974 resultados para Cross-flow


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The phenomenon of self-induced vibrations of prismatic beams in a cross-flow has been studied for decades, but it is still of great interest due to their important effects in many different industrial applications. This paper presents the experimental study developed on a prismatic beam with H-section.The aim of this analysis is to add some additional insight into the behaviour of the flow around this type of bodies, in order to reduce galloping and even to avoid it. The influence of some relevant geometrical parameters that define the H-section on the translational galloping behaviour of these beams has been analysed. Wind loads coefficients have been measured through static wind tunnel tests and the Den Hartog criterion applied to elucidate the influence of geometrical parameters on the galloping properties of the bodies under consideration.These results have been completed with surface pressure distribution measurements and, besides, dynamic tests have been also performed to verify the static criterion. Finally, the morphology of the flow past the tested bodies has been visualised by using smoke visualization techniques. Since the rectangular section beam is a limiting case of the H-section configuration, the results here obtained are compared with the ones published in the literature concerning rectangular configurations; the agreement is satisfactory.

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O fenômeno de vibração induzida por vórtices (VIV) é um problema fundamental dentro da Mecânica dos Fluidos e um exemplo importante de interação fluido-estrutura. Esta tese investiga fenômeno de VIV quando um cilindro rígido, submetido a escoamento uniforme, está livre para oscilar na direção transversal e alinhada com a corrente incidente. A tese foi estruturada ao redor de sete perguntas relacionadas ao fenômeno de VIV: 1) O fenômeno e os resultados experimentais são repetitivos? 2) Como ocorre a transição entre ramos de resposta? 3) Qual é o papel da inércia da estrutura oscilante? 4) Qual é o papel de sua rigidez? 5) Quais são as frequências naturais mais importantes da estrutura? 6) Quais padrões de esteira se desenvolvem para VIV com dois graus de liberdade? 7) Quais são os efeitos do movimento na direção alinhada com a corrente no processo de formação e desprendimento de vórtices? O fenômeno de VIV é estudado de maneira experimental em uma base elástica pendular capaz de oscilar com o mesmo momento de inércia e frequência natural nas duas direções. Os experimentos de VIV foram realizados em canal de água recirculante e com diferentes condições de inércia e rigidez. A técnica de velocimetria por imagem de partículas foi usada e permitiu identificar diferentes padrões de esteira de vórtices. Verificou-se que o VIV é repetitivo a nível de amplitudes médias e frequências dominantes. A transição dos ramos pode ocorrer de maneira intermitente ou com histerese. Os parâmetros de inércia e rigidez da estrutura são capazes de mudar o regime de oscilação e, para algumas condições, suprimir as vibrações alinhadas com a corrente. Dentre os padrões de esteira observados, um deles não havia sido relatado na literatura e é definido nesta tese. O novo modo de emissão apresenta dois vórtices com circulação oposta e elevada intensidade emitidos por ciclo. A influência da direção alinhada com o escoamento está relacionada a dois efeitos: a velocidade relativa entre o cilindro e o fluido, responsável pelo aumento da circulação dos vórtices na esteira, e o ângulo de fase do movimento nas direções alinhada e transversal, capaz de mudar o processo de formação dos vórtices.

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Após o aumento de potência do reator IEA-R1 de 2 MW para 5 MW observou-se um aumento da taxa de corrosão nas placas laterais de alguns elementos combustíveis e algumas dúvidas surgiram com relação ao valor de vazão utilizada nas análises termo-hidráulicas. A fim de esclarecer e medir a distribuição de vazão real pelos elementos combustíveis que compõe o núcleo do reator IEA-R1, um elemento combustível protótipo, sem material nuclear, chamado DMPV-01 (Dispositivo para Medida de Pressão e Vazão), em escala real, foi projetado e construído em alumínio. A vazão no canal entre dois elementos combustíveis é muito difícil de estimar ou ser medida. Esta vazão é muito importante no processo de resfriamento das placas laterais. Este trabalho apresenta a concepção e construção de um elemento combustível instrumentado para medir a temperatura real nestas placas laterais para melhor avaliar as condições de resfriamento do combustível. Quatorze termopares foram instalados neste elemento combustível instrumentado. Quatro termopares em cada canal lateral e quatro no canal central, além de um termopar no bocal de entrada e outro no bocal de saída do elemento. Existem três termopares para medida de temperatura do revestimento e um para a temperatura do fluido em cada canal. Três séries de experimentos, para três configurações distintas, foram realizadas com o elemento combustível instrumentado. Em dois experimentos uma caixa de alumínio foi instalada ao redor do núcleo para reduzir o escoamento transverso entre os elementos combustíveis e medir o impacto na temperatura das placas externas. Dada a tamanha quantidade de informações obtidas e sua utilidade no projeto, melhoria e capacitação na construção, montagem e fabricação de elementos combustíveis instrumentados, este projeto constitui um importante marco no estudo de núcleos de reatores de pesquisa. As soluções propostas podem ser amplamente utilizadas para outros reatores de pesquisa.

