Transient instability of the flow induced by an impulsively started rotating cylinder

The onset of instability induced by transient momentum diffusion in a boundary layer over an impulsively started rotating cylinder is examined. Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) have conducted experiments and reported anomalously large Taylor numbers of up to 20×10⁶, far exceeding the well-known value of 1708 for Taylor vortices in steady flow. In this paper, we argue that it is inappropriate to treat the phenomenon as a steady-state wide-gap Couette flow, because the unstable boundary layer in their experiments was very thin. The instability in the fluid induced by momentum diffusion is an unsteady-state phenomenon analogous to transient thermal instability, whose mathematical equivalence for the steady-state cases have been established by Taylor (Philos. Trans. R. Soc. London A 223 (1923) 289). We find that the onset of instability can be predicted from a transient Taylor number defined as Ta=y⁵(∂u/∂y)²/ν²R_i. The maximum transient Taylor number is found to occur at a critical depth , where Ta_max=1.461U_i²(νt)^1.5/ν²R_i. Ta_max bears a theoretical critical value of 1100 from linear stability analysis. The experimental data of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) agree remarkably well with this value. The critical time can thus be predicted with good accuracy from a critical value of the maximum transient Taylor number of 1100. The theoretical critical dimension of the toroidal plume formed after the boundary layer becomes unstable is found to be , which agrees well with measurements. The average critical dimensionless wavenumber of the experiments of Kirchner and Chen (J. Fluid Mech. 40 (1970) 39) is found to be 3.05, which is very close to the theoretical value of 2.9.     

The onset of Taylor-Görtler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

The onset of Taylor-Görtler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as V _i ∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (V _i =constant). Based on the present τ _c and the Foster’s [1969] comment, the manifest stability guideline is suggested.     

On the relative importance of the kinetic and frictional contributions to granular motion in an annular Couette flow

A quantitative assessment is made on the relative importance of the kinetic and frictional contributions to the motion of dry granular materials under shear in an annular Couette flow configuration. The assessment is based on comparing the modelling results using the kinetic-frictional model with the experiments. It is shown that the kinetic-theory-based model with equal weight of the collisional and frictional contributions, commonly used in the literature, gives a great deviation from the experimental results in the point of view of the dominant solids motion, while an increase in the weight of the frictional contribution improves the modelling towards the experimental results. An increase in the weight of the frictional contribution by 25-50% leads to the best match, suggesting the current constitutive relationship with equal weight of the kinetic and frictional contributions need to be refined in order to reflect the real dense granular flows.     

The onset of Taylor-Görtler vortices during impulsive spin-down to rest

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using the propagation theory. The primary transient swirl flow is laminar but for an initially high rotating speed secondary motion sets in at a certain time. It is found here that the critical Reynolds number Re_c=320, below which the flow is unconditionally stable. For Re>Re_c the dimensionless critical time τ_c to mark the onset of a fastest growing instability is presented as a function of the Reynolds number Re. Available experimental data and also predictions show that deviation of the velocity profiles from their primary ones occurs starting from a certain time τ≈4τ_c. This means that secondary motion is detected experimentally at this characteristic time. It seems that during τ_c?τ?4τ_c secondary motion is relatively very weak.     

Influence of orientation upon the hydrodynamics of gas-liquid flow for square channels in monolith supports

Monoliths are being used increasingly as catalyst supports for two-phase gas-liquid reactions, yet substantial differences in the mass transfer performance between different configurations have not been thoroughly explained using either mass transfer or hydrodynamic arguments. In this paper, investigations of the differences in hydrodynamics between up-flow and down-flow have been made in a single channel using square glass capillaries of either 1.5 or 2 mm section. The fluids used were either water or 30%_v/v isopropanol/water mixture and air. Predictive flow maps are presented for down-flow: annular, Taylor (slug) flow, bubbly and churn flow were observed. In the Taylor flow regime, slug velocities and lengths measured using an optoelectronic technique were found to be in good agreement with the drift flux model [Zuber, N., Findlay, J.A., 1965. Average volumetric concentration in two-phase flow systems. Journal of Heat Transfer 87, 453-468]. Non-zero drift velocities were obtained. Particle image velocimetry (PIV) was used to investigate the velocity fields within the liquid slugs. For short slugs (slug length less than the tube hydraulic diameter), a flow is developed where the axial velocity component is only a function of position in the tube cross-section. The velocity profile is relatively flat, with the maximum observed velocity at the axis of the tube, V_max, being 0.8-1 times the bubble velocity, V_B. For long slugs, the axial velocity component depends on both the axial position and the position in the tube cross-section. Close to parabolic profiles are developed with V_max/V_B≈1.1-1.7. The location of the centre of the recirculation vortices produced in long slugs was found to be closer to the tube centre in down-flow compared with up-flow. Recirculation times in up-flow were 3 times faster: this has implications for the models used to predict rates of mass transfer and residence time distribution.     

