitude, and Kα SRS improved by 3 orders of magnitude. 2. The high-efficiency multi-scale mixings in SRS were attributed to weak back-mixing and uniform energy release along axial and radial directions. 3. In SRS the two high-frequency reversing fields of high gravity and static pressure co-produced intensive secondary flow and vigorous shear stress. 4. In the initial semi-circle channel, SRS can generate ultrafast mixing process. After 15
that, it only can realize fast mixing process. 5. PRF and SRS are separately suitable for generating PEF and NES. At the initial stage of SRS, the ultrafast mixing is derived from the unity of NES and PEF.
Nomenclature Definitions Primary rotating flow (PRF)
a rotating flow whose direction is always constant
Secondary rotating stream (SRS)
a rotating stream whose direction reverses every 180° rotation
a rotating stream whose direction reverses every 360。/N
Nth rotating stream
rotation Multiscale mixings
mixing process involves macro-, meso- and micro-mixings
Reversing high-gravity field
a high-gravity field whose direction is reversing at a certain frequency;
Positive energy flow (PEF) Negative energy stream (NES)
a flow whose mechanical energy is increasing; a stream whose mechanical energy is decreasing;
Symbols dC/dt
increase rate of iodine concentration in the aqueous phase [mol/L s]
Kα
volumetric mass transfer coefficient [ s-1]
Kα
average volumetric mass transfer coefficient
C∞ C
bulk concentration in water phase after infinite mixing time [mol/L] bulk concentration in water phase [mol/L] 16
Pc
volumetric mixing power consumption [W/mL or MPa/s]
PC
average volumetric mixing power consumption
d
width of semi-circle channel
r
inner radius of semi-circle channel
Re
Reynolds number
D
Dean number
V0
Total flux [ml/s]
VR
Volume of the semi-circle channels [ml]
v
Average flow velocity [m/s]
Greek symbols
ρ
Density [kg/m3]
μ
Viscosity [mPa s]
τ
Space time [s]
Subscripts PRF
the PRF blender
SRS
the SRS mixer
References and Notes: [1] J. García-Serna, L. Pérez-Barrigón, M. J. Cocero, New trends for design towards sustainability in chemical engineering: Green engineering. Chem. Eng. J. 133(s 1–3) (2007) 7-30. [2] R. F. Service, The next big(ger) thing. Science 335 (2012) 1167. [3] E. L. Paul, V. A. Atiemo-Obeng, S. M. Kresta, Handbook of Industrial Mixing: 17
Science and Practice, Wiley & Sons, Hoboken, 2004. [4] C. Ramshaw, Higee distillation––an example of process intensification, Chem. Eng. 90 (2) (1983) 13–14. [5] J. D. Robert, R. B. John, Rapid micromixing by the impingement of thin liquid sheets, Ind. Eng. Chem. Res. 28 (1989) 825-839. [6] N. Nam-Trung, W. Zhigang, Micromixers—a review, J. Micromech. Microeng. 15 (2005) R1–R16. [7] J. Lindley, T. J. Mason. Sonochemistry. Part 2 - Synthetic applications, Chem. Soc. Rev. 16 (1987) 275-311. [8] M. Jasińska, J. Bałdyga, M. Cooke, A. Kowalski, Investigations of mass transfer with chemical reactions in two-phase liquid–liquid systems, Chem. Eng. Res. Des. 91(2013) 2169-2178. [9] P. Patrick, M. R. Dominique, M. Arturo, Liquid–liquid flow regimes and mass transfer in various micro-reactors, Chem. Eng. J. 300 (2016) 9–19. [10] J. R. Bourne, J. Garcia-Rosas, Rotor-stator mixer for rapid micromixing, Chem. Eng. Res. 61 (1986) 11-17. [11] C. J. Kobus, G. Shumway, An experimental investigation into impinging forced convection heat transfer from stationary isothermal circular disks, Int. Heat. Mass. Tran. 49 (2006) 411-414. [12] J. F. Chen, Y. H. Wang, F. Guo, C. Zheng, Synthesis of Nanoparticles with Novel Technology: High-Gravity Reactive Precipitation, Ind. Eng. Chem. Res. 39 (2000) 948-954. 18
[13] H. Zhao, L. Shao, J. F. Chen, High-gravity process intensification technology and application, Chem. Eng. J. 156 (2010) 588-593. [14] Q. Sun, B. Chen, X. Wu, M. Wang, C. Zhang, X. F. Zeng, J. X. Wang, J. F. Chen. Preparation of transparent suspension of lamellar magnesium hydroxide nanocrystals using a high-gravity reactive precipitation combined with surface modification, Ind. Eng. Chem. Res. 54 (2015) 666-671. [15] Z. B. Zhang, M. L. Xie, Y. Y. Kuang, J. X. Wang, Y. Le, X. F. Zeng, J. F. Chen, Preparation of amorphous drug nanoparticles by high-gravity reactive precipitation technique, Chem. Eng. Process. 104 (2016) 253–261. [16] A. Ghanem, T. Lemenand, D. D. Valle, H. Peerhossaini, Static mixers: Mechanisms, applications, and characterization methods – A review. Chem. Eng. Res. Des. 92(2014) 205-228. [17] D. G. Wang, B. K. Zhu, H. C. Tao, Preparation of Fe3O4/MnOOH core-shell nanoparticles by a high-frequency impinging stream reactor, Chin. J. Chem. Eng. 23 (2015) 727–735. [18] G. C. Rajib, P. Santanu, Core/Shell Nanoparticles: Classes, Properties, Synthesis Mechanisms, Characterization, and Applications, Chem. Rev. 112 (2012) 2373–2433. [19] W. R. Dean, Note on the motion of fluid in a curved pipe. Philos. Mag. 20 (1927) 208-223. [20] J. H. Horlock, B. Lakshminarayana, Secondary flows: Theory, experiment, andapplication in turbomachinery aerodynamics, Ann. Rev. Fluid. Mech. 5 (1973) 247-280. 19
[21] W. R. Briley, H. Medonald, Three-dimensional viscous flows with large secondary velocity, J. Fluid. Mech. 144(1984) 47-77. [22] N. R. Rosaguti, F. F. David, S. H. Brian, Low-Reynolds number heat transfer enhancement in sinusoidal channels, Chem. Eng. Sci. 62 (2007) 694-702.
