New techniques for measuring and modeling cavern dimensions in a Bingham plastic fluid

A model for predicting the mixing cavern dimensions for Bingham plastic fluids based on the assumption of equal torque is developed. Experimental data has been collected for the purpose of verifying this model, using a novel technique, for both axial and radial flow impellers in a tank of Heinz ketchup. The mixing caverns were found to be the shape of an elliptical torus. The ellipse aspect ratios were determined for both impeller types and are assumed to be constant. The model was able to predict the cavern diameter and cavern height within the experimental uncertainty.     

Laminar flow of power-law fluids in the entrance region of a pipe

The study is concerned with developing laminar flow of a power-law fluid in a circular tube. The analysis extends the filled-region concept, used previously to study Newtonian fluid flow, to the more general class of power-law fluids. Flow is analyzed in both the inlet and filled regions using an integral boundary layer method. Results obtained provide the lengths of the entrance, inlet and filled regions as a function of the generalized Reynolds number and the power-law fluid index. In addition, the variations of the local friction factor, the pressure drop and the centerline velocity along the axial coordinate are also provided. The available models are compared with the present one on the basis of experimental data. The present results are found to reach asymptotically the fully developed values, and also to be in good agreement with all available experimental data.     

Shear rates investigation in a scraped surface heat exchanger

The electrodiffusion technique was performed in order to investigate the shear rate on a scraped surface heat exchanger. Microelectrodes were placed inside: the walls of the outer cylinder; the inlet and outlet bowls; the rotor and the blades. Highly viscous Newtonian fluid (Emkarox HV45 solutions) and non-Newtonian model fluid (aqueous solutions of CMC) were used. The electrodiffusion method allowed us to measure wall shear rates. Maximum shear rate was observed at the scraping surface and caused by blades scraping, high shear rate was also measured on the leading edge of the blades. In the other parts of the exchanger, shear rate remained low but the development of Taylor vortices completely modified the scraped surface heat exchangers behaviour inside the surface of the bowls. A dimensionless representation of the friction factor was established for the inner and outer wall surface of the exchanger.     

Gas displacing liquids from tubes: high capillary number flow of a power law liquid including inertia effects

Computer simulation has been used as a virtual experimental tool to investigate the displacement of a shear thinning Power Law liquid from a cylindrical tube by a gas, in the limit of high capillary number and in the absence of gravity effects. Two scenarios have been considered. In the first, gas enters at a steady rate, and the gas penetration velocity and residual wall layer thickness attain steady values. In the second, a constant gas pressure is applied at the inlet, and the gas penetration rate accelerates as the column of liquid ahead of it becomes shorter. The first set of experiments confirm that the developed wall layer thickness falls with increased degrees of shear thinning and with increased Reynolds Number, and quantifies the latter effect for the first time. The relationship is summarized by a correlation formula for dimensionless layer thickness as a function of Power Law index, n, and an appropriately defined Reynolds group in the range 0.1?n?1.0,0.001?Re?100. The flow pattern ahead of the gas bubble throughout the range of these experiments was always of the ‘by-pass’ type, consistent with a generalized criterion for the transition between by-pass and re-circulating flow which is derived for a Power Law liquid. In the second set of experiments, where a constant gas inlet pressure is applied, giving accelerating gas penetration, a comparison of layer thickness values at various axial positions, with those obtained at corresponding Reynolds number in steady flow, showed close agreement, though a small discrepancy for the highest Reynolds numbers could indicate some influence of inertia in the accelerating liquid column. At higher Reynolds number, in both steady and accelerating flow, the gas bubble near to the inlet shows a concave region on the axis, with re-circulation in the liquid ahead of it. As the bubble moves down the tube, the radius of this concavity decreases and a steady convex profile is eventually attained, with reversion of the flow to by-pass type. We show that the origin of this is inertial.The results have applications in a number of technologies, including gas-assisted injection moulding of plastics and certain gas liquid reactors.     

