Motions of a porous particle in stokes flow part 2. Linear flows near a fluid interface

Analytical results are presented for the motion of a porous sphere in the vicinity of a plane fluid-fluid interface. The fluids are assumed to undergo a linear undisturbed flow and the viscosily ratio of the two fluids is assumed to be arbitrary. The analysis consists of the method of reflections, coupled with an application of fundamental singularity solutions for Stokes flow to calculate the hydrodynamic force and torque on the particle. The fundamental relationships for Ihe force and torque are then applied, in combination with Ihe corresponding solutions obtained in earlier publications for the translation and rotalion through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow.     

Prediction of pressure drop and void-fraction in annular two-phase flows

The polynomial vvelocity profile due to Pai (1953), applicable to transition and turbulent conditions in single phase flow, has been used to solve the equations of two-phase annular flow with appropriate matching conditions at the interface and at the boundaries. The results obtained enable one to predict the pressure drop and the void-fraction, when the interfacial friction factor is specified. Entrainment of the liquid in the core of the flowing gas has been taken into account by using the empirical relation of Hutchinson and Whalley (1973). It has been shown that the theory provides results in agreement with horizontal tube and vertical tube adiabatic flow data, in addition to predicting the liquid film thickness accurately.     

The shape of a fluid drop approaching an interface

The shape of a fluid drop approaching an interface does not change appreciably with time and is very close to the equilibrium dimensions, in spite of the large pressure gradient which is present in the draining film. This is because the net vertical force due to the excess pressure in the draining film above that in the drop is identical with that for an equilibrium film being zero for a plane interface and —2Rσ sin² ? for a deformable interface. Employing this result in a force balance around the drop which is independent of the bulk interface shows that the area A of the draining film between a fluid drop of volume V and a deformable fluid-liquid interface is given by where σ is the interfacial tension and Δρ the density difference between the drop and surrounding fluid, 1/b is the curvature at the top of the drop and h is the distance between this point and the edge of the draining film which is inclined to the horizontal at an angle ?. When the interface is a rigid plane the overall curvature 1/R of the draining film and the volume v enclosed by it, together with the angle ? are all zero. The limiting cases of the expression for very small and very large drops agree with those previously established for both deformable and rigid interfaces. An approximate expression which applies when cV^2/3 (where c = Δρg/σ) is between 0.6 and 13.5 and which gives A to within ± e% is where for a rigid plane interface and for a deformable interface When the densities of the drop and bulk heavy fluids are equal, but their respective interfacial tensions σ₁₂ and σ₂₃ with the light fluids are different, the expression becomes which estimates A/V^2/3 to within about ± 25% for σ₁₂/σ₂₃ in the range 0.11 to 9.0 and cV^2/3 (where c = Δρg/σ₁₂) between 0.6 and 13.5.     

微通道内流体压力降研究进展

从微通道构型出发,总结了恒定截面通道、变径通道、复杂通道内流体压降研究的最新进展,介绍了哈根?泊肃叶定律用于恒定截面通道的研究进展,提出了变径通道的截面变化对压降的影响,总结了复杂构型微通道内流体压降研究的难点,讨论了粘度、滑移、特征尺寸及其测量方式对压降的影响,为构建压降预测模型提供了思路. 对该领域今后主要的研究方向进行了展望.     

Adaptive linear quadratic gaussian (LQG) control of a bioreactor

The paper deals with the modelling and adaptive control of a continuous-flow fermentation process for the production of alcohol. The fermenter model has been developed from mass balance and leads to nonlinear differential equations. In practice, control strategies are difficult to derive using this non-linear model. The dilution rate and the substrate concentration have been considered as control and controlled variables, respectively. The adaptive control algorithm implemented is based on the linear quadratic control approach, where the associated Riccati equation is iterated until the system closed-loop poles belong to a restricted stability domain which is included in the unit circle. A single input/output model is used for control purposes. The model parameters are estimated on-line using a robust identification algorithm which includes: data normalization, time-varying forgetting factor, covariance matrix factorization, etc. Experimental results show the performance of this adaptive scheme and its ability to control biotechnological processes.     