Acknowledgments: We acknowledge the early financial supports provided by the National Key Technology R&D Program of China (No. 2009BAB47B08) and the Science & Technical Project of China Petroleum Chemical Co. (No. 314109).
20
Fig. 1.Experimental set-up (A) of SRS mixer and photographs (B-D) of its inner structure.
21
Fig. 2.Agitation process in PRF blender. (A) Photograph of the agitation process. (B) Distribution diagram of the H2O, emulsion, and CCl4 layers.
22
Fig. 3.Mixing characteristics of PRF blender. (A) Sample points, regression curve, three theoretical curves, and the line of ܥஶ . (B) Curve of KαPRF versus operation time.
(A)
Concentration (mg/L)
20
16
12
Sample point Regression curve -1 Ka PRF=0.00147 s
8
-1
Ka PRF=0.0030 s 4
-1
Ka PRF=0.0050 s C∞=18.1mg/L
0 0
400
800
1200
1600
2000
Operation time (s)
(B) 0.05
Ka PRF ( s-1)
0.04 0.03
Curve of Ka PRF
0.02
Ka PRF, min =0.00147 s
-1
0.01 0.00 0
300
600
900
1200
1500
Operation time (s)
23
1800
Fig. 4.Mixing characteristics of SRS mixer. (A) Concentrations versus space times of തതതതௌோௌ versus τ. (C) all the samples obtained from the five exits. (B) Curves of ߙܭ Curves of high-gravity level and reverse frequency versus τ, corresponding to the group of samples obtained from Exit 3. (D) Curves of pressure drop versus exit.
(A)
Concentration (mg L-1)
18
15
12 Samples from Exit 1 Samples from Exit 2 Samples from Exit 3 Samples from Exit 4 Samples from Exit 5 Equilibrium line
9
6
3 0.0
0.2
0.4
0.6
0.8
1.0
Space time (s)
(B) 75
-1
Ka SRS ( s )
60
Samples from Exit 1 Samples from Exit 2 Samples from Exit 3 Samples from Exit 4 Samples from Exit 5 Equal flux curve
45
30
15
0 0.0
0.2
0.4
0.6
Space time (s)
24
0.8
1.0
1.2
(C)
160 140
Curve of high gravity level Curve of reverse frequency
250
120 100
200
80
150
60 100 40 50
20
0
0 0.10
0.15
0.20
0.25
0.30
0.35
0.40
Space time (s)
(D)
P0
1
3
2
Exit
5
4
-1 V0=18.77 mL s -1 V0=18.70 mL s -1 V0=18.94 mL s -1 V0=18.58 mL s -1 V0=16.10 mL s
Gauge pressure (KPa)
500
400
300
200
100
0 0
10
20
30
40
50
Semi-circle channels
25
60
70
Reverse frequency (Hz)
High gravity level (g)
300
Fig. 5. Mesh density of the simulated SRS. (A) Mesh density in a 3-D graph. (B) Mesh density on a cross-section. (C) Mesh density along the axial direction.
26
Fig. 6.Simulations of SRS. (A) Diagram of axial pressure distribution. (B) Diagram of two rotating flows merging together. (C) Diagram of axial velocity distribution as well as the position of five flow cross sections. (D) Diagrams of velocity distribution in five flow cross sections.
27
Fig. 7.Model curve of KαSRS versus semi-circle channels.
