反应釜外文翻译---气体诱导涡轮搅拌的搅拌反应釜中的二相流的研究.docx

附录B：英文原文及翻译A study on the two-phase flow in a stirred tank reactor agitated by a gas-inducing turbineabstractExperimental and numerical studies of a gasliquid two-phase flow have been applied to a non-baffled laboratory-scale stirred tank reactor, mechanically agitated by a gas-inducing turbine. The dispersion of air as gas phase into isopropanol as liquid phase at room temperature under different stirrer speeds was investigated. The X-ray cone beam computed tomography (CBCT) measurements have been taken at five different stirrer speeds starting from 1000 rpm at which the gas inducement occurs for the given operating conditions.The considerable difficulties in acquiring the phase distribution due to beam hardening and radiation scattering effects have been overcome by developing a suitable measurement setup as well as by calibration and software correction methods to achieve high accuracy. The computational fluid dynamics analyses of the stirred tank reactor have been performed in 3D with CFX 10.0 numerical software. The simplified numerical setup of mono-dispersed bubbles, constant drag coefficient and the ke turbulence model was able to capture both the bubble induction and dispersion and the free surface vortex formation. Despite the assumed simplifications, the numerical predictions exhibit a good agreement with the experimental data.Keywords:Stirred tank reactor; Gas-inducing impeller; CFD; X-ray computed tomography Mixing.1. IntroductionGasliquid mixing in stirred tank reactors is a common process in the industry. It is regarded as one of the most difficult to tackle because of its complexities in terms of flow regimes and multiphase operations. Traditionally, the gasliquid stirred tank reactor is equipped with an impeller responsible for dispersing the gas phase, which is usually supplied via a single pipe or a ring sparger mounted beneath the impeller. The gas-inducing impellers provide an alternative gas injection, in which case the gas is sucked via a hollow shaft and fed directly into the stirrer region (Evans et al., 1990). More gas bubbles can be broken-up into small ones when such configuration is applied, which consequently could provide higher mass transfer (Rigby and Evans, 1998). Among the long lasting efforts to establish precise but practical measurement techniques for the analysis of multiphase fluid dynamic processes in chemical reactors (Boyer et al., 2002), methods based on ionising radiation are most promising since they are applicable at higher gas fractions,and they give linear measurements regardless of the structure complexity inside the vessel. An advanced tomographic technique is cone beam X-ray computed tomography (CBCT). With CBCT, a volume density distribution is reconstructed from a set of two-dimensional radiographs obtained from an object at different projection angles. This technique is especially suitable for time-integrated gas fraction measurements.The use of X-ray CT for gas hold-up measurements has been described by Pike et al. (1965), and recently by Hervieu et al. (2002), with application to two-phase flow in a pipe, by Kantzas and Kalogerakis (1996), who monitored the fluidisation characteristics of a fluidised bed reactor, by Reinicke et al.(1998), and Toye et al. (1998), who used it in packed catalyst beds, and by Vinegar and Wellington(1987),who measured fluid transport in porous media. All the above-mentioned techniques yield time-averaged rather than instantaneous phase distribution images. Rotationally symmetric material distributions such as the phase distribution in an un-baffled reactor enables even a rather fast tomography, since one radiographic projection is sufficient to compute a complete axial and radial gas hold up profile. Though CBCT is widely used today in medical imaging and material research, it has two inherent problems that must be addressed for quantitative gas fraction measurements in a stirred chemical reactor. It is inevitably necessary, in particular, to devise special correction steps to account for beam hardening and scattered radiation. With such corrections, the calculated gas fraction values will fit within the error limits of less than four percent(Boden et al., 2005).Modelling a stirred tank using computational fluid dynamics (CFD) requires consideration of many aspects of the process (Marden Marshall and Bakker, 2002). The geometry of the stirred tank, even in the case of a complex one especially when the impeller is explicitly modelled, needs to be embedded in a computational grid. Special care has to be taken to account for the impeller motion especially at low rotating speed when the turbulence and the corresponding turbulence damping wall functions have significant effect on the flow (Ranade, 2002).Lane et al. (2005), along the lines proposed by Brucato et al.(1998), have shown that in order to acquire the correct phase distribution in the vessel, inclusion of the non-drag forces and modification of the drag laws were necessary. Micale et al. (2000) have reached similar conclusions when studying solid suspension in agitated vessels. However, Torre et al. (2007) managed to obtain good agreement between the numerical simulations and the experimental observation of the free surface vortex plotted for a gas void of 0.50.9 with simplifying assumptions of a constant bubble size, a constant drag coefficient and the use of the ke turbulence model. Using advanced X-ray computed tomography, the current study demonstrates the CFD abilities of predicting the two-phase flow in the stirred vessel when gas inducing impeller is employed.2. Experimental investigationA detailed description of the measurement setup, the correction and reconstruction calculations and their evaluation is given elsewhere (Boden et al., 2005), and is only briefly reviewed here.2.1. Tomography measurement setupThe cone beam tomography