多层搅拌式生物反应器内溶液流变性质对流场特性影响的研究
|
摘要
目前计算流体力学(CFD)方法已经在生物过程反应器的设计和放大过程得到了应用。但是CFD方法与生物反应过程模型相结合来预测生物反应过程,并实现过程优化与放大是有困难的。反应器内多相流的流动、混合和传递过程是复杂和多维的,然而生物反应器内非牛顿型的发酵体系的流体动力学行为则更为复杂。本文以多层搅拌式生物反应器为对象,开展了单相、以及不同溶液中的气液两相流的实验流体力学与计算流体力学研究。
采用角度解析的大涡PIV流场测试技术发现径流RT和HBT桨在桨叶的后方形成一对相反方向的尾涡,而翼型WHHd和WHu桨在桨叶后方形成一个尾涡。并且发现角度解析的最大湍动能的值约为时间平均的最大湍动能的2倍,最大湍动能耗散率约为时间平均的最大湍动能耗散率的3.5倍。实验结果发现湍能耗散率积分值依赖于模型参数Cs,当取Cs=0.12,大涡PIV方法得到的湍动能耗散率体积积分的功率与扭矩的测得的功率便能相等。3RT桨的桨叶区的功率占22.1%,桨叶排出区占45.2%,主流区占32.7%。对于上翻操作的3WHu组合的桨叶区的功率占39.2%,桨叶排出区占23.3%,主流区占37.5%。组合桨中的每层桨都具有自己的特征。RT桨的最大湍动能耗散率与平均的湍动能耗散率的比值(εmax/εavg)的平均值为18.6,HBT桨的εmax/εavg为26.9～34.1,WHd桨的εmax/εavg的平均值为22.8,WHu桨的εmax/εavg的值为14.7～23.1。
空气-水溶液两相体系中,在低表观气速时(通气量为0.2vvm)上翻型搅拌器的传质能力优于下压型搅拌器,3WHu的传质系数比HBT+2WHd高53%, HBT+2WHu和3RT的传质能力居中。而表观气速较高时(通气量为1.0vvm),在相同的比功率输入情况下所有搅拌组合的传质能力相近。开发的三电导探针测得了局部的气含率表明：对于3RT,最高的气含率位于底层桨叶排出区,其次是中层和顶层桨排出流的上下方靠近壁面的位置。HBT+2WHd的底层桨的气含率与RT桨相似,主体区气含率分布比较均匀。HBT+2WHu和3WHu组合中,两层上翻型桨叶之间的气含率较高,项层桨上方的气含率相对较低。气泡的速度场分布表明在通气情况下,RT桨同样形成两个循环,但下方的循环比上方的更靠近器壁。在搅拌控制的条件下,混合时间随着通气量的增加而增加。总的来说,上翻型桨叶组合3WHu和HBT+2WHu组合的传质和混合特性是比较好的。
采用低浓度的CMC溶液替代菌丝发酵液来研究反应器内气泡大小和传质特性。发现相同功率输入时,上翻操作的桨型组合的气含率要高于下压操作以及3RT组合产生的气含率,气含率εG∝(正比于)(PG/V)0·3VG0.62。相同的通气功率下,Sauter平均直径大小依次是：3Whu>HBT+2WHu>HBT+2WHd>3RT,而相界面积大小排序是：3RT> HBT+2WHd>HBT+2WHu>3Whu,这是因为上翻桨叶气泡的聚并现象比较严重,Sauter平均直径d32∝(PG/V),)-0.12μGa0.32εG0.14,相间面积a∞(PG/V)-0.4VG0.5μa-0.5。低浓度的CMC溶液上翻操作的桨型组合的传质能力最好,但是随着粘度的增加,上翻桨叶组合的传质能力下降较快,气液传质系数kLα∝=(PG/V)0.5VG0.45μα-0.78。WHu、HBT+2WHu的kL是3RT、HBT+2WHd的kL的1.5-2倍,液相氧传质系数kL∝=(PG/V)0.11μα-0.24。气液传质依赖于桨型结构性质,实质是取决于不同桨型结构产生不同的流场,与物性一起决定了气泡的动力学和传质性能。
本文研究发现高粘黄原胶溶液要达到相同功率消耗,小直径桨型组合的转速随着浓度的增加而增加,而大直径桨型的转速随着浓度的增加而降低。局部kLα分布发现黄原胶溶液的浓度为1.Owt%时,小直径桨型组合罐内的流体混合较好,kLα分布比较均匀,但随黄原胶浓度增加时壁面基本上变成传递的死区。而大直径桨型组合除了罐底部区域,kLa基本分布比较均匀,但是随着浓度的增加,大直径桨型组合基本丧失了气体分散的能力。实验发现桨型组合的平均kLa值大小排序为3RT> HBT+2WHu> HBT+2WHd> EG> HBT+2MIG> HBT+DHR。且发现功率与表观粘度对kLα影响较大,通气量对kLα的影响较小。小直径桨组合的混合时间要大于大直径桨叶的组合,同时也发现粘度对混合时间的影响要大于功率消耗对混合时间的影响。
采用不同桨型组合研究流场特性对黑曲霉产糖化酶的发酵实验的影响。结果发现保证OUR趋势一致的情况下,三种桨型最终的转速3WHu>3RT> HBT+2WHu,对应的功率输入是3RT>3WHu> HBT+2WHu。而最终3RT的菌体酶活是最低的,上翻式桨叶组合HBT+2WHu和3WHu的菌体酶活比较接近。3RT由于高剪切而延迟菌球出现的时间并且菌球的浓度较低,上翻式桨叶组合由于较小的剪切,其菌球出现早而且其浓度也大于平叶桨的菌球浓度。发酵过程的发酵液流变特性的测试表明HBT+2WHu的表观粘度要低于3RT罐内的表观粘度。这也说明菌球的形成确实有利于降低发酵液的黏度,促进反应器的流动性,从而提高了产酶效率。建立了HBT+2WHu桨型组合的发酵过程kLa关联式。这些研究结果为未来的工艺优化及放大提供了有益的线索和理论指导。
对于3RT的单相数值模拟,基于雷诺平均的湍流粘性模型计算得到速度值比PIV测试值的要大,湍动能的值都要比实验值低40-80%。而LES得到的流场与PIV测试的非常相似,包括速度与湍动能分布,排出区的湍动能比实验值约低15-30%,主流区的湍动能和PIV测的湍动能吻合很好。对于气液两相流的模拟采用CFD和PBM耦合求解。采用Ishii-Zuber曳力模型模拟形成的气含率较低,改用修正的Brucato曳力模型能获得比较满意的气含率。High Resolution对流差分格式与修正的Brucato曳力模型,增强系数4.5×10-6的模拟方法预测的气含率、相界面积以及kLα与实验值比较接近。kLα的增加是其通过增加曳力来增加相界面积,且认为CFD模拟的kLα值比实验值低的主要原因是低估了罐内的湍动能耗散率,其次低估了曳力。
Computational fluid dynamics (CFD) method has been used in the bio-process for reactor design and process optimization. Combination CFD method with bio-processes model to predict bio-processes and achieve process optimization is difficult. The flow field, mixing and mass transfer of multiphase flow are very complex. The hydrodynamic of the bioreactors are more complex due to the non-Newtonian broths. In this paper, stirred bioreactors with multiple impellers were employed to study the hydrodynamics in single-phase and gas-liquid flow with different media by experimental and CFD methods.
It can be found that there are a pair of trailing vortices behind the blade of RT and HBT impellers, while only a trailing vortex behind the blade of WHd and WHu impellers by the angle-resolved large eddy PIV measurement techniques. The maximum turbulent kinetic energy of angle-resolved is about2times of that obtained by the time-averaged, and maximum turbulent energy dissipation is about3.5times of that obtained by time-averaged. When Cs=0.12, the power getted from volume integral of turbulent energy dissipation is equal to the power calculated by the measured torque. For3RT,22.1%of the total input energy is dissipated in the impeller region,45.2%in the stream region and32.7%in the remaining volume of the tank. For3WHu,39.2%of the total input energy is dissipated in the impeller region,23.3%in the stream region and37.5%in the remaining volume of the tank. Each impeller of the combination has own characteristic even the same type. εmax/εavg is the ratio of maximum turbulent energy dissipation to the average turbulent energy dissipation. The average εmax/εavg of RT impellers is18.6, the εmax/εavg of HBT impellers is26.9-34.1, the average εmax/εavg of WHd impellers is22.8, the εmax/εavg of WHu impellers is14.7-23.1.
In the air-water system,3WHu produces53%higher mass transfer coefficient than HBT+2WHd, HBT+2WHu and3RT lie between them at gas superficial velocity. At high gas superficial velocity, however, all the tested configurations give almost similar mass transfer coefficient under equivalent power input. For3RT, highest hold-up is in the bottom impeller discharge stream and near the wall for the middle and top impellers. For the HBT+2WHd combination, there was no large variations of gas hold up in the bulk except region around the bottom impeller. For HBT+2WHu and3WHu, high gas hold-up was observed between the two up pumping impellers, and moderately low gas hold-up above the top impeller. Under gassed condition, each RT also generates two loops, but the lower loop is more near the wall than the upper loop. the mixing time increases with the gas flow rate increases in the agitator-dominated regime. Overall, mass transfer and mixing characteristics are quite good for the3WHu and HBT+2WHu combinations.
CMC solutions with different concentrations which are preferred to mycelial fermentation broth were used for the study of bubble size and mass transfer characteristics in bioreactor. At same power input, the impeller combinations with up-pumping produce higher gas holdup than that of other combinations, gas holdup εG∝(PG/V)0.3VG0.62. At same power input, the rank of Sauter mean diameter is:3Whu> HBT+2WHu> HBT+2WHd>3RT, and the rank of interfacial area is:3RT> HBT+2WHd> HBT+2WHu>3Whu, this is due to more bubble coalescence for up-pumping impeller. Sauter mean diameter d32∝(PG/V)-0.12μα0.32εG0.14, while interfacial area α∝(PG/V)-0.14VG0.5μα-0.5. At low concentration of CMC solutions, impeller combinations with up-pumping give best mass transfer, the mass transfer coefficient kLα∝(PG/V)0.5VG0.45μα-0.78. Liquid phase mass transfer coefficient kL of WHu and HBT+2WHu is1.5-2times higher than that of3RT and HBT+2WHd, and kL∝(PG/V)0.11μα-0.24. Mass transfer depends on the flow fields gernerated by impellers and physical properties, because they determine the bubble dynamics and mass transfer performance.
For highly viscosity xanthan gum solutions, in order to gain the same power input, the rotating speed of "small-diameter" impeller combinations increases as the concentration of xanthan gum increases, while it decrease for "large-diameter" impeller combinations.. For the "small-diameter" impeller combinations, the kLα value near the wall drop faster than other areas as the concentration of xanthan gum increases. While for the "large-diameter" impeller combinations, the kLα distribution is homogenous except the bottom area but with poor gas dispersion capability as concentration of xanthan gum increases. The rank of average kLα is:3RT> HBT+2WHu> HBT+2WHd> EG> HBT+2MIG> HBT+DHR. The obtained correlation shows that the kLα is heavily depend on specific power and viscosity, but less influenced by the gassing rate. The mixing time of small-diameter impeller combinations is greater than that of large-diameter combinations, the effect of viscosity on the mixing time is greater than that of power consumption on the mixing time.
The fermentation of Aspergillus niger to produce glucoamylase with different impeller combinations, in order to keep same OUR, the final impeller speed is3WHu>3RT> HBT+2WHu, corresponds to the power input is3RT>3WHu> HBT+2WHu. Ultimately, the emzyme activity of3RT is the lowest, the emzyme activity of HBT+2WHu and3WHu are closer. High shear strain rate of3RT delays the formation of pellets and gains lower pellet concentration. Howerver, low shear strain rate of HBT+2WHu accelerates the formation of pellets and gains higher pellet concentration. The rheological properties of the fermentation broth show that the apparent viscosity in the bioreactor with HBT+2WHu is lower than that in the bioreactor with3RT. This also show that the formation of pellets do help to reduce the viscosity of the fermentation broth, and promote the mobility of the reactor, thereby increase the production efficiency of enzyme. Impellers with up-pumping have excellent mixing and low shear rate for the fermentation of filamentous fungi, and the kLα correlation for fermentation process have established for HBT+2WHu. These results provide useful clues and theoretical guidance for future process optimization.
For the single-phase numerical simulation of3RT, the speeds obtained from Reynolds-averaged turbulence model are larger than the PIV data, but turbulent kinetic energy values are40-80%lower than the experimental values. The flow field getted by LES simulation are very similar with the PIV results, the values of turbulent energy dissipation are approximately15-30%lower than that of the experimental values in the stream region. The values of turbulent kinetic energy in other regions agree well with PIV results. CFD coupled PBM model was employed for numerical simulation of multi-phase flow. Simulated gas holdup is low using Ishii-Zuber drag force model. The modified Brucato drag force model can obtain satisfactory gas holdup. The simulation method of Hi Resolution convection difference scheme combining modified Brucato drag force model, enhancement factor4.5×10-6can predict well the gas holdup, interfacial area and kLα. the kLα value increases is due to the increase of the interfacial area results from the increase of drag force. The simulated kLα value is ower than the experimental value is mainly due to underestimation of the turbulent energy dissipation in the tank, followed by underestimation of the drag force.
