Fibre orientation distribution in turbulent fibre suspensions flowing through an axisymmetric contraction

The Reynolds averaged Navier–Stokes equation was solved numerically with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in turbulent fibre suspensions flowing through an axisymmetric contraction. The fluctuating fluid velocity was represented as a Fourier series with random coefficients. Then the slender‐body theory was used to predict the fibre orientation distribution and orientation tensor. Some numerical results are compared with the experimental ones in the turbulent fibre suspensions flowing through a contraction with a rectangular cross‐section. The results show that the fibres with high aspect ratio tend to align its principal axis with the flow direction much easier. High contraction ratio makes the fibre alignment with the flow direction much easier. The contraction ratio has a strong effect on the fibre orientation distribution. Only a small part of the fibre is aligned with the flow direction in the inlet region, while most fibres are aligned with the flow direction when they approach to exit. The fibres are aligned with the flow direction rapidly in the inlet region, after that the fibre orientations change little in the most of the downstream region. The fibres with high aspect ratio are aligned with the flow direction faster when they enter the contraction. The randomising effect of the turbulence becomes significant in the downstream region because of the high turbulent intensity.     

Laminar‐forced convection mass transfer to ordered and disordered single layer arrays of spheres

Laminar forced convection mass transfer to single layers of equidistantly and nonequidistantly spaced spheres perpendicular to the flow direction is studied. Average Sherwood numbers are reported as a function of geometric configurations and flow conditions, for open frontal area fractions between 0.25 and 0.95, Schmidt numbers between 0.7 and 10, and Reynolds numbers (based on the sphere diameter and the free stream velocity) between 0.1 and 100. For equidistantly spaced arrays of spheres, a general analytical expression is proposed for the average Sherwood number as a function of the Reynolds number, Schmidt number and the open frontal area fraction, as well as asymptotic scaling rules for small and large Reynolds. For all studied Schmidt numbers, equidistant arrays exhibit decreasing average Sherwood numbers for decreasing open frontal area fractions at low Reynolds numbers. For high Reynolds numbers, the Sherwood number approaches that of a single sphere, independent of the open frontal area fraction. For equal open frontal area fractions, the Sherwood number in nonequidistant arrays is lower than in equidistant arrays for intermediate Reynolds numbers. For very low and high Reynolds numbers, nonuniformity does not influence mass transfer. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1400–1408, 2013     

On the link between experimentally-measured turbulence quantities and polymer-induced drag reduction in pipe flows

In this study, we investigate the hydrodynamics of polymer-induced drag reduction (DR) in horizontal turbulent pipe flows. We provide spatiotemporally resolved information of velocity and its gradients obtained with particle image velocimetry measurements in solutions of water with dissolved polyethylene oxide of three different molecular weights (MWs), at various dilute concentrations and with flow Reynolds numbers from 35,000 to 210,000. We find that the local magnitudes of important turbulent flow variables correlate with the measured levels of DR irrespective of the flow Reynolds number, polymer weight, and concentration. Contour maps illustrate the spatial characteristics of this correlation. A relationship between the DR and the turbulent flow variables is found. The effects of the polymer MW, its concentration, and the Reynolds number on the flow are further examined through joint probability distributions of the fluctuations of the streamwise and spanwise velocity components.     

Mass/heat transfer from a neutrally buoyant sphere in simple shear flow at finite Reynolds and Peclet numbers

Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non‐zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006;96:134503; Subramanian and Koch, Phys Fluids. 2006;18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow‐gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier‐Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233–240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow‐gradient plane. However, the wake near the flow‐gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Direct simulations of spherical particle motion in Bingham liquids

The present work deals with the development of a direct simulation strategy for solving the motion of spherical particles in a Bingham liquid. The simulating strategy is based on a lattice-Boltzmann flow solver and the dual-viscosity Bingham model. Validation of the strategy is first performed for single phase (lid-driven cavity flow) and then for two phase flows. Lid-driven cavity flow results illustrate the flow's response to an increase of the yield stress. We show how the settling velocity of a single sphere sedimenting in a Bingham liquid is influenced by the yield stress of the liquid. The hydrodynamic interactions between two spheres are studied at low and moderate Reynolds number. At low Reynolds number, two spheres settle with equal velocity. At moderate Reynolds number, the yield effects are softened and the trailing sphere approaches the leading sphere until collision occurs.     

Laminar and turbulent entry flow of polymer solutions

Entry lengths and contraction losses have been determined for 0.01, 0.2 and 0.6% aqueous solutions of Separan AP-30. The Reynolds numbers ranged between 10² and 10⁵ in 1/2-in. and 2-in. tubes. At Reynolds numbers in excess of 2100, the entry lengths and contraction losses for the polymer solutions are significantly larger than those for Newtonian fluids. These effects are shown to be related to the transitional flow phenomena which occur with drag reducing polymer solutions. At low Reynolds number the contraction loss data show expected trends but are in quantitative disagreement with predictions based on recent studies in capillary tubes. These indicate that the analyses based on small tubes are less general than anticipated.     