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When a gas is introduced at high velocity through a nozzle into a packed bed, it creates a raceway in the packed bed. It has been found that the raceway size is larger when it is formed by decreasing the gas velocity from its highest value than when it is formed by increasing the gas velocity. This phenomenon is known as raceway hysteresis. A hypothesis has been oroposed to explain the hysteresis phenomenon based on a force-balance approach which includes frictional, bed-weight, and pressure forces. According to this hypothesis, the frictional force acts in different directions when the raceway is expanding and contracting. In this article, the entire packed bed has been divided into radial and Cartesian co-ordinate systems, and the forces acting on the raceway have been solved analytically for a simplified one-dimensional case. Based on the force-balance approach, a general equation has been obtained to predict the diameter of the raceway for increasing And decreasing velocities. A reasonable agreement has been found between the theoretical predictions and experimental observations. The model has also been compared with published experimental and plant data. The hysteresis mechanism in the packed beds can be described reasonably by taking into consideration the direction of frictional forces for the increasing- and decreasin-velocity cases. The effects of the particleshape factor and void fraction on the raceway hysteresis are examined.

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Polymeric microdrops of low viscosity, elastic fluids have been generated in T-shaped microfluidic devices using a cross-flow shear-induced drop generation process. Dilute (c/c* similar to 0.5) aqueous solutions of polyethylene oxide (PEO) of various molecular weights (3 x 10(5) -2 x 10(6) g/mol) were used as the drop phase fluids whilst silicone oils (5 mPa s

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This research deals with the production of pectic oligosaccharides (POS) from agro-industrial residues, with specific focus on development of continuous cross flow enzyme membrane reactor. Pectic oligosaccharides have recently gained attention due to their prebiotic activity. Lack of information on the continuous production of POS from agro-industrial residues formed the basis for the present study. Four residues i.e sugar beet pulp, onion hulls, pressed pumpkin cake and berry pomace were taken to study their pectin content. Based on the presence of higher galacturonic acid and arabinose (both homogalacturonan and rhamnogalacturonan) in sugar beet pulp and galacturonic acid (only homogalacturonan) in onion hulls, further optimization of different extraction methods of pectin (causing minimum damage to pectic chain) from these residues were done. The most suitable extractant for sugar beet pulp and onion hulls were nitric acid and sodium hexametaphosphate respectively. Further the experiments on the continuous production of POS from sugar beet pulp in an enzyme membrane reactor was initiated. Several optimization experiments indicated the optimum enzyme (Viscozyme) as well as feed concentration (25 g/L) to be used for producing POS from sugar beet pulp in an enzyme membrane reactor. The results highlighted that steady state POS production with volumetric and specific productivity of 22g/L/h and 11 g/gE/h respectively could be achieved by continuous cross flow filtration of sugar beet pulp pectic extract over 10 kDa membrane at residence time of 20 min. The POS yield of about 80% could be achieved using above conditions. Also, in this thesis preliminary experiments on the production and characterization of POS from onion hulls were conducted. The results revelaed that the most suitable enzyme for POS production from onion hulls is endo-polygalacturonase M2. The POS produced from onion hulls were present in the form of DP1 -DP10 in substituted as well as unsubstituted forms. This study clearly demonstrates that continuous production of POS from pectin rich sources can be achieved by using cross flow continuous enzyme membrane reactor.