采用角度解析的大涡PIV流场测试技术发现径流RT和HBT桨在桨叶的后方形成一对相反方向的尾涡,而翼型WHHd和WHu桨在桨叶后方形成一个尾涡。并且发现角度解析的最大湍动能的值约为时间平均的最大湍动能的2倍,最大湍动能耗散率约为时间平均的最大湍动能耗散率的3.5倍。实验结果发现湍能耗散率积分值依赖于模型参数Cs,当取Cs=0.12,大涡PIV方法得到的湍动能耗散率体积积分的功率与扭矩的测得的功率便能相等。3RT桨的桨叶区的功率占22.1%,桨叶排出区占45.2%,主流区占32.7%。对于上翻操作的3WHu组合的桨叶区的功率占39.2%,桨叶排出区占23.3%,主流区占37.5%。组合桨中的每层桨都具有自己的特征。RT桨的最大湍动能耗散率与平均的湍动能耗散率的比值(εmax/εavg)的平均值为18.6,HBT桨的εmax/εavg为26.9～34.1,WHd桨的εmax/εavg的平均值为22.8,WHu桨的εmax/εavg的值为14.7～23.1。
空气-水溶液两相体系中,在低表观气速时(通气量为0.2vvm)上翻型搅拌器的传质能力优于下压型搅拌器,3WHu的传质系数比HBT+2WHd高53%, HBT+2WHu和3RT的传质能力居中。而表观气速较高时(通气量为1.0vvm),在相同的比功率输入情况下所有搅拌组合的传质能力相近。开发的三电导探针测得了局部的气含率表明：对于3RT,最高的气含率位于底层桨叶排出区,其次是中层和顶层桨排出流的上下方靠近壁面的位置。HBT+2WHd的底层桨的气含率与RT桨相似,主体区气含率分布比较均匀。HBT+2WHu和3WHu组合中,两层上翻型桨叶之间的气含率较高,项层桨上方的气含率相对较低。气泡的速度场分布表明在通气情况下,RT桨同样形成两个循环,但下方的循环比上方的更靠近器壁。在搅拌控制的条件下,混合时间随着通气量的增加而增加。总的来说,上翻型桨叶组合3WHu和HBT+2WHu组合的传质和混合特性是比较好的。
采用低浓度的CMC溶液替代菌丝发酵液来研究反应器内气泡大小和传质特性。发现相同功率输入时,上翻操作的桨型组合的气含率要高于下压操作以及3RT组合产生的气含率,气含率εG∝(正比于)(PG/V)0·3VG0.62。相同的通气功率下,Sauter平均直径大小依次是：3Whu>HBT+2WHu>HBT+2WHd>3RT,而相界面积大小排序是：3RT> HBT+2WHd>HBT+2WHu>3Whu,这是因为上翻桨叶气泡的聚并现象比较严重,Sauter平均直径d32∝(PG/V),)-0.12μGa0.32εG0.14,相间面积a∞(PG/V)-0.4VG0.5μa-0.5。低浓度的CMC溶液上翻操作的桨型组合的传质能力最好,但是随着粘度的增加,上翻桨叶组合的传质能力下降较快,气液传质系数kLα∝=(PG/V)0.5VG0.45μα-0.78。WHu、HBT+2WHu的kL是3RT、HBT+2WHd的kL的1.5-2倍,液相氧传质系数kL∝=(PG/V)0.11μα-0.24。气液传质依赖于桨型结构性质,实质是取决于不同桨型结构产生不同的流场,与物性一起决定了气泡的动力学和传质性能。
本文研究发现高粘黄原胶溶液要达到相同功率消耗,小直径桨型组合的转速随着浓度的增加而增加,而大直径桨型的转速随着浓度的增加而降低。局部kLα分布发现黄原胶溶液的浓度为1.Owt%时,小直径桨型组合罐内的流体混合较好,kLα分布比较均匀,但随黄原胶浓度增加时壁面基本上变成传递的死区。而大直径桨型组合除了罐底部区域,kLa基本分布比较均匀,但是随着浓度的增加,大直径桨型组合基本丧失了气体分散的能力。实验发现桨型组合的平均kLa值大小排序为3RT> HBT+2WHu> HBT+2WHd> EG> HBT+2MIG> HBT+DHR。且发现功率与表观粘度对kLα影响较大,通气量对kLα的影响较小。小直径桨组合的混合时间要大于大直径桨叶的组合,同时也发现粘度对混合时间的影响要大于功率消耗对混合时间的影响。
采用不同桨型组合研究流场特性对黑曲霉产糖化酶的发酵实验的影响。结果发现保证OUR趋势一致的情况下,三种桨型最终的转速3WHu>3RT> HBT+2WHu,对应的功率输入是3RT>3WHu> HBT+2WHu。而最终3RT的菌体酶活是最低的,上翻式桨叶组合HBT+2WHu和3WHu的菌体酶活比较接近。3RT由于高剪切而延迟菌球出现的时间并且菌球的浓度较低,上翻式桨叶组合由于较小的剪切,其菌球出现早而且其浓度也大于平叶桨的菌球浓度。发酵过程的发酵液流变特性的测试表明HBT+2WHu的表观粘度要低于3RT罐内的表观粘度。这也说明菌球的形成确实有利于降低发酵液的黏度,促进反应器的流动性,从而提高了产酶效率。建立了HBT+2WHu桨型组合的发酵过程kLa关联式。这些研究结果为未来的工艺优化及放大提供了有益的线索和理论指导。
对于3RT的单相数值模拟,基于雷诺平均的湍流粘性模型计算得到速度值比PIV测试值的要大,湍动能的值都要比实验值低40-80%。而LES得到的流场与PIV测试的非常相似,包括速度与湍动能分布,排出区的湍动能比实验值约低15-30%,主流区的湍动能和PIV测的湍动能吻合很好。对于气液两相流的模拟采用CFD和PBM耦合求解。采用Ishii-Zuber曳力模型模拟形成的气含率较低,改用修正的Brucato曳力模型能获得比较满意的气含率。High Resolution对流差分格式与修正的Brucato曳力模型,增强系数4.5×10-6的模拟方法预测的气含率、相界面积以及kLα与实验值比较接近。kLα的增加是其通过增加曳力来增加相界面积,且认为CFD模拟的kLα值比实验值低的主要原因是低估了罐内的湍动能耗散率,其次低估了曳力。
Computational fluid dynamics (CFD) method has been used in the bio-process for reactor design and process optimization. Combination CFD method with bio-processes model to predict bio-processes and achieve process optimization is difficult. The flow field, mixing and mass transfer of multiphase flow are very complex. The hydrodynamic of the bioreactors are more complex due to the non-Newtonian broths. In this paper, stirred bioreactors with multiple impellers were employed to study the hydrodynamics in single-phase and gas-liquid flow with different media by experimental and CFD methods.
It can be found that there are a pair of trailing vortices behind the blade of RT and HBT impellers, while only a trailing vortex behind the blade of WHd and WHu impellers by the angle-resolved large eddy PIV measurement techniques. The maximum turbulent kinetic energy of angle-resolved is about2times of that obtained by the time-averaged, and maximum turbulent energy dissipation is about3.5times of that obtained by time-averaged. When Cs=0.12, the power getted from volume integral of turbulent energy dissipation is equal to the power calculated by the measured torque. For3RT,22.1%of the total input energy is dissipated in the impeller region,45.2%in the stream region and32.7%in the remaining volume of the tank. For3WHu,39.2%of the total input energy is dissipated in the impeller region,23.3%in the stream region and37.5%in the remaining volume of the tank. Each impeller of the combination has own characteristic even the same type. εmax/εavg is the ratio of maximum turbulent energy dissipation to the average turbulent energy dissipation. The average εmax/εavg of RT impellers is18.6, the εmax/εavg of HBT impellers is26.9-34.1, the average εmax/εavg of WHd impellers is22.8, the εmax/εavg of WHu impellers is14.7-23.1.
In the air-water system,3WHu produces53%higher mass transfer coefficient than HBT+2WHd, HBT+2WHu and3RT lie between them at gas superficial velocity. At high gas superficial velocity, however, all the tested configurations give almost similar mass transfer coefficient under equivalent power input. For3RT, highest hold-up is in the bottom impeller discharge stream and near the wall for the middle and top impellers. For the HBT+2WHd combination, there was no large variations of gas hold up in the bulk except region around the bottom impeller. For HBT+2WHu and3WHu, high gas hold-up was observed between the two up pumping impellers, and moderately low gas hold-up above the top impeller. Under gassed condition, each RT also generates two loops, but the lower loop is more near the wall than the upper loop. the mixing time increases with the gas flow rate increases in the agitator-dominated regime. Overall, mass transfer and mixing characteristics are quite good for the3WHu and HBT+2WHu combinations.
CMC solutions with different concentrations which are preferred to mycelial fermentation broth were used for the study of bubble size and mass transfer characteristics in bioreactor. At same power input, the impeller combinations with up-pumping produce higher gas holdup than that of other combinations, gas holdup εG∝(PG/V)0.3VG0.62. At same power input, the rank of Sauter mean diameter is:3Whu> HBT+2WHu> HBT+2WHd>3RT, and the rank of interfacial area is:3RT> HBT+2WHd> HBT+2WHu>3Whu, this is due to more bubble coalescence for up-pumping impeller. Sauter mean diameter d32∝(PG/V)-0.12μα0.32εG0.14, while interfacial area α∝(PG/V)-0.14VG0.5μα-0.5. At low concentration of CMC solutions, impeller combinations with up-pumping give best mass transfer, the mass transfer coefficient kLα∝(PG/V)0.5VG0.45μα-0.78. Liquid phase mass transfer coefficient kL of WHu and HBT+2WHu is1.5-2times higher than that of3RT and HBT+2WHd, and kL∝(PG/V)0.11μα-0.24. Mass transfer depends on the flow fields gernerated by impellers and physical properties, because they determine the bubble dynamics and mass transfer performance.
For highly viscosity xanthan gum solutions, in order to gain the same power input, the rotating speed of "small-diameter" impeller combinations increases as the concentration of xanthan gum increases, while it decrease for "large-diameter" impeller combinations.. For the "small-diameter" impeller combinations, the kLα value near the wall drop faster than other areas as the concentration of xanthan gum increases. While for the "large-diameter" impeller combinations, the kLα distribution is homogenous except the bottom area but with poor gas dispersion capability as concentration of xanthan gum increases. The rank of average kLα is:3RT> HBT+2WHu> HBT+2WHd> EG> HBT+2MIG> HBT+DHR. The obtained correlation shows that the kLα is heavily depend on specific power and viscosity, but less influenced by the gassing rate. The mixing time of small-diameter impeller combinations is greater than that of large-diameter combinations, the effect of viscosity on the mixing time is greater than that of power consumption on the mixing time.
The fermentation of Aspergillus niger to produce glucoamylase with different impeller combinations, in order to keep same OUR, the final impeller speed is3WHu>3RT> HBT+2WHu, corresponds to the power input is3RT>3WHu> HBT+2WHu. Ultimately, the emzyme activity of3RT is the lowest, the emzyme activity of HBT+2WHu and3WHu are closer. High shear strain rate of3RT delays the formation of pellets and gains lower pellet concentration. Howerver, low shear strain rate of HBT+2WHu accelerates the formation of pellets and gains higher pellet concentration. The rheological properties of the fermentation broth show that the apparent viscosity in the bioreactor with HBT+2WHu is lower than that in the bioreactor with3RT. This also show that the formation of pellets do help to reduce the viscosity of the fermentation broth, and promote the mobility of the reactor, thereby increase the production efficiency of enzyme. Impellers with up-pumping have excellent mixing and low shear rate for the fermentation of filamentous fungi, and the kLα correlation for fermentation process have established for HBT+2WHu. These results provide useful clues and theoretical guidance for future process optimization.
For the single-phase numerical simulation of3RT, the speeds obtained from Reynolds-averaged turbulence model are larger than the PIV data, but turbulent kinetic energy values are40-80%lower than the experimental values. The flow field getted by LES simulation are very similar with the PIV results, the values of turbulent energy dissipation are approximately15-30%lower than that of the experimental values in the stream region. The values of turbulent kinetic energy in other regions agree well with PIV results. CFD coupled PBM model was employed for numerical simulation of multi-phase flow. Simulated gas holdup is low using Ishii-Zuber drag force model. The modified Brucato drag force model can obtain satisfactory gas holdup. The simulation method of Hi Resolution convection difference scheme combining modified Brucato drag force model, enhancement factor4.5×10-6can predict well the gas holdup, interfacial area and kLα. the kLα value increases is due to the increase of the interfacial area results from the increase of drag force. The simulated kLα value is ower than the experimental value is mainly due to underestimation of the turbulent energy dissipation in the tank, followed by underestimation of the drag force.
引文
[1]张嗣良.发酵工程技术发展现状与趋势.生物产业技术.2011,(1)：26-32.
[2]H. Unadkat, C. D. Rielly, et al. PIV study of the flow field generated by a sawtooth impeller. Chemical Engineering Science.2011,66(21):5374-5387.
[3]A. Gabriele, A. W. Nienow, et al. Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank. Chemical Engineering Science.2009,64(1):126-143.
[4]N. N. Clark, R. Turton. Chord length distributions related to bubble size distributions in multiphase flows. International Journal of Multiphase Flow.1988,14(4):413-424.
[5]W. Liu, N. N. Clark. Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters. International Journal of Multiphase Flow.1995,21(6):1073-1089.
[6]K. E. Morud, B. H. Hjertager. LDA measurements and CFD modelling of gas-liquid flow in a stirred vessel. Chemical Engineering Science.1996,51(2):233-249.
[7]A. A. Kulkarni, J. B. Joshi, et al. Simultaneous measurement of hold-up profiles and interfacial area using LDA in bubble columns:predictions by multiresolution analysis and comparison with experiments. Chemical Engineering Science.2001,56(21-22):6437-6445.
[8]V. V. Ranade, M. Perrard, et al. Influence of Gas Flow Rate on the Structure of Trailing Vortices of a Rushton Turbine:PIV Measurements and CFD Simulations. Chemical Engineering Research and Design.2001,79(8):957-964.
[9]A. R. Khopkar, A. R. Rammohan, et al. Gas-liquid flow generated by a Rushton turbine in stirred vessel:CARPT/CT measurements and CFD simulations. Chemical Engineering Science.2005,60(8-9):2215-2229.
[10]M. Barigou, M. Greaves. Bubble-size distributions in a mechanically agitated gas—liquid contactor. Chemical Engineering Science.1992,47(8):2009-2025.
[11]K. Takahashi, W. J. McManamey, et al. Bubble size distributions in impeller region in a gas-sparged vessel agitated by a Rushton turbine. Journal of Chemical Engineering of Japan.1992,25:427-432.
[12]V. Machon, A. W. Pacek, et al. Bubble Sizes in Electrolyte and Alcohol Solutions in a Turbulent Stirred Vessel. Chemical Engineering Research and Design.1997,75(3):339-348.
[13]M. Laakkonen, P. Moilanen, et al. Local Bubble Size Distributions in Agitated Vessel: Comparison of Three Experimental Techniques. Chemical Engineering Research and Design.2005,83(1):50-58.
[14]G. A. Hughmark. Power Requirements and Interfacial Area in Gas-Liquid Turbine Agitated Systems. Industrial & Engineering Chemistry Process Design and Development. 1980,19(4):638-641.
[15]B. J. Michel, S. A. Miller. Power requirements of gas-liquid agitated systems. AICHE Journal.1962,8(2):262-266.
[16]S. Nagata. Mixing principle and application. Tokyo:A Halsted press.1975.
[17]A. W. Nienow, D. J. Wisdom, et al. The effect of scale and geometry on flooding, recirculation, and power in gassed stirred vessels [M]. Second European Conf on Mixin. Cambridge, England.1977.