Gas displacing liquids from non-circular tubes: high capillary number flow of a shear-thinning liquid

Transient, three-dimensional finite element analysis has been used to investigate the displacement of a shear thinning liquid from prismatic channels of square, rectangular and trapezoidal cross sections. Inertia, gravity and surface tension effects are neglected and the results therefore apply in the limits of low Reynolds and high capillary numbers. The analysis is carried out in a fixed frame of reference and gas penetration is modelled as the bubble moves down the tube, which is long relative to its transverse dimension. Results are provided for the thickness of the layers left on the channel walls under developed conditions, and the fraction of the cross section occupied by liquid, as a function of the channel cross-sectional geometry and the degree of shear thinning, modelled using the power law. Interface contours on the channel cross sections are displayed. It is found for the Newtonian liquid that the fingering instability arises in the rectangular channel when the aspect ratio reaches about five. Shear thinning delays the onset of the instability to higher aspect ratios. The results are systematized, and insights gained into the influence of channel geometry and shear thinning, by noting a qualitative, inverse relationship between the deposited layer thickness and the shear rate at the wall in the flow ahead of the bubble.     

Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime

A computational fluid dynamics (CFD) model of flow in a mixing tank with a single axial-flow impeller was developed with the Fluent^TM software. The model consists of an unstructured hexagonal mesh (158,000 total cells), dense in the region from the surface of the impeller. The flow was modeled as laminar and a multiple reference frame approach was used to solve the discretized equations of motion in one-quarter of a baffled tank. A solution of 0.1% Carbopol in water, a shear-thinning fluid, was found to be clear enough to measure impeller discharge angles using laser Doppler velocimetry. This is the first time that impeller discharge angles have been reported in the literature for a shear-thinning fluid with a hydrofoil impeller. Rheological measurements indicated that the Carbopol solution can be characterized by the power law (K=9,n=0.2) under the range of shear conditions (0.1- expected near the impeller in the mixing tank. The CFD model accurately predicted the dependence of power number and discharge angle on Reynolds number (as predicted by Metzner and Otto), for an A200 (pitched blade turbine or PBT) and an A315 (Hydrofoil) impeller operating in the transitional flow regime (Reynolds numbers: 25-400) with glycerin and 0.1% Carbopol solutions. Subsequently, the results of a systematic CFD study with power law fluids indicated that the power number and discharge angle of an axial-flow impeller in the transitional flow regime depends not only on the Reynolds number (as determined by Metzner and Otto's method) but also on the flow behavior index n. Consequently, an alternative to Metzner and Otto's method was pursued. The results of converged CFD simulations indicate that the near-impeller “average shear rate” increases not only with increasing RPM (as proposed by Metzner and Otto), but also with decreasing flow behavior index (n) and discharge angle in the transitional flow regime. Considering this result, an improved method of estimating the power number and discharge angle for power law fluids in the transitional flow regime is proposed.     

Experimental study of drag reduction by a polymeric additive in slug two-phase flow of crude oil and air in horizontal pipes

In this study the effect of the presence of a drag reducing agent (DRA) on the pressure drop in cocurrent horizontal pipes carrying slug two-phase flow of air and crude oil is investigated. An experimental set-up is erected. The test section of the experimental set-up is consisted of: a smooth pipe of polycarbonate with 10.3 m long and 2.54 cm ID, a rough pipe of galvanized iron with 8.8 m long and 2.54 cm ID and a rough pipe of galvanized iron with 8.8 m long and 1.27 cm ID. The employing DRA is a Polyalpha-olefin (Polyisobutylene). The percent drag reduction (%DR) is calculated using the obtained experimental data, in presence of the DRA. The results show that addition of DRA could be effective up to some doses of DRA after which the pressure drop is kept constant. A %DR of about 40 is obtained for some experimental conditions.     