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Two key issues defined the focus of this research in manufacturing plasmid DNA for use In human gene therapy. First, the processing of E.coli bacterial cells to effect the separation of therapeutic plasmid DNA from cellular debris and adventitious material. Second, the affinity purification of the plasmid DNA in a Simple one-stage process. The need arises when considering the concerns that have been recently voiced by the FDA concerning the scalability and reproducibility of the current manufacturing processes in meeting the quality criteria of purity, potency, efficacy, and safety for a recombinant drug substance for use in humans. To develop a preliminary purification procedure, an EFD cross-flow micro-filtration module was assessed for its ability to effect the 20-fold concentration, 6-time diafiltration, and final clarification of the plasmid DNA from the subsequent cell lysate that is derived from a 1 liter E.coli bacterial cell culture. Historically, the employment of cross-flow filtration modules within procedures for harvesting cells from bacterial cultures have failed to reach the required standards dictated by existing continuous centrifuge technologies, frequently resulting in the rapid blinding of the membrane with bacterial cells that substantially reduces the permeate flux. By challenging the EFD module, containing six helical wound tubular membranes promoting centrifugal instabilities known as Dean vortices, with distilled water between the Dean number's of 187Dn and 818Dn,and the transmembrane pressures (TMP) of 0 to 5 psi. The data demonstrated that the fluid dynamics significantly influenced the permeation rate, displaying a maximum at 227Dn (312 Imh) and minimum at 818Dn (130 Imh) for a transmembrane pressure of 1 psi. Numerical studies indicated that the initial increase and subsequent decrease resulted from a competition between the centrifugal and viscous forces that create the Dean vortices. At Dean numbers between 187Dn and 227Dn , the forces combine constructively to increase the apparent strength and influence of the Dean vortices. However, as the Dean number in increases above 227 On the centrifugal force dominates the viscous forces, compressing the Dean vortices into the membrane walls and reducing their influence on the radial transmembrane pressure i.e. the permeate flux reduced. When investigating the action of the Dean vortices in controlling tile fouling rate of E.coli bacterial cells, it was demonstrated that the optimum cross-flow rate at which to effect the concentration of a bacterial cell culture was 579Dn and 3 psi TMP, processing in excess of 400 Imh for 20 minutes (i.e., concentrating a 1L culture to 50 ml in 10 minutes at an average of 450 Imh). The data demonstrated that there was a conflict between the Dean number at which the shear rate could control the cell fouling, and the Dean number at which tile optimum flux enhancement was found. Hence, the internal geometry of the EFD module was shown to sub-optimal for this application. At 579Dn and 3 psi TMP, the 6-fold diafiltration was shown to occupy 3.6 minutes of process time, processing at an average flux of 400 Imh. Again, at 579Dn and 3 psi TMP the clarification of the plasmid from tile resulting freeze-thaw cell lysate was achieved at 120 Iml1, passing 83% (2,5 mg) of the plasmid DNA (6,3 ng μ-1 10.8 mg of genomic DNA (∼23,00 Obp, 36 ng μ-1 ), and 7.2 mg of cellular proteins (5-100 kDa, 21.4 ngμ-1 ) into the post-EFD process stream. Hence the EFD module was shown to be effective, achieving the desired objectives in approximately 25 minutes. On the basis of its ability to intercalate into low molecular weight dsDNA present in dilute cell lysates, and be electrophoresed through agarose, the fluorophore PicoGreen was selected for the development of a suitable dsDNA assay. It was assesseel for its accuracy, and reliability, In determining the concentration and identity of DNA present in samples that were eleclrophoresed through agarose gels. The signal emitted by intercalated PicoGreen was shown to be constant and linear, and that the mobility of the PicaGreen-DNA complex was not affected by the intercalation. Concerning the secondary purification procedure, various anion-exchange membranes were assessed for their ability to capture plasmid DNA from the post-EFD process stream. For a commercially available Sartorius Sartobind Q15 membrane, the reduction in the equilibriumbinding capacity for  ctDNA in buffer of increasing ionic demonstrated that DNA was being.adsorbed by electrostatic  interactions only. However, the problems associated with fluid distribution across the membrane demonstrated that the membrane housing was the predominant cause of the .erratic breakthrough curves. Consequently, this would need to be rectified before such a membrane could be integrated into the current system, or indeed be scaled beyond laboratory scale. However, when challenged with the process material, the data showed that considerable quantities of protein (1150 μg) were adsorbed preferentially to the plasmid DNA (44 μg). This was also shown for derived Pall Gelman UltraBind US450 membranes that had been functionalised by varying molecular weight poly-L~lysine and polyethyleneimine ligands. Hence the anion-exchange membranes were shown to be ineffective in capturing plasmid DNA from the process stream. Finally, work was performed to integrate a sequence-specific DNA·binding protein into a single-stage DNA chromatography, isolating plasmid DNA from E.coli cells whilst minimising the contamination from genomic DNA and cellular protein. Preliminary work demonstrated that the fusion protein was capable of isolating pUC19 DNA into which the recognition sequence for the fusion-protein had been inserted (pTS DNA) when in the presence of the conditioned process material. Althougth the pTS recognition sequence differs from native pUC19 sequences by only 2 bp, the fusion protein was shown to act as a highly selective affinity ligand for pTS DNA alone. Subsequently, the scale of the process was scaled 25-fold and positioned directly following the EFD system. In conclusion, the integration of the EFD micro-filtration system and zinc-finger affinity purification technique resulted in the capture of approximately 1 mg of plasmid DNA was purified from 1L of E.coli  culture in a simple two stage process, resulting in the complete removal of genomic DNA and 96.7% of cellular protein in less than 1 hour of process time.