[18]A. W. Nienow, H. Liu, et al. The use of large ring spargars to improve the performance of fermenters agitated by single and multiple standard rushton turbines [M].2th Int Conf on Bioreactor fluid dynamics. Cambridge, Engiand.1988.
[19]K. Van't Riet, J. Tramper. Basic Bioreactor Design. New York Marcel Dekker, Inc. 1991.
[20]Warmoeskerker, G. M.M.C, et al. Impeller loading in multi-turbine vessels [M].2th Int Conf on Bioreactor fluid dynamics. held at Cambridge, England.1988.
[21]Y. Q. Cui, R. G. J. M. van der Lans, et al. Local power uptake in gas-liquid systems with single and multiple rushton turbines. Chemical Engineering Science.1996,51(11):2631-2636.
[22]T. Koloni, I. Plazl, et al. Power consumption, gas hold-up and interfacial area in aerated non-newtonian suspensions in stirred tanks of square cross-section. Chem Eng Res Des. 1989,67:526-536.
[23]T. Moucha, V. Linek, et al. Improved power and mass transfer correlations for design and scale-up of multi-impeller gas-liquid contactors. Chemical Engineering Science.2009, 64(3):598-604.
[24]M. Taghavi, R. Zadghaffari, et al. Experimental and CFD investigation of power consumption in a dual Rushton turbine stirred tank. Chemical Engineering Research and Design.2011,89(3):280-290.
[25]S. M. Kresta, P. E. Wood. The flow field produced by a pitched blade turbine: Characterization of the turbulence and estimation of the dissipation rate. Chemical Engineering Science.1993,48(10):1761-1774.
[26]H. Wu, G. K. Patterson. Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer. Chemical Engineering Science.1989,44(10):2207-2221.
[27]R. Escudie, A. Line. Experimental analysis of hydrodynamics in a radially agitated tank. AICHE Journal.2003,49(3):585-603.
[28]K. V. Sharp, R. J. Adrian. PIV study of small-scale flow structure around a Rushton turbine. AICHE Journal.2001,47(4):766-778.
[29]S. Michelet. Turbulence et Dissipation au Sein d'un Re'acteur agite'parune Turbine Rushton-Ve 'locime' trie Laser Doppler a'Deux de Mesure. [D]. Lorraine, France; L Institut National Polytechnique de Lorraine,1998.
[30]A. Ducci, M. Yianneskis. Direct determination of energy dissipation in stirred vessels with two-point LDA. AICHE Journal.2005,51(8):2133-2149.
[31]P. Saarenrinne, M. Piirto, et al. Experiences of turbulence measurement with PIV. Measurement Science and Technology.2001,12(11):1904.
[32]J. Sheng, H. Meng, et al. A large eddy PIV method for turbulence dissipation rate estimation. Chemical Engineering Science.2000,55(20):4423-4434.
[33]J. Smagorinsky. General circulation experiments with the primitive equation 1 the basic experiment. Monthly Weather Review.1963,91(3):99-164.
[34]S. Liu, C. Meneveau, et al. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. Journal of Fluid Mechanics.1994,275(-1):83-119.
[35]R. A. Clark, J. H. Ferziger, et al. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J Fluid Mech.1979,91(1):1-16.
[36]G. Zhou, S. M. Kresta. Impact of tank geometry on the maximum turbulence energy dissipation rate for impellers. AICHE Journal.1996,42(9):2476-2490.
[37]S. Baldi, M. Yianneskis. On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements. Chemical Engineering Science.2004,59(13):2659-2671.
[38]F. R. Khan. Investigation of Turbulent Flows and Instabilities in a Stirred Vessel Using Particle Image Velocimetry [D]. Loughborough, UK; Loughborough University,2005.
[39]S. Baldi, M. Yianneskis. On the Direct Measurement of Turbulence Energy Dissipation in Stirred Vessels with PIV. Industrial& Engineering Chemistry Research.2003,42(26): 7006-7016.
[40]J. Kilander, A. Rasmuson. Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements. Chemical Engineering Science. 2005, 60(24): 6844-6856.
[41]W.-M. Lu, S.-J. Ju. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. The Chemical Engineering Journal. 1987, 35(1): 9-17.
[42]V. V. Ranade, M. Pcrrard, ct al. Trailing Vortices of Rushton Turbine: PIV Measurements and CFD Simulations with Snapshot Approach. Chemical Engineering Research and Design. 2001,79(1): 3-12.
[43]N. Deen. An Experimental and Computational Study of Fluid Dynamics in Gas-Liquid Chemical Reactors [D]. Esbjerg; Aalborg University, 2001.
[44]B. Loiseau, N. Midoux, et al. Some hydrodynamics and power input data in mechanically agitated gas-liquid contactors. AICHE Journal. 1977, 23(6): 931-935.
[45]N. Midoux, J. C. Charpenticr. Mechanically agitated gas-liquid reactors parti: Hydrodynamics. International Chemical Engineering. 1984, 24: 249-287.
[46]Y. Nagase, II. Yasui. Fluid motion and mixing in a gas-liquid contactor with turbine agitators Chemical Engineering Journal. 1983, 27: 33.
[47]I. Zun, B. Fiiipic, et al. Phase discrimination in void fraction measurements via genetic algorithms. Review of Scientific Instruments. 1995, 66(10): 5055-5064.
[48]A. Bombac, I. Zun, et al. Gas-filled cavity structures and local void fraction distribution in aerated stirred vessel. AICI IE Journal. 1997, 43( 11): 2921 -2931.
[49]J. O. Hinze. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AICI IE Journal. 1955, 1(3): 289-295.
[50]P. H. Calderbank. The interfacial area in gas-liquid contacting with mechanical agitation. Trans Instrum Chem Eng. 1958, 36: 443-463.
[51]S. P. S. Andrews. Gas-liquid mass transfer in microbiological reactors. Trans IChemE. 1982,60: 3-10.
[52]R. Parthasarathy, G. J. Jameson, et al. Bubble break-up in stirred vessels predicting the Sauter mean diameter. Trans IChemE Symposium Series. 1991, 69(A): 295-301.
[53]R. Parthasarathy, N. M. Ahmed. Sauter mean and maximum bubble diameters in aerated stirred vessels. Trans IChemE. 1994, 72(A): 565-572.
[54]S. S. Alves, C. I. Maia, ct al. Bubble size in aerated stirred tanks. Chemical Engineering Journal. 2002, 89(1-3): 109-117.
[55]T. Martin, C. M. Me Farlane, et al. The influence of liquid properties and impeller type on bubble coalescence behaviour and mass transfer in sparged, agitated reactors. Institution of Chemical Engineers Symposium Series. 1994, 136: 57-64.
[56]M. Bouaifi, M. Roustan. Bubble size and mass transfer coefficients in dual-impeller agitated reactors. Canadian Journal of Chemical Engineering. 1998. 76(3): 390-397.
[57]M. Laakkonen, P. Moilanen, et al. Local bubble size distributions in agitated vessels Chemical Engineering Journal. 2005. 106(2): 133-143.
[58j G. Montante, D. Horn, et al. Gas-liquid flow and bubble size distribution in stirred tanks. Chemical Engineering Science. 2008. 63(8): 2107-2118.
[59]Y. Bao, L. Chen, et al. Local void fraction and bubble size distributions in cold-gassed and hot-sparged stirred reactors. Chemical Engineering Science. 2010, 65(2): 976-984.
[60]T. Sridhar, O. E. Potter. Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels. Industrial & Engineering Chemistry Fundamentals. 1980, 19(1): 21-26.
[61]M. Barigou, M. Greaves. Gas holdup and interfacial area distributions in a mechanically agitated gas-liquid contactor. Chemical Engineering Research and Design. 1996, 74: 397-405.
[62]H. Yagi, F. Yoshida. Gas Absorption by Newtonian and Non-Newtonian Fluids in Sparged Agitated Vessels. Industrial & Engineering Chemistry Process Design and Development. 1975, 14(4): 488-493.
[63]M. M. L. de Figueiredo, P. II. Calderbank. The scale-up of aerated mixing vessels for specified oxygen dissolution rates. Chemical Engineering Science.1979,34(11):1333-1338.
[64]K. Van't Riet. Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels. Industrial & Engineering Chemistry Process Design and Development.1979,18(3):357-364.
[65]M. Nishikawa, M. Nakamura, et al. Gas absorption in aerated mixing vessels. Journal of Chemical Engineering of Japan.1981,14:219-226.
[66]K. Chandrasekharan, P. H. Calderbank. Further observations on the scale-up of aerated mixing vessels. Chemical Engineering Science.1981,36:819-823.
[67]S. M. Davies, L. G. Gibilaro, et al. The application of two novel techniques for mass transfer coefficient determination to the scale up of gas sparged agitated vessels [M]. Proc Eur Conf Mix.1985.
[68]V. Linek, J. Sinkule, et al. Critical assessment of gassing-in method measuring kLa in fermentors. Biotechnol Bioeng.1991,38:323-330.
[69]A. G. Pedersen, M. Bundgaard-Nielsen, et al. Characterization of mixing in stirred tank bioreactors equipped with Rushton turbines. Biotechnology and Bioengineering.1994, 44(Compendex):1013-1017.
[70]H. Gagnon, M. Lounes, et al. Power consumption and mass transfer in agitated gas-liquid columns:A comparative study. The Canadian Journal of Chemical Engineering.1998, 76(3):379-389.
[71]S. J. Arjunwadkar, K. Sarvanan, et al. Gas-liquid mass transfer in dual impeller bioreactor. Biochemical Engineering Journal.1998,1(2):99-106.
[72]J. M. T. Vasconcelos, S. C. P. Orvalho, et al. Effect of Blade Shape on the Performance of Six-Bladed Disk Turbine Impellers. Industrial and Engineering Chemistry Research.2000, 39(1):203-213.
[73]F. Garcia-Ochoa, E. Gomez. Mass transfer coefficient in stirred tank reactors for xanthan gum solutions. Biochemical Engineering Journal.1998,1(1):1-10.
[74]M. S. Puthli, V. K. Rathod, et al. Gas-liquid mass transfer studies with triple impeller system on a laboratory scale bioreactor. Biochemical Engineering Journal.2005,23(1): 25-30.
[75]Y. Zhu, P. C. Bandopadhayay, et al. Measurement of Gas-Liquid Mass Transfer in an Agitated Vessel— A Comparison between Different Impellers. Journal of Chemical Engineering of Japan.2001,34(5):579-584.
[76]M. S. Puthli, V. K. Rathod, et al. Gas-liquid mass transfer studies with triple impeller system on a laboratory scale bioreactor. Biochemical engineering journal.2005,23(1):25-30.
[77]J. F. Perez, O. C. Sandall. Gas absorption by non-Newtonian fluids in agitated vessels. AICHE Journal.1974,20:770-775.
[78]E. Costa, A. Lucas, et al. Transferencia de materia en tanques agitados:burbujeo de gases en liquidos newtonianos y no newtonianos. I. Turbinas de 6 paletas y difusor plano. An Quim.1982,78:387-392.
[79]R. S. Albal, Y. T. Shah, et al. Mass transfer in multiphase agitated contactors. Chem Eng J. 1983,27:61-80.
[80]V. Schluter, W. D. Deckwer. Gas/liquid mass transfer in stirred vessels. Chemial Engineering Science.1992,47:2357-2362.
[81]W. G. Whitman. Preliminary experimental confirmation of the two-film theory of gas absorption. Chem Metall Eng.1923,29:146-169.
[82]R. Higbie. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Inst Chem Eng.1935,35:36-60.
[83]P. V. Danckwerts. Significance of liquid-film coefficients in gas absorption. Ind Eng Chem. 1951,43:1460-1467.
[84]J. C. Lamont, D. S. Scott. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChEJ. 1970, 16(513-519):
[85]H. L. Toor, J. M. Marchelo. Film-penetration model for mass transfer and heat transfer. AIChEJ 1958,4:97-101.
[86]II. Hocker, G. Langer, et al. Mass transfer in aerated Newtonian and non-Newtonian liquids in stirred reactors. Ger Chem Eng 1981, 4: 51-62.
[87]J. B. Joshi. Computational flow modelling and design of bubble column reactors. Chemical Engineering Science. 2001, 56(21-22): 5893-5933.
[88]M. Ishii, N. Zuber. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AICHE Journal. 1 979, 25: 843-855.
[89]M. Atenas, M. Clark, et al. Holdup and Liquid Circulation Velocity in a Rectangular Air-Lift Bioreactor. Industrial & Engineering Chemistry Research. 1999, 38(3): 944-949.
[90]M. Rafique, P. Chen, et al. Computational modeling of gas-liquid flow in bubble columns. Reviews in Chemical Engineering. 2004, 20: 225-375.
[91]N. H. Thomas, T. R. Auton, et al. Entrapment and transport of bubbles in transient large eddies in multiphase turbulent shear flows. International Conference on the Physical Modelling of Multiphase Flows. 1983: 169-184.
192] A. Tomiyama. Struggle with computational bubble dynamics. Multiphase Sci Tech. 1998, 10:369-405.
[93]S. Ledakowicz, M. Stelmachowski, et al. Mcthanol synthesis in bubble column slurry reactors. Chem ling Proc. 1992, 31(4): 213-219.
[94]T. Frank, A. D. B. Bums, et al. Drag model for turbulent dispersion in Eulerian multi-phase flows [M]. Insthlntemational Conference on Multi PhaseFlow. Yokohama,Japan. 2004.
[95]S. P. Antal, R. T. Lahey, et al. Analysis of phase distribution in fully developed laminar bubble two-phase flow. International Journal of Multiphase Flow. 1991, 17: 635-652.
[96]P. Ranganathan, S. Sivaraman. Investigations on hydrodynamics and mass transfer in gas-liquid stirred reactor using computational fluid dynamics. Chemical Engineering Science. 2011, 66(14): 3108-3124.
[97]R. I. Issa, A. D. Gosman. The computation of three dimensional turbulent two-phase flows in mixer vessels [M]. Numerical Methods in Laminar and Turbulent Flow. Swansea; Pineridge Press. 1981:827-839.
[98]A. D. Gosman, C. Lekakou, et al. Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE Journal. 1992, 38(12): 1946-1956.
[99]W. A. M. Bakker. H. J. L. van Can, et al. Hydrodynamics and mixing in a multiple air-lift loop reactor. Biotechnology and Bioengineering. 1993, 42(8): 994-1001.
[100]M. J. Prince, H. W. Blanch. Bubble coalescence and break-up in air-sparged bubble columns. AICIIE Journal. 1990. 36(10): 1485-1499.
