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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Non-Newtonian multi-phase flows: On drag reduction, pressure drop and liquid wall friction factor

The present work focuses on the non-Newtonian liquid drag reduction by gas injection. Two regimes are taken in consideration: fully stratified gas shear-thinning liquid flow and gas shear-thinning liquid slug flow regimes.Predictions of drag reduction ratio and holdup are presented for the stratified flow of gas and non-Newtonian Ostwald-de Waele liquid. Fully stratified flow is considered and the approach developed in Taitel and Dukler (1976) is used. For these regimes, CMC (CarboxyMethyl Cellulose) solution is used in order to investigate the behaviour of the gas and non-Newtonian liquids in horizontal pipes. Results have been reformulated and an extension to interfacial Andreussi and Persen (1987) correlation has been carried out for stratified regimes.For slug flow regimes, the mechanistic slug unit model is adopted in order to estimate the pressure gradients along the slug unit. The slug unit model is rearranged and reinterpreted as inviscid Burgers's equation for incompressible phases.For both stratified and slug flow regimes, three dimensional CFD (computational fluid dynamics) simulations were performed in order to compare the drag reduction ratio and pressure gradients. In stratified flows, CFD is also used in an attempt to evaluate the liquid wall friction factor and to compare the obtained values with those given by empirical standard correlations.     

Transition between stratified and non-stratified horizontal oil-water flows. Part II: Mechanism of drop formation

The conditions and mechanism of drop formation at the interface of oil-water wavy stratified flows that lead to the onset of drop entrainment and the transition to dual continuous flow pattern were investigated both experimentally and theoretically. Experimentally, high-speed video imaging was used to capture the mechanism of drop detachment from waves during oil and water stratified flow in a diameter horizontal acrylic pipe. The visual observations revealed that the faster phase undercuts the other one while the waves present in both phases deform until drops are detached. The wave deformation was attributed to the drag force, that originates from the relative movement between the two phases, exceeding the stabilising surface tension force. Based on this force balance an equation was developed that related the wavelength to the amplitude that can lead to drop detachment. This drop entrainment equation and the wave stability equation suggested in part I of the paper [Al-Wahaibi, T., Angeli, P., 2007. Transition between stratified and non-stratified horizontal oil-water flows. Part I: Stability analysis. Chemical Engineering Science, in press, doi:10.1016/j.ces.2007.01.024 ], defined three regions in a wave amplitude versus length graph, namely the stable waves, the unstable waves and the drop entrainment region. The intersection of the lines produced by these two equations gives the critical minimum wave characteristics for drop formation. These agreed well with experimental data when a new correlation for the drag coefficient on the waves was used, suitable for liquid-liquid flows. Also the characteristics of waves that were experimentally found to form drops fell within the predicted entrainment region.     

Residence time distribution of a purely viscous non-Newtonian fluid in helically coiled or spatially chaotic flows

This work is dedicated to an experimental study of residence time distributions (RTD) of a pseudoplastic fluid in different configurations of helically coiled or chaotic systems. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean cells. Fluid particle trajectories become chaotic through a geometrical perturbation obtained by rotating the curvature plane of each bend of ±90° with respect to the neighboring ones (alternated or twisted curved ducts). Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the device. The experimental RTD is modeled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for generalized Reynolds numbers varying from 30 to 270. The Péclet number based on the diameter of the pipe is found to increase with the Reynolds number whatever the number of bends in the system. This reduction in axial dispersion is due to both the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction, which is one of the characteristic parameters of the model, increases with the Reynolds number, whatever the number of bends, to reach a maximum value ranging from 90% to 100%. For Reynolds numbers less than 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube center. Results have been compared with those previously obtained using Newtonian fluids. The values of the Péclet number are greater for the pseudoplastic fluid, the local change of apparent viscosity affecting the secondary flow. For pseudoplastic fluids, the apparent viscosity is lower near the wall and higher at the center of the cross section. The maximum axial velocity is flattened as the flow behavior index is reduced, inducing a decrease of the secondary flow in the central part of the pipe and an acceleration of it near the wall, which reduces the axial dispersion. These results are encouraging for the use of this system as continuous mixer for complex fluids in laminar regime, particularly for small Reynolds numbers.     

3-D computational fluid dynamics for gas and gas-particle flows in a cyclone with different inlet section angles

A three-dimensional computational fluid dynamics (CFD) Reynolds stress model (RSM) was used to describe the gas and gas-solid flow in a cyclone with a scroll inlet duct at three different inlet section angles in relation to the cyclone body. The effects of the inlet section angles on the fluid dynamics inside the cyclone and on the performance parameters (collection efficiency and pressure drop) were analyzed by means of the finite volume method using a computational code and an industrial-sized cyclone for separation of gas-particle phases operated by Votorantim Cimentos Company. The numerical results show that the value for overall collection efficiency in this work increased to 77.2% for the 45° inlet section angle, while that for the normal inlet duct was 54.4% under the same operating conditions.     

Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems

Abstract. This article describes a polynomial estimation technique based on the state‐space model and develops an estimation method for the quadratic estimation problem by applying the multivariate recursive least squares (RLS) Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete‐time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The augmented signal vector is modelled in terms of an autoregressive model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is found to be considerably improved in comparison with the existing RLS Wiener estimators. The proposed method may be applied advantageously to the quadratic estimations of wide‐sense stationary stochastic signals in general.