HYPERLINK "http://dx.doi.org/10.1016/j.expthermflusci.2012.10.008" \h Experimental Thermal and Fluid Science 45 (2013) 6374Contents lists available at SciVerse ScienceDirect Experimental tiina termic i Fluidjournal h omepage: www.else vier.com/locate/etfs nelegerea hidrodinamic bule n coloane de buleAmir Sheikhi 1, Rahmat Sotudeh-Gharebagh , Reza Zarghami, Navid Mostou, Mehrdad AlMultiphase Systems Research Lab., Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Irana r t i c l e i n f o Article history:Received 31 March 2012Received in revised form 19 July 2012Accepted 9 October 2012Available online 30 October 2012Keywords: Gasliquid column Hydrodynamics Vibration inspection Pressure uctuations Frequency analysis Wavelet transform
a b s t r a c t Comparativ cu coloane clasice cu bule de gaz - lichid , coloane de gaz lichid , inclusiv cu gaz i fluxurile de lichide au fost investigate mai puin , datorit hidrodinamicii lor complexe i dificulti operaionale . n acest studiu , metode non- intruzive simultane de vibraii coaj de coloan i de fluctuaie presiune msurtorile s-au cuplat cu fotografia direct i analiz de imagine pentru caracterizarea bule . Diferite analize sta - tistic i frecven au fost efectuate pe semnalelor de acceleraie i de presiune fluctuaii a determina capacitatea lor de a interpreta comportamentul bule n interiorul coloanei . Deviaia standard a semnalelor de vibraie a artat o sensibilitate mai mic la un comportament bule n comparaie cu cel al fluctuaiile de presiune . Skewness de vibraii i de presiune fluctuaii ar putea detecta cu bule puncte de tranziie regim la toate vitezele gazelor studiat i lichide timp de vibraii i de presiune fluctuaii exces ar putea detecta doar punctul de tranziie principal al coloanei , la o vitez de lichid moderat . Sa constatat c n afar de metode statistice periodice , energia de semnale de presiune ar putea prezice puncte de tranziie regim bule succes complet . n timp ce de control pe baz de vibraii a aratat mai mult sensibilitate la distribuia mrimii bule ( similar cu deviaia standard de semnale de presiune ) , analiza frecvenei pe semnale de presiune s-au dovedit a fi un reprezentant puternic de bule Sauter medie cu diametrul de modificare de variaie a fluxului de lichid la gaz constante energie cinetica - ities . Mai mult dect att , prin transformare wavelet discrete pe baz de energie , am definitexact cale - calea diferitelor sub- semnal evoluii graduale a lungul unei game largi de condiii de funcionare a gazului i vitezelor lichide i capturat puncte de tranziie de regim n consecin . Metodele propuse n aceast lucrare pot fi utilizate pentru caracterizarea hidrodinamic non- intruziv n coloanele cu bule industriale. 2012 Elsevier Inc. All rights reserved.
1. IntroductionGasliquid contactors are widely used in various industries such as chemical , biochemical, biotechnology , biomed- ical , petrochemical and rening [9,10], environmental, separa- tion and purication , nanotechnology [19,20] and gas processing industries . Among such contactors, bubble col- umns, with or without liquid ow, are of a considerable impor- tance in numerous process units. Industrial plants which are dealing with physical  and/or chemical interactions between gas and liquid phases as well as gasliquidsolid  contactors prot from the ease of construction , high interfacial area and consequently high mass  and heat  transfer rates, sta- ble temperature , the ease of energy providence and the high liquid hold up  of bubble columns .Successful design, operation, scales up and optimization of bubble columns highly depends on the hydrodynamics of such Corresponding author. Tel.: +98 21 6697 6863; fax: +98 21 6646 1024.E-mail addresses: email@example.com (A. Sheikhi), firstname.lastname@example.org(R. Sotudeh-Gharebagh).1 Present address: Chemical Engineering Department, McGill University, Montreal, Quebec H3A 0C5, Canada.