[101]S. Kumar, D. Ramkrishna. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science. 1996, 51(8): 1311-1332.
[102]H. Euo, H. F. Svendsen. Theoretical model for drop and bubble breakup in turbulent dispersions. AICIIE Journal. 1996, 42(5): 1225-1233.
[103]G. Fleisher, S. Becker, et al. Detailed modeling of the chemisorption of CO? into NaOH in a bubble column. Chemical Engineering Science. 1996, 51: 1715-1724.
[104]D. P. Patil, J. R. G. Andrews. An analytical solution to continuous population balance model describing floe coalescence and breakage-A special case. Chemical Engineering Science. 1998, 53(3): 599-601.
[105]S. E. Pratsinis, S. K. Friedlander, et al. Aerosol reactor theory: Stability and dynamics of a continuous stirred tank aerosol reactor. AICHE Journal. 1986, 32(2): 177-185.
[106]II. Luo. Coalescence, breakup and liquid circulation in bubble column reactors [D]. Norges TeklliskeHogskole; Universitetet I Trondheim. 1993.
[107]F. Lehr, M. Millies, et al. Bubble size distributions and flow fields in bubble columns. AICHE Journal.2002,48(11):2426-2443.
[108]F. Lehr, M. Millies, et al. Bubble-size distributions and flow fields in bubble columns. AICHE Journal.2002,48(11):2426-2443.
[109]T. Wang, J. Wang. Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model. Chemical Engineering Science.2007,62(24):7107-7118.
[110]B. C. H. Venneker, J. J. Derksen, et al. Population balance modeling of aerated stirred vessels based on CFD. AICHE Journal.2002,48(4):673-685.
[111]M. Petitti, A. Nasuti, et al. Bubble size distribution modeling in stirred gas-liquid reactors with QMOM augmented by a new correction algorithm. AICHE Journal.2010,56(1):36-53.
[112]H. Yang, D. G. Allen. Model-based scale-up strategy for mycelial fermentation processes. The Canadian Journal of Chemical Engineering.1999,77(5):844-854.
[113]S. Schmalzriedt, M. Jenne, et al. Integration of physiology and fluid dynamics. Advances in biochemical engineering/biotechnology.2003,80:19-68.
[114]J.-Y. Xia, Y.-H. Wang, et al. Fluid dynamics investigation of variant impeller combinations by simulation and fermentation experiment. Biochemical Engineering Journal.2009,43(3):252-260.
[115]W. Feng, J. Wen, et al. Modeling of local dynamic behavior of phenol degradation in an internal loop airlift bioreactor by yeast Candida tropicalis. Biotechnology and Bioengineering.2007,97(2):251-264.
[116]G. Zhou, S. M. Kresta. Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank. Chemical Engineering Science.1998,53(11):2063-2079.
[117]K. C. Lee, M. Yianneskis. Turbulence properties of the impeller stream of a Rushton turbine. AICHE Journal.1998,44(1):13-24.
[118]M. Assirelli, W. Bujalski, et al. Intensifying micromixing in a semi-batch reactor using a Rushton turbine. Chemical Engineering Science.2005,60(8-9):2333-2339.
[119]F. R. Khan, C. D. Rielly, et al. Angle-resolved stereo-PIV measurements close to a down-pumping pitched-blade turbine. Chemical Engineering Science.2006,61(9):2799-2806.
[120]G. Zhou, S. M. Kresta. Distribution of energy between convective and turbulent flow for three frequently used impellers. Chemical Enginering Research and Design.1996,74(A): 379-389.
[121]R. J. Adrian. Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry. Applied Optics.1986,25(21):3855-3858.
[122]P. Gupta, M. H. Al-Dahhan, et al. A novel signal filtering methodology for obtaining liquid phase tracer responses from conductivity probes. Flow Measurement and Instrumentation.2000,11(2):123-131.
[123]A. W. Nienow. Hydrodynamics of Stirred Bioreactors. Applied Mechanics Reviews.1998, 51(1):3-32.
[124]D. K. Lilly:University Corporation for Atmospheric Research,1966.
[125]J. Meyers, P. Sagaut. On the model coefficients for the standard and the variational multi-scale Smagorinsky model. Journal of Fluid Mechanics.2006,569:287-319.
[126]S. B. Pope. Ten questions concerning the large-eddy simulation of turbulent flows.2004.
[127]J. Meyers, B. J. Geurts, et al. A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model. Journal of Computational Physics.2007,227(1):156-173.
[128]L. A. Cutter. Flow and turbulence in a stirred tank. AICHE Journal.1966,12(1):35-45.
[129]Z. Jaworskia, I. Fortb. Energy dissipation rate in a baffled vessel with pitched blade turbine impeller. Collection of Czechoslovak Chemical Communications.1991.56:1856- 1867.
[130]A. A. Gunkel, M. E. Weber. Flow phenomena in stirred tanks. Part Ⅰ. The impeller stream. AICHE Journal. 1975, 21(5): 931-939.
[131]V. V. Ranade, J. R. Bourne, et al. Fluid mechanics and blending in agitated tanks. Chemical Engineering Science. 1991,46(8): 1883-1893.
[132]S. M. Kresta, P. E. Wood. Prediction of the three-dimensional turbulent flow in stirred tanks. AICHE Journal. 1991, 37(3): 448-460.
[133]A. Togatorop. Computational fluid mixing in stirred vessels [D]; UMIST, UK, 1995.
[134]K. Ng, M. Yianneskis. Observations on the Distribution of Energy Dissipation in Stirred Vessels. Chemical Engineering Research and Design. 2000, 78(3): 334-341.
[135]A. W. Nienow. Agitators for mycelial fermentations. Trends in Biotechnology. 1990, 8(0): 224-233.
[136]A. W. Nienow. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chemical Engineering Science. 1997, 52(15): 2557-2565.
[137]R. K. Grenville, A. W. Nienow. Handbook of Industrial Mixing: Science and Practice. Hoboken, New Jersey: John Wiley & Sons. 2004.
[138]M. Cooke. Processing of Solid-liquid Suspensions. UK: Butterworth-Heinemann. 1988.
[139]T. E. Rodgers, L. Gangolf, et al. Mixing times for process vessels with aspect ratios greater than one. Chemical Engineering Science. 2011, 66(13): 2935-2944.
[140]P. R. Gogate, A. A. C. M. Beenackers, et al. Multiple-impeller systems with a special emphasis on bioreactors: a critical review. Biochemical Engineering Journal. 2000, 6(2): 109-144.
[141]S. J. Arjunwadkar, K. Saravanan, ct al. Optimizing the impeller combination for maximum hold-up with minimum power consumption. Biochemical Engineering Journal. 1998, 1(1): 25-30.
[142]A. Lara, E. Galindo. et al. Living with heterogeneities in bioreactors. Molecular Biotechnology. 2006, 34(3): 355-381.
[143]P. Vrabel, R. G. J. M. Van der Lans, et al. Compartment Model Approach: Mixing in Large Scale Aerated Reactors with Multiple Impellers. Chemical Engineering Research and Design. 1999, 77(4): 291-302.
[144]T. Moucha, V. Linek, et al. Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations. Chemical Engineering Science. 2003, 58(9): 1839-1846.
[145]P. Vrabel, R. G. J. M. van der Lans, et al. Mixing in large-scale vessels stirred with multiple radial or radial and axial up-pumping impellers: modelling and measurements. Chemical Engineering Science. 2000, 55(23): 5881-5896.
[146]D. Pinelli, F. Magelli. Analysis of the Fluid Dynamic Behavior of the Liquid and Gas Phases in Reactors Stirred with Multiple Hydrofoil Impellers. Industrial and Engineering Chemistry Research. 2000, 39(9): 3202-3211.
[147]S. D. Shewale, A. B. Pandit. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science. 2006, 61(2): 489-504.
[148]M. Fujasova, V. Linek, et al. Mass transfer correlations for multiple-impeller gas-liquid contactors. Analysis of the effect of axial dispersion in gas and liquid phases on "local" kLa values measured by the dynamic pressure method in individual stages of the vessel. Chemical Engineering Science. 2007, 62(6): 1650-1669.
[149]R. Sardeing. J. Aubin, et al. Gas-Liquid Mass Transfer: A Comparison of Down- and Up-pumping Axial Flow Impellers with Radial Impellers. Chemical Engineering Research and Design. 2004, 82(12): 1589-1596.
[150]D. Pinelli, A. Bakker, et al. Some F'eatures of a Novel Gas Dispersion Impeller in a Dual-Impeller Configuration. Chemical Engineering Research and Design. 2003, 81(4): 448- 454.
[151]M. Cooke, P. J. Heggs. Advantages of the hollow (concave) turbine for multi-phase agitation under intense operating conditions. Chemical Engineering Science.2005,60(20): 5529-5543.
[152]P. Jiisten, G. C. Paul, et al. Dependence of Penicillium chrysogenum growth, morphology, vacuolation, and productivity in fed-batch fermentations on impeller type and agitation intensity. Biotechnology and Bioengineering.1998,59(6):762-775.
[153]J.-H. Heo, V. Ananin, et al. Impeller types and feeding modes influence the morphology and protein expression in the submerged culture of Aspergillus oryzae. Biotechnology and Bioprocess Engineering.2004,9(3):184-190.
[154]X. Li, J. Zhang, et al. Effects of flow field on the metabolic characteristics of'Streptomyces lincolnensis in the industrial fermentation of lincomycin. J Biosci Bioeng.2013,115(1): 27-31.
[155]V. Linek, T. Moucha, et al. Gas-liquid mass transfer in vessels stirred with multiple impellers—Ⅰ. Gas-liquid mass transfer characteristics in individual stages. Chemical Engineering Science.1996,51(12):3203-3212.
[156]Y. Chisti, U. J. Jauregui-Haza. Oxygen transfer and mixing in mechanically agitated airlift bioreactors. Biochemical Engineering Journal.2002,10(2):143-153.
[157]P. Weiland, U. Onken. Fluid dynamics and mass transfer in an airlift fermenter with external loop. German Chemical Engineering.1981,4:42-50.
[158]S. P. Godbole, A. Schumpe, et al. Hydrodynamics and mass transfer in non-Newtonian solutions in a bubble column. AICHE Journal.1984,30(2):213-220.
[159]F. Garcia-Ochoa, E. Gomez. Bioreactor scale-up and oxygen transfer rate in microbial processes:an overview. Biotechnology Advances.2009,27(2):153-176.
[160]M. L. Jackson, C.-C. Shen. Aeration and mixing in deep tank fermentation systems. AICHE Journal.1978,24(1):63-71.
[161]D. Zhao, L. Guo, et al. An experimental study on local interfacial area concentration using a double-sensor probe. International Journal of Heat and Mass Transfer.2005,48(10): 1926-1935.
[162]M. R. Rampure, A. A. Kulkarni, et al. Hydrodynamics of Bubble Column Reactors at High Gas Velocity:Experiments and Computational Fluid Dynamics (CFD) Simulations. Industrial and Engineering Chemistry Research.2007,46(25):8431-8447.
[163]S. T. Revankar, M. Ishii. Theory and measurement of local interfacial area using a four sensor probe in two-phase flow. International Journal of Heat and Mass Transfer.1992, 36(12):2997-3007.
[164]Wang, Z.-S. Mao, et al. Experimental and Numerical Investigation on Gas Holdup and Flooding in an Aerated Stirred Tank with Rushton Impeller. Industrial and Engineering Chemistry Research.2006,45(3):1141-1151.
[165]T. Hibiki, S. Hogsett, et al. Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow. Nuclear Engineering and Design.1998,184(2-3): 287-304.
[166]S. Hogsett, M. Ishii. Local two-phase flow measurements using sensor techniques. Nuclear Engineering and Design.1997,175(1-2):15-24.
[167]M. A. Young, R. G. Carbonell, et al. Airlift bioreactors:Analysis of local two-phase hydrodynamics. AICHE Journal.1991,37(3):403-428.
[168]C.-S. Lo, S.-J. Hwang. Local hydrodynamic properties of gas phase in an internal-loop airlift reactor. Chemical Engineering Journal.2003,91(1):3-22.
[169]S. G. Dias, F. A. Franca, et al. Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes. International Journal of Multiphase Flow.2000,26(11):1797-1830.
[170]A. Matsuura, L.-S. Fan. Distribution of bubble properties in a gas-liquid-solid fluidized bed. AICHE Journal. 1984, 30(6): 894-903.
[171]A. Yasunishi, M. Fukuma, et al. Measurement of behavior of gas bubbles and gas hold-up in a slurry bubble column by a dual electro-resistivity probe method. Journal of Chemical Engineering of Japan. 1986, 19(5): 444-449.
[172]F. A. Holland, R. Bragg. Fluid Flow for Chemical Engineers. London. 1995.
[173]V. Abardi, G. Rovero, et al. Sparged vessels agitated by multiple turbines [M]. Proceedings of the Sixth European Conference on Mixing. 1988: 329-336.
[174]A. W. Nienow. Gas-liquid mixing studies : A comparison of Rushton turbines with some modern impellers. Chemical Engineering Research and Design. 1996, 74(A): 417-423.
[175]M. Nocentini, D. Fajner, et al. Gas-liquid mass transfer and holdup in vessels stirred with multiple Rushton turbines: water and water-glycerol solutions. Industrial and Engineering Chemistry Research. 1993,32(1): 19-26.
[176]D. Pinelli, M. Nocentini, et al. Hold-up in low viscosity gas-liquid systems stirred with multiple impellers. Comparison of different agitator types and sets [M]. Institution of Chemical Engineers Symposium Series. 1994: 81-88.
[177]J. M. T. Vasconcelos, J. M. L. Rodrigues, et al. Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors. Chemical Engineering Science. 2003, 58(8): 1431-1440.
[178]J. M. Smith. Simple Performance Correlations for Agitated Vessels [M]. Proceedings of 7th European Congress on Mixing. Brugge,Belgium. 1991: 233-241.
[179]T. Murugesan. Dispersed phase hold-up in mechanically agitated gas-liquid contactors. Journal of Chemical Technology and Biotechnology. 1998, 72(3): 221-226.
[180]Y. Bao, Z. Ilao, et al. Gas dispersion and solid suspension in three-phase stirred tank with multiple impellers. Chemical Engineering Communications. 2006, 193(7): 801-825.
[181]Y. Kawse, M. Moo-Yong. Volumetric mass transfer coefficients in aerated stirred tank reactors with Newtonian and non-Newtonian media. Chemical Engineering Research and Design. 1988, 66(3): 284-288.