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Accurate prediction of shellside pressure drop in a baffled shell-and-tube heat exchanger is very difficult because of the complicated shellside geometry. Ideally, all the shellside fluid should be alternately deflected across the tube bundle as it traverses from inlet to outlet. In practice, up to 60% of the shellside fluid may bypass the tube bundle or leak through the baffles. This short-circuiting of the main flow reduces the efficiency of the exchanger. Of the various shellside methods, it is shown that only the multi-stream methods, which attempt to obtain the shellside flow distribution, predict the pressure drop with any degree of accuracy, the various predictions ranging from -30% to +70%, generally overpredicting. It is shown that the inaccuracies are mainly due to the manner in which baffle leakage is modelled. The present multi-stream methods do not allow for interactions of the various flowstreams, and yet it is shown that three main effects are identified, a) there is a strong interaction between the main cross flow and the baffle leakage streams, enhancing the crossflow pressure drop, b) there is a further short-circuit not considered previously i.e. leakage in the window, and c) the crossflow does not penetrate as far, on average, as previously supposed. Models are developed for each of these three effects, along with a new windowflow pressure drop model, and it is shown that the effect of baffle leakage in the window is the most significant. These models developed to allow for various interactions, lead to an improved multi-stream method, named the "STREAM-INTERACTION" method. The overall method is shown to be consistently more accurate than previous methods, with virtually all the available shellside data being predicted to within ±30% and over 60% being within ±20%. The method is, thus, strongly recommended for use as a design method.

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The separation performance of a semicontinuous counter-current chromatographic refiner (SCCR7), consisting of twelve 5.4 cm id x 75cm long columns packed with calcium charged cross-linked polysytrene resin (KORELA VO7C), was optimised. An industrial barley syrup was used containing 42% fructose, 52% glucose and 6% maltose and oligosaccharides. The effects of temperature, flow rates and concentration on the distribution coefficients were evaluated and quantified by deriving general relationships. The effects of flow rates, feed composition and concentration on the separation performance of the SCCR7 were identified and general relationships between them and the switch time, which was found to be the controlling parameter, were developed. Fructose rich (FRP) and glucose rich (GRP) product purities of 99.9% were obtained at 18.6% w/v feed concentrations. When a 66% w/v feed concentration was used and product splitting technique was employed, the throughput was 32.1 kg sugar solids/m3 resin/hr. The GRP contained less than 4.5% fructose, the FRP was over 95% pure, and the respective concentrations were 22.56 and 11.29% w/v. Over 94% of the glucose and 95.78% of the fructose in the feed were recovered in the GRP and FRP respectively. By recycling the dilute product split fractions, the GRP and FRP concentrations were increased to 25.4 and 12.96% w/v; the FRP was 90.2% pure and the GRP contained 6.69% w/v fructose. A theoretical link between batch and semicontinuous chromatographic equipments has been determined. A computer simulation was developed predicting successfully the purging concentration profiles at `pseudo-equilibrium', and also certain system design parameters. An important further aspect of the work has been to study the behaviour of chromatographic bioreactor-separators. Such batch systems of 5.4cm id and lengths varying between 30 and 230cm, were used to investigate the effect of scaling up on the conversion of sucrose into dextran and fructose in the presence of the dextransucrase enzyme. Conversions of over 80% were achieved at 4 hr sucrose residence times. The crude dextransucrase was purified using centrifugation, ultrafiltration and cross-flow microfiltration techniques. Better enzyme stability was obtained by first separating the non-solid impurities using cross-flow microfiltration, and then removing the cells from the enzyme immediately before use by continuous centrifugation.