28
Table 1. Mixing experimental results from the PRF blender.
t(s)
5
10
15
20
40
60
90
120
180
300
C(mg/L)
4.451
7.913
10.30
11.13
12.53
13.60
13.44
14.01
14.42
15.08
t(s)
450
600
750
900
1050
1200
1350
1500
1650
1800
C(mg/L)
16.23
15.66
16.82
17.47
17.23
17.80
17.64
17.64
18.05
18.05
29
Table 2. Mixing experimental results from the SRS mixer. Exit 1 (VR, 0.259 ml)
Exit 2 (0.950 ml)
Exit 3 (2.072 ml)
Exit 4 (4.144 ml)
Exit 5 (6.216 ml)
τ(s)
0.0308
0.0222
0.0175
0.0153
0.0138
C (mg/L)
9.310
10.10
11.03
11.18
11.37
τ (s)
0.116
0.0865
0.0664
0.0594
0.0506
C (mg/L)
13.10
13.98
14.39
14.24
14.68
τ (s)
0.3816
0.2429
0.1855
0.1460
0.1321
0.1093
C (mg/L)
11.13
13.11
13.68
13.60
14.75
15.20
τ (s)
0.7480
0.4682
0.3740
0.2922
0.2580
0.2232
C (mg/L)
11.54
14.01
14.34
15.33
15.33
15.74
τ (s)
1.1364
0.7480
0.5575
0.4409
0.3861
C (mg/L)
13.27
14.01
14.01
15.74
16.40
30
Table 3. Comparisons of mixing parameters and performances between two mixers. Performances
PRF blender
SRS mixer
Operation mode
Batch operation
Continuous operation
Liquid holdup, ml
3.0
2.072
Mixing power, W
20
5.68
rotary diameter, mm
25
10
Total treated volume, ml
200
200
Total mixing time, s
300
10.6
—
0.109
Total energy consumption, J
6000
60
Kα , s-1
0.00610
16.7
Pc, MPa/s
0.10
2.74
Average mixing time of fluid element, s
31
Table 4. Simulation conditions and physical properties in this work. Property
Value
Average flow speeds
1.9 m/s
The viscosity of mixture
1.0 mPa s
Density of aqueous stream
1.0 g/ml
Density of CCl4 stream
1.8 g/ml
Wall roughness in the semi-circle channel
0.01 mm
32
Graphical abstract
33
Highlights 1. Secondary rotating stream (SRS) is a novel supplement of Higee technology. 2. Many excellent performances of SRS reactor are close to those of ideal fast reactor. 3. The mixing efficiency of SRS was not far from that of ideal fast reactor. 4. The reversing high-gravity field generates intensive convection and shear stress. 5. The initial SRS generates ultrafast mixing. After that, it forms fast mixing.
34
S1385-8947(16)31792-2 http://dx.doi.org/10.1016/j.cej.2016.12.040 CEJ 16234
Received Date: Revised Date: Accepted Date:
31 July 2016 8 December 2016 10 December 2016
Please cite this article as: High-efficiency mixing process in secondary rotating stream, Chemical Engineering Journal (2016), doi: http://dx.doi.org/10.1016/j.cej.2016.12.040
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
High-efficiency mixing process in secondary rotating stream
Dong-guang Wanga,*, Yu-hua Wang a, Zhen-yu Sunb, Rong-tao Zhouc, Bai-Kang Zhua, Ren-Kun Zhang a, a
Petrochemical &Energy Engineering School, Zhejiang Ocean University, 1 Haida
South Road, Lincheng New District, Zhoushan 316022, Zhejiang, P.R. China. b
State Key Laboratory of Organic–Inorganic Composites, Beijing University of
Chemical Technology, 15 Third Ring Road, Chaoyang District, Beijing 100029, P.R. China. c
State Key Laboratory of Multiphase Complex Systems, Institute of Process
Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, P.R. China.
1
Abstract Primary rotating flow (PRF) and secondary rotating stream (SRS) are two basic rotating flow patterns. We compared their mixing performances via the iodine transfer process from CCl4 to water. When the mixing power consumptions of the SRS mixer and PRF blender were approximated, the maximum value of KαSRS exceeded 71.7 s-1. Kα SRS was higher than Kα PRF 3 orders of magnitude, but the total energy
consumption of the SRS mixer was lower than that of the PRF blender 2 orders of magnitude. It was also found that Kα SRS increased sharply with the decrease of τ, which is consistent with the typical characteristics of Higee technology. Furthermore, computational fluid dynamics (CFD) was applied to simulate the pressure and flow field distributions of SRS. Based on the analysis of the velocity distribution mappings, it is concluded that SRS spontaneously generates intensive convection and vigorous shear stress under the reversing high-gravity field. The curve of KαSRS versus semi-circle channels is composed of a peak line and a wave line. In theory, we systematically illustrated the reasons for the high efficiency of SRS from four perspectives: time mixing, thermodynamics, momentum and mass transfers, opposite energy flows. Having many advantages and potentials, SRS will be widely explored and applied in chemical engineering field.