[182]Y. Kawasc. M. Moo-Young. Mathematical models for design of bioreactors: Applications of: Kolmogoroffs theory of isotropic turbulence. Chemical Engineering Journal. 1990, 43(1): B19-B41.
[183]J. C. Lamont, D. S. Scott. An eddy cell model of mass transfer into the surface of a turbulent liquid. AICHE Journal. 1970, 16(4): 513-519.
[184]M. Bouaiil, G. I Iebrard, et al. A comparative study of gas hold-up, bubble size, interfacial area and mass transfer coefficients in stirred gas-liquid reactors and bubble columns. Chemical Engineering and Processing. 2001, 40(2): 97-111.
[185]K. M. Ge/.ork. W. Bujalski, et al. Mass Transfer and Hold-up Characteristics in a Gassed, Stirred Vessel at Intensified Operating Conditions. Chemical Engineering Research and Design. 2001, 79(8): 965-972.
[186]P. R. Gogate. A. B. Pandit. Survey of measurement techniques for gas-liquid mass transfer coefficient in bioreactors. Biochemical Engineering Journal. 1999, 4(1): 7-15.
[187]P. A. Gibbs, R. J. Seviour, et al. Growth of Filamentous Fungi in Submerged Culture: Problems and Possible Solutions. Critical Reviews in Biotechnology. 2000. 20(1): 17-48.
[188]M. O. Albaek, K. V. Gernaey, et al. Modeling enzyme production with Aspergillus oryzae in pilot scale vessels with different agitation, aeration, and agitator types. Biotechnol Bioeng. 2011, 108(8): 1828-1840.
[189]E. Olsvik, B. Kristiansen. Rheology of filamentous fermentations. Biotechnology Advances. 1994. 12(1): 1-39.
[190]J. C. Gabelle, E. Jourdier, et al. Impact of rheology on the mass transfer coefficient during the growth phase of Trichoderma recsei in stirred bioreactors. Chemical Engineering Science. 2012, 75(0): 408-417.
[191]J. C. Gabelle, F. Augier. et al. Effect of tank size on kLa and mixing time in aerated stirred reactors with non-newtonian fluids. The Canadian Journal of Chemical Engineering.2011, 89(5):1139-1153.
[192]A. Amanullah, P. Justen, et al. Agitation induced mycelial fragmentation of Aspergillus oryzae and Penicillium chrysogenum. Biochemical Engineering Journal.2000,5(2):109-114.
[193]V. R. Ranade, J. J. Ulbrecht. Influence of polymer additives on the gas-liquid mass transfer in stirred tanks. AICHE Journal.1978,24(5):796-803.
[194]S. Dronawat, C. Svihla, et al. Effect of impeller geometry on gas-liquid mass transfer coefficients in filamentous suspensions. Applied Biochemistry and Biotechnology.1997, 63-65:363-373.
[195]N. Benchapattarapong, W. A. Anderson, et al. Rheology and Hydrodynamic Properties of Tolypocladium inflatum Fermentation Broth and Its Simulation. Bioprocess and Biosystems Engineering.2005,27(4):239-247.
[196]S. Sideman, O. Hortacsu, et al. Mass transfer in gas-liquid contacting systems. Industrial and Engineering Chemistry Research.1966,58(7):32-47.
[197]R. Shinnar. On the behaviour of liquid dispersions in mixing vessels. Journal of Fluid Mechanics.1961,10(02):259-275.
[198]J. C. Lee, D. L. Meyrick. Gas-liquid interfacial areas in salt solutions in an agitated tank. Trans IChemE.1970,48:T37-T45.
[199]W. D. Deckwer. Bubble Column Reactors. New York,. USA:John Wiley & Sons.1992.
[200]K. G. Clarke, L. D. C. Correia. Oxygen transfer in hydrocarbon-aqueous dispersions and its applicability to alkane bioprocesses:A review. Biochemical Engineering Journal.2008, 39(3):405-429.
[201]A. Schumpe, W. D. Deckwer. Gas holdups, specific interfacial areas, and mass transfer coefficients of aerated carboxymethyl cellulose solutions in a bubble column. Industrial& Engineering Chemistry Process Design and Development.1982,21(4):706-711.
[202]C. T. O'Connor, E. W. Randall, et al. Measurement of the effects of physical and chemical variables on bubble size. International Journal of Mineral Processing.1990,28(1-2):139-149.
[203]R. Lemoine, B. I. Morsi. An algorithm for predicting the hydrodynamic and mass transfer parameters in agitated reactors. Chemical Engineering Journal.2005,114(1-3):9-31.
[204]P. H. Calderbank, M. B. Moo-Young. The continuous phase heat and mass transfer properties of dispersions. Chemical Engineering Science.1995,50(24):3921-3934.
[205]C. W. Robinson, C. R. Wilke. Simultaneous measurement of interfacial area and mass transfer coefficients for a well—mixed gas dispersion in aqueous electrolyte solutions. AICHE Journal.1974,20(2):285-294.
[206]P. H. Calderbank, M. B. Moo-Young. The continuous phase heat and mass-transfer properties of dispersions. Chemical Engineering Science.1961,16(1-2):39-54.
[207]F. Yoshida, Y Miura. Gas absorption in agitated gas-liquid contactors. Industrial& Engineering Chemistry Process Design and Development.1963,2(4):263-268.
[208]J. F. Kennedy, I. J. Bradshaw. Production, properties, and applications of xanthan. Progress in Industrial Microbiology.1984,19:319-371.
[209]R. Ben Salah, K. Chaari, et al. Optimisation of xanthan gum production by palm date (Phoenix dactylifera L.) juice by-products using response surface methodology. Food Chemistry.2010,121(2):627-633.
[210]R. B. Salah, K. Chaari, et al. Production of xanthan gum from xanthomonas campestris nrrl b-1459 by fermentation of date juice palm by-products(phoenix dactyliferal.) Journal of Food Process Engineering.2010:no-no.
[211]E. Galindo, B. Torrestiana, et al. Rheological characterization of xanthan fermentation broths and their reconstituted solutions. Bioprocess and Biosystems Engineering.1989, 4(3):113-117.
[212]A. Amanullah, L. Serrano-Carreon, et al. The influence of impeller type in pilot scale Xanthan fermentations. Biotechnology and Bioengineering.1998,57(1):95-108.
[213]L. Pakzad, F. Ein-Mozaffari, et al. Using electrical resistance tomography and computational fluid dynamics modeling to study the formation of cavern in the mixing of pseudoplastic fluids possessing yield stress. Chemical Engineering Science.2008,63(9): 2508-2522.
[214]J. Aubin, C. Xuereb. Design of multiple impeller stirred tanks for the mixing of highly viscous fluids using CFD. Chemical Engineering Science.2006,61(9):2913-2920.
[215]I.-S. Suh, H. Herbst, et al. The molecular weight of xanthan polysaccharide produced under oxygen limitation. Biotechnology Letters.1990,12(3):201-206.
[216]M. Papagianni, S. K. Psomas, et al. Xanthan production by Xanthomonas campestris in batch cultures. Process Biochemistry.2001,37(1):73-80.
[217]F. Garcia-Ochoa, V. E. Santos, et al. Xanthan gum production in a laboratory aerated stirred tank bioreactor. Chemical and Biochemical Engineering Quarterly.1997,11:69-74.
[218]S. Kraitschev, V. Lossev, et al. Energy saving in gas-liquid mixing using the NS-impeller. Institution of Chemical Engineer Symposium Series.1999,146:245-252.
[219]T. Moucha, V. Linek, et al. Effect of liquid axial mixing on local kLa values in individual stages of multiple-impeller vessel. Collection of Czechoslovak Chemical Communications. 1998,63:2103-2113.
[220]M. Laakkonen, P. Moilanen, et al. Dynamic modeling of local reaction conditions in an agitated aerobic fermenter. AICHE Journal.2006,52(5):1673-1689.
[221]F. Cabaret, S. Bonnot, et al. Mixing Time Analysis Using Colorimetric Methods and Image Processing. Industrial & Engineering Chemistry Research.2007,46(14):5032-5042.
[222]M. H. Xie, J. Y. Xia, et al. Hydrodynamics Characterization of an Ellipse Gate Impeller by Experimental and Numerical Studies. Chemical Engineering & Technology.2013, 36(1):115-122.
[223]M. O. Albaek, K. V. Gernaey, et al. Evaluation of the energy efficiency of enzyme fermentation by mechanistic modeling. Biotechnology and Bioengineering.2012,109(4): 950-961.
[224]M. McIntyre, C. Miiller, et al. Metabolic Engineering of the Morphology of Aspergillus. Springer Berlin Heidelberg.2001.
[225]M. Papagianni. Fungal morphology and metabolite production in submerged mycelial processes. Biotechnology Advances.2004,22(3):189-259.
[226]Z. J. Li, V. Shukla, et al. Effects of Increased Impeller Power in a Production-Scale Aspergillusoryzae Fermentation. Biotechnology Progress.2002,18(3):437-444.
[227]B. McNeil, L. M. Harvey. Viscous Fermentation Products. Critical Reviews in Biotechnology.1993,13(4):275-304.
[228]夏建业.基于流体力学与微生物生理学的搅拌生物反应器流场模拟研究[D]；华东理工大学,2008.
[229]唐文俊.基于菌体形态特征、生理参数及反应器工程特性的黑曲霉发酵过程优化[D]；华东理工大学,2013.
[230]J. L. Casas Lopez, J. A. Sanchez Perez, et al. Pellet morphology, culture rheology and lovastatin production in cultures of Aspergillus terreus. Journal of Biotechnology.2005, 116(1):61-77.
[231]A. Lapin, J. Schmid, et al. Modeling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor--A structured-segregated approach. Chemical Engineering Science.2006,61(14):4783-4797.
[232]X. Jia, X. Wang, et al. CFD modelling of phenol biodegradation by immobilized Candida tropicalis in a gas-liquid-solid three-phase bubble column. Chemical Engineering Journal. 2010,157(2-3):451-465.
[233]Y. Liao, D. Lucas. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chemical Engineering Science.2009,64(15):3389-3406.
[234]T. Wang, J. Wang, et al. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science.2003,58(20):4629-4637.
[235]S. Kumar, D. Ramkrishna. On the solution of population balance equations by discretization—Ⅱ. A moving pivot technique. Chemical Engineering Science.1996,51(8): 1333-1342.
[236]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 3—generalized daughter distribution functions. Chemical Engineering Science.2002,57(19):4187-4198.
[237]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 2—moment models and distribution reconstruction. Chemical Engineering Science.2002,57(12):2211-2228.
[238]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 1—analytical solution of the steady-state population balance. Chemical Engineering Science.2002,57(12):2193-2209.
[239]A. R. Khopkar, G. R. Kasat, et al. CFD simulation of mixing in tall gas-liquid stirred vessel:Role of local flow patterns. Chemical Engineering Science.2006,61(9):2921-2929.
[240]A. Brucato, F. Grisafi, et al. Particle drag coefficients in turbulent fluids. Chemical Engineering Science.1998,53(18):3295-3314.
[241]M. Petitti, D. L. Marchisio, et al. Effect of drag modeling on the prediction of critical regime tran-sitions in agitated gas-liquid reactors with bubble size distribution modelling. Multiphase Science and Technology.2009,21(1-2):95-106.
[242]M. Martin, F. J. Montes, et al. Mass transfer rates from bubbles in stirred tanks operating with viscous fluids. Chemical Engineering Science.2010,65(12):3814-3824.
[243]F. Kerdouss, A. Bannari, et al. Two-phase mass transfer coefficient prediction in stirred vessel with a CFD model. Computers & Chemical Engineering.2008,32(8):1943-1955.
[244]J. Derksen. Assessment of Large Eddy Simulations for Agitated Flows. Chemical Engineering Research and Design.2001,79(8):824-830.
[245]A. Bakker, L. M. Oshinowo. Modelling of Turbulence in Stirred Vessels Using Large Eddy Simulation. Chemical Engineering Research and Design.2004,82(9):1169-1178.
[246]Z. Li, Y. Bao, et al. PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks. Chemical Engineering Science.2011,66(6):1219-1231.
[247]B. N. Murthy, J. B. Joshi. Assessment of standard k-ε, RSM and LES turbulence models in a baffled stirred vessel agitated by various impeller designs. Chemical Engineering Science.2008,63(22):5468-5495.
[248]M. Laakkonen, V. Alopaeus, et al. Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel. Chemical Engineering Science. 2006,61(1):218-228.
[249]P. Moilanen, M. Laakkonen, et al. Modelling mass transfer in an aerated 0.2 m3 vessel agitated by Rushton, Phasejet and Combijet impellers. Chemical Engineering Journal. 2008,142(1):95-108.
[250]S. S. Alves, C. I. Maia, et al. Gas-liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering and Processing: Process Intensification.2004,43(7):823-830.
[2]H. Unadkat, C. D. Rielly, et al. PIV study of the flow field generated by a sawtooth impeller. Chemical Engineering Science.2011,66(21):5374-5387.
[3]A. Gabriele, A. W. Nienow, et al. Use of angle resolved PIV to estimate local specific energy dissipation rates for up- and down-pumping pitched blade agitators in a stirred tank. Chemical Engineering Science.2009,64(1):126-143.
[4]N. N. Clark, R. Turton. Chord length distributions related to bubble size distributions in multiphase flows. International Journal of Multiphase Flow.1988,14(4):413-424.
[5]W. Liu, N. N. Clark. Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters. International Journal of Multiphase Flow.1995,21(6):1073-1089.
[6]K. E. Morud, B. H. Hjertager. LDA measurements and CFD modelling of gas-liquid flow in a stirred vessel. Chemical Engineering Science.1996,51(2):233-249.
[7]A. A. Kulkarni, J. B. Joshi, et al. Simultaneous measurement of hold-up profiles and interfacial area using LDA in bubble columns:predictions by multiresolution analysis and comparison with experiments. Chemical Engineering Science.2001,56(21-22):6437-6445.
[8]V. V. Ranade, M. Perrard, et al. Influence of Gas Flow Rate on the Structure of Trailing Vortices of a Rushton Turbine:PIV Measurements and CFD Simulations. Chemical Engineering Research and Design.2001,79(8):957-964.
[9]A. R. Khopkar, A. R. Rammohan, et al. Gas-liquid flow generated by a Rushton turbine in stirred vessel:CARPT/CT measurements and CFD simulations. Chemical Engineering Science.2005,60(8-9):2215-2229.