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Liquid desiccant systems are of potential interest as a means of cooling greenhouses to temperatures below those achieved by conventional means. However, only very little work has been done on this technology with previous workers focussing on the cooling of human dwellings using expensive desiccants such as lithium salts. In this study we are designing a system for greenhouse cooling based on magnesium chloride desiccant which is an abundant and non-toxic substance. Magnesium chloride is found in seawater, for example, and is a by-product from solar salt works. We have carried out a detailed experimental study of the relevant properties of magnesium rich solutions. In addition we have constructed a test rig that includes the main components of the cooling system, namely a dehumidifier and solar regenerator. The dehumidifier is a cross-flow device that consists of a structured packing made of corrugated cellulose paper sheets with different flute angles and embedded cooling tubes. The regenerator is of the open type with insulated backing and fabric covering to spread the flow of desiccant solution. Alongside these experiments we are developing a mathematical model in gPROMS® that combines and simulates the heat and mass transfer processes in these components. The model can be applied to various geographical locations. Here we report predictions for Havana (Cuba) and Manila (Philippines), where we find that average wet-bulb temperatures can be lowered by 2.2 and 3°C, respectively, during the month of May.

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The sequence-specific affinity chromatographic isolation of plasmid DNA from crude lysates of E. coli DH5α fermentations is addressed. A zinc finger-GST fusion protein that binds a synthetic oligonucleotide cassette containing the appropriate DNA recognition sequence is described. This cassette was inserted into the Smal site of pUC19 to enable the affinity isolation of the plasmid. It is shown that zinc finger-GST fusion proteins can bind both their DNA recognition sequence and a glutathione-derivatized solid support simultaneously. Furthermore, a simple procedure for the isolation of such plasmids from clarified cell lysates is demonstrated. Cell lysates were clarified by cross-flow Dean vortex microfiltration, and the permeate was incubated with zinc finger-GST fusion protein. The resulting complex was adsorbed directly onto glutathione-Sepharose. Analysis of the glutathione-eluted complex showed that plasmid DNA had been recovered, largely free from contamination by genomic DNA or bacterial cell proteins. © 2002 Wiley Periodicals, Inc.

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There is currently significant interest in particle-stabilized emulsions for a variety of applications and as precursors to other materials such as micro-capsules or colloidosomes. A prerequisite for many applications is the ability to produce stable droplets with a well-controlled size. The preparation of oil-in-water (o/w) emulsions stabilized by silica colloids has been demonstrated here using membrane ulsification techniques. Emulsions were produced using both a cross-flow membrane device and a rotating membrane reactor. Under the correct conditions, highly stable emulsions with very narrow droplet size distributions can be produced. Investigations into the effects of changing the cross-flow shear rate at a fixed droplet production rate illustrate the fine control over mean droplet size that is possible with these emulsification techniques. Evidence for the importance of particle adsorption kinetics onto growing droplets prior to detachment from the membrane surface was obtained by varying the droplet production rate under fixed shear conditions. The presence of a critical surface coverage by the stabilizing particles to prevent droplet coalescence was clearly seen. Comparison with samples produced using conventional high-shear homogenization highlights the improved control over size distribution available from these membrane techniques.