Conduction and dissipation in the shearing flow of granular materials modeled as non-Newtonian fluids

After providing a brief review of the constitutive modeling of the stress tensor for granular materials using non-Newtonian fluid models, we study the flow between two horizontal flat plates. It is assumed that the granular media behaves as a non-Newtonian fluid (of the Reiner-Rivlin type); we use the constitutive relation derived by Rajagopal and Massoudi [Rajagopal, K. R. and M. Massoudi, “A Method for measuring material moduli of granular materials: flow in an orthogonal rheometer,” Topical Report, DOE/PETC/TR-90/3, 1990] which can predict the normal stress differences. The lower plate is fixed and heated, and the upper plate (which is at a lower temperature than the lower plate) is set into motion with a constant velocity. The steady fully developed flow and the heat transfer equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers and viscous dissipation are discussed.     

Dynamic prediction of milk ultrafiltration performance: A neural network approach

Neural network models were tested in connection with the dynamic prediction of permeate flux (J_P), total hydraulic resistance (R_T) and the solutes rejection for the crossflow ultrafiltration of milk at different transmembrane pressure (TMP) and temperature (T). This process has complex non-linear dependencies on the operating conditions. Thus it provides demanding test of the neural network approach to the process variables prediction. Two neural network models with single hidden layer were constructed to predict the time dependent rate of J_P/R_T and rejections from a limited number of training data. The modelling results showed that there is an excellent agreement between the experimental data and predicted values, with average errors less than 1%. The experimental results showed that the R_T and solutes rejection (except for protein) increased greatly with time at each value of TMP and T, whereas the J_P decreased significantly for the same conditions. Increasing TMP at constant T led to an increase in the J_P, R_T and solutes rejection, but increasing T at constant TMP had no significant effect on the J_P, R_T and rejection of components.     

Dynamic modelling of the deformation of a drop in a four-roll mill

The deformation of a drop flowing along the centre streamline of a four-roll mill (4RM) has been investigated. The velocities and elongation rates along the centre streamline in the 4RM were measured using particle tracking velocimetry. The deformation and position of the deforming drops were photographed with a video camera. A dynamic, one-dimensional, analytical simulation model describing the drop deformation has been developed. The model is based on Taylor's [1964. International Congress on Applied Mechanics, vol. 11, 790-796] static conical drop shape model, but has been extended to include elliptic drops undergoing rapid deformation. The model was incorporated into a numerical scheme using Matlab and the drop deformation in the 4RM was simulated. The simulations were compared with the results of the experiments with the help of a dynamic Weber number incorporating the exact effect of the continuous phase stress on the deformation of the drop. With a dynamic Weber number of 0.42 the agreement between the experiments and the simulations along the whole deformation process was excellent for all three drop diameters studied. With this model the deformation of drops of all sizes in different elongation fields can be calculated, for example sub-micron-sized drops in a high-pressure homogeniser.     

Mixed convection in the heated semi-circular lid-driven cavity for nonNewtonian power-law fluids: Effect of presence and shape of the block

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the liddriven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for twodimensional, steady-state, laminar and for non-Newtonian power-law fluids. The semi-circular cavity has a diameter of D. The horizontal wall/lid is sliding with a uniform horizontal velocity(u = U) and is subjugated to the ambient thermal condition; while the curved surface is subjugated to a higher isothermal temperature.The convective characteristics inside the system is explored for the broad range of Richardson number(0.1 ≤Ri ≤ 10), Prandtl number(1 ≤ Pr ≤ 100) and non-Newtonian power-law index(0.5 ≤ n ≤ 1.5) at a constant Grashof number of 10~4. Apart from this, the effect of shape(cross-section) of the inserted block, i.e., circular, square and triangular on heat transfer characteristics has also been explored. It is observed that the shear thickening fluids display better cooling characteristics. Besides, the cavity with immersed triangular block shows better heat transfer results than the circular and square blocks. The deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number(Nu~N). The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the cavity. In the end, the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number, power-law index, and Richardson number.     