[10]M. Barigou, M. Greaves. Bubble-size distributions in a mechanically agitated gas—liquid contactor. Chemical Engineering Science.1992,47(8):2009-2025.
[11]K. Takahashi, W. J. McManamey, et al. Bubble size distributions in impeller region in a gas-sparged vessel agitated by a Rushton turbine. Journal of Chemical Engineering of Japan.1992,25:427-432.
[12]V. Machon, A. W. Pacek, et al. Bubble Sizes in Electrolyte and Alcohol Solutions in a Turbulent Stirred Vessel. Chemical Engineering Research and Design.1997,75(3):339-348.
[13]M. Laakkonen, P. Moilanen, et al. Local Bubble Size Distributions in Agitated Vessel: Comparison of Three Experimental Techniques. Chemical Engineering Research and Design.2005,83(1):50-58.
[14]G. A. Hughmark. Power Requirements and Interfacial Area in Gas-Liquid Turbine Agitated Systems. Industrial & Engineering Chemistry Process Design and Development. 1980,19(4):638-641.
[15]B. J. Michel, S. A. Miller. Power requirements of gas-liquid agitated systems. AICHE Journal.1962,8(2):262-266.
[16]S. Nagata. Mixing principle and application. Tokyo:A Halsted press.1975.
[17]A. W. Nienow, D. J. Wisdom, et al. The effect of scale and geometry on flooding, recirculation, and power in gassed stirred vessels [M]. Second European Conf on Mixin. Cambridge, England.1977.
[18]A. W. Nienow, H. Liu, et al. The use of large ring spargars to improve the performance of fermenters agitated by single and multiple standard rushton turbines [M].2th Int Conf on Bioreactor fluid dynamics. Cambridge, Engiand.1988.
[19]K. Van't Riet, J. Tramper. Basic Bioreactor Design. New York Marcel Dekker, Inc. 1991.
[20]Warmoeskerker, G. M.M.C, et al. Impeller loading in multi-turbine vessels [M].2th Int Conf on Bioreactor fluid dynamics. held at Cambridge, England.1988.
[21]Y. Q. Cui, R. G. J. M. van der Lans, et al. Local power uptake in gas-liquid systems with single and multiple rushton turbines. Chemical Engineering Science.1996,51(11):2631-2636.
[22]T. Koloni, I. Plazl, et al. Power consumption, gas hold-up and interfacial area in aerated non-newtonian suspensions in stirred tanks of square cross-section. Chem Eng Res Des. 1989,67:526-536.
[23]T. Moucha, V. Linek, et al. Improved power and mass transfer correlations for design and scale-up of multi-impeller gas-liquid contactors. Chemical Engineering Science.2009, 64(3):598-604.
[24]M. Taghavi, R. Zadghaffari, et al. Experimental and CFD investigation of power consumption in a dual Rushton turbine stirred tank. Chemical Engineering Research and Design.2011,89(3):280-290.
[25]S. M. Kresta, P. E. Wood. The flow field produced by a pitched blade turbine: Characterization of the turbulence and estimation of the dissipation rate. Chemical Engineering Science.1993,48(10):1761-1774.
[26]H. Wu, G. K. Patterson. Laser-Doppler measurements of turbulent-flow parameters in a stirred mixer. Chemical Engineering Science.1989,44(10):2207-2221.
[27]R. Escudie, A. Line. Experimental analysis of hydrodynamics in a radially agitated tank. AICHE Journal.2003,49(3):585-603.
[28]K. V. Sharp, R. J. Adrian. PIV study of small-scale flow structure around a Rushton turbine. AICHE Journal.2001,47(4):766-778.
[29]S. Michelet. Turbulence et Dissipation au Sein d'un Re'acteur agite'parune Turbine Rushton-Ve 'locime' trie Laser Doppler a'Deux de Mesure. [D]. Lorraine, France; L Institut National Polytechnique de Lorraine,1998.
[30]A. Ducci, M. Yianneskis. Direct determination of energy dissipation in stirred vessels with two-point LDA. AICHE Journal.2005,51(8):2133-2149.
[31]P. Saarenrinne, M. Piirto, et al. Experiences of turbulence measurement with PIV. Measurement Science and Technology.2001,12(11):1904.
[32]J. Sheng, H. Meng, et al. A large eddy PIV method for turbulence dissipation rate estimation. Chemical Engineering Science.2000,55(20):4423-4434.
[33]J. Smagorinsky. General circulation experiments with the primitive equation 1 the basic experiment. Monthly Weather Review.1963,91(3):99-164.
[34]S. Liu, C. Meneveau, et al. On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. Journal of Fluid Mechanics.1994,275(-1):83-119.
[35]R. A. Clark, J. H. Ferziger, et al. Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J Fluid Mech.1979,91(1):1-16.
[36]G. Zhou, S. M. Kresta. Impact of tank geometry on the maximum turbulence energy dissipation rate for impellers. AICHE Journal.1996,42(9):2476-2490.
[37]S. Baldi, M. Yianneskis. On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements. Chemical Engineering Science.2004,59(13):2659-2671.
[38]F. R. Khan. Investigation of Turbulent Flows and Instabilities in a Stirred Vessel Using Particle Image Velocimetry [D]. Loughborough, UK; Loughborough University,2005.
[39]S. Baldi, M. Yianneskis. On the Direct Measurement of Turbulence Energy Dissipation in Stirred Vessels with PIV. Industrial& Engineering Chemistry Research.2003,42(26): 7006-7016.
[40]J. Kilander, A. Rasmuson. Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements. Chemical Engineering Science. 2005, 60(24): 6844-6856.
[41]W.-M. Lu, S.-J. Ju. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. The Chemical Engineering Journal. 1987, 35(1): 9-17.
[42]V. V. Ranade, M. Pcrrard, ct al. Trailing Vortices of Rushton Turbine: PIV Measurements and CFD Simulations with Snapshot Approach. Chemical Engineering Research and Design. 2001,79(1): 3-12.
[43]N. Deen. An Experimental and Computational Study of Fluid Dynamics in Gas-Liquid Chemical Reactors [D]. Esbjerg; Aalborg University, 2001.
[44]B. Loiseau, N. Midoux, et al. Some hydrodynamics and power input data in mechanically agitated gas-liquid contactors. AICHE Journal. 1977, 23(6): 931-935.
[45]N. Midoux, J. C. Charpenticr. Mechanically agitated gas-liquid reactors parti: Hydrodynamics. International Chemical Engineering. 1984, 24: 249-287.
[46]Y. Nagase, II. Yasui. Fluid motion and mixing in a gas-liquid contactor with turbine agitators Chemical Engineering Journal. 1983, 27: 33.
[47]I. Zun, B. Fiiipic, et al. Phase discrimination in void fraction measurements via genetic algorithms. Review of Scientific Instruments. 1995, 66(10): 5055-5064.
[48]A. Bombac, I. Zun, et al. Gas-filled cavity structures and local void fraction distribution in aerated stirred vessel. AICI IE Journal. 1997, 43( 11): 2921 -2931.
[49]J. O. Hinze. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AICI IE Journal. 1955, 1(3): 289-295.
[50]P. H. Calderbank. The interfacial area in gas-liquid contacting with mechanical agitation. Trans Instrum Chem Eng. 1958, 36: 443-463.
[51]S. P. S. Andrews. Gas-liquid mass transfer in microbiological reactors. Trans IChemE. 1982,60: 3-10.
[52]R. Parthasarathy, G. J. Jameson, et al. Bubble break-up in stirred vessels predicting the Sauter mean diameter. Trans IChemE Symposium Series. 1991, 69(A): 295-301.
[53]R. Parthasarathy, N. M. Ahmed. Sauter mean and maximum bubble diameters in aerated stirred vessels. Trans IChemE. 1994, 72(A): 565-572.
[54]S. S. Alves, C. I. Maia, ct al. Bubble size in aerated stirred tanks. Chemical Engineering Journal. 2002, 89(1-3): 109-117.
[55]T. Martin, C. M. Me Farlane, et al. The influence of liquid properties and impeller type on bubble coalescence behaviour and mass transfer in sparged, agitated reactors. Institution of Chemical Engineers Symposium Series. 1994, 136: 57-64.
[56]M. Bouaifi, M. Roustan. Bubble size and mass transfer coefficients in dual-impeller agitated reactors. Canadian Journal of Chemical Engineering. 1998. 76(3): 390-397.
[57]M. Laakkonen, P. Moilanen, et al. Local bubble size distributions in agitated vessels Chemical Engineering Journal. 2005. 106(2): 133-143.
[58j G. Montante, D. Horn, et al. Gas-liquid flow and bubble size distribution in stirred tanks. Chemical Engineering Science. 2008. 63(8): 2107-2118.
[59]Y. Bao, L. Chen, et al. Local void fraction and bubble size distributions in cold-gassed and hot-sparged stirred reactors. Chemical Engineering Science. 2010, 65(2): 976-984.
[60]T. Sridhar, O. E. Potter. Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels. Industrial & Engineering Chemistry Fundamentals. 1980, 19(1): 21-26.
[61]M. Barigou, M. Greaves. Gas holdup and interfacial area distributions in a mechanically agitated gas-liquid contactor. Chemical Engineering Research and Design. 1996, 74: 397-405.
[62]H. Yagi, F. Yoshida. Gas Absorption by Newtonian and Non-Newtonian Fluids in Sparged Agitated Vessels. Industrial & Engineering Chemistry Process Design and Development. 1975, 14(4): 488-493.
[63]M. M. L. de Figueiredo, P. II. Calderbank. The scale-up of aerated mixing vessels for specified oxygen dissolution rates. Chemical Engineering Science.1979,34(11):1333-1338.
[64]K. Van't Riet. Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels. Industrial & Engineering Chemistry Process Design and Development.1979,18(3):357-364.
[65]M. Nishikawa, M. Nakamura, et al. Gas absorption in aerated mixing vessels. Journal of Chemical Engineering of Japan.1981,14:219-226.
[66]K. Chandrasekharan, P. H. Calderbank. Further observations on the scale-up of aerated mixing vessels. Chemical Engineering Science.1981,36:819-823.
[67]S. M. Davies, L. G. Gibilaro, et al. The application of two novel techniques for mass transfer coefficient determination to the scale up of gas sparged agitated vessels [M]. Proc Eur Conf Mix.1985.
[68]V. Linek, J. Sinkule, et al. Critical assessment of gassing-in method measuring kLa in fermentors. Biotechnol Bioeng.1991,38:323-330.
[69]A. G. Pedersen, M. Bundgaard-Nielsen, et al. Characterization of mixing in stirred tank bioreactors equipped with Rushton turbines. Biotechnology and Bioengineering.1994, 44(Compendex):1013-1017.
[70]H. Gagnon, M. Lounes, et al. Power consumption and mass transfer in agitated gas-liquid columns:A comparative study. The Canadian Journal of Chemical Engineering.1998, 76(3):379-389.
[71]S. J. Arjunwadkar, K. Sarvanan, et al. Gas-liquid mass transfer in dual impeller bioreactor. Biochemical Engineering Journal.1998,1(2):99-106.
[72]J. M. T. Vasconcelos, S. C. P. Orvalho, et al. Effect of Blade Shape on the Performance of Six-Bladed Disk Turbine Impellers. Industrial and Engineering Chemistry Research.2000, 39(1):203-213.
[73]F. Garcia-Ochoa, E. Gomez. Mass transfer coefficient in stirred tank reactors for xanthan gum solutions. Biochemical Engineering Journal.1998,1(1):1-10.
[74]M. S. Puthli, V. K. Rathod, et al. Gas-liquid mass transfer studies with triple impeller system on a laboratory scale bioreactor. Biochemical Engineering Journal.2005,23(1): 25-30.
[75]Y. Zhu, P. C. Bandopadhayay, et al. Measurement of Gas-Liquid Mass Transfer in an Agitated Vessel— A Comparison between Different Impellers. Journal of Chemical Engineering of Japan.2001,34(5):579-584.
[76]M. S. Puthli, V. K. Rathod, et al. Gas-liquid mass transfer studies with triple impeller system on a laboratory scale bioreactor. Biochemical engineering journal.2005,23(1):25-30.
[77]J. F. Perez, O. C. Sandall. Gas absorption by non-Newtonian fluids in agitated vessels. AICHE Journal.1974,20:770-775.
[78]E. Costa, A. Lucas, et al. Transferencia de materia en tanques agitados:burbujeo de gases en liquidos newtonianos y no newtonianos. I. Turbinas de 6 paletas y difusor plano. An Quim.1982,78:387-392.
[79]R. S. Albal, Y. T. Shah, et al. Mass transfer in multiphase agitated contactors. Chem Eng J. 1983,27:61-80.
[80]V. Schluter, W. D. Deckwer. Gas/liquid mass transfer in stirred vessels. Chemial Engineering Science.1992,47:2357-2362.
[81]W. G. Whitman. Preliminary experimental confirmation of the two-film theory of gas absorption. Chem Metall Eng.1923,29:146-169.
[82]R. Higbie. The rate of absorption of a pure gas into a still liquid during short periods of exposure. Inst Chem Eng.1935,35:36-60.
[83]P. V. Danckwerts. Significance of liquid-film coefficients in gas absorption. Ind Eng Chem. 1951,43:1460-1467.
[84]J. C. Lamont, D. S. Scott. An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChEJ. 1970, 16(513-519):
[85]H. L. Toor, J. M. Marchelo. Film-penetration model for mass transfer and heat transfer. AIChEJ 1958,4:97-101.
[86]II. Hocker, G. Langer, et al. Mass transfer in aerated Newtonian and non-Newtonian liquids in stirred reactors. Ger Chem Eng 1981, 4: 51-62.
[87]J. B. Joshi. Computational flow modelling and design of bubble column reactors. Chemical Engineering Science. 2001, 56(21-22): 5893-5933.
[88]M. Ishii, N. Zuber. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AICHE Journal. 1 979, 25: 843-855.
[89]M. Atenas, M. Clark, et al. Holdup and Liquid Circulation Velocity in a Rectangular Air-Lift Bioreactor. Industrial & Engineering Chemistry Research. 1999, 38(3): 944-949.
[90]M. Rafique, P. Chen, et al. Computational modeling of gas-liquid flow in bubble columns. Reviews in Chemical Engineering. 2004, 20: 225-375.
[91]N. H. Thomas, T. R. Auton, et al. Entrapment and transport of bubbles in transient large eddies in multiphase turbulent shear flows. International Conference on the Physical Modelling of Multiphase Flows. 1983: 169-184.
192] A. Tomiyama. Struggle with computational bubble dynamics. Multiphase Sci Tech. 1998, 10:369-405.
