Pii: s0896-8446(02)00084-0

Journal of Supercritical Fluids 24 (2002) 231 – 237 The characteristics of coherent structures in the rapid expansion flow of the supercritical carbon dioxide Xiao-Yu Sun, Ting-Jie Wang *, Zhi-Wen Wang, Yong Jin Department of Chemical Engineering, Tsinghua Uni6ersity, Beijing 100084, People’s Republic of China Received 29 October 2001; received in revised form 1 March 2002; accepted 17 April 2002 Abstract
By the use of a tiny pressure-transferring probe and capacitor-type sensor, the dynamic pressure signals in the jet flow of the rapid expansion of supercritical carbon dioxide are measured, which distinctively shows the characteristicsof quasi-periodical coherent structures. After Fast Fourier Transform (FFT) conversion of the time series signals ofthe dynamic pressure, there exist three dominant frequency bands in the power spectrum, which correlate with thescale of the dominant eddies in the turbulent field. The dominant frequencies change little with the distance from thenozzle exit or the pre-expansion pressure, while the power density of the dominant frequencies, which correlates withthe energy of the dominant eddies in the turbulence, attenuates along the axial direction and with the decrease of thepre-expansion pressure. Through analysis, it is inferred that the nozzle structure and initial conditions remarkablyaffect the coherent structures in the expansion flow which should be the important factors in the particle nucleationand its growth process in ultra-fine particle preparation by rapid expansion of supercritical fluid solution (RESS).
2002 Elsevier Science B.V. All rights reserved.
Keywords: Rapid expansion; RESS process; Supercritical fluids; Turbulence; Jet flow 1. Introduction
increase of supersaturation and rapid density dropprompt an outburst of homogeneous nuclei, and In the rapid expansion of supercritical fluid ultra-fine particles with a narrow size distribution solution (RESS) process, the supercritical fluid are expected to form. With mild operational tem- solution expands rapidly through a narrow throt- perature and without organic solvents, the RESS tling structure, e.g. capillary or orifice nozzle, to a process promises a solvent-free product with high low pressure and low temperature state, which purity in a single process, and has the potential leads to a very high supersaturation at an ultra- for eliminating the disadvantages of the conven- short time interval of about 10−7 s. The steep tional methods in fine particle preparation in suchareas as chemical engineering, pharmaceutical in-dustry, material science and biotechnology etc.
* Corresponding author. Tel.: + 86-10-6278-8993; fax: + Most experimental and theoretical researches in literature focus on the effects of various parame- E-mail address: (T.-J. Wang).
0896-8446/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 8 9 6 - 8 4 4 6 ( 0 2 ) 0 0 0 8 4 - 0 X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 ters, including pre- and post-expansion tempera- 2. Fundamental
ture, pressure and concentration, nozzle geome-try, upon the product characteristics, e.g. size and Before 1980s, it was considered that the coher- morphology. But the experimental results are usu- ent structures of the eddy only exist in the flow ally available only for the specified conditions.
with low Reynolds number, and in the fully devel- Various solute and solvent systems usually show oped turbulence the periodical signals should not different characteristics of the process [1 – 9].
exist. Afterwards, more and more experimental Debenedetti et al. [1,2,9] developed a one-dimen- results showed that the coherent structures exist in sional compressible model of sub-sonic flow to almost all kinds of turbulent fields, even in the study the dynamics of particle nucleation and flow with high Reynolds number of 107 [10]. The growth in the RESS process. Shaub et al. [5] formation of the structures is not random but calculated the adiabatic process of the free jet correlates with the initial conditions and inner expansion from the nozzle into vacuum with su- non-linear specialities of the turbulence [10 – 18].
percritical carbon dioxide (SC-CO ) as a solvent The coherent structures in turbulent flow can be and phenanthrene as a solute. These calculations analyzed theoretically [13] [17] or experimentally are helpful for understanding the qualitative [11,12] [14 – 16]. The scale and energy information trends, but not able to predict the quantitative of eddies in the turbulence can be analyzed from results. To produce fine and mono-dispersed par- the power spectrum of the dynamic pressure or ticles with a narrow size distribution, the sug- velocity signals. The frequency band where the gested way is preventing the supercritical fluid eddy energy concentrates densely reflects the char- solution from phase separation until it expands at acteristics of the dominant eddy in the turbulence.
