30 resultados para Modified k-epsilon model
em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland
Resumo:
In a centrifugal compressor the flow around the diffuser is collected and led to the pipe system by a spiral-shaped volute. In this study a single-stage centrifugal compressor with three different volutes is investigated. The compressorwas first equipped with the original volute, the cross-section of which was a combination of a rectangle and semi-circle. Next a new volute with a fully circular cross-section was designed and manufactured. Finally, the circular volute wasmodified by rounding the tongue and smoothing the tongue area. The overall performance of the compressor as well as the static pressure distribution after the impeller and on the volute surface were measured. The flow entering the volute was measured using a three-hole Cobra-probe, and flow visualisations were carriedout in the exit cone of the volute. In addition, the radial force acting on theimpeller was measured using magnetic bearings. The complete compressor with thecircular volute (inlet pipe, full impeller, diffuser, volute and outlet pipe) was also modelled using computational fluid dynamics (CFD). A fully 3-D viscous flow was solved using a Navier-Stokes solver, Finflo, developed at Helsinki University of Technology. Chien's k-e model was used to take account of the turbulence. The differences observed in the performance of the different volutes were quite small. The biggest differences were at low speeds and high volume flows,i.e. when the flow entered the volute most radially. In this operating regime the efficiency of the compressor with the modified circular volute was about two percentage points higher than with the other volutes. Also, according to the Cobra-probe measurements and flow visualisations, the modified circular volute performed better than the other volutes in this operating area. The circumferential static pressure distribution in the volute showed increases at low flow, constant distribution at the design flow and decrease at high flow. The non-uniform static pressure distribution of the volute was transmitted backwards across the vaneless diffuser and observed at the impeller exit. At low volume flow a strong two-wave pattern developed into the static pressure distribution at the impeller exit due to the response of the impeller to the non-uniformity of pressure. The radial force of the impeller was the greatest at the choke limit, the smallest atthe design flow, and moderate at low flow. At low flow the force increase was quite mild, whereas the increase at high flow was rapid. Thus, the non-uniformityof pressure and the force related to it are strong especially at high flow. Theforce caused by the modified circular volute was weaker at choke and more symmetric as a function of the volume flow than the force caused by the other volutes.
Resumo:
Crystal growth is an essential phase in crystallization kinetics. The rate of crystal growth provides significant information for the design and control of crystallization processes; nevertheless, obtaining accurate growth rate data is still challenging due to a number of factors that prevail in crystal growth. In industrial crystallization, crystals are generally grown from multi-componentand multi-particle solutions under complicated hydrodynamic conditions; thus, it is crucial to increase the general understanding of the growth kinetics in these systems. The aim of this work is to develop a model of the crystal growth rate from solution. An extensive literature review of crystal growth focuses on themodelling of growth kinetics and thermodynamics, and new measuring techniques that have been introduced in the field of crystallization. The growth of a singlecrystal is investigated in binary and ternary systems. The binary system consists of potassium dihydrogen phosphate (KDP, crystallizing solute) and water (solvent), and the ternary system includes KDP, water and an organic admixture. The studied admixtures, urea, ethanol and 1-propanol, are employed at relatively highconcentrations (of up to 5.0 molal). The influence of the admixtures on the solution thermodynamics is studied using the Pitzer activity coefficient model. Theprediction method of the ternary solubility in the studied systems is introduced and verified. The growth rate of the KDP (101) face in the studied systems aremeasured in the growth cell as a function of supersaturation, the admixture concentration, the solution velocity over a crystal and temperature. In addition, the surface morphology of the KDP (101) face is studied using ex situ atomic force microscopy (AFM). The crystal growth rate in the ternary systems is modelled on the basis of the two-step growth model that contains the Maxwell-Stefan (MS) equations and a surface-reaction model. This model is used together with measuredcrystal growth rate data to develop a new method for the evaluation of the model parameters. The validation of the model is justified with experiments. The crystal growth rate in an imperfectly mixed suspension crystallizer is investigatedusing computational fluid dynamics (CFD). A solid-liquid suspension flow that includes multi-sized particles is described by the multi-fluid model as well as by a standard k-epsilon turbulence model and an interface momentum transfer model. The local crystal growth rate is determined from calculated flow information in a diffusion-controlled crystal growth regime. The calculated results are evaluated experimentally.
Resumo:
Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.