Observation and modelling of capillary flow occlusion resulting from the capture of superparamagnetic nanoparticles in a magnetic field

The magnetic field mediated capture of 10 nm diameter superparamagnetic nanoparticles, in the form of agglomerates of mean diameter 330 and 580 nm, from microcapillary flows has been observed and modelled. The steady state thickness of the captured layer in microcapillaries of diameter 400- could be predicted for both the 330 and the 580 nm diameter agglomerates at flow rates of between 0.1 and . The model provides insight into blockage formation at a constant flow rate as a precursor to the prediction of thrombotic embolism in magnetic directed therapies. Capillary constriction was particularly acute for the 580 nm agglomerates in large microcapillaries with flow rates of . From this model, agglomerates of diameter 330 nm or less offer the potential for minimal microcapillary occlusion in a range of flow rates.     

A novel approach for determining the flow patterns in centrifuges by means of Laser-Doppler-Anemometry

The flow pattern in process machinery has a significant impact on the product quality, because it influences the residence time, the mixing of components and the stability of chemical reactions. Hence the determination of the residence time and the measurement of the flow patterns have been the emphasis of many studies. The work presented shows a novel approach for the determination of the tangential and axial velocity profiles in a tubular bowl centrifuge. For the first time, flow velocities inside a fast rotating centrifuge have been measured using Laser-Doppler-Anemometry. The rotor of the centrifuge is made of carbon fibre reinforced plastic with an inner diameter of 100 mm and a length of 200 mm. The maximum rotational speed is 20,000 rpm, creating the multiple of 22,400 times the earth gravitational force. No failure of the material was detected at any process parameters. The centrifuge is operated with two different setups. One setup employs an assembly of two coaxial cylinders, in which the void between them is entirely filled with water. In the second arrangement, only the outer rotor is assembled and the centrifuge is operated like an overflow centrifuge. The Laser-Doppler measurements of the axial fluid velocity are confirmed by determining the residence time distribution at various parameters. The results obtained show an effective tangential acceleration; the liquid exhibits a rigid body rotation for rotational speeds up to 8000 rpm for throughputs between 0.5 and 1.8 l/min. The axial flow pattern depend on the volume flux and the rotational speed. The cross-section through which the liquid flows was in most cases between 60% and 100% of the overall area. The influence of the inlet subsides towards the outlet with an inlet zone of 15% of the length of the rotor. No boundary layer flow was detected in the overflow setup, which is due to the plunged inlet and the effective tangential acceleration of the incoming liquid.     

Computational analysis of the flow of pseudoplastic power-law fluids in a microchannel plate

The flow of pseudoplastic power-law fluids with different flow indexes at a microchannel plate was studied using computational fluid dynamic simulation.The velocity distribution along the microchannel plate and especially in the microchannel slits,flow pattern along the outlet arc and the pressure drop through the whole of microchannel plate were investigated at different power-law flow indexes.The results showed that the velocity profile in the microchannel slits for low flow index fluids was similar to the plug flow and had uniform pattern.Also the power-law fluids with lower flow indexes had lower stagnation zones near the outlet of the microchannel plate.The pressure drop through the microchannel plate showed huge differences between the fluids.The most interesting result was that the pressure drops for power-law fluids were very smaller than that of Newtonian fluids.In addition,the heat transfer of the fluids through the microchannel with different channel numbers in a wide range of Reynolds number was investigated.For power-law fluid with flow index (n =0.4),the Nusselt number increases continuously as the number of channels increases.The results highlight the potential use of using pseudoplastic fluids in the microheat exchangers which can lower the pressure drop and increase the heat transfer efflciency.     