The characteristics of the turbulent flow can be Nevertheless, another important factor in the modified through the control of the coherent RESS process, i.e. the strong turbulence in the structures, which can be intensified by the period- expansion flow, has not been investigated suffi- ical stimulations upon the flow [10] or weakened ciently. Just like the particle preparation in by the addition of small polymer particles into the aqueous solution, the turbulence in the jet flow may remarkably affect the particle nucleation and The rapid expansion of supercritical fluids, con- growth even during ultra-short residence time.
sidered as a supersonic or at least subsonic free The turbulent characteristics of the expansion jet, brings out tempestuous turbulence, which flow may be the key factor affecting the particle forms a large number of eddies in different scales.
preparation by the RESS process. This paper When a series of eddies pass through the probe set studies the characteristics of the rapid expansion in the jet flow, time series signals of dynamic flow of pure supercritical carbon dioxide. Coher- pressure will be detected, which are converted ent structures in the expansion flow are shown from the eddy momentum. Smaller eddy size or faster change of the velocity in the eddy reflectshigher frequency in detected signals. Thus theeddy parameters in the turbulent flow can beevaluated from the pressure signals of time series,as shown in Fig. 1.
Based on the acoustic scattering principle, Baudet et al. [12] set up an experimental techniqueallowing the direct probing of the vorticity field ina turbulent flow. The spatial correlation length ofdiscrete vorticity events was measured to revealthe time continuous transfer of energy from thelargest scales towards smaller scales. It is claimed Fig. 1. Formation of dynamic pressure signals from the mov-ing eddy at the probe top.
that the recourse to time – frequency distributions X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 turbulence may remarkably affects the particlesize and morphology. It is supposed that strongerand more uniform turbulence in microscopic scalehas advantages on the formation of super-fineparticles with a narrow size distribution.
3. Experimental
The experimental apparatus and flow sheet are schematically shown in Fig. 2. The CO from a bomb is cooled in a cooler with the setting tem- Fig. 2. Schematic diagram of the experimental apparatus and perature of 263 K, then fed into a tank with the flow sheet of the RESS system. (1) CO bomb, (2) cooler, (3) volume of 1.5 l through a high-pressure pump.
high pressure pump, (4) extracting tank, (5) constant tempera- The temperature of the CO in the tank can be ture bath, (6) nozzle, (7) fixed micrometer caliper, (8) probe controlled from room temperature to 573 K and sensor, (9) data sampling computer.
within 1 K, and the pressure can be controlledfrom 0 to 40 MPa within 0.1 MPa. After thetemperature and pressure of the CO in the tank are stabilized at the scheduled values, the CO2fluid is let out to a coil pipe in a second constanttemperature bath, in which more accurate pre-ex-pansion temperature is controlled within 0.1 K. Astainless steel capillary, which is 15 mm long and100 mm in inner diameter, is used as jet nozzle.
Another stainless steel capillary 15 mm long and600 mm in inner diameter is also used to explaininfluence of the nozzle structure on the coherentstructure in the jet flow. This paper mainly dealswith the experimental results of the former nozzle.
A probe is axially set in the expansion flow todetect the dynamic pressure signals, which is fixedon the movable part of a fixed micrometer caliper Fig. 3. The structure and position of the sensor and probe in to locate the exact position along the axis.