Resumo:
Fluid particle breakup and coalescence are important phenomena in a number of industrial flow systems. This study deals with a gas-liquid bubbly flow in one wastewater cleaning application. Three-dimensional geometric model of a dispersion water system was created in ANSYS CFD meshing software. Then, numerical study of the system was carried out by means of unsteady simulations performed in ANSYS FLUENT CFD software. Single-phase water flow case was setup to calculate the entire flow field using the RNG k-epsilon turbulence model based on the Reynolds-averaged Navier-Stokes (RANS) equations. Bubbly flow case was based on a computational fluid dynamics - population balance model (CFD-PBM) coupled approach. Bubble breakup and coalescence were considered to determine the evolution of the bubble size distribution. Obtained results are considered as steps toward optimization of the cleaning process and will be analyzed in order to make the process more efficient.
Resumo:
Työssä on tutkittu CFX ja Fluent virtauslaskentaohjelmien soveltavuutta kuristet-tujen isotermisten vesivirtausten kolmidimensionaaliseen mallintamiseen. Teoriaosassa on esitelty virtausta hallitsevat perusyhtälöt sekä eri kavitaatioteori-oita kavitaatiokuplan syntymisestä tuhoutumiseen. Laskennallisessa osassa esitellään käytetyt virtauslaskentaohjelmat ja laskentatapaukset sekä verrataan saatuja tuloksia aiemmin suoritettuihin mittauksiin. Työn pääpaino oli tutkia käytettyjen virtauslaskentaohjelmien soveltuvuutta kuris-tettujen virtauksien mallinnukseen.
Resumo:
Tässä työssä esitetään tuloilmalaitteen virtausten laskennallinen tarkastelu huonetilassa virtauslaskentaohjelmiston avulla. Tarkastelu suoritetaan kolmiulotteisena sekä isotermisille että termisille tapauksille, jolloin huonetilan joihinkin pintoihin asetetaan lämpövuo ja epäpuhtauslähde. Työn tarkoituksena on arvioida CFX -virtauslaskentaohjelmiston soveltuvuutta huonetilavirtausten mallintamiseen ja tarkastella huonetilan ilmanvaihdon tehokkuutta eri tapauksissa. Arviointi suoritetaan vertaamalla laskentatuloksia mittaustuloksiin. Turbulenssimallien vaikutusta on arvioitu käyttämällä nollan yhtälön ja standardi k-e turbulenssimalleja. CFX:n k-e turbulenssimallilla lasketut nopeuden alenemat eri tilavuusvirroilla vastasivat paremmin mittaustuloksia kuin nollan yhtälön turbulenssimallilla, jolla erot olivat huomattavia. Huonetilan ilmanvaihdon tehokkuus vaihteli suuresti tuloilmalaitteen sijoituspaikan ja lämpövuon mukaan.
Resumo:
The aim of this work is to study flow properties at T-junction of pipe, pressure loss suffered by the flow after passing through T-junction and to study reliability of the classical engineering formulas used to find head loss for T-junction of pipes. In this we have compared our results with CFD software packages with classical formula and made an attempt to determine accuracy of the classical formulas. In this work we have studies head loss in T-junction of pipes with various inlet velocities, head loss in T-junction of pipes when the angle of the junction is slightly different from 90 degrees and T-junction with different area of cross-section of the main pipe and branch pipe. In this work we have simulated the flow at T-junction of pipe with FLUENT and Comsol Multiphysics and observed flow properties inside the T-junction and studied the head loss suffered by fluid flow after passing through the junction. We have also compared pressure (head) losses obtained by classical formulas by A. Vazsonyi and Andrew Gardel and formulas obtained by assuming T-junction as combination of other pipe components and observations obtained from software experiments. One of the purposes of this study is also to study change in pressure loss with change in angle of T-junction. Using software we can have better view of flow inside the junction and study turbulence, kinetic energy, pressure loss etc. Such simulations save a lot of time and can be performed without actually doing the experiment. There were no real life experiments made, the results obtained completely rely on accuracy of software and numerical methods used.