Simulation of the newtonian flow through an abruptly contracted tube using a mixed finite element method

The solutions of the Navier-Stokes equation for a Newtonian flow through a 4/1 contraction tube were obtained numerically using the Galerkin finite element method with the nine-node Lagrangian element which was believed to be one of the most accurate tools for mixed-type interpolating formulations. It was proved from this study that the vortex occurrence in the entrance corner region were confirmed but its size was gradually decreased with the increase of Reynolds numbers, and that the velocity profiles and pressure distributions along the applied mesh layers were in agreement with the experimental and the previously reported numerical results.     

环形通道内层流入口段换热及流体变物性的影响

采用SIMPLER算法对环形通道内二维定常轴对称入口段流动与换热进行了数值计算, 研究了两种边界条件下的层流流动与换热规律, 给出了不同Prandtl数以及半径比率下沿程Nusselt数的变化曲线,同时还给出了流体物性随温度变化对流动与换热的影响, 最后还拟合出了不同半径比率下平均Nusselt数的关联式.计算结果还表明,环形通道能强化传热,强化程度随半径比率减小而增大,且入口段的换热强化与其较高的径向速度有关.     

Influence of Tortuous Geometry on the Hydrodynamic Characteristics of Laminar Flow in Microchannels

Flow visualizations are performed to study the hydrodynamic characteristics of laminar flow in tortuous microchannels for a wide range of Reynolds numbers. The detailed flow patterns in wavy channels are identified and found to be greatly affected by geometrical parameters. In wavy channels, steady flow exists at low Reynolds numbers, but above a critical number unsteady flow develops. The critical Reynolds number is found to depend on the characteristics of the channel path. Recirculation zones form immediately after the inner corners of the sharp bends, with their size and magnitude of the recirculation velocity increasing with higher Reynolds numbers. Large fluctuations in recirculation zone locations highlight the importance of these flow features in the development of transient flow. The flow behaviors play very important roles in determining the pressure drop in wavy channels relative to straight channels.     

Joule-Thomson effects on turbulent graetz problem for gas flows in pipes with uniform wall temperature

The Joule-Thomson effect is known to be important in arctic gas pipelines. The Joule-Thomson effects on forced convective heat transfer in the thermal entrance region of pipes with uniform wall temperature are studied for steady fully developed turbulent gas flows by the Graetz method. Thermal entrance heat transfer results are presented for Prandtl number 0.72, Reynolds number 10⁵ and Brinkman number ± 0.1, ± 1.0 with Joule-Thomson parameter Jμ ranging from 0 to 1.0 to cover the possible range in practical applications. Bulk temperatures and Nusselt numbers are also presented for fully developed flow with Reynolds numbers from 5 × 10³ to 10⁶. For given Prandtl and Reynolds numbers, the asymptotic Nusselt number is found to be dependent on the Joule-Thomson parameter only and is independent of Brinkman number. The fully developed bulk temperature is a linear function of Brinkman number and a linear relationship exists between the bulk temperature parameter (-θ_bf/Br) and the Joule-Thomson parameter Jμ for given Prandtl and Reynolds numbers.     

Transitional flow in a Rushton turbine stirred tank

The way in which the single phase flow of Newtonian liquids in the vicinity of the impeller in a Rushton turbine stirred tank goes through a laminar‐turbulent transition has been studied in detail experimentally (with Particle Image Velocimetry) as well as computationally. For Reynolds numbers equal to or higher than 6000, the average velocities and velocity fluctuation levels scale well with the impeller tip speed, that is, show Reynolds independent behavior. Surprising flow structures were measured—and confirmed through independent experimental repetitions—at Reynolds numbers around 1300. Upon reducing the Reynolds number from values in the fully turbulent regime, the trailing vortex system behind the impeller blades weakens with the upper vortex weakening much stronger than the lower vortex. Simulations with a variety of methods (direct numerical simulations, transitional turbulence modeling) and software implementations (ANSYS‐Fluent commercial software, lattice‐Boltzmann in‐house software) have only partial success in representing the experimentally observed laminar‐turbulent transition. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3610–3623, 2017     

Laminar and turbulent flow in annuli of unit eccentricity

Experimental results are presented for the flow of water in eccentric annuli having unit eccentricity in the laminar, transition and turbulent flow regimes at Reynolds numbers between 200 and 20,000. In both the laminar and turbulent regimes the interesting result is obtained that, for a given Reynolds number, the friction factor is a minimum at a diameter ratio of about 0.750. The experimental results are compared with previous theoretical analyses in the laminar region, and with previous experimental data at Reynolds numbers exceeding 20,000 in the turbulent region. A further interesting result relates to the transition region where, at intermediate diameter ratios, the transition from laminar to turbulent flow becomes more diffuse. This appears to be a consequence of the gradual change from laminar to turbulent flow brought about by the variation in local Reynolds number from zero to a maximum value within the eccentric annulus. It is believed that sufficent experimental data are now available for the pressure gradient to be predicted for flow in eccentric annuli of unit eccentricity over a relatively wide range of Reynolds number.     