The probe is 1 mm in inner diameter, 1.5 mm in outer diameter and 13 mm long, the top of which (TFD) leads to an operational definition of coher- is designed to reduce the influence on the flow ent structures associated with phase stationarity in field due to its existence, as shown in Fig. 3. The circular and sharp shape of the probe can also The experimental results in the following text lighten the shock wave caused by the speedy flow.
will show that the expansion flow in the RESS The probe is connected with the sensor. The process obviously contains coherent structures, capacitor-type sensor (64 – 170 dB, 0.98 mV/Pa, which should be one of the important factors inherent frequency: 70 kHz) with high accuracy is affecting the particle nucleation and growth in employed to detect the pressure signals. Even so, fine particle preparation. Although the residence some very small turbulence could possibly not be time of the nuclei is as short as 10−7 s, the report measured due to the capillary filtration on high of simulated growth rate of the nuclei is as high as frequency signals and the limitation of the sensor 1026 m/s [9], which indicates that the expansion inherent frequency or the sampling frequency of X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 the computer. The dynamic pressure signals prop- influence of the probe on the expansion flow and agate by the elastic gas in the probe to the sensor.
the accuracy of the measurement, the nearest axial They are converted to electric signals through the distance is limited to 2 mm. The experiments sensor, then magnified and sampled by the com- reflecting the influence of the pre-expansion pres- puter. The sampling frequency is 16 000 points at sure ranged from 5 to 20 MPa are carried out at each interval of 0.33 s. The sampled signals of intervals of 0.5 MPa, with the pre-expansion tem- time series are converted into power spectrum for analysis through the Fast Fourier Transform When the pre-expansion pressure is 20 MPa, Before measurements the noise from the back- and pre-expansion temperature is 373 K, the mass ground is detected in order to exclude possible flow through the nozzle of 100 mm is calculated disturbance from the environment variables.
through the pressure drop during a certain time When the pressure and temperature in the extrac- and the Reynold number of the flow in the nozzle tion tank reach the setting value and are stable, is estimated at about 104. In the rapid expansion the exit valve is opened to the maximum, starting of supercritical carbon dioxide, there should be the rapid expansion. When the jet flow is stable, Joule – Thompson effect in the process. In the the pressure signals are sampled, and then the jet experimental conditions, dry ice does not form in flow is shut for next measurement. The conditions in steady state are insured in the measurements.
The measurement process lasts about 10 s. Thepressure decrease ( 4. Results and discussion
tank in each measurement are recovered throughthe high-pressure pump and the temperature con- 4.1. The inherent characteristics of the turbulent troller. Parallel experiments are carried at each condition to insure the measurement resultavailable.
The detected signals of dynamic pressure re- The dynamic pressure signals are detected along markably show quasi-periodical characteristics of the axis of the expansion flow of pure solvent CO coherent structures. The power spectrum from under certain thermodynamic conditions. The ax- FFT conversion contains three frequency bands, ial distance between the probe top and the nozzle the energy of which concentrates on each peak exit ranges from 0 to 50 mm. Considering the value respectively. In order to easily characterizethe coherent structures and compare the differ-ence under various conditions, the power spec-trum in gray line is smoothed by taking theaverage of every 50 adjacent points into a blackline, as shown in Fig. 4. Three dominant fre-quency peaks are at 2300, 15 500 and 30 000 Hz,respectively. The half width of the dominant fre-quency bands is about 1000 – 2000 Hz. The lowfrequency band has the most of the turbulentenergy and the high frequency band has the least.
To examine the possible error from the probe, experimental measurements with different probesin varied shape, length and inner diameter arecarried out. It is found that the power spectrumof the measured pressure signals does not change Fig. 4. Power spectrum of the coherent structure with capillary with the shape of the probe. The inherent fre- nozzle inner diameter of 100 mm (L/d=150, z=19 mm, 373K, 20 MPa).
quency of the sensor is 70 kHz, which is much X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 4.2.1. Influence of the nozzle structure In the RESS process, the initial and boundary conditions of the expansion flow are the keyfactors affecting the formation of coherent struc-tures. Besides fluid velocity in the expansion flow,the most important boundary condition is thenozzle structure. In this research, the coherentstructures of the expansion flow with the capillarynozzle of 600 mm in inner diameter and 15 mmlong are measured. The result in Fig. 5 shows thatthere is only one dominant frequency band rang- Fig. 5. Power spectrum of the coherent structure with capillary ing from 10 000 to 20 000 Hz, and the energy of nozzle inner diameter of 600 mm (L/d=25, z=10 mm, 373 K,20 MPa).