Effects of wall-heating on the linear instability characteristics of pressure-driven two-layer channel flow

The linear stability analysis of a pressure-driven two-layer channel flow of two immiscible, Newtonian and incompressible fluids is considered. The walls of the channel are maintained at different constant temperatures and Nahme's law is applied to model the temperature dependence of the fluid viscosity. A modified Orr–Sommerfeld equation for the disturbance streamfunction coupled to a linearized energy equation is derived and solved using a spectral collocation method. Our results indicate that increasing the dimensionless top wall temperature has a non-monotonic effect on the linear stability characteristics. We also found that increasing the thermal conductivity and density ratios stabilise the flow for the set of parameter values considered; the viscosity ratio has a non-monotonic effect on the maximal growth rate. An energy ‘budget’ analysis shows that the most dangerous mode is of ‘interfacial’ type.     

Regimes of Multiple Emulsions of W1/O/W2 and O1/W/O2 Type in the Continuous Couette‐Taylor Flow Contactor

The flow regimes of multiple emulsions in the continuous Couette‐Taylor flow (CTF) contactor and characterization of the dispersion state are reported. The proposed method of multiple emulsion preparation is a one‐step procedure on the contrary to the classical two‐step procedure. The effect of operating parameters in the CTF contactor on multiple emulsion appearance, structure (drop size and packing), and rheological behavior is discussed. The key factors affecting multiple emulsion preparation in the CTF apparatus were the phases ratio, the rotational flow, and an annular gap width. The influence of an axial flow was more significant in the range of small rotational rates. The operating conditions were optimized to find the best characteristic multiple emulsions (largest interfacial area). The paper presents the same exemplary data of using W₁/O/W₂ emulsions as emulsion liquid membranes (ELMs) in the extraction process and O₁/W/O₂ for control active agent (drug) release.     

Migration of air channels: An instability of air flow in mobile saturated porous media

A set of two-dimensional laboratory visualization experiments reveals a previously unrecognized gas-flow instability in a porous medium saturated with a glycerine-water solution. The medium is a non-fixed vertically placed packing of grains of crushed fused silica glass. The interaction of the injected air flow and the medium structure leads to mobilization of the medium and an instability, which causes the air channel to migrate. This instability is dominated by a dimensionless number α, which can be interpreted as a normalization of a critical velocity with a dipole velocity for saturated conditions. The channel migration appears as a sequence of previous channels collapsing and new channels opening. The channel migration comes to a stop after some time, leaving one thin and stable channel. The process is studied by calculating the cumulated lateral movement distance of a channel and the lateral width of the area affected by the migration, both scaled by α with an empirical power of 0.25. Another dimensionless number f is defined to qualify the migration under different grain size, height of bed, and air flow rate.     

An experimental study of the flow of nonspherical grains in a rotating cylinder

The effect of particle aspect ratio on the rheology of the flow of granular materials is studied experimentally in a quasi–two‐dimensional rotating cylinder, using two varieties of prolate spheroidal grains with different aspect ratios. Image analysis of high speed videos is used to obtain the flow profiles near the centre of the cylinder. The dynamic angle of repose and apparent viscosity in the medium show significant increase with increasing aspect ratio. The mean velocity, root mean square velocity and shear rate profiles are qualitatively similar for nonspherical and spherical particles, however, their magnitudes increase with increasing aspect ratio. A simple scaling is shown to predict the maximum thickness of the flowing layer for all the particles. The predictions of a model for the flow match with the measured mean velocity profiles and layer thickness. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4307–4315, 2017     

Mass‐transfer enhancement by a reversible chemical reaction across the interface of a bubble rising under Stokes flow

Mass transfer around a bubble rising in a liquid under Stokes regime is investigated when a reversible chemical reaction, , is taken into account. Four dimensionless parameters control the interfacial transfer rate: the Péclet and Damköhler numbers, the ratio of the diffusion coefficient of both species, and the reaction equilibrium constant. The mass‐transfer equations are solved numerically with a finite element technique. A boundary layer approach is also proposed and solved with a coupled technique of finite difference and Chebyshev‐spectral method. The equilibrium constant and the ratio of diffusion coefficients have a strong influence on the coupling between the chemical reaction and mass transfer leading to an increase of the Sherwood number. The interaction between the chemical reaction and advection is clearly established by the simulations. Conditions corresponding to Péclet number larger than the Damköhler number reduces the effect of the chemical reaction. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3376–3388, 2014     

Effect of Cylinder Rotation on Flow Characteristics of the Annular Region in Annular Centrifugal Extractor

The flow patterns in the annular region of a 50 mm annular centrifugal extractor (ACE) were studied using phase particle image velocimetry (PIV), by which the distributions of radial velocity, axial velocity, vorticity, turbulent kinetic energy (TKE), and micromixing time of a fluid under different rotating Reynolds numbers were investigated. In the center of the annular region, both the radial and axial velocities of the fluid are close to zero, regardless of the rotating Reynolds number changes. The TKE of the fluid along the radial direction is small at center and large on the edge. The results show that the mixing process mainly occurs at the region near the outer cylinder’s sidewall, and the mixing time in this region is less than that in the internal annular region. Besides, the whole mixing efficiency is proportional to the rotational speed when the speed is below a certain level, and then gradually reaches a plateau when the speed is further increased.     