[93]S. Ledakowicz, M. Stelmachowski, et al. Mcthanol synthesis in bubble column slurry reactors. Chem ling Proc. 1992, 31(4): 213-219.
[94]T. Frank, A. D. B. Bums, et al. Drag model for turbulent dispersion in Eulerian multi-phase flows [M]. Insthlntemational Conference on Multi PhaseFlow. Yokohama,Japan. 2004.
[95]S. P. Antal, R. T. Lahey, et al. Analysis of phase distribution in fully developed laminar bubble two-phase flow. International Journal of Multiphase Flow. 1991, 17: 635-652.
[96]P. Ranganathan, S. Sivaraman. Investigations on hydrodynamics and mass transfer in gas-liquid stirred reactor using computational fluid dynamics. Chemical Engineering Science. 2011, 66(14): 3108-3124.
[97]R. I. Issa, A. D. Gosman. The computation of three dimensional turbulent two-phase flows in mixer vessels [M]. Numerical Methods in Laminar and Turbulent Flow. Swansea; Pineridge Press. 1981:827-839.
[98]A. D. Gosman, C. Lekakou, et al. Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE Journal. 1992, 38(12): 1946-1956.
[99]W. A. M. Bakker. H. J. L. van Can, et al. Hydrodynamics and mixing in a multiple air-lift loop reactor. Biotechnology and Bioengineering. 1993, 42(8): 994-1001.
[100]M. J. Prince, H. W. Blanch. Bubble coalescence and break-up in air-sparged bubble columns. AICIIE Journal. 1990. 36(10): 1485-1499.
[101]S. Kumar, D. Ramkrishna. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science. 1996, 51(8): 1311-1332.
[102]H. Euo, H. F. Svendsen. Theoretical model for drop and bubble breakup in turbulent dispersions. AICIIE Journal. 1996, 42(5): 1225-1233.
[103]G. Fleisher, S. Becker, et al. Detailed modeling of the chemisorption of CO? into NaOH in a bubble column. Chemical Engineering Science. 1996, 51: 1715-1724.
[104]D. P. Patil, J. R. G. Andrews. An analytical solution to continuous population balance model describing floe coalescence and breakage-A special case. Chemical Engineering Science. 1998, 53(3): 599-601.
[105]S. E. Pratsinis, S. K. Friedlander, et al. Aerosol reactor theory: Stability and dynamics of a continuous stirred tank aerosol reactor. AICHE Journal. 1986, 32(2): 177-185.
[106]II. Luo. Coalescence, breakup and liquid circulation in bubble column reactors [D]. Norges TeklliskeHogskole; Universitetet I Trondheim. 1993.
[107]F. Lehr, M. Millies, et al. Bubble size distributions and flow fields in bubble columns. AICHE Journal.2002,48(11):2426-2443.
[108]F. Lehr, M. Millies, et al. Bubble-size distributions and flow fields in bubble columns. AICHE Journal.2002,48(11):2426-2443.
[109]T. Wang, J. Wang. Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model. Chemical Engineering Science.2007,62(24):7107-7118.
[110]B. C. H. Venneker, J. J. Derksen, et al. Population balance modeling of aerated stirred vessels based on CFD. AICHE Journal.2002,48(4):673-685.
[111]M. Petitti, A. Nasuti, et al. Bubble size distribution modeling in stirred gas-liquid reactors with QMOM augmented by a new correction algorithm. AICHE Journal.2010,56(1):36-53.
[112]H. Yang, D. G. Allen. Model-based scale-up strategy for mycelial fermentation processes. The Canadian Journal of Chemical Engineering.1999,77(5):844-854.
[113]S. Schmalzriedt, M. Jenne, et al. Integration of physiology and fluid dynamics. Advances in biochemical engineering/biotechnology.2003,80:19-68.
[114]J.-Y. Xia, Y.-H. Wang, et al. Fluid dynamics investigation of variant impeller combinations by simulation and fermentation experiment. Biochemical Engineering Journal.2009,43(3):252-260.
[115]W. Feng, J. Wen, et al. Modeling of local dynamic behavior of phenol degradation in an internal loop airlift bioreactor by yeast Candida tropicalis. Biotechnology and Bioengineering.2007,97(2):251-264.
[116]G. Zhou, S. M. Kresta. Correlation of mean drop size and minimum drop size with the turbulence energy dissipation and the flow in an agitated tank. Chemical Engineering Science.1998,53(11):2063-2079.
[117]K. C. Lee, M. Yianneskis. Turbulence properties of the impeller stream of a Rushton turbine. AICHE Journal.1998,44(1):13-24.
[118]M. Assirelli, W. Bujalski, et al. Intensifying micromixing in a semi-batch reactor using a Rushton turbine. Chemical Engineering Science.2005,60(8-9):2333-2339.
[119]F. R. Khan, C. D. Rielly, et al. Angle-resolved stereo-PIV measurements close to a down-pumping pitched-blade turbine. Chemical Engineering Science.2006,61(9):2799-2806.
[120]G. Zhou, S. M. Kresta. Distribution of energy between convective and turbulent flow for three frequently used impellers. Chemical Enginering Research and Design.1996,74(A): 379-389.
[121]R. J. Adrian. Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry. Applied Optics.1986,25(21):3855-3858.
[122]P. Gupta, M. H. Al-Dahhan, et al. A novel signal filtering methodology for obtaining liquid phase tracer responses from conductivity probes. Flow Measurement and Instrumentation.2000,11(2):123-131.
[123]A. W. Nienow. Hydrodynamics of Stirred Bioreactors. Applied Mechanics Reviews.1998, 51(1):3-32.
[124]D. K. Lilly:University Corporation for Atmospheric Research,1966.
[125]J. Meyers, P. Sagaut. On the model coefficients for the standard and the variational multi-scale Smagorinsky model. Journal of Fluid Mechanics.2006,569:287-319.
[126]S. B. Pope. Ten questions concerning the large-eddy simulation of turbulent flows.2004.
[127]J. Meyers, B. J. Geurts, et al. A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model. Journal of Computational Physics.2007,227(1):156-173.
[128]L. A. Cutter. Flow and turbulence in a stirred tank. AICHE Journal.1966,12(1):35-45.
[129]Z. Jaworskia, I. Fortb. Energy dissipation rate in a baffled vessel with pitched blade turbine impeller. Collection of Czechoslovak Chemical Communications.1991.56:1856- 1867.
[130]A. A. Gunkel, M. E. Weber. Flow phenomena in stirred tanks. Part Ⅰ. The impeller stream. AICHE Journal. 1975, 21(5): 931-939.
[131]V. V. Ranade, J. R. Bourne, et al. Fluid mechanics and blending in agitated tanks. Chemical Engineering Science. 1991,46(8): 1883-1893.
[132]S. M. Kresta, P. E. Wood. Prediction of the three-dimensional turbulent flow in stirred tanks. AICHE Journal. 1991, 37(3): 448-460.
[133]A. Togatorop. Computational fluid mixing in stirred vessels [D]; UMIST, UK, 1995.
[134]K. Ng, M. Yianneskis. Observations on the Distribution of Energy Dissipation in Stirred Vessels. Chemical Engineering Research and Design. 2000, 78(3): 334-341.
[135]A. W. Nienow. Agitators for mycelial fermentations. Trends in Biotechnology. 1990, 8(0): 224-233.
[136]A. W. Nienow. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chemical Engineering Science. 1997, 52(15): 2557-2565.
[137]R. K. Grenville, A. W. Nienow. Handbook of Industrial Mixing: Science and Practice. Hoboken, New Jersey: John Wiley & Sons. 2004.
[138]M. Cooke. Processing of Solid-liquid Suspensions. UK: Butterworth-Heinemann. 1988.
[139]T. E. Rodgers, L. Gangolf, et al. Mixing times for process vessels with aspect ratios greater than one. Chemical Engineering Science. 2011, 66(13): 2935-2944.
[140]P. R. Gogate, A. A. C. M. Beenackers, et al. Multiple-impeller systems with a special emphasis on bioreactors: a critical review. Biochemical Engineering Journal. 2000, 6(2): 109-144.
[141]S. J. Arjunwadkar, K. Saravanan, ct al. Optimizing the impeller combination for maximum hold-up with minimum power consumption. Biochemical Engineering Journal. 1998, 1(1): 25-30.
[142]A. Lara, E. Galindo. et al. Living with heterogeneities in bioreactors. Molecular Biotechnology. 2006, 34(3): 355-381.
[143]P. Vrabel, R. G. J. M. Van der Lans, et al. Compartment Model Approach: Mixing in Large Scale Aerated Reactors with Multiple Impellers. Chemical Engineering Research and Design. 1999, 77(4): 291-302.
[144]T. Moucha, V. Linek, et al. Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations. Chemical Engineering Science. 2003, 58(9): 1839-1846.
[145]P. Vrabel, R. G. J. M. van der Lans, et al. Mixing in large-scale vessels stirred with multiple radial or radial and axial up-pumping impellers: modelling and measurements. Chemical Engineering Science. 2000, 55(23): 5881-5896.
[146]D. Pinelli, F. Magelli. Analysis of the Fluid Dynamic Behavior of the Liquid and Gas Phases in Reactors Stirred with Multiple Hydrofoil Impellers. Industrial and Engineering Chemistry Research. 2000, 39(9): 3202-3211.
[147]S. D. Shewale, A. B. Pandit. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science. 2006, 61(2): 489-504.
[148]M. Fujasova, V. Linek, et al. Mass transfer correlations for multiple-impeller gas-liquid contactors. Analysis of the effect of axial dispersion in gas and liquid phases on "local" kLa values measured by the dynamic pressure method in individual stages of the vessel. Chemical Engineering Science. 2007, 62(6): 1650-1669.
[149]R. Sardeing. J. Aubin, et al. Gas-Liquid Mass Transfer: A Comparison of Down- and Up-pumping Axial Flow Impellers with Radial Impellers. Chemical Engineering Research and Design. 2004, 82(12): 1589-1596.
[150]D. Pinelli, A. Bakker, et al. Some F'eatures of a Novel Gas Dispersion Impeller in a Dual-Impeller Configuration. Chemical Engineering Research and Design. 2003, 81(4): 448- 454.
[151]M. Cooke, P. J. Heggs. Advantages of the hollow (concave) turbine for multi-phase agitation under intense operating conditions. Chemical Engineering Science.2005,60(20): 5529-5543.
[152]P. Jiisten, G. C. Paul, et al. Dependence of Penicillium chrysogenum growth, morphology, vacuolation, and productivity in fed-batch fermentations on impeller type and agitation intensity. Biotechnology and Bioengineering.1998,59(6):762-775.
[153]J.-H. Heo, V. Ananin, et al. Impeller types and feeding modes influence the morphology and protein expression in the submerged culture of Aspergillus oryzae. Biotechnology and Bioprocess Engineering.2004,9(3):184-190.
[154]X. Li, J. Zhang, et al. Effects of flow field on the metabolic characteristics of'Streptomyces lincolnensis in the industrial fermentation of lincomycin. J Biosci Bioeng.2013,115(1): 27-31.
[155]V. Linek, T. Moucha, et al. Gas-liquid mass transfer in vessels stirred with multiple impellers—Ⅰ. Gas-liquid mass transfer characteristics in individual stages. Chemical Engineering Science.1996,51(12):3203-3212.
[156]Y. Chisti, U. J. Jauregui-Haza. Oxygen transfer and mixing in mechanically agitated airlift bioreactors. Biochemical Engineering Journal.2002,10(2):143-153.
[157]P. Weiland, U. Onken. Fluid dynamics and mass transfer in an airlift fermenter with external loop. German Chemical Engineering.1981,4:42-50.
[158]S. P. Godbole, A. Schumpe, et al. Hydrodynamics and mass transfer in non-Newtonian solutions in a bubble column. AICHE Journal.1984,30(2):213-220.
[159]F. Garcia-Ochoa, E. Gomez. Bioreactor scale-up and oxygen transfer rate in microbial processes:an overview. Biotechnology Advances.2009,27(2):153-176.
[160]M. L. Jackson, C.-C. Shen. Aeration and mixing in deep tank fermentation systems. AICHE Journal.1978,24(1):63-71.
[161]D. Zhao, L. Guo, et al. An experimental study on local interfacial area concentration using a double-sensor probe. International Journal of Heat and Mass Transfer.2005,48(10): 1926-1935.
[162]M. R. Rampure, A. A. Kulkarni, et al. Hydrodynamics of Bubble Column Reactors at High Gas Velocity:Experiments and Computational Fluid Dynamics (CFD) Simulations. Industrial and Engineering Chemistry Research.2007,46(25):8431-8447.
[163]S. T. Revankar, M. Ishii. Theory and measurement of local interfacial area using a four sensor probe in two-phase flow. International Journal of Heat and Mass Transfer.1992, 36(12):2997-3007.
[164]Wang, Z.-S. Mao, et al. Experimental and Numerical Investigation on Gas Holdup and Flooding in an Aerated Stirred Tank with Rushton Impeller. Industrial and Engineering Chemistry Research.2006,45(3):1141-1151.
[165]T. Hibiki, S. Hogsett, et al. Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow. Nuclear Engineering and Design.1998,184(2-3): 287-304.
[166]S. Hogsett, M. Ishii. Local two-phase flow measurements using sensor techniques. Nuclear Engineering and Design.1997,175(1-2):15-24.
[167]M. A. Young, R. G. Carbonell, et al. Airlift bioreactors:Analysis of local two-phase hydrodynamics. AICHE Journal.1991,37(3):403-428.
[168]C.-S. Lo, S.-J. Hwang. Local hydrodynamic properties of gas phase in an internal-loop airlift reactor. Chemical Engineering Journal.2003,91(1):3-22.
[169]S. G. Dias, F. A. Franca, et al. Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes. International Journal of Multiphase Flow.2000,26(11):1797-1830.
[170]A. Matsuura, L.-S. Fan. Distribution of bubble properties in a gas-liquid-solid fluidized bed. AICHE Journal. 1984, 30(6): 894-903.
[171]A. Yasunishi, M. Fukuma, et al. Measurement of behavior of gas bubbles and gas hold-up in a slurry bubble column by a dual electro-resistivity probe method. Journal of Chemical Engineering of Japan. 1986, 19(5): 444-449.
[172]F. A. Holland, R. Bragg. Fluid Flow for Chemical Engineers. London. 1995.
[173]V. Abardi, G. Rovero, et al. Sparged vessels agitated by multiple turbines [M]. Proceedings of the Sixth European Conference on Mixing. 1988: 329-336.