Keywords: Secondary rotating stream; Reversing high-gravity field; Multiscale mixings; Mass transfer; Computational fluid dynamics (CFD); Process intensification;
2
1. Introduction Mixing operation is an important component of modern industry engineering. Especially in chemical reaction engineering, ideal multiscale-mixing is benefit to fast reaction process by controllable intrinsic kinetics. Therefore, the development of green and clean chemical industry [1] urgently needs to go forward to exploring an ideal fast reactor with the following excellent performances [2, 3]: such as continuous operation, ultrafast multiscale mixings without back-mixing, small volume with high yield, the lowest energy consumption, uniform feeding distribution, excellent maneuverability, good tightness and machinability, easy cleaning, simulating, and scale-up. The same as those available mixing technologies [4-10], the ideal fast reactor firstly must be able to generate intensive convection and vigorous shear stress. Compared with impinging forced convection [11], rotating forced convection is characterized by smaller energy dissipation and larger scale mixings. PRF always has serious back-mixing and inertial spin. During inertial spin, the shear stress between flow layers is extremely low. The whirl style of SRS not only inhibits back-mixing and large-scale inertial spin, but also reverses the direction of centrifugal force field every 180° rotation. High-gravity is derived from centrifugal force, which is much higher than normal gravity. Conventional high-gravity (Higee) technology, being carried out in a rotating packed bed (RPB), has exhibited prominent process intensification characteristics including vigorous shear stress, rapid surface renewal, ultrafast mass transfer and micro-mixing, miniaturization, high efficiency, high-quality product and easy scale-up [12-15], etc. Dynamic high-gravity reactor 3
only create static high-gravity field, but static SRS mixer [16] generates dynamic high-frequency-reversing high-gravity field. The reverse frequency is much higher than that of hand shaking a cuvette. Nth rotating stream (N>2) is derived from SRS. At the same angular velocity of rotation, Nth rotating stream has higher reverse frequency than SRS. In our recent work [17], SRS and large-scale feeding distribution were combined together to achieve fast multiscale mixings. As a result, well-defined Fe3O4/MnOOH nanocomposites with 12.5 % of optimal coating ratio were continuously rapid synthesized in 0.2 s. The film-coating time was shorter than that of traditional method [18] 3~4 orders of magnitude. This feeding mode of SRS has enormous potentials for large-scaled and low-cost production of complicated materials. Furthermore, SRS and its derivatives may prove high-efficient multiscale mixing in many actual or potential industry processes, such as ionic liquid catalysis, nanoparticle fluidized catalysis, supercritical extraction, hydrothermal synthesis, polymerization, and precipitation, etc. In these processes, the transfer steps will be significantly accelerated by the reversing high-gravity field. Here we first quantitatively compared the differences of mixing performances between SRS mixer and PRF blender by unitary mass transfer process. The purpose is looking forward to realize fast ionic liquid catalytic reaction by using SRS reactor instead of stirred autoclave. The pressure and flow field distributions of SRS were simulated and discussed. Finally, we proposed the concept of mechanical energy circulation system. 4
2. Experimental The iodine transfer process from CCl4 phase to H2O phase was selected as the model system. During the mixing experiments, the volumes or flow rates of the two phases were basically equal. 2.1 Equipment 2.1.1. PRF blender The PRF blender was composed of a 250mL reagent bottle, a magnetic paddle with 25 mm-length and 10 mm-thickness, and a magnetism mixer (85-2 Model; Mei-Xiang Co., Shanghai, China). The liquid holdup of the rotating magnetic paddle was 3.0 ml. The stirring power was kept at the maximum value (20 W), as the maximum stirring speed at 2600 rpm. 2.1.2. SRS mixer As shown in Fig. 1(A), the SRS mixer had two inlets and five outlets. The impinging angle between the two feeding streams was 120°. The secondary rotating channel was composed of three parts in series (I, II, and III). Each part comprised 24 semi-circle channels with a total volume (VR) of 2.072 ml. All the semi-circle channels had the same inner diameter (10 mm) and the same cross section with 1.0 mm width and 5.0 mm depth. The 1.0 mm of hydraulic width reduced the consumption of CCl4 reagent, and is the minimum size of macro-channel. The 5.0 mm depth will increase the heat exchange area. P0 was the entrance pressure. Every exit could discharge liquid or connect with a pressure meter. For example, Exit 2 was used to measure pressure, see Fig. 1(B-D). In order to minimize the impact of the branch 5
channel on the pressure drop, a 1 mm diameter of stainless steel rod was filed and then inserted into the fork of the branch channel. When Exit 2 was used to discharge emulsion, the uniformity rod and 1mm thickness of silicone rubber were inserted into the main channel. 2.2. Experimental procedure We firstly prepared CCl4 solution containing 1000 mg/L I2, deionized water, 1g/L of KI solution, and standard iodine solution containing 7.30 mg/L I2 and 1.0 g/L KI. The used reagents (Sinopharm) were of analytical grade. In each PRF blender experiment, 100 ml CCl4 solution and 100 ml deionized water were added to the reagent bottle in order, and the bottle was sealed by a lid. Subsequently, the magnetism mixer was opened to the maximum and timed. When a mixing operation was stopped, the liquid stood for 30 min. Subsequently, 5 mL clear aqueous solution was transferred into a 100 mL volumetric flask and immediately diluted with the KI solution to volume. Finally, the sample was prepared. CCl4 solution and deionized water were separately poured into the two tanks, as shown in Fig. 1. High pressure air of 0.8 MPa was introduced into the two tanks to drive the two streams flow into the SRS mixer. The two flow rates were regulated to a pre-set equal flux by two liquid flow meters. Subsequently, we collected 200 mL of the discharged emulsion into a measuring cylinder. The collected volume and time were recorded to calculate the total flux. The emulsion shortly separated into aqueous layer and CCl4 layer in the cylinder. The actual volumes of the two layers were also recorded. The volume difference between the two layers must be less than 5 mL. 6