Resumo:
Centrifugal compressors are widely used for example in refrigeration processes, the oil and gas industry, superchargers, and waste water treatment. In this work, five different vaneless diffusers and six different vaned diffusers are investigated numerically. The vaneless diffusers vary only by their diffuser width, so that four of the geometries have pinch implemented to them. Pinch means a decrease in the diffuser width. Four of the vaned diffusers have the same vane turning angle and a different number of vanes, and two have different vane turning angles. The flow solver used to solve the flow fields is Finflo, which is a Navier-Stokes solver. All the cases are modeled with the Chien's k – έ- turbulence model, and selected cases are modeled also with the k – ώ-SST turbulence model. All five vaneless diffusers and three vaned diffusers are investigated also experimentally. For each construction, the compressor operating map is measured according to relevant standards. In addition to this, the flow fields before and after the diffuser are measured with static and total pressure, flow angle and total temperature measurements. When comparing the computational results to the measured results, it is evident that the k – ώ-SST turbulence model predicts the flow fields better. The simulation results indicate that it is possible to improve the efficiency with the pinch, and according to the numerical results, the two best geometries are the ones with most pinch at the shroud. These geometries have approximately 4 percentage points higher efficiency than the unpinched vaneless diffusers. The hub pinch does not seem to have any major benefits. In general, the pinches make the flow fields before and after the diffuser more uniform. The pinch also seems to improve the impeller efficiency. This is down to two reasons. The major reason is that the pinch decreases the size of slow flow and possible backflow region located near the shroud after the impeller. Secondly, the pinches decrease the flow velocity in the tip clearance, leading to a smaller tip leakage flow and therefore slightly better impeller efficiency. Also some of the vaned diffusers improve the efficiency, the increment being 1...3 percentage points, when compared to the vaneless unpinched geometry. The measurement results confirm that the pinch is beneficial to the performance of the compressor. The flow fields are more uniform with the pinched cases, and the slow flow regions are smaller. The peak efficiency is approximately 2 percentage points and the design point efficiency approximately 4 percentage points higher with the pinched geometries than with the un- pinched geometry. According to the measurements, the two best geometries are the ones with the most pinch at the shroud, the case with the pinch only at the shroud being slightly better of the two. The vaned diffusers also have better efficiency than the vaneless unpinched geometries. However, the pinched cases have even better efficiencies. The vaned diffusers narrow the operating range considerably, whilst the pinch has no significant effect on the operating range.
Resumo:
The objective of this thesis was to study the removal of gases from paper mill circulation waters experimentally and to provide data for CFD modeling. Flow and bubble size measurements were carried out in a laboratory scale open gas separation channel. Particle Image Velocimetry (PIV) technique was used to measure the gas and liquid flow fields, while bubble size measurements were conducted using digital imaging technique with back light illumination. Samples of paper machine waters as well as a model solution were used for the experiments. The PIV results show that the gas bubbles near the feed position have the tendency to escape from the circulation channel at a faster rate than those bubbles which are further away from the feed position. This was due to an increased rate of bubble coalescence as a result of the relatively larger bubbles near the feed position. Moreover, a close similarity between the measured slip velocities of the paper mill waters and that of literature values was obtained. It was found that due to dilution of paper mill waters, the observed average bubble size was considerably large as compared to the average bubble sizes in real industrial pulp suspension and circulation waters. Among the studied solutions, the model solution has the highest average drag coefficient value due to its relatively high viscosity. The results were compared to a 2D steady sate CFD simulation model. A standard Euler-Euler k-ε turbulence model was used in the simulations. The channel free surface was modeled as a degassing boundary. From the drag models used in the simulations, the Grace drag model gave velocity fields closest to the experimental values. In general, the results obtained from experiments and CFD simulations are in good qualitative agreement.
Resumo:
Supersonic axial turbine stages typically exhibit lower efficiencies than subsonic axial turbine stages. One reason for the lower efficiency is the occurrence of shock waves. With higher pressure ratios the flow inside the turbine becomes relatively easily supersonic if there is only one turbine stage. Supersonic axial turbines can be designed in smaller physical size compared to subsonic axial turbines of same power. This makes them good candidates for turbochargers in large diesel engines, where space can be a limiting factor. Also the production costs are lower for a supersonic axial turbine stage than for two subsonic stages. Since supersonic axial turbines are typically low reaction turbines, they also create lower axial forces to be compensated with bearings compared to high reaction turbines. The effect of changing the stator-rotor axial gap in a small high (rotational) speed supersonic axial flow turbine is studied in design and off-design conditions. Also the effect of using pulsatile mass flow at the supersonic stator inlet is studied. Five axial gaps (axial space between stator and rotor) are modeled using threedimensional computational fluid dynamics at the design and three axial gaps at the off-design conditions. Numerical reliability is studied in three independent studies. An additional measurement is made with the design turbine geometry at intermediate off-design conditions and is used to increase the reliability of the modelling. All numerical modelling is made with the Navier-Stokes solver Finflo employing Chien’s k ¡ ² turbulence model. The modelling of the turbine at the design and off-design conditions shows that the total-to-static efficiency of the turbine decreases when the axial gap is increased in both design and off-design conditions. The efficiency drops almost linearily at the off-design conditions, whereas the efficiency drop accelerates with increasing axial gap at the design conditions. The modelling of the turbine stator with pulsatile inlet flow reveals that the mass flow pulsation amplitude is decreased at the stator throat. The stator efficiency and pressure ratio have sinusoidal shapes as a function of time. A hysteresis-like behaviour is detected for stator efficiency and pressure ratio as a function of inlet mass flow, over one pulse period. This behaviour arises from the pulsatile inlet flow. It is important to have the smallest possible axial gap in the studied turbine type in order to maximize the efficiency. The results for the whole turbine can also be applied to some extent in similar turbines operating for example in space rocket engines. The use of a supersonic stator in a pulsatile inlet flow is shown to be possible.