Entrance flows of polymeric materials: Pressure drop and flow patterns

Flow at the entrance of a tube or channel is of interest in many polymer processes. Except for mathematical treatments at high Reynolds numbers and in creeping Newtonian flow, one must turn to empirical correlating equations and qualitative observations. These are discussed in two parts, one on pressure drop and the other on flow patterns. The discussion of pressure drop is largely a review, dealing with inertial, viscous, and elastic contributions to the pressure drop in tapered and sharp-edged entrances; also presented are new data for a viscoelastic polymer solution in tapered cone entrances. In the section on flow patterns, stress birefringent data for a very elastic solution flowing into a channel entrance show an unusual effect: stress discontinuities, not unlike “shock waves,” upstream and downstream of the entrances. This is in contrast to Newtonian and less elastic materials in which the stress patterns change gradually between the developed flow region and the entrance region.     

Minimum fluid flowrate,pressure drop and stability of a conical spouted bed

A model for calculating the minimum spouting flowrate and pressure drop in a conical spouted bed has been developed and described in our previous paper (Had?ismajlovi et al., 1986). In the present work, this model was examined at a wider range of experimental conditions and it was found that measured and predicted values of the minimum spouting flowrate and pressure drop differed by about 10.3% and 20.0%, respectively. It is shown that the spouted bed in a conical column is stable when the inlet tube diameter is less than 25 particle diameters.     

Air flows and pressure drop modelling for different pleated industrial filters

A dimensionless model was developed to determine the pressure drop across clean pleated filters, according to filter medium type, geometric characteristics of the pleating (distance between two pleats, pleat height, etc) and air flow parameters (filtration velocity, air density, etc). The model was derived from both experimental and numerical results obtained from nuclear and automotive filters — high efficiency particulate air (HEPA) and low efficiency particulate (LE), respectively. The major findings were that a more homogeneous air flow distribution occured over the surface of the pleated HEPA filter, while geometric characteristics had a greater influence on the initial pressure drop across the LE filter. The numerical model highlighted the fundamental importance of the filter medium's air flow resistance on air flow distribution.     

Single and two-phase flows in a horizontal pipe with a Kenics static mixer: Effect of pressure drop on mixing

Single and two-phase flows pressure drops through a Kenics static mixer were investigated, for liquid and gas Reynolds numbers ranging from 8110 < Re_L < 18 940 to 1730 < Re_G < 8680, respectively. New friction factor correlations were established for single and two-phase flows, showing better agreement than those available in the literature. Dissipated energy and characteristic time constants were estimated from experimental data. For instance, a dissipated energy with a maximum value of 510 W/kg was calculated in two-phase flow with the drift-flux model. The dispersed phase reduced the characteristic mixing times and its influence was more important than the continuous phase for all the characteristic mixing time investigated. Furthermore, the macroscopic characteristic mixing time was shown to be the governing mixing process for almost all gas and liquid flow rates explored.     

非闪蒸型气液二相流压降计算的计算机程序化

确定气液二相流的流动形式对于两相流的压力降计算非常重要,而在流型判断中,使用Baker图和GriffithWallis图进行手算尚可,却不利于计算机编程。基于此,应用Origin软件对Baker图和Griffith-Wallis图进行数据回归,得到划分区域线条的函数,再使用C++语言进行编程,实现整个计算过程的计算机程序化,可快捷、准确地判断垂直管道和水平管道的二相流流型,并使用均相法和杜克勒法计算出二相流管道压力降。计算机编程能大幅度提高计算效率,在处理杜克勒法压力降计算中的迭代运算时尤为实用。经过规范中例题的验证和工程实例运行结果,证明该方法是可行和准确的。     

Predictions of heat transfer and pressure drop for a modified power law fluid flow in a square duct

Numerical Solutions for the Nusselt Numbers (CHF and CWT) and the Friction Factor times Reynolds Number have been obtained for fully developed laminar flow of a MPL (Modified Power Law) fluid within a square duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian at low shear rates through a transition region to power law behavior at higher shear rates. A shear rate parameter is identified, which allows the prediction of the shear rate range for a specified set of operating conditions. Numerical results of the Nusselt numbers (CHF and CWT) and the Friction factors times Reynolds number for the Newtonian and power law regions are compared with previous published results, showing agreement with 0.02% in Newtonian region and 4.0% in power law region.     