Otherwise, we had to repeat the operation until the requirement was met. Then, the aqueous layer was poured into a reagent bottle. After the reagent bottle stood for 30 min, a sample was prepared as described above. A series of standard solutions were prepared by diluting the standard iodine solution to 5%, 10%, 15%, 20%, and 25% with the KI solution. Thereafter, a visible spectrophotometer (Model- 722G; Shanghai Jingke Co., China) was used to measure the absorbance values of the standard solutions and the samples at the maximum absorption wavelength of 370 nm. The validity of the standard solutions and samples was limited in 24 h. The sample concentrations were eventually calculated from the standard curve. 3. Results and discussion The iodine transfer processes from CCl4 phase to H2O phase is described as dC = K α ⋅ ∆C dt
(1)
During the data processing, since the iodine distribution coefficient between two phases is more than 50, ΔC was treated as the concentration gradient between the equilibrium bulk concentration (C∞ ) and the bulk concentration (C) in the aqueous phase. Pc is the volumetric mixing power consumption, W/ml or MPa/s. PcPRF was always kept at 0.10 MPa/s. PcSRS was expressed by
PcSRS =
∆P
τ
≈
P0 ⋅ V0 VR
(2)
3.1. PRF blender The experimental results are shown in Table 1. During the mixing process, the 7
emulsion layer was formed only when the bottom of the aqueous layer fully touched the magnetic paddle, as shown in Fig. 3. The formation of emulsion layer significantly increased the mass transfer area between the two phases. If Kα PRF does not change with time, then Eq. (1) is integrated to t =
1
Kα PRF
C∞ ⋅ I n . C∞ − C
(3)
Fig. 4(A) shows the regression curve of sample concentration versus operation time. This curve was determined by Kα PRF, whose variation was synchronous with that of the momentum transfer. At the beginning, the momentum transfer instantaneously reached the maximum because the velocity gradient between the PRF and the magnetic paddle was the largest. With the decrease of velocity gradient, the PRF gradually entered inertia spin state. According to this trend, the sample points at the inertia spin state were regressed to a smooth curve based on Eq. (3). C∞ and the minimum of KαPRF were derived from the curve. Subsequently, the points at the second stage were regressed along the above regression curve based on the fact that the decline of KαPRF slowed down as time progresses. Fig. 4(B) shows the variation curve of KαPRF with time. The variation of KαPRF involved three stages: first, it rose to the maximum (t<5 s); then, it monotonically reduced to the lowest level (t<400 s); finally, it stayed at the lowest level (t>400 s). The maximum of KαPRF was roughly 30 times higher than the minimum. 3.2. SRS mixer The experimental results are shown in Table 2. During data processing, the SRS mixer was approximated as a plug flow reactor because secondary flow made the 8
residence times of all fluid elements tend to be equal. The two fluxes were approximately equal to half of V0. The basic equation of the mixing process was expressed as τ =
VR
V0
=
1 Kα SRS
C∞ ⋅ I n C∞ − C .
(4)
Eqs. (3) and (4) are basically same except for Kα SRS and τ. Figure 5(A) shows the concentrations versus τ of all the samples. At the same initial and terminal concentrations, the τ in the SRS mixer was usually 2–4 orders of magnitude shorter than the operation time in the PRF blender. Thus, Kα SRS of every sample was calculated according to Eq. (4). The results are shown in Fig. 5(B). The five curves corresponded to five groups of samples separately obtained from the five exits. One curve corresponded to a group of samples obtained at the approximate flux of 18.7 ml s-1. Their actual fluxes are shown in Fig. 5(D). Strikingly, the maximum of Kα SRS reached 71.7 s-1. From Fig. 5(B), it was concluded that Kα SRS increased with τ
being shortened. Two aspects were relevant. When V0 was constant but VR was increased, Kα SRS reduced from 71.7 s-1 to 9.13 s-1. This tendency was similar to the curve of KαPRF versus operation time. This suggests that small-scale inertia spin still occurred in SRS and derived from secondary flow [19], because the spin direction of secondary flow was unvaried in the flow field of SRS. When VR was unchanged but V0 was elevated, Kα SRS increased sharply with the decrease of τ. Fig. 5(C) indicates the reversing high-gravity field versus τ. The unit of high-gravity level is g, the acceleration of normal gravity field. The two intensities of the reversing high-gravity field also increased sharply with the decrease of τ. The synchronism demonstrated that 9