Resumo:
This master thesis presents a study on the requisite cooling of an activated sludge process in paper and pulp industry. The energy consumption of paper and pulp industry and it’s wastewater treatment plant in particular is relatively high. It is therefore useful to understand the wastewater treatment process of such industries. The activated sludge process is a biological mechanism which degrades carbonaceous compounds that are present in waste. The modified activated sludge model constructed here aims to imitate the bio-kinetics of an activated sludge process. However, due to the complicated non-linear behavior of the biological process, modelling this system is laborious and intriguing. We attempt to find a system solution first using steady-state modelling of Activated Sludge Model number 1 (ASM1), approached by Euler’s method and an ordinary differential equation solver. Furthermore, an enthalpy study of paper and pulp industry’s vital pollutants was carried out and applied to revise the temperature shift over a period of time to formulate the operation of cooling water. This finding will lead to a forecast of the plant process execution in a cost-effective manner and management of effluent efficiency. The final stage of the thesis was achieved by optimizing the steady state of ASM1.
Resumo:
Työn tavoitteena oli laatia Tieliikelaitoksen tutkimus- ja kehitysprojektien kannattavuuden arvioinnin toimintamalli ja laskentamalli. Työn tavoitteena oli myös kehittääTieliikelaitoksen tutkimus- ja kehitysprojektin kannattavuuden arviointia ja tuottaa informaatiota t&k -projektien valintatilanteisiin. Työ koostuu teoriasta, haastatteluista, t&k -projektien kannattavuuden arvioinnin toimintamallista ja laskentamallista. Työssä käsitellään kirjallisuudesta ja haastatteluista esille tulleita käytäntöjä ja menetelmiä, joiden avulla tutkimus- ja kehitysprojektien kannattavuutta voidaan arvioida. Työssä kuvataan myös arviointimenetelmien käyttöä t&k -prosessin eri vaiheissa. Työn merkittävimpinä tuloksina ovat laaditut toimintamalli ja laskentamalli Tieliikelaitoksen t&k -projektien kannattavuuden arviointiin. Lisäksi työssä tuloksena oli, että arviointimenetelmiä tulee käyttää monipuolisesti ja projektien arviointi tulee olla jatkuvaa. Projektien kannattavuuden arviointi ei voi perustua pelkästään taloudellisiin menetelmiin vaan arviointiin tulee valita sekä taloudellisia että laadullisia menetelmiä. Projektien jatkuvalla arvioinnilla ja arviointimenetelmien käytön monipuolisuudella varmistetaan oikeiden ja kannattavien projektien toteuttaminen.