A practical method for predicting the friction factor of power-law fluids in a rectangular duct

This article presents a simple and unique method for predicting the friction factor for the fully developed, laminar flow of power-law fluids in ducts with a rectangular cross-section by means of an engineering calculation for rapid equipment design. The relationship between friction factor f and the Reynolds number defined by Metzner–Reed (Re_MR) for a rectangular cross-section was investigated and rearranged with very good engineering accuracy using the results of very simple correlations based on the application of the well-known and long-established coefficient for Newtonian fluid flow. The investigated value of the flow index was up to 2, and the aspect ratio ranged from 0 to 1, with calculation error not higher than 3.5%. The proposed method was compared with conventional methods from the literature, and was validated by means of numerical computations, and also with experimental data from the literature. The product of friction factor and Re_MR is a linear function of geometrical parameter C and flow behavior index n and also the proposed method predicts the friction factor as accurately as conventional and traditional methods.     

Transition of the flow in a symmetric channel with periodically expanded grooves

Transition of the flow in a periodically grooved channel is numerically investigated for periodicity indices m=1 up to 6 by assuming the two-dimensional and fully developed flow field, where m is defined as a number of grooves in which the flow repeats periodically. Critical Reynolds numbers for the onset of a self-sustained oscillatory flow from a steady-state flow are evaluated by numerical simulations. It is found that the bifurcations occur at the critical Reynolds numbers as a result of Hopf bifurcation, and a period in the streamwise direction of the oscillatory flow is twice as long as the groove pitch of the channel. In addition, flow visualization with the aluminum dust method is carried out to confirm the results obtained from the numerical simulations. The experimental results are in good agreement with the numerical ones.     

Forces on the surface of small ellipsoidal particles immersed in a linear flow field

Knowledge of the forces which a fluid motion exerts on the surface of suspended material is important for many processes in which the particles are broken apart by the hydrodynamic forces. In this paper, we examine the stresses on a small ellipsoidal particle which is immersed in either a constant, simple shear, two-dimensional straining or axisymmetric straining flow. Calculations have been performed using Oberbeck's and Jeffery's models and have been appropriately visualized. Furthermore, the motion and orientation of the ellipsoid have been examined and the extreme values of stresses have been analyzed. A simple criterion for the break-up of particles is proposed. The analysis shows that the straining flows are particular important for the load on particles. In contrast, simple shear flows are less crucial as the presence of vorticity leads to a rotation of the particles.     

Fluid dynamics and mixing of single-phase flow in a stirred vessel with a grid disc impeller: Experimental and numerical investigations

We report experimental and numerical investigations of a novel grid disc impeller for mixing of single-phase flow in stirred vessels. We performed detailed mean velocity measurements using LDA to understand the flow generated by the grid disc impeller and we also measured the mixing time and power consumption of the grid disc impeller. Measurements showed that the performance of the grid disc impeller, which has radial flow characteristics, is equivalent to a standard propeller in terms of the degree of mixing achieved per unit power consumption. We also performed numerical simulations to predict the flow generated by the grid disc impeller and its mixing performance. It was shown that the present computational model predicts the mean velocities, power consumption and mixing time in good agreement with the measurements. The experimentally validated computational model was further used to understand the effects of impeller rotational speed and grid disc configuration on the fluid dynamics and mixing performance of the grid disc impeller.     

Experimental studies on the flow of two immiscible fluids in porous media using X-ray computed tomography: The case when the viscosities of the fluids are equal

Experiments were carried out to demonstrate the dispersion that occurs at the interface between fluids when two immiscible fluids flow in porous structures. In this work the porous medium was cellulosic absorbent and the fluids, decyl alcohol and water, were modified so as to cover a range of flow rates and identical fluid viscosities. Computerized Tomography (CT) was used to generate dynamic three-dimensional images of two-phase saturations and provided quantitative information of time evolution of fluid saturation at each position. Thus, use of CT made characterization of two-phase displacement history in cellulosic porous media possible. This work could relate experimental fluid saturation to theoretical model of immiscible fluids flow.