the reversing high-gravity field significantly improved Kα SRS . This is the typical characteristic of Higee technology. Thus, SRS comprises two opposite actions: small-scale inertia spin versus reversing high-gravity field. Fig. 5(D) shows the pressure distributions in the SRS mixer. The distribution of pressure drop in the three parts of the secondary rotating channels was relatively uniform, but that in the first part was obviously different. 3.3. Comparison of mixing performances To compare the mixing performances of the two mixers, we separately selected two samples. One was collected from the Exit 3 of the SRS mixer when V0 was 18.94 mL/s. The other was obtained after being agitated for 300 s in the PRF blender. Both had the same terminal concentration of 15.2 mg/L. The comparison results are shown in Table 3. Surprisingly, PcSRS was only 27.4 times higher than PcPRF, but Kα SRS was 2700 times higher than Kα PRF . This growth mode was completely nonlinear. Moreover, the total energy consumption and mixing time of the PRF blender were separately 100 times and 28.4 times higher than those of the SRS mixer. In the PRF blender, all the emulsion drops were generated from the rotating paddle. Table 3 indicates that the liquid holdup, rotary diameter and mixing power consumption of the paddle were close to those of the 24 semi-circle channels. The most difference between them was that the liquid did not repeat into the SRS mixer, but always repeated into the paddle. This led to a significant difference in the driving force of mass transfer (ΔC) between them. The driving force in the SRS mixer always maintained at the highest level, yet that in the PRF kept at the lowest level. Therefore, 10
the weak back-mixing is the first reason for the high-efficiency of SRS. During the above experiments, the waste CCl4 solution containing slightly less than 1 g/L of iodine was collected and decolorized by Na2S2O3 solution. According to the stoichiometric formula, 1 g of I2 consumes 1.246 g of Na2S2O3. When 100 mL of the waste liquid was treated by 100 mL, 1.25 g/L of Na2S2O3 solution in the PRF blender, the decolorization time lasted about 90 s～120 s. This process was accomplished readily in the SRS mixer (see Video). It was observed that when the total flux was higher than 23.1 mL s-1 and the outlet position was Exit 3, the collected CCl4 phase was colorless. The decolorization time in the SRS mixer was three orders of magnitude shorter than that in the PRF blender. 4. CFD simulation 4.1. Procedure We simulated the flow pattern of SRS in the first three representative semi-circle channels of the SRS mixer. The swept hexahedral meshes were used to discretize the domain for the computational efficiency and accuracy, as shown in Fig. 2(A). Both the axial and cross-sectional meshes were constructed to provide accurate resolution of the flow field throughout the domain, see Fig. 2(B-C). The total amount of the meshes was 735,060. The operating conditions and physical properties are shown in Table 4. The model involves two immiscible liquids, and the basic equations in the simulation are conservation of mass, momentum, and energy. The two-phase mixture model was used to simulate the 3D two-phase flow by using FLUENT package. 11
Turbulence is modeled by the standard k-ε mixture model. The schiller-naumann drag model is used to describe momentum exchange between phases. The first order upwind scheme is applied for the discretization of all the equations. SIMPLE method was adopted for the pressure-velocity coupling. 4.2. Results The simulation results of pressure and flow field distributions are displayed in Fig. 6. Fig. 6(A) indicates that the total pressure drop is 76.5 kPa, close to the measured values from 80 to 150 kPa. The simulated impingement between the two streams brings about 26.5 kPa of pressure drop. Although the impingement can greatly intensify micro-mixing [5], its instantaneous energy consumption is too high. Therefore, it is imagined that inelastic merging of two rotating flows will not only lower the feeding power consumption but also further accelerate the multi-scale mixings, as shown in Fig. 6(B). Furthermore, it can be seen from Fig. 6(A) that the axial distribution of the 50 kPa pressure drop is essentially uniform, and the radial distribution is reversed by the reversing high gravity. This suggests that the mechanical energy in the SRS is uniformly dissipated along the axial direction. In the 24 semi-circle channels, the energy dissipation time and distance were 0.109 s and 360 mm, respectively. However, the two values of the stirring paddle were just very low. The pressure drop curve of SRS was not far from that of an ideal reversible mixing process. According to the second law of thermodynamics, the ideal process has the highest mixing efficiency. Therefore, the energy efficiency of SRS was much higher than that of the stirring paddle. The uniform pressure drop distribution of SRS 12
is another reason for its high-efficiency. At the simulated conditions, the high-gravity level and reverse frequency are 287 g and 110 Hz, respectively. The two reversing fields of high gravity and static pressure generate the disturbed flow regions along axial direction, as shown in Fig. 6(C). It can be seen that there are obvious velocity boundary layers in SRS. Before SRS reaches to the center of a disturbed region, its boundary layer becomes thin. After it flows through the center, its boundary layer becomes thick. During this process, the shear stress has an obvious fluctuation, which makes KαSRS fluctuation above the static baseline. When ρ andμ of the emulsion are estimated to be 1400 kg/m3 and 1 mPa s, Re and D are calculated to be 5300 and 1700, according to the following two formulas: Re =
dv ρ
µ ,
d 2r
0. 5
D = Re
(5)
The two values are an order of magnitude higher than the two critical numbers of Dean vortices [20-22]. Fig. 6(D) shows the flow field distribution maps of five cross sections. It can be seen from Fig. 6(D) that secondary flow or its derivative Dean vortices are distributed in each cross section map. Astonishingly, the intensities of secondary flows in the 1-1 cross section are much stronger than those in the other four cross sections. In the five cross section maps, the intensities of secondary flows are arranged in the following order: 1-1≫2-2≈4-4>3-3≈5-5. In 1-1, the spontaneously high-speed rotating Dean vortexes are generated in less than 2.5 ms by the vigorous and balanced shear stress distribution, which also brings about the balanced KαSRS and concentration distributions. From 2-2 to 5-5, Dean 13