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows,we investigated the transformation of single drop breakup from binary to ternary and multiple.Silicone oil and deionized water were the dispersed phase and con-tinuous phase,respectively.The probability of binary,ternary,and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number.To address the underlying mechanisms of this transfor-mation of drop breakup,we performed two-dimensional particle image velocimetry(PIV)experiments of single-phase jet flows.With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field,these transformation conditions can be estimated:the capillary number ranges from 0.17 to 0.27,and the Weber number ranges from 55 to 111.     

A pressure drop correlation for low Reynolds number Newtonian flows through a rectangular orifice in a similarly shaped micro-channel

Current microfabrication methods mean that rectangular orifices in similarly shaped micro-channels are often found in microfluidic devices. The power required to overcome the pressure drop across such orifices is often of importance. In the contribution reported here, numerical results for low Reynolds number incompressible Newtonian fluid flow through rectangular orifice in similarly shaped micro-channel have been used to develop a correlation for pressure drop arising from the orifice. The correlation, which was motivated by theoretical developments, indicates that the pressure drop is proportional to the average velocity through the orifice, and a function of the orifice contraction ratio, length-to-width ratio and, most particularly, aspect ratio.     

Experimental and CFD studies of fluid dynamic gauging in duct flows

Experimental and computational fluid dynamics (CFD) studies of the technique of fluid dynamic gauging (FDG) in duct flows have been performed. Experiments were performed using a stainless steel gauging nozzle located on the centreline of a Perspex duct of square cross section. The test fluid was water, flowing through the duct at 0.0077-0.74 m/s (Re_duct 116-11 100). The success of the experiments was confirmed by the results of Tuladhar et al. [2003. Dynamic gauging in duct flows. Canadian Journal of Chemical Engineering 81, 279-284].For the first time, CFD has been applied to simulate FDG in an imposed flow for steady, incompressible, laminar flows. Experimental data and simulation results agreed to within 6%, supporting the validity of both the experiments and the assumptions underpinning the simulation. CFD simulations predicted the stresses beneath the lip of the nozzle and confirmed the practical working range of the gauge (0.1<h/d_t<0.25). This is a major achievement, proving that CFD can be used to model this flow-FDG accurately, which is valuable for future work in this area, namely fouling in food, crude oil and cross-flow membrane systems.     

Observation of linear and quadratic magnetic field-dependence of magneto-photocurrents in InAs/GaSb superlattice

We experimentally studied the magneto-photocurrents generated by direct interband transition in InAs/GaSb type II superlattice. By varying the magnetic field direction, we observed that an in-plane magnetic field induces a photocurrent linearly proportional to the magnetic field; however, a magnetic field tilted to the sample plane induces a photocurrent presenting quadratic magnetic field dependence. The magneto-photocurrents in both conditions are insensitive to the polarization state of the incident light. Theoretical models involving excitation, relaxation and Hall effect are utilized to explain the experimental results.     

细小尺度下潜热型功能热流体压降与传热特性

实验研究了相变微胶囊颗粒(囊芯材料为正十六烷,壳材为尿素-甲醛树脂)和去离子水混合制成的潜热型功能热流体流过等热流细小圆管的流动与传热特性,同时以去离子水作为传热工质在相同条件下进行了对比实验。得到了压降随质量流量的变化规律,实验段出、入口温度以及量纲1出口温度随Reynolds数变化规律,量纲1壁面温度沿轴向的分布规律,平均Nusselt数随Reynolds数的变化关系。结果表明,相变微胶囊颗粒的加入会导致流动压降增大,但随着流量增加,流动压降逐渐与单相液体的接近;出口温度及壁面温度要比相同条件下单相液体的低;含有较小相变微胶囊颗粒浓度的潜热型功能热流体的平均Nusselt数是相同条件下单相液体的2.0～4.0倍。     

Pressure drop of the fluid and the flow patterns of the phases in multistage fluidisation

Staging of a fluidisation column with horizontal screens reduces the axial mixing of the phases and limits the formation and growth of the bubbles. The pressure drop of the fluid and the flow patterns of the phases differ markedly with the mode of operation of the multistage fluidised bed. These aspects with respect to the theoretical models, the experimental data and the range of applicability are discussed along with the correlations to predict the characteristics of the bed.