contactors. Although various theoretical efforts to model two- phase gasliquid contactors have been undertaken , new experimental approaches for hydrodynamic inspections are of great interests in industrial and R&D communities. Wall pressure uctuations were used to study the effect of various sparger geom- etries on bubble ow regimes in bubble columns . Flow pattern and structure were investigated by means of pressure uctua- tions combined with particle image velocimetry . Chaotic behavior of bubbles were studied using pressure signals and laser-phototransistor . Also, bubbling-to-jetting regime transi- tion was investigated by plenum pressure uctuations monitoring . Turbulence in the heterogeneous bubble regime was charac- terized by chaos analysis on pressure uctuations .Simonnet et al. studied the drag coefcient on the gas bubble swarm using laser Doppler velocimetry . Harteveld et al.  and Olmos et al.  used laser Doppler anemometry for the accu- rate estimation of turbulence power spectra and ow regime tran- sition identication, respectively. Magnetic resonance imaging was utilized to characterize hydrodynamics of opaque multiphase sys- tems such as slurry bubble columns . Also, particle image velocimetry was found to be able to dene bubble velocity and ow regimes inside a two-phase gasliquid column . Similar advanced, non-intrusive but expensive methods, such as
0894-1777/$ - see front matter 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermusci.2012.10.008
Nomenclatureak approximation sub-signalAn amplitude in a time series at a certain frequency of fn(kPa or m/s2)CWT continuous wavelet transform
N data point number in a sampleL segment (window) number in a time seriesp indicating pressure uctuation experimentsPxx average power spectrum (kPa2/Hz or m2/s4 Hz)
n 2 2 4
de equivalent bubble diameter (m)
power spectrum for each segment (kPa /Hz or m /s
dm,j minor length (smallest Feret diameter) of bubbles (m)dM,j major length (largest Feret diameter) of bubbles (m)dS Sauter mean diameter of bubbles (m)Dk detail sub-signalX(f) discrete Fourier transformDWT discrete wavelet transformE energy of PSDF (kPa2 or m2/s4)Ea energy of approximation sub-signal coefcient (kPa2 or m2/s4)ED energy of detail sub-signal coefcient (kPa2 or m2/s4)f desired frequency (Hz)i imaginary unitk sub-signal numberK kurtosis or the forth momentn counternj bubble number with equivalent diameter of de,j
PSDF power spectral density function (kPa2/Hz or m2/s4 Hz)q time-lag coefcientS skewness or the third momentt time (s)Ug gas velocity (m/s)Ul liquid velocity (m/s)v indicating vibration (acceleration) experimentsxn time series data (kPa or m/s2)Greek symbolsd scale factorr standard deviations shift factorw mother wavelet function
computer-automated radioactive particle tracking , computed tomography , electrical resistance  and capacitance  tomography have also been used by a variety of researchers.Recently, Abbasi et al. suggested the non-intrusive measure- ment and analysis of vibrations in both time  and frequency  domains to characterize the hydrodynamics of gassolid uid- ized beds. They were able to dene main transition points inside the bed as well as bubble behavior using regular signal processing methods. Sheikhi et al.  have shown that vibration inspection can also be used as a reliable method for the hydrodynamic char- acterization of liquidsolid uidized beds. They predicted mini- mum liquid-uidization and solid-regime transition conditions. Yet, no effort has been made to characterize gasliquid contactors by means of simultaneous vibration and pressure uctuations analyses. The aim of this work is a critical comparative study on the applicability of vibration and pressure uctuation signal pro- cessing for the hydrodynamic characterization of bubble behavior inside bubble columns. Electrical signals obtained from vibration inspection and pressure uctuations were processed in time and frequency domains and the extracted information were used to determine the hydrodynamic state of a bubble column at a wide range of industrial gasliquid two-phase reactor operating conditions.2. Materials and methods2.1. Experimental set-upThe bubble column used in this study was made of a 2 m height Plexiglas column with an inner diameter of 0.09 m, presented in Fig. 1. Air at ambient temperature, produced by a compressor, was introduced into the 0.1 m high gasliquid engagement section from the bottom of the bed using a cylindrical porous ceramic air sparger with a 0.03 m diameter and 0.085 m length consisting of0.0001 m pores. Tap water, as the continuous phase, was pumped into the engagement section. Engagement section was lled with0.01 m glass beads for better mixing of air and water. The mixture of gas and liquid was then sent into the bed through a perforated plate distributor including 110 holes of