vortexes are difficult to be detected. The obvious uneven speed distributions of secondary flows suggest the uneven KαSRS and concentration distributions. The consequence of the two uneven distributions is very similar to that of back-mixing, i.e., the significant reduction of total KαSRS. Therefore, the Kα SRS of the first semi-circle channel is much higher than the average value of 71.7 s-1, and then a high peak line of KαSRS is formed. Therefore, we conjecture the model curve of KαSRS versus semi-circle channels, as shown in Fig.7. The peak line is fit for one-time feeding with ultrafast mixing, and the wave line is fit for continuous feeding with fast mixing. Since the Kα and concentration distributions are completely inhomogeneous in the PRF blender, this is the third reason for the high-efficiency of SRS. Obviously, the ideal reversible mixing process means that the wall friction is zero, and the reversing high gravity, reversing static pressure, as well as shear stress form the first dynamic balance. The second dynamic balance is formed between shear stress and surface tension, and the shear force distribution is completely uniform along the radial direction. Only ideal fast reactor can realize the ideal reversible mixing process. 5. PEF and NES From another perspective, a centrifugal pump and an SRS mixer can constitute a high-efficiency mechanical energy circulation system. In a split second, the former generates high positive energy flow (PEF) and the latter forms high negative energy stream (NES). Attraction, dependence, and transformation relations exist between PEF and NES. When sucked into the centrifugal pump, NES along axial direction is transformed into PEF along radial direction. The center of PEF is NES and both are 14
separated. Upon entering into the SRS mixer, a primary flow with high mechanical energy becomes SRS. SRS is NES along axial direction and develops Dean vortices along radial direction. Dean vortices belong to PEF during its development. The energy of PEF is derived from NES and both are completely integrated together. In the SRS mixer, PEF can directly absorb and largely transform the high pressure energy of NES into vigorous shear stress. In centrifugal pump, the existence time of PEF is extended with the intensity of high-gravity field being increased. If the two intensities of reversing high-gravity field in the SRS mixer are also increased, its PEF will also have longer existence time. 6. Conclusion SRS is a novel supplement of Higee technology. Many excellent performances of SRS reactor are close to those of ideal fast reactor. In this study, the mixing performances of SRS were quantitative analyzed and simulated. The mainly conclusions are as follows: 1. The mixing efficiency of the SRS mixer was not far from that of ideal fast reactor. Compared with the PRF blender, its mixing energy consumption lowered by 2 orders of magnitude, and Kα SRS improved by 3 orders of magnitude. 2. The high-efficiency multi-scale mixings in SRS were attributed to weak back-mixing and uniform energy release along axial and radial directions. 3. In SRS the two high-frequency reversing fields of high gravity and static pressure co-produced intensive secondary flow and vigorous shear stress. 4. In the initial semi-circle channel, SRS can generate ultrafast mixing process. After 15
that, it only can realize fast mixing process. 5. PRF and SRS are separately suitable for generating PEF and NES. At the initial stage of SRS, the ultrafast mixing is derived from the unity of NES and PEF.
Nomenclature Definitions Primary rotating flow (PRF)
a rotating flow whose direction is always constant
Secondary rotating stream (SRS)
a rotating stream whose direction reverses every 180° rotation
a rotating stream whose direction reverses every 360。/N
Nth rotating stream
rotation Multiscale mixings
mixing process involves macro-, meso- and micro-mixings
Reversing high-gravity field
a high-gravity field whose direction is reversing at a certain frequency;
Positive energy flow (PEF) Negative energy stream (NES)
a flow whose mechanical energy is increasing; a stream whose mechanical energy is decreasing;
Symbols dC/dt
increase rate of iodine concentration in the aqueous phase [mol/L s]
Kα
volumetric mass transfer coefficient [ s-1]
Kα
average volumetric mass transfer coefficient
C∞ C
bulk concentration in water phase after infinite mixing time [mol/L] bulk concentration in water phase [mol/L] 16
Pc
volumetric mixing power consumption [W/mL or MPa/s]
PC
average volumetric mixing power consumption
d
width of semi-circle channel
r
inner radius of semi-circle channel
Re
Reynolds number
D
Dean number
V0
Total flux [ml/s]
VR
Volume of the semi-circle channels [ml]
v
Average flow velocity [m/s]
Greek symbols
ρ
Density [kg/m3]
μ
Viscosity [mPa s]
τ
Space time [s]
Subscripts PRF
the PRF blender
SRS
the SRS mixer
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Acknowledgments: We acknowledge the early financial supports provided by the National Key Technology R&D Program of China (No. 2009BAB47B08) and the Science & Technical Project of China Petroleum Chemical Co. (No. 314109).
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Fig. 1.Experimental set-up (A) of SRS mixer and photographs (B-D) of its inner structure.
21
Fig. 2.Agitation process in PRF blender. (A) Photograph of the agitation process. (B) Distribution diagram of the H2O, emulsion, and CCl4 layers.
22
Fig. 3.Mixing characteristics of PRF blender. (A) Sample points, regression curve, three theoretical curves, and the line of ܥஶ . (B) Curve of KαPRF versus operation time.