setup consists essentially of a rotating anode X-ray source (DI-104H-22/60-150, COMET AG, Switzerland) fed by a medical type high voltage generator (MP601, Ro ntgenwerk Bochum, Germany) and a two dimensional digital X-ray flat panel imager (RID1640AL1, Perkin-Elmer Optoelectronics GmbH & Co. KG, Germany) arranged opposite to each other as shown in Fig. 1. The X-ray source may be operated at voltages up to 125 kV and electron currents of maximum 800 mA in single exposure mode. The detector provides 1024 by 1024 pixels, each 0.4 mm by 0.4 mm in size. The X-ray setup was assembled inside a shielded box. The stirred reactor was placedbetween the source and the detector at the distances given in Fig. 1.To ensure the quantitative radiographic image quality for each single exposure, a special data acquisition procedure described below was adopted. The detectors dark current signal was determined before each exposure and was subsequently subtracted from acquired image data. Quantitative X-ray intensity measurements synchronized to the Xray generation may be degraded due to the detectors delaying behaviour (also known as image lag). Therefore, the detectors signal integration time was set to persist well beyond the shutoff of each individual X-ray exposure. The duration of an X-ray exposure was 6.3 s which was the longest permissible time given by the X-ray generator. For the particular reactor geometry under investigation,this integration time period was found to be sufficient to achieve the required signal to noise ratio which means that dynamic processes with timeconstants of several seconds, such as changing of the stirrer speed, feeding, extraction, and mixing, can be observed in real time.Fig. 1 Schematic view of the CBCT setup.The model fluid used was isopropanol at normal pressure and room temperature. The critical stirrer speed at which gas dispersion at the stirrer blades occurs was estimated by optical observation to be of 1020 rpm. Then, the stirrer was successively driven with speeds in the range of 10001200 rpm at 50 rpm intervals. For each operation point, a CBCT scan was performed.2.3. Scattering correctionIn an additional measurement, a moving slit technique (Jaffe and Webster, 1975) was applied to synthesise an almost scattering free radiographic image of the reactor at moderate stirrer speed well below its critical value. The difference between such an image and an un-collimated cone beam Xray radiography of the same arrangement gives a measured value for the amount of scattered radiation intensity distribution in the detector plane. Subsequently acquired X-ray intensity distributions have been reduced by that amount to eliminate the contribution of scattered radiation which otherwise would ultimately lead to quantitative errors in the reconstruction process. This approach is reasonable,since by dispersing little amount of gas into the fluid, the overall mass of the object is conserved and there are only slight changes in the material distribution and thus only slight changes in the amount of scattered radiation are expected.2.4. Beam hardening correctionPolyenergetic X-ray radiation would be hardened when penetrating thick materials, as the effective attenuation coefficient becomes smaller with increasing penetration depth. If uncorrected, this leads to systematic errors in quantitative X-ray measurements. The adopted method for beam hardening correction can be illustrated with the experimental setup presented in Fig. 1. Two radiograms, one of the reactors completely filled with the fluid and another for the same arrangement plus an additional acrylic plate of thickness d = 0.01 m between reactor vessel and the detectorwere taken. Both images were synthesised from a series of slit images according to the method described above, and thus are assumed to be almost free of scattered radiation. From both images, the calibration extinction radiogram E c (r S , r D ) can be computed according to the following equation (1)where I denotes the measured intensities, is the effective attenuation coefficient of the acrylic plate according to a certain ray path between source and detector position r S , r D , and is the angle between the ray and the detector normal. The indexes S and D stand for source and detector respectively. After that, the plate is removed. Now any image taken from the reactor with another fluidgas distribution inside is processed to the extinction radiogram (2)where is the effective attenuation coefficient of the fluid and e denotes the void fraction distribution. Here, intensity measurements should be corrected for scattered radiation as described above. Taking the ratio of both extinction radiograms gives (3)Thereby, plate denotes the attenuation coefficient of the plate. It is important to note that in the second term the attenuation coefficients m fluid and are ray-dependent due to the beam hardening, whereas in the right hand term the ratio is being considered as energy and thus ray independent. This is reasonably accurate for materials with similar radiological properties such as PMMA and organic fluids or water. Furthermore, the ratio can be determined by measurement. Ray dependence in the case under investigation was significant, since the stirred vessel was composed of materials with largely varying attenuation properties. This is obvious, if one considers the energy spectra of photons passing though the metallic stirrer shaft, which attenuates much more low energy radiation compared to the energy spectra of photons passing only through the reactor glass wall.2.5. Tomographic reconstructionThe FDK algorithm (Feldkamp et al., 1984; Kak and Slaney,1988) was implemented in order to recover the gas fraction distribution e(r) directly by computational inversion of the X ray transform according to Eq. (3). An assumption that the examined object the time averaged gas distribution field