the coherent structures in the turbulence is muchweaker than that with the capillary nozzle of 100mm inner diameter shown in Fig. 4. It is inferredthat the coherent structures can be obviouslychanged by the change of the boundary conditionof the nozzle.
higher than the dominant frequencies. The reso-nant frequencies of the probe can be calculated 4.2.2. Coherent structures along the axis The axial measurements are carried out under the conditions with pre-expansion temperature of 323 and 373 K, pre-expansion pressure of 10 and 20 MPa, respectively, using the capillary with is the in-situ sound velocity and L is inner diameter of 100 mm and 15 mm long as the pipe length of the probe. The resonant fre- nozzle. The power spectrum of the measured pres- quencies of 4.8 × n kHz (n = 1, 2, 3.) are also sure signals indicates that there exist three domi- different from the dominant frequencies. There- nant frequency bands, which reflect three kinds of fore, it can be confirmed that the dominant fre- coherent structures in the expansion flow. The quencies reflect the inherent characteristics of the dominant frequency and their power density expansion flow, instead of coming from the mea- change along the axis under pre-expansion ther- modynamic conditions of 20 MPa and 373 K, as The results of measurement show that there shown in Fig. 6. The higher frequency bands exist eddies in various scales in the jet flow, and becomes obvious at certain positions, and the the turbulent energy mainly concentrates on the dominant frequency bands change little along the eddies of the three group scales. The large eddies axis, while the power density gradually decreases correspond to the low frequencies and the small along the axis. Similar results can be obtained eddies correspond to the high frequencies. The formation and composition of the eddies should be affected by the turbulence and flow field at the Therefore, it can be inferred that the coherent nozzle exit, i.e. affected by the thermodynamic structure scale of the eddy in the jet flow do not and flow conditions of the supercritical fluid, and change much, while the eddy energy decreases the nozzle structure etc. The disturbance due to along the axis. The eddy energy in the jet flow the shear between the peripheral layer of the jet mainly concentrates on the fore part of the jet and the ambient atmosphere may also contribute flow close to the nozzle exit, which is similar to to the pressure signals of measured.
the reported result in the incompressible free jet, X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 that the energy of the jet flow in the vicinity of the with the increase of pre-expansion pressure. Ex- nozzle accounts for 50% of the energy in the total perimental results also indicate that the pre-ex- pansion temperature has little effect on thedominant frequency bands and their powerdensities.
4.2.3. Influence of pre-expansion pressure The increase of pre-expansion pressure nor- The dominant frequencies and their power den- mally results in the increase of the expansion sities changing with pre-expansion pressure at pre- Mach number, and enhances the energy intensity expansion temperature of 373 K, 10 mm from the through the disturbance caused by the momentary nozzle exit is shown in Fig. 7. The high frequency expansion. It is the phase transformation and bands are not very obvious in the experiments.
supersonic/subsonic expansion flow that make the When the pre-expansion pressure is higher than RESS process different from other free jet flows, 13 MPa, the high frequency band can be obvi- and these two factors should be the important ously observed. The power densities of the three conditions to form the coherent structures in the dominant frequency bands increase remarkably Fig. 6. Power spectrum of the coherent structure changing with the axial distance from nozzle exit (L/d = 150, d = 100 mm, 373 K,20 MPa).
Fig. 7. Power spectrum of the coherent structure changing with the pre-expansion pressure (L/d = 150, d = 100 mm, z=10 mm, 373K).