(A)
Concentration (mg/L)
20
16
12
Sample point Regression curve -1 Ka PRF=0.00147 s
8
-1
Ka PRF=0.0030 s 4
-1
Ka PRF=0.0050 s C∞=18.1mg/L
0 0
400
800
1200
1600
2000
Operation time (s)
(B) 0.05
Ka PRF ( s-1)
0.04 0.03
Curve of Ka PRF
0.02
Ka PRF, min =0.00147 s
-1
0.01 0.00 0
300
600
900
1200
1500
Operation time (s)
23
1800
Fig. 4.Mixing characteristics of SRS mixer. (A) Concentrations versus space times of തതതതௌோௌ versus τ. (C) all the samples obtained from the five exits. (B) Curves of ߙܭ Curves of high-gravity level and reverse frequency versus τ, corresponding to the group of samples obtained from Exit 3. (D) Curves of pressure drop versus exit.
(A)
Concentration (mg L-1)
18
15
12 Samples from Exit 1 Samples from Exit 2 Samples from Exit 3 Samples from Exit 4 Samples from Exit 5 Equilibrium line
9
6
3 0.0
0.2
0.4
0.6
0.8
1.0
Space time (s)
(B) 75
-1
Ka SRS ( s )
60
Samples from Exit 1 Samples from Exit 2 Samples from Exit 3 Samples from Exit 4 Samples from Exit 5 Equal flux curve
45
30
15
0 0.0
0.2
0.4
0.6
Space time (s)
24
0.8
1.0
1.2
(C)
160 140
Curve of high gravity level Curve of reverse frequency
250
120 100
200
80
150
60 100 40 50
20
0
0 0.10
0.15
0.20
0.25
0.30
0.35
0.40
Space time (s)
(D)
P0
1
3
2
Exit
5
4
-1 V0=18.77 mL s -1 V0=18.70 mL s -1 V0=18.94 mL s -1 V0=18.58 mL s -1 V0=16.10 mL s
Gauge pressure (KPa)
500
400
300
200
100
0 0
10
20
30
40
50
Semi-circle channels
25
60
70
Reverse frequency (Hz)
High gravity level (g)
300
Fig. 5. Mesh density of the simulated SRS. (A) Mesh density in a 3-D graph. (B) Mesh density on a cross-section. (C) Mesh density along the axial direction.
26
Fig. 6.Simulations of SRS. (A) Diagram of axial pressure distribution. (B) Diagram of two rotating flows merging together. (C) Diagram of axial velocity distribution as well as the position of five flow cross sections. (D) Diagrams of velocity distribution in five flow cross sections.
27
Fig. 7.Model curve of KαSRS versus semi-circle channels.
28
Table 1. Mixing experimental results from the PRF blender.
t(s)
5
10
15
20
40
60
90
120
180
300
C(mg/L)
4.451
7.913
10.30
11.13
12.53
13.60
13.44
14.01
14.42
15.08
t(s)
450
600
750
900
1050
1200
1350
1500
1650
1800
C(mg/L)
16.23
15.66
16.82
17.47
17.23
17.80
17.64
17.64
18.05
18.05
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Table 2. Mixing experimental results from the SRS mixer. Exit 1 (VR, 0.259 ml)
Exit 2 (0.950 ml)
Exit 3 (2.072 ml)
Exit 4 (4.144 ml)
Exit 5 (6.216 ml)
τ(s)
0.0308
0.0222
0.0175
0.0153
0.0138
C (mg/L)
9.310
10.10
11.03
11.18
11.37
τ (s)
0.116
0.0865
0.0664
0.0594
0.0506
C (mg/L)
13.10
13.98
14.39
14.24
14.68
τ (s)
0.3816
0.2429
0.1855
0.1460
0.1321
0.1093
C (mg/L)
11.13
13.11
13.68
13.60
14.75
15.20
τ (s)
0.7480
0.4682
0.3740
0.2922
0.2580
0.2232
C (mg/L)
11.54
14.01
14.34
15.33
15.33
15.74
τ (s)
1.1364
0.7480
0.5575
0.4409
0.3861
C (mg/L)
13.27
14.01
14.01
15.74
16.40
30
Table 3. Comparisons of mixing parameters and performances between two mixers. Performances
PRF blender
SRS mixer
Operation mode
Batch operation
Continuous operation
Liquid holdup, ml
3.0
2.072
Mixing power, W
20
5.68
rotary diameter, mm
25
10
Total treated volume, ml
200
200
Total mixing time, s
300
10.6
—
0.109
Total energy consumption, J
6000
60
Kα , s-1
0.00610
16.7
Pc, MPa/s
0.10
2.74
Average mixing time of fluid element, s
31
Table 4. Simulation conditions and physical properties in this work. Property
Value
Average flow speeds
1.9 m/s
The viscosity of mixture
1.0 mPa s
Density of aqueous stream
1.0 g/ml
Density of CCl4 stream
1.8 g/ml
Wall roughness in the semi-circle channel
0.01 mm
32
Graphical abstract
33
Highlights 1. Secondary rotating stream (SRS) is a novel supplement of Higee technology. 2. Many excellent performances of SRS reactor are close to those of ideal fast reactor. 3. The mixing efficiency of SRS was not far from that of ideal fast reactor. 4. The reversing high-gravity field generates intensive convection and shear stress. 5. The initial SRS generates ultrafast mixing. After that, it forms fast mixing.
34