in the stirred chemical reactor is rotationally symmetric was made. For simplification, the additional requirement that the axis of symmetry is equal to centre of the tomography setup was employed. The X-ray transform is then no longer dependent on the projection angle of the setup. Thus, from a single measurement at source position r S,0 and from a set of virtual source positions r S, virt on a virtual circular or bit including r S,0 the rotationally symmetric distribution can be reconstructed. Due to rotational symmetry, the FDK algorithm .was implemented in such a way that only the radial and axial gas hold-up distributions in the central vertical slice were computed with considerable reduction in computational load. Finally, it is important to note that the reconstruction from a single projection at virtual source positions is equal to rotational averaging of the reconstruction result. This, however, results in a space variant noise distribution in the reconstructed data. The signal to noise ratio of voxels residing at the outer boundary of the supporting circular reconstruction grid will ultimately rise due to the greater circumference length and thus of the greater number of voxels during averaging.3. Numerical investigationsThe computational fluid dynamics analyses of the stirred tank reactor were performed with CFX 10.0 numerical software.Although the non-baffled vessel exhibits to some extent an axi-symmetric behaviour on a macro-mixing scale, the process was regarded as three-dimensional in order to demonstrate the local variations in the gas hold-up associatedwith the blades positions. In such a way, cavity presence behind the impeller blades was theoretically predicted. An unstructured tetrahedral mesh, which explicitly includes the impeller geometry, with about 1,500,000 elements was used for the solution of the flow field in the stirred vessel. The mesh was globally refined since a detailed view in the whole tank was required. Additional simulations were performed on differently sized grids to establish grid independence of the results. There was no additional refinement of the mesh at wall since the wall turbulence damping function are known to work well at high Reynolds numbers as in the particular case.The stirred tank was broken down into four domains: threerotating and one stationary. The choice of having four domains instead of two, one stationary and one rotating was made because of some difficulties when meshing the geometry in 3D. The three rotating domains comprise the impeller, the part of the stirrer shaft in the impeller region and the stirrer shaft above the impeller. A multiple frames of references interaction scheme was used in the simulations to bond the stationary and the rotating domains. Wall boundary conditions with free slip for the gaseous and no slip for the liquid phases were the only ones required as the vessel was closed at the top. Four steady state simulations at stirrer speed from 200 to 800 rpm were conducted to obtain an initial guess of the flow field and the phase distribution for the simulation at 1000 rpm. Zero velocity fields for both phases have been taken as initial conditions for the simulation at stirrer speed of 200 rpm. The numerical predictions above 1000 rpm used the previous simulation results as an initial guess. Starting from 1000 rpm, five simulations have been performed at stirrer speed intervals of 50 rpm. The gas phase was modelled as dispersed fluid with a mean bubble diameter of 1 mm and the liquid phase as continuous fluid. According to Laakkonen et al. (2005), the mean bubble diameter for an airwater system in a stirred reactor agitated by a Rushton turbine at stirrer speed around 250 rpm was close to 3 mm. However, in the current experimental setup the stirrer was rotated with a speed above 1000 rpm and the holes on the impeller shaft had a diameter of 2 mm. The choice of 1 mm in size bubbles was also based on additionally performed high-speed camera measurements. For an isothermal two-phase flow with no mass transfer, the mass (4)and momentum(5)governing equations can be applied to both phases. The phases in this case have separate velocities and other related to the phases fields, but share the common pressure field. Additionally, the volume conservation equation, expressing the constraint that the volume fractions sum to unity , is relevant. In the above equations, r denotes the density, m the dynamic viscosity, p the pressure and U the velocity. A quantity subscribed with or refers to the value of the quantity of the particular phase or . S Ma denotes the momentum source due to external body forces. M a describes the interfacial forces acting on phase a due to the presence of phase , for which the drag force, was taken into account. The drag between the phases was modelled with a constant drag coefficient model, C D = 0.44 as the bubble Reynolds number was large enough to ensure domination of the inertial over the viscous effects. The interfacial transfer of momentum is determined by the contact surface area between the two phases.This is characterised by the interfacial area per unit volume between phase and phase , known as the interfacial area density . The interfacial area density between the continuous phase, the isopropanol, and the dispersed phase, the air,was modelled assuming that the air (phase ) is present as spherical particles of mean diameter = 1 mm according to (6)The turbulence was considered using phase-dependent turbulent models. For the gas phase the dispersed phase zero equation (AEA Technology and CFX International, 2004) was adopted. Different turbulence models, available in CFX TM software package, and their suitability have been considered for the liquid phase but the turbulence model was finally implemented because of numerical stability. Although the model is generally acknowledged as not suitable for rotating flow,