X.-Y. Sun et al. / J. of Supercritical Fluids 24 (2002) 231 – 237 5. Conclusion
[5] G.R. Shaub, J.F. Brennecke, M.J. McCready, Radial model for panicle formation from the rapid expansion ofsupercritical solutions, J. Supercrit. Fluids 8 (1995) 318 – Experimental results indicate that there exist coherent structures in the rapid expansion flow of [6] M. Tu¨rk, Formation of small organic particles by RESS: the supercritical carbon dioxide. Three dominant experimental and theoretical investigations, J. Supercrit.
frequency bands were found in the quasi-periodi- cal dynamic pressure signals under the experimen- [7] E. Reverchon, G. DellaPorta, R. Taddeo, P. Pallado, A.
tal conditions, which correspond to the different Stassi, Solubility and micronization of griseofulvin in eddy scales in the jet flow respectively. The domi- supercritical CHF , Ind. Eng. Chem. Res. 34 (1995) nant frequencies change little with the axial dis- [8] C. Domingo, E. Berends, G.M. vanRosmalen, Precipita- tance or pre-expansion pressure. The power tion of ultrafine organic crystals from the rapid expansion density that reflects the intensity of the eddy of supercritical solutions over a capillary and a frit nozzle, energy attenuates along the axis of the expansion J. Supercrit. Fluids 10 (1997) 39 – 55.
flow and with the decrease of the pre-expansion [9] X. Kwauk, P.G. Debenedetti, Mathematical modeling of pressure. The coherent structures should have aerosol formation by rapid expansion of supercriticalsolutions in a converging nozzle, J. Aerosol. Sci. 24 (1993) strong effect on the microscopic environment in which the fine particles nucleate and grow. As one [10] J.Z. Lin, The Coherent Structures in Turbulence, China of the boundary conditions, the nozzle structure is an important factor affecting the dominant fre- [11] J. Dunyak, X. Gilliam, R. Peterson, Coherent gust detec- quency value and power density of the coherent tion by wavelet transform, J. Wind Eng. Ind. Aerodynam.
structures. It is expected that by the design of appropriate nozzle structure and setting suitable [12] C. Baudet, O. Michela, W.J. Williams, Detection of co- herent vorticity structures using time-scale resolved acous- initial conditions, the coherent structure of the tic spectroscopy, Physica. D. 128 (1999) 1 – 17.
[13] G. Haller, G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D 147(2000) 352 – 370.
[14] B.H. Timmerman, D.W. Wat, P.J. Bryanston-Cross, Acknowledgements
Quantitative visualization of high-speed 3D turbulentflow structures using holographic interferometric tomog- The authors wish to express their appreciation raphy, Optics Laser Technol. 31 (1999) 53 – 65.
for the financial support of this study by the [15] Q.L. Fan, H.Q. Zhang, Y.C. Guo, X.L. Wang, W.Y. Lin, National Natural Science Foundation of China.
Experimental studies of two-phase round turbulent jet The grant number is NSFC No. 29906004.
coherent structures, Tsinghua Sci. Technol. 5 (2000) 105 –108.
[16] H.-L. Zhou, Z.M. Lu, X.-T. Ren, X.-L. Xie, The experi- mental study of the chaotic phenomena of heated jets, References
Acta Mechanica Sinica 31 (1999) 603 – 610.
[17] F. de Souza, J. Delville, J. Lewalle, J.P. Bonnet, Large scale coherent structures in a turbulent boundary layer [1] R.S. Mohamed, P.G. Debenedetti, R.K. Prud’homme, Effects of process conditions on crystals obtained from interacting with a cylinder wake, Exp. Thermal Fluid Sci.
supercritical mixtures, AIChE J. 35 (1989) 325 – 332.
[2] P.G. Debenedetti, Homogeneous nucleation in supercriti- [18] Z.-S. Yu, Interactions of the rigid-rodlike polymer and cal fluids, AIChE J. 36 (1990) 1289 – 1298.
the coherent structures in a mixing layer, Acta Mechanica [3] A.K. Lele, A.D. Shine, Effect of RESS dynamics on polymer morphology, Ind. Eng. Chem. Res. 33 (1994) [19] Nanjing University of Aeronautices and Astronautics, Beijing University of Aeronautices and Astronautics, The [4] C.J. Chang, A.D. Randolph, Solvent expansion and so- principle of sensors. National Defense Industry Press. (In lute solubility predictions in gas-expanded liquids, AIChE

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