Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.     

Effect of drag reducing polymers on oil–water flow in a horizontal pipe

Measurements of drag-reduction are presented for oil–water flowing in a horizontal 0.0254 m pipe. Different oil–water configurations were observed. The injection of water soluble polymer solution (PDRA) in some cases produced drag reduction of about 65% with concentration of only 10–15 ppm. The results showed a significant reduction in pressure gradient due to PDRA especially at high mixture velocity which was accompanied by a clear change in the flow pattern. Phase inversion point in dispersed flow regime occurred at a water fraction range of (0.33–0.35) indicated by its pressure drop peak which was disappeared by injecting only 5 ppm (weight basis) of PDRA. Effect of PDRA concentration and molecular weight on flow patterns and pressure drops are presented in this study. Influence of salt content in the water phase on the performance of PDRA is also examined in this paper.     

Numerical investigations on gas–solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas–solid circulating fluidized bed (CFB) riser by including the cluster information collected from image processing and wavelet analysis into the calculation of system drag. The performance of the proposed drag model is compared with some commonly used drag models. A good agreement with the experimental data is achieved by the proposed cluster-based drag model. Error analysis of the proposed cluster-based drag model based on the local distributions of solids holdup and particle velocity is conducted. The clustering phenomenon in the low-density and high-density CFB risers and the effect of the cluster size on the simulation accuracy are also numerically studied by the proposed drag model.     

Review on vertical gas–liquid slug flow

Vertical slug flow is characterized by the rise of long bullet-shaped gas bubbles with a diameter almost matching that of the tube - Taylor bubbles. Liquid slugs separate consecutive Taylor bubbles, which may interact and coalesce if the distance between them is small. Slug flow has numerous industrial applications, being also observed on physiological and geological systems. In spite of the contribution of the development of non-intrusive experimental techniques to a deeper understanding of slug flow features, the complexity of this flow pattern requires the combined use of numerical approaches to overcome some of the optical problems reported in experimental methods, and other limitations related to the flow aperiodic behavior.The need to systematize the large amount of data published on the subject and to understand the limitations of the techniques employed constitutes the motivation for this review. In the present work, literature on vertical gas–liquid slug flow, with Newtonian fluids, from 1943 to 2015, covering theoretical, experimental and numerical approaches, is reviewed. Focus is given to single and trains of Taylor bubbles rising through stagnant and co-current liquids.It should be emphasized, however, that further research still needs to be conducted in some particular areas, namely the hydrodynamics of the liquid film surrounding the Taylor bubbles, the interaction between consecutive bubbles, and a more detailed approach to the flow of Taylor bubbles through co-current liquids.     

A review of research on nanoparticulate flow undergoing coagulation

Nanoparticulate flows occur in a wide range of natural phenomena and engineering applications and, hence,have attracted much attention. The purpose of the present paper is to provide a review of the research conducted over the last decade. The research covered relates to the Brownian coagulation of monodisperse and polydisperse particles, the Taylor-series expansion method of moment, and nanoparticle distributions due to coagulation in pipe and channel flow,jet flow, and the mixing layer and in the process of flame synthesis and deposition.     

Thermocapillary flow without return flow–linear flow

The experimental realization of thermocapillary flow without return flow is reported. This type of flow (linear flow) was proposed and analyzed theoretically by Smith and Davis (J. Fluid Mech., 132:119–144, 1983). We suppressed the return flow by providing channels and side channels with lower flow resistance compared to that of the return flow. Cooling the layer with linear flow from above results in the Marangoni instability of longitudinal rolls as the most dangerous mode. Strong linear flow stabilizes the system against longitudinal rolls. We report preliminary results on the threshold and on the wavelength of the longitudinal rolls.     

Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations

A new analytical model was developed to predict the gravity wave drag (GWD) induced by an isolated 3-dimensional mountain, over which a stratified, non-rotating non-Boussinesq sheared flow is impinged. The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height. The modified Taylor-Goldstein equation with variable coefficients is solved with a Wentzel-Kramers-Brillouin (WKB) approximation, formally valid at high Richardson numbers. With this WKB solution, generic formulae of second order accuracy, for the GWD and surface pressure perturbation (both for hydrostatic and non-hydrostatic flow) are presented, enabling a rigorous treatment on the effects by vertical variations in wind profiles. In an ideal test to the circular bell-shaped mountain, it was found that when the wind is linearly sheared, that the GWD decreases as the Richardson number decreases. However, the GWD for a forward sheared wind (wind increases with height) decreases always faster than that for the backward sheared wind (wind deceases with height). This difference is evident whenever the model is hydrostatic or not.     

End wall effect on particle motion in a chute flow

The influence of the end wall of a chute on the rotation of internal characteristic particles is mainly on the z-axis.A measurement device based on inertial measurement technology does not require the assistance of external information;hence,it is especially suitable for measuring the angular and translational velocities of internal characteristic particles.To study the influence of the end wall of the chute on the motions of the internal characteristic particles,the z-axis rotational and translational velocities of the internal characteristic particles in the chute were measured,and it was found that the rotational velocity about the z-axis differs according to the initial position.The z-axis angular velocity of a characteristic particle at the centre fluctuates near 0,and the average value approaches 0.The z-axis angular velocity of a characteristic particle at the left end wall is typically negative.This phenomenon is due to the influence of the end wall on the rotational motions of particles with initial positions that are near the end wall.In addition,the average translational velocity of the characteristic particles is also affected by the end wall.The distributions of the average z-axis angular velocity and the average translational velocity are quantitatively analysed,and the correlation between the tilt angle of the chute and the end wall effect is studied.     

Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

Effect of heat flow on heat‐transfer characteristics for a supersonic spatial flow around a spherically blunted cone

Heattransfer processes for a supersonic spatial flow around a spherically blunted cone were studied by solving direct and inverse threedimensional problems taking into account heat flow along the longitudinal and circumferential coordinates. It is shown that highly heatconducting materials can be used to advantage to decrease the maximum temperatures on the windward side of streamline bodies.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.     

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convectionflows, the surface of the cylinder is maintained by the uniform surface temperature(UST)or the uniform heat flux(UHF) condition. The governing equations corresponding to theflow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids(n > 1) than the other fluids(n≤1).The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.     

Experimental study on interfacial waves in stratified horizontal oil–water flow

Interfacial wave characteristics were studied experimentally in horizontal oil–water pipe flows during stratified flow and at the transition to dual continuous flow, where drops of one phase appear into the other (onset of entrainment). The experimental investigations were carried out in a stainless steel test section with 38 mm ID with water and oil (density 828 kg/m³and viscosity 5.5 mPas) as test fluids. Wave characteristics were obtained with a high speed video camera and a parallel wires conductivity probe that measured the instantaneous fluctuations of the interface. Experiments were conducted at 2 m and at 6 m from the inlet. Visual observations revealed that no drops are formed when interfacial waves are absent. It was also found that waves have to reach a certain amplitude before drops can detach from their crests. Wave amplitudes are increased as the superficial velocities of both phases increase. In the stratified region, the mean wave amplitude decreases by increasing the oil–water input ratio while mean wavelength increases as the slip velocity between the two-phase decreases. At the onset of entrainment, the mean amplitude and length are found to be a function of the relative velocity between the oil and water layers and of the turbulence in each layer.     

Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis

When a two-dimensional (2D) imaging system is used to visualize particle motion in a 3D gas–solid flow, the particle rotation speed was found extremely difficult to be accurately measured due to the fact that the direction of rotation axis was usually random and hard to be distinguished. The paper presents a method to calculate the particle rotation speed from particle images based on the identification of its rotation axis using two or more characteristic points on its surface. The idea was analyzed and realized in a mathematical way and based on which a calculation program was given. The measurement method was verified with an experiment using a small sphere with known rotation axis and rotation speed. The effects of several factors, including the direction of the particle rotation axis, the particle image resolution, the types and positions of characteristic points, etc., on the measurement error are discussed. The error is found to be acceptable for most cases. The measurement method was finally applied to those small glass beads in a real 3D gas–solid flow inside a cold circulating fluidized bed (CFB) riser, which indicates that the problems of 2D imaging system applying to 3D particulate system could be solved by using this mathematical method.     

Soret and Dufour effects on magnetohydrodynamic （MHD） flow of Casson fluid

This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.     

Study on the instability in separating–reattaching flow over a surface-mounted rib

A numerical study on the flow structure and instability in the separated–reattached flow over a surface-mounted rib at Re = 1000 is performed using large eddy simulation. It is found that the phenomenon of vortex pairing, which has been extensively observed in similar flows, exists in the separation zone. Based on the spectral analysis, the Kelvin–Helmholtz (K-H) instability of shear layer at St ≈ 0.361 (St ≡ fh/U₀) and its subharmonic at St ≈ 0.18 are found. It is assumed that the K-H instability reduces to its subharmonic through the vortex pairing. This process is further confirmed by the flow visualisation. The two-dimensional (2D) structures are subjected to sinusoidal undulation along the spanwise and observed to undergo helical pairing process, which is attributed to the transformation of 2D structures into 3D. However, the low frequency due to flapping of the shear layer is not found.     

Bubble–wall interaction and two-phase flow parameters on a full-scale boat boundary layer

Full scale bubbly flow experiments were performed on a 6 m flat bottom survey boat, measuring the void fraction, bubble velocity and size distributions as the bubbles naturally entrained at the bow of the boat interact with the boat’s boundary layer. Double-tip sapphire optical probes capable of measuring bubbles down to 50 μm in diameter were specifically designed and built for this experiment. The probes were positioned under the hull at the bow near the bubble entrainment region and at the stern at the exit of the bottom flat plate. Motorized positioners were used to vary the probe distance to the wall from 0 to 50 mm. The experiments were performed in fresh water (Coralville Lake, IA) and salt water (Panama City Beach, FL), at varying velocities with most data analysis performed at 10, 14 and 18 knots. The results indicate that the bubbles interact significantly with the boundary layer. At low velocity in fresh water, bubble accumulation under the hull and coalescence are evident by the presence of large bubbles at the stern. At high speeds bubble breakup dominates and very small bubbles are produced near the wall. It is also observed that salt water inhibits coalescence, even at low boat speeds. The void fraction increases with speed beyond 10 knots and peaks near the wall. Bubble velocities show slip with the wall at all speeds and exhibit large RMS fluctuations, increasing near the wall.