Resumo:
Työssä tutkittiin sulfonoitujen polystyreenidivinyylibentseenirunkoisten geeli-, meso- ja makrohuokoistenioninvaihtohartsien rakennetta käyttäen useita eri karakterisointimenetelmiä. Lisäksi työssä tutkittiin hartsien huokoskoon vaikutusta aminohappojen kromatografisessa erotuksessa. Työn pääpaino oli hartsien huokoskoon ja huokoisuuden määrittämisessä. Sen selvittämiseksi käytettiin hyväksi elektronimikroskopiaa, typpiadsorptiomittauksia, sekä käänteistä kokoekskluusiokromatografiaa. Parhaat tulokset saatiin käänteisellä kokoekskluusiokromatografialla, joka perustuu erikokoisten dekstraanipolymeerien käyttöön mallimolekyyleinä. Menetelmä sopii meso- ja makrohuokoisuuden tutkimiseen, mutta sen heikkoutena on erittäin pitkä mittausaika. Menetelmä antaa myös huokoskokojakauman, mutta yhden hartsin mittaaminen voi kestää viikon. Menetelmää muutettiin siten, että käytettiin määritettävää huokoskokoaluetta kuvaavien kahden dekstraanipolymeerin seosta. Kromatografiset ajo-olosuhteet optimoitiin sellaisiksi, että injektoidussa seoksessa olevien dekstraanien vastehuiput erottuivat toisistaan. Tällöin voitiin luotettavasti määrittää tutkittavan stationaarifaasin suhteellinen huokoisuus. Tätä työssä kehitettyä nopeaa käänteiseen kokoekskluusiokromatografiaan perustuvaa menetelmää kutsutaan kaksipistemenetelmäksi. Hartsien sulfonihapporyhmien määrää ja jakautumista tutkittiin määrittämällä hartsien kationinvaihtokapasiteetti sekä tutkimalla hartsin pintaa konfokaali-Raman-spektroskopian avulla. Sulfonihapporyhmien ioninvaihtokyvyn selvittämiseksi mitattiin K+-muotoon muutetusta hartsista S/K-suhde poikkileikkauspinnasta. Tulosten perusteella hartsit olivat tasaisesti sulfonoituneet ja 95 % rikkiatomeista oli toimivassa ioninvaihtoryhmässä. Aminohappojen erotuksessa malliaineina oli lysiini, seriini ja tryptofaani. Hartsi oli NH4+-muodossa ja petitilavuus oli 91 mL. Eluenttina käytettiin vettä, jonka pH oli 10. Paras tulos saatiin virtausnopeudella 0,1 mL/min, jolla kaikki kolme aminohappoa erottuivat toisistaan Finex Oy:n mesohuokoisella KEF78-hartsilla. Muilla tutkituilla hartseilla kaikki kolme aminohappoa eivät missään ajo-olosuhteissa erottuneet täysin.
Resumo:
Tutkimuksen tavoitteena oli löytää yritysten välisten tutkimus- ja kehityshankkeiden valintaan liittyviä kriittisiä tekijöitä ja luoda T&K-verkostojen analysointiin soveltuva malli, jonka avulla tutkimuksen caseyritys VR Cargo voi tehdä päätöksiä panostuksistaan eri hankkeisiin ja ylipäätänsä siitä, missä kannattaa olla mukana sekä kuinka löytää strategisia kehityskumppaneita. Työn teoriaosuus tehtiin kirjallisuuskatsauksena aiempaan T&K-tutkimukseen ja empiria osuus suoritettiin tekemällä teemahaastatteluja VR Cargossa sekä kahdessa vertailuyrityksessä. Tutkimuksessa havaittiin useita erilaisia kriittisiä tekijöitä T&K-yhteistyöhankkeisiin liittyen. Yrityksen on mm. huomioitava T&K-hankkeen strateginen sopivuus ja lisäarvo, määriteltävä motiivit ja riskit, yrityskohtaisten tekijöiden ovat oltava kunnossa, on tiedettävä millainen on yritykselle hyvä ja sopiva partneri sekä yhteistyötason tekijät on huomioitava. Tutkimuksessa rakennettua hankkeiden valintaan liittyvää päätöspuumallia, ei ole tarkoitettu tekemään lopullista valintapäätöstä, vaan sen tarkoituksena on helpottaa ja tukea valintaprosessia ja alentaa näin todennäköisyyttä unohtaa jokin tärkeä seikka valintaprosessissa.
Resumo:
Membrane filtration has become increasingly attractive in the processing of both foodand biotechnological products. However, the poor selectivity of the membranes and fouling are the critical factors limiting the development of UF systems for the specific fractionation of protein mixtures. This thesis gives an overview on fractionation of proteins from model protein solutions or from biological solutions. An attempt was made to improve the selectivity of the available membranes by modifying the membranes and by exploiting the different electrostatic interactions between the proteins and the membrane pore surfaces. Fractionation and UF behavior of proteins in the model solutions and in the corresponding biological solutions were compared. Characterization of the membranes and protein adsorptionto the membrane were investigated with combined flux and streaming potential studies. It has been shown that fouling of the membranes can be reduced using "self-rejecting" membranes at pH values where electrostatic repulsion is achieved between the membrane and the proteins in solution. This effect is best shown in UF of dilute single protein solutions at low ionic strengths and low pressures. Fractionation of model proteins in single, binary, and ternary solutionshas been carried out. The results have been compared to the results obtained from fractination of biological solutions. It was generally observed that fractination of proteins from biological solutions are more difficult to carry out owingto the presence of non studied protein components with different properties. Itcan be generally concluded that it is easier to enrich the smaller protein in the permeate but it is also possible to enrich the larger protein in the permeateat pH values close to the isoelectric point of the protein. It should be possible to find an optimal flux and modification to effectively improve the fractination of proteins even with very similar molar masses.