Determination of the interfacial area and mass transfer coefficients in the Taylor gas–liquid flow in a microchannel

The interfacial area in the Taylor (slug) gas–liquid flow in a microchannel was measured by the Danckwerts' (chemical) method, using CO₂ absorption from the CO₂/N₂ mixture into KHCO₃/K₂CO₃ buffer solutions, containing NaOCl as a catalyst. The rate of absorption was determined and the Danckwerts' plots were constructed. Reasonable agreement with the geometrical area measured photographically was obtained. This fact allowed to determine for the first time the mass transfer coefficients separately for liquid film and liquid caps. A correlation for the calculation of mass transfer coefficients has been proposed.     

The hydrodynamics of ejector-Venturi scrubbers and their modelling by an annular flow/boundary layer model

The performance of ejector-Venturi scrubbers has been studied experimentally. Data have been obtained on overall pressure drop, axial pressure profiles and droplet sizes. The effect of throat diameter, length and spray angle was investigated. Empirical models for pressure drop across Venturis have been tested against the data. Only when the model is tuned to the experimental data they are successful. The model of Azzopardi et al. which incorporates all the important physical mechanisms, has been successfully adapted to handle ejector-Venturi. It has been found to give accurate predictions.     

CFD approaches for the simulation of hydrodynamics and heat transfer in Taylor flow

Previous studies on heat and mass transfer in the Taylor flow regime in microchannels have shown the transport (heat/mass) rates to be dependent on the length of the liquid slug. In order to understand the effect of slug length on transport rates and to have a one-to-one comparison with experimental data, a computational approach is required to simulate flows with liquid slugs and bubbles of controlled lengths.Here we describe and benchmark two approaches. The first, and conceptually simplest, is to generate bubbles and slugs in a long tube using a time-dependent boundary condition. In the second method, the flow and heat transfer in a single unit cell, consisting of a bubble surrounded by liquid slugs, is solved in a frame of reference moving with the bubble velocity. Both methods were implemented in ANSYS-Fluent.Simulations for a two-phase (liquid-only) Reynolds number of 713, Capillary number of 0.004 and void fraction of 0.366 for nitrogen-water flow were performed to compare the two techniques. There was a very large difference between the required computational mesh sizes and times for the two methods, with a wall clock time of 38 h on a single processor for the moving domain compared with 1460 h using four processors for the stationary domain approach. In addition, for a constant wall heat flux boundary condition, even with 14 bubbles present in a long tube thermal development was not achieved. The hydrodynamic and heat transfer results obtained from the two approaches were found to be very similar to each other and with results from our earlier verification and validation studies, giving a high degree of confidence in the implementation of both methods.     

三角槽道低Reynolds数脉动流的流动特性分析

以水为工质对三角槽道低Reynolds数脉动流的流动特性进行了实验研究与理论分析。通过流动实验,分析了Reynolds数（Re）、Womersley数（W）、脉动振幅（A）等参数对流动阻力的影响。同时,建立了脉动流压降的数学模型,从理论层面解析了各脉动参数对流动阻力产生影响的作用机理,揭示了瞬时流速曲线与瞬时压降曲线之间相位差产生的原因。研究发现,相较于稳态流,脉动流会增加流动阻力,这是因为脉动流压降方程中存在三角函数项Δp_r,其周期平均值P始终大于0;就脉动参数而言,W对总压降的形阻压降部分影响较为显著,而A与总压降呈正相关;相位差的产生是由于总压降方程中存在加速度压降,而相位差的大小取决于沿程阻力、形阻压降、加速度压降三者对总压降波动的影响程度。     

Experimental study of the slug/churn flow transition in a single Taylor bubble

A study is presented of the hydrodynamic behaviour of very long gas slugs, rising co-currently with water along a 20 mm i.d. vertical tube. Visual observation (supported by pictures from video and still cameras) and the signals from a set of three fast response differential pressure transducers, were used to elucidate the flow behaviour of individual slugs of argon, with densities in the range 6.6-21.5 kg/m³ (corresponding to operating pressures in the range 0.4-1.3 MPa), as they rose in water that moved up the tube, with constant average velocity in the range 0.17-1.4 m/s. For the lower gas densities and liquid velocities the slugs were stable, but for the higher liquid velocities and/or gas densities, the slugs would become unstable, as a result of flooding in the wetted wall flow around them. The video sequences show clearly that, at the higher pressures, liquid from the film was dragged up by the gas, while the still pictures document the corresponding transition to churn flow in the lower regions of the rising slugs.