[174]A. W. Nienow. Gas-liquid mixing studies : A comparison of Rushton turbines with some modern impellers. Chemical Engineering Research and Design. 1996, 74(A): 417-423.
[175]M. Nocentini, D. Fajner, et al. Gas-liquid mass transfer and holdup in vessels stirred with multiple Rushton turbines: water and water-glycerol solutions. Industrial and Engineering Chemistry Research. 1993,32(1): 19-26.
[176]D. Pinelli, M. Nocentini, et al. Hold-up in low viscosity gas-liquid systems stirred with multiple impellers. Comparison of different agitator types and sets [M]. Institution of Chemical Engineers Symposium Series. 1994: 81-88.
[177]J. M. T. Vasconcelos, J. M. L. Rodrigues, et al. Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors. Chemical Engineering Science. 2003, 58(8): 1431-1440.
[178]J. M. Smith. Simple Performance Correlations for Agitated Vessels [M]. Proceedings of 7th European Congress on Mixing. Brugge,Belgium. 1991: 233-241.
[179]T. Murugesan. Dispersed phase hold-up in mechanically agitated gas-liquid contactors. Journal of Chemical Technology and Biotechnology. 1998, 72(3): 221-226.
[180]Y. Bao, Z. Ilao, et al. Gas dispersion and solid suspension in three-phase stirred tank with multiple impellers. Chemical Engineering Communications. 2006, 193(7): 801-825.
[181]Y. Kawse, M. Moo-Yong. Volumetric mass transfer coefficients in aerated stirred tank reactors with Newtonian and non-Newtonian media. Chemical Engineering Research and Design. 1988, 66(3): 284-288.
[182]Y. Kawasc. M. Moo-Young. Mathematical models for design of bioreactors: Applications of: Kolmogoroffs theory of isotropic turbulence. Chemical Engineering Journal. 1990, 43(1): B19-B41.
[183]J. C. Lamont, D. S. Scott. An eddy cell model of mass transfer into the surface of a turbulent liquid. AICHE Journal. 1970, 16(4): 513-519.
[184]M. Bouaiil, G. I Iebrard, et al. A comparative study of gas hold-up, bubble size, interfacial area and mass transfer coefficients in stirred gas-liquid reactors and bubble columns. Chemical Engineering and Processing. 2001, 40(2): 97-111.
[185]K. M. Ge/.ork. W. Bujalski, et al. Mass Transfer and Hold-up Characteristics in a Gassed, Stirred Vessel at Intensified Operating Conditions. Chemical Engineering Research and Design. 2001, 79(8): 965-972.
[186]P. R. Gogate. A. B. Pandit. Survey of measurement techniques for gas-liquid mass transfer coefficient in bioreactors. Biochemical Engineering Journal. 1999, 4(1): 7-15.
[187]P. A. Gibbs, R. J. Seviour, et al. Growth of Filamentous Fungi in Submerged Culture: Problems and Possible Solutions. Critical Reviews in Biotechnology. 2000. 20(1): 17-48.
[188]M. O. Albaek, K. V. Gernaey, et al. Modeling enzyme production with Aspergillus oryzae in pilot scale vessels with different agitation, aeration, and agitator types. Biotechnol Bioeng. 2011, 108(8): 1828-1840.
[189]E. Olsvik, B. Kristiansen. Rheology of filamentous fermentations. Biotechnology Advances. 1994. 12(1): 1-39.
[190]J. C. Gabelle, E. Jourdier, et al. Impact of rheology on the mass transfer coefficient during the growth phase of Trichoderma recsei in stirred bioreactors. Chemical Engineering Science. 2012, 75(0): 408-417.
[191]J. C. Gabelle, F. Augier. et al. Effect of tank size on kLa and mixing time in aerated stirred reactors with non-newtonian fluids. The Canadian Journal of Chemical Engineering.2011, 89(5):1139-1153.
[192]A. Amanullah, P. Justen, et al. Agitation induced mycelial fragmentation of Aspergillus oryzae and Penicillium chrysogenum. Biochemical Engineering Journal.2000,5(2):109-114.
[193]V. R. Ranade, J. J. Ulbrecht. Influence of polymer additives on the gas-liquid mass transfer in stirred tanks. AICHE Journal.1978,24(5):796-803.
[194]S. Dronawat, C. Svihla, et al. Effect of impeller geometry on gas-liquid mass transfer coefficients in filamentous suspensions. Applied Biochemistry and Biotechnology.1997, 63-65:363-373.
[195]N. Benchapattarapong, W. A. Anderson, et al. Rheology and Hydrodynamic Properties of Tolypocladium inflatum Fermentation Broth and Its Simulation. Bioprocess and Biosystems Engineering.2005,27(4):239-247.
[196]S. Sideman, O. Hortacsu, et al. Mass transfer in gas-liquid contacting systems. Industrial and Engineering Chemistry Research.1966,58(7):32-47.
[197]R. Shinnar. On the behaviour of liquid dispersions in mixing vessels. Journal of Fluid Mechanics.1961,10(02):259-275.
[198]J. C. Lee, D. L. Meyrick. Gas-liquid interfacial areas in salt solutions in an agitated tank. Trans IChemE.1970,48:T37-T45.
[199]W. D. Deckwer. Bubble Column Reactors. New York,. USA:John Wiley & Sons.1992.
[200]K. G. Clarke, L. D. C. Correia. Oxygen transfer in hydrocarbon-aqueous dispersions and its applicability to alkane bioprocesses:A review. Biochemical Engineering Journal.2008, 39(3):405-429.
[201]A. Schumpe, W. D. Deckwer. Gas holdups, specific interfacial areas, and mass transfer coefficients of aerated carboxymethyl cellulose solutions in a bubble column. Industrial& Engineering Chemistry Process Design and Development.1982,21(4):706-711.
[202]C. T. O'Connor, E. W. Randall, et al. Measurement of the effects of physical and chemical variables on bubble size. International Journal of Mineral Processing.1990,28(1-2):139-149.
[203]R. Lemoine, B. I. Morsi. An algorithm for predicting the hydrodynamic and mass transfer parameters in agitated reactors. Chemical Engineering Journal.2005,114(1-3):9-31.
[204]P. H. Calderbank, M. B. Moo-Young. The continuous phase heat and mass transfer properties of dispersions. Chemical Engineering Science.1995,50(24):3921-3934.
[205]C. W. Robinson, C. R. Wilke. Simultaneous measurement of interfacial area and mass transfer coefficients for a well—mixed gas dispersion in aqueous electrolyte solutions. AICHE Journal.1974,20(2):285-294.
[206]P. H. Calderbank, M. B. Moo-Young. The continuous phase heat and mass-transfer properties of dispersions. Chemical Engineering Science.1961,16(1-2):39-54.
[207]F. Yoshida, Y Miura. Gas absorption in agitated gas-liquid contactors. Industrial& Engineering Chemistry Process Design and Development.1963,2(4):263-268.
[208]J. F. Kennedy, I. J. Bradshaw. Production, properties, and applications of xanthan. Progress in Industrial Microbiology.1984,19:319-371.
[209]R. Ben Salah, K. Chaari, et al. Optimisation of xanthan gum production by palm date (Phoenix dactylifera L.) juice by-products using response surface methodology. Food Chemistry.2010,121(2):627-633.
[210]R. B. Salah, K. Chaari, et al. Production of xanthan gum from xanthomonas campestris nrrl b-1459 by fermentation of date juice palm by-products(phoenix dactyliferal.) Journal of Food Process Engineering.2010:no-no.
[211]E. Galindo, B. Torrestiana, et al. Rheological characterization of xanthan fermentation broths and their reconstituted solutions. Bioprocess and Biosystems Engineering.1989, 4(3):113-117.
[212]A. Amanullah, L. Serrano-Carreon, et al. The influence of impeller type in pilot scale Xanthan fermentations. Biotechnology and Bioengineering.1998,57(1):95-108.
[213]L. Pakzad, F. Ein-Mozaffari, et al. Using electrical resistance tomography and computational fluid dynamics modeling to study the formation of cavern in the mixing of pseudoplastic fluids possessing yield stress. Chemical Engineering Science.2008,63(9): 2508-2522.
[214]J. Aubin, C. Xuereb. Design of multiple impeller stirred tanks for the mixing of highly viscous fluids using CFD. Chemical Engineering Science.2006,61(9):2913-2920.
[215]I.-S. Suh, H. Herbst, et al. The molecular weight of xanthan polysaccharide produced under oxygen limitation. Biotechnology Letters.1990,12(3):201-206.
[216]M. Papagianni, S. K. Psomas, et al. Xanthan production by Xanthomonas campestris in batch cultures. Process Biochemistry.2001,37(1):73-80.
[217]F. Garcia-Ochoa, V. E. Santos, et al. Xanthan gum production in a laboratory aerated stirred tank bioreactor. Chemical and Biochemical Engineering Quarterly.1997,11:69-74.
[218]S. Kraitschev, V. Lossev, et al. Energy saving in gas-liquid mixing using the NS-impeller. Institution of Chemical Engineer Symposium Series.1999,146:245-252.
[219]T. Moucha, V. Linek, et al. Effect of liquid axial mixing on local kLa values in individual stages of multiple-impeller vessel. Collection of Czechoslovak Chemical Communications. 1998,63:2103-2113.
[220]M. Laakkonen, P. Moilanen, et al. Dynamic modeling of local reaction conditions in an agitated aerobic fermenter. AICHE Journal.2006,52(5):1673-1689.
[221]F. Cabaret, S. Bonnot, et al. Mixing Time Analysis Using Colorimetric Methods and Image Processing. Industrial & Engineering Chemistry Research.2007,46(14):5032-5042.
[222]M. H. Xie, J. Y. Xia, et al. Hydrodynamics Characterization of an Ellipse Gate Impeller by Experimental and Numerical Studies. Chemical Engineering & Technology.2013, 36(1):115-122.
[223]M. O. Albaek, K. V. Gernaey, et al. Evaluation of the energy efficiency of enzyme fermentation by mechanistic modeling. Biotechnology and Bioengineering.2012,109(4): 950-961.
[224]M. McIntyre, C. Miiller, et al. Metabolic Engineering of the Morphology of Aspergillus. Springer Berlin Heidelberg.2001.
[225]M. Papagianni. Fungal morphology and metabolite production in submerged mycelial processes. Biotechnology Advances.2004,22(3):189-259.
[226]Z. J. Li, V. Shukla, et al. Effects of Increased Impeller Power in a Production-Scale Aspergillusoryzae Fermentation. Biotechnology Progress.2002,18(3):437-444.
[227]B. McNeil, L. M. Harvey. Viscous Fermentation Products. Critical Reviews in Biotechnology.1993,13(4):275-304.
[228]夏建业.基于流体力学与微生物生理学的搅拌生物反应器流场模拟研究[D]；华东理工大学,2008.
[229]唐文俊.基于菌体形态特征、生理参数及反应器工程特性的黑曲霉发酵过程优化[D]；华东理工大学,2013.
[230]J. L. Casas Lopez, J. A. Sanchez Perez, et al. Pellet morphology, culture rheology and lovastatin production in cultures of Aspergillus terreus. Journal of Biotechnology.2005, 116(1):61-77.
[231]A. Lapin, J. Schmid, et al. Modeling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor--A structured-segregated approach. Chemical Engineering Science.2006,61(14):4783-4797.
[232]X. Jia, X. Wang, et al. CFD modelling of phenol biodegradation by immobilized Candida tropicalis in a gas-liquid-solid three-phase bubble column. Chemical Engineering Journal. 2010,157(2-3):451-465.
[233]Y. Liao, D. Lucas. A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chemical Engineering Science.2009,64(15):3389-3406.
[234]T. Wang, J. Wang, et al. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science.2003,58(20):4629-4637.
[235]S. Kumar, D. Ramkrishna. On the solution of population balance equations by discretization—Ⅱ. A moving pivot technique. Chemical Engineering Science.1996,51(8): 1333-1342.
[236]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 3—generalized daughter distribution functions. Chemical Engineering Science.2002,57(19):4187-4198.
[237]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 2—moment models and distribution reconstruction. Chemical Engineering Science.2002,57(12):2211-2228.
[238]R. B. Diemer, J. H. Olson. A moment methodology for coagulation and breakage problems:Part 1—analytical solution of the steady-state population balance. Chemical Engineering Science.2002,57(12):2193-2209.
[239]A. R. Khopkar, G. R. Kasat, et al. CFD simulation of mixing in tall gas-liquid stirred vessel:Role of local flow patterns. Chemical Engineering Science.2006,61(9):2921-2929.
[240]A. Brucato, F. Grisafi, et al. Particle drag coefficients in turbulent fluids. Chemical Engineering Science.1998,53(18):3295-3314.
[241]M. Petitti, D. L. Marchisio, et al. Effect of drag modeling on the prediction of critical regime tran-sitions in agitated gas-liquid reactors with bubble size distribution modelling. Multiphase Science and Technology.2009,21(1-2):95-106.
[242]M. Martin, F. J. Montes, et al. Mass transfer rates from bubbles in stirred tanks operating with viscous fluids. Chemical Engineering Science.2010,65(12):3814-3824.
[243]F. Kerdouss, A. Bannari, et al. Two-phase mass transfer coefficient prediction in stirred vessel with a CFD model. Computers & Chemical Engineering.2008,32(8):1943-1955.
[244]J. Derksen. Assessment of Large Eddy Simulations for Agitated Flows. Chemical Engineering Research and Design.2001,79(8):824-830.
[245]A. Bakker, L. M. Oshinowo. Modelling of Turbulence in Stirred Vessels Using Large Eddy Simulation. Chemical Engineering Research and Design.2004,82(9):1169-1178.
[246]Z. Li, Y. Bao, et al. PIV experiments and large eddy simulations of single-loop flow fields in Rushton turbine stirred tanks. Chemical Engineering Science.2011,66(6):1219-1231.
[247]B. N. Murthy, J. B. Joshi. Assessment of standard k-ε, RSM and LES turbulence models in a baffled stirred vessel agitated by various impeller designs. Chemical Engineering Science.2008,63(22):5468-5495.
[248]M. Laakkonen, V. Alopaeus, et al. Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel. Chemical Engineering Science. 2006,61(1):218-228.
[249]P. Moilanen, M. Laakkonen, et al. Modelling mass transfer in an aerated 0.2 m3 vessel agitated by Rushton, Phasejet and Combijet impellers. Chemical Engineering Journal. 2008,142(1):95-108.
[250]S. S. Alves, C. I. Maia, et al. Gas-liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering and Processing: Process Intensification.2004,43(7):823-830.