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Nos dias de hoje a sociedade exige níveis qualitativos de vida cada vez mais elevados, o que torna prioritária a conceção de sistemas eficientes, não poluidores, económicos e diversificados que permitam uma gestão integrada e racionalizada de recursos tão escasso como é o da água e da energia. Em sistemas de abastecimento de água, o uso de válvulas redutoras de pressão (VRP) visa a uniformização e controlo de pressões, promovendo uma perda de carga localizada que dissipa a energia hidráulica presente através da redução dos valores de pressão a jusante. Estas são fundamentais no controlo e redução de pressão. A utilização de microturbinas é uma alternativa sustentável para o controle de pressão e, simultaneamente, para a produção de energia elétrica. Trata-se de um método de mitigação para controlar as perdas referidas convergindo no âmbito da eficiência energética. Na perspetiva de promover um aproveitamento de energia nas redes de abastecimento de água, o presente trabalho sugere a substituição de válvulas redutoras de pressão (VRP) por microturbinas. Desse modo, apresenta-se um método automático de seleção de (i) local para implementação e (ii) projeto de microturbinas para sistemas de abastecimento de água. Para a modelação do funcionamento dos sistemas hidráulicos recorre-se ao simulador hidráulico EPANET. Esta ferramenta possibilita avaliação de caudais e pressões em todos os pontos da rede durante um determinado intervalo de tempo. A metodologia desenvolvida permite selecionar o local ideal no sistema hidráulico através de uma análise de cada secção conduta-nó escolhendo-se a melhor opção baseada na produção de energia. Depois da localização procede-se à seleção do tipo de turbina (Kaplan, Francis, Pelton e Cross-flow) que vai depender das características do sistema hidráulico. Na etapa seguinte apresenta-se os resultados obtidos pela turbina nomeadamente a produção de energia elétrica anual, o investimento necessário, o tempo de retorno e a rentabilização ao final de um período de 25 anos. Na última etapa da metodologia, de forma avaliar o comportamento do sistema final, realiza-se uma nova simulação da rede mas tendo em conta a introdução da microturbina no local. Apresentam-se alguns casos de estudo que validam a ferramenta desenvolvida. A metodologia desenvolvida é comparada com um caso de estudo real. Em ambos os exemplos simulados a metodologia aplicada permite obter soluções com ganhos energéticos significativos associados ao sistema. Apenas num dos exemplos se observaram que a implementação da microturbina no sistema hidráulico não seria economicamente rentável.

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Lääkeaineiden poistaminen jätevedestä on tärkeää lääkeainejäämien ympäristöön pääsyn ehkäisemiseksi. Tämän työn tavoitteena on selvittää, soveltuvatko katalyyttiset membraanit lääkeaineiden poistoon jätevedestä ja saadaanko membraanisuodatusta tehostettua katalyyttisellä prosessilla. Työ käsittelee katalyyttisistä prosesseista fotokatalyysiä, joka perustuu valoa absorboivan katalyytin käyttöön. Kirjallisuustyössä tarkastellaan kahden erilaisen fotokatalyyttisen prosessin toimivuutta membraanisuodatuksen kanssa lääkeaineiden poistossa jätevedestä. Lisäksi tutkitaan fotokatalyysissä käytettävän katalyytin ja ultraviolettisäteilyn vaikutusta membraaniin. Tutkimukset ovat osoittaneet, että katalyyttisillä membraaneilla voidaan poistaa lääkeaineita jätevedestä tehokkaasti. Parhaan lääkeaineiden poistotehokkuuden saamiseksi katalyytin määrä on optimoitava hajotusprosessin kannalta. Myös katalyytin sijainti membraanissa vaikuttaa tehokkuuteen. Katalyytti voi sijaita membraanista myös erillään. Tällöin saadaan käsiteltyä myös jatkuvatoimisessa membraanisuodatuksessa syntyvä lääkeaineita sisältävä konsentraattivirta. Kun katalyyttisellä membraanilla hajotetaan lääkeaineita, täytyy prosessin turvallisuuden kannalta olla hyvin selvillä mahdollisista syntyvistä myrkyllisistä välituotteista. Tutkimuksissa on myös todettu, että katalyyttisen membraanin käyttö vähentää membraanin likaantumista.

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In this study, the dynamic response of a vertical flexible cylinder vibrating at low mode numbers with combined x-y motion was investigated in a towing tank. The uniform flow was simulated by towing the flexible cylinder along the tank in still water; therefore, the turbulence intensity of the free flow was negligible in obtaining more reliable results. A lower branch of dominant frequencies with micro vibration amplitude was found in both cross-flow and in-line directions. This justifiable discrepancy was likely caused by an initial lock-in. The maximum attainable amplitude, modal analysis and x-y trajectory in cross-flow and in-line directions are reported here and compared with previous literature, along with some good agreements and different observations that were obtained from the study. Drag and lift coefficients are also evaluated by making use of a generalized integral transform technique approach, yielding an alternative method to study fluid force acting upon a flexible cylinder.