Electroviscous effects in low Reynolds number liquid flow through a slit-like microfluidic contraction

A finite volume numerical method is used to predict electroviscous effects in steady state, pressure-driven liquid flow in a slit-like microfluidic contraction at low Reynolds number. A uniform charge density is assumed on the channel walls and the liquid is taken to be a symmetric 1:1 electrolyte. It is shown that predicted profiles of electrical potential, charge, and velocity across the channel at locations half way along the contraction and outlet sections are almost coincident with their uniform slit counterparts. A simple theory is developed that calculates the pressure drop along the channel by adding the pressure losses in the inlet, contraction and outlet sections (based on the classical fully developed electrokinetic flow solution in a uniform slit) to the entry and exit losses due to the contraction, approximated using the low Reynolds number analytical solution for a slit orifice without electrokinetic effects. For the parameter range investigated, the simple theory overestimates the apparent viscosity by up to 5-10%, compared with that determined by the numerical solution, but the differences are smaller when the surface charge density or EDL thickness is small, or the overall pressure drop is large (as occurs for long contractions).     

Reappearance of azimuthal waves in turbulent Taylor-Couette flow at large aspect ratio

Velocity field data were acquired for Taylor-Couette flow in the annular gap between an inner rotating cylinder and a stationary concentric outer cylinder using particle image velocimetry (PIV) in a meridional plane of the annulus. Data were acquired for several rotational Reynolds numbers with the ratio of the rotational and critical Reynolds numbers ranging from 6 to 200, corresponding to flow states ranging from laminar wavy Taylor vortex flow to turbulent Taylor vortex flow. Spatial correlations of velocity fluctuations were found to exhibit a sharp decrease as R, the ratio of Reynolds number to the critical Reynolds number, increases from 16, indicating the disappearance of azimuthal waves and the onset of turbulence, reaching a minimum at R=18. However, correlation lengths subsequently increase with increasing R, displaying a secondary peak from 20?R?38, suggesting the reappearance of azimuthal waves. The reemergence of azimuthal waves was confirmed through other methods including analysis of the axial velocity. At still higher Reynolds numbers, correlation lengths decay once again. The magnitude and Reynolds number associated with the secondary peak in the fluctuation velocity correlations were found to be dependent on the location of the basis point used in the calculations. Specifically, correlation lengths were longest near the outer cylinder in the inflow boundary and near the inner cylinder in the outflow boundary. This was shown to be due to the spatial dependence of Reynolds stresses in turbulent Taylor-Couette flow.     

Computational Modelling on Heat Transfer Study of Molten Silicon During Multi-crystalline Silicon Growth Process for PV Applications

Multi-crystalline silicon is an important material with advantages of low-production cost and high conversion efficiency for photovoltaic solar cells. Directional solidifi cation has become the main technique for producing mc-Si ingots for solar cell applications. The study is performed in the framework of the incompressible Navier-Stokes equation in the Boussinesq approximation with convection-conduction equations. The computations are carried out in a two dimensional (2D) axisymmetric model by the finite- element method. The influence of the Reynolds numbers, total heat flux and velocity streamline pattern on the silicon melt was simulated and analyzed for various Rayleigh numbers between 10 to 10 ⁶ with the help of a numerical technique. The following key findings are presented in this paper. The velocity field value is increased above 0.02(m/s), heat flux value is increased to 10 ⁴(W/m ²), when the Rayleigh number is increased above 1000. Reynolds numbers are also studied in five parallel horizontal cross-sections of the melt silicon region for various Prandtl numbers at a critical Rayleigh number of 1000. Reynolds numbers are varied between 100 and 10 ⁵ for the Rayleigh numbers between 10 to 10 ⁶. Meanwhile, the melt has high fluctuation when the Prandtl number is increased above 0.01. The flow is converted from laminar to turbulence at a critical Rayleigh number 1000 and Prandtl number 0.01. These results provide important information for controlling the melt fluctuations during the solidification process which are used to increase the average grain size in growing silicon multicrystals and reduce the dislocation density.     

Fine particle turbulence modulation

Streamwise turbulence intensities of fine particulate suspensions were studied in a 26 mm N.B. horizontal pipe loop. Colloidal silica spheres were prepared in 10^?4M and 1M KNO₃ solutions to control the degree of aggregate formation in the suspension. Using an ultrasonic Doppler velocity profiling sensor, the turbulence intensities of the fine particle suspensions were compared with those of a particle‐free flow over a range of Reynolds numbers. At low electrolyte concentration, the silica particles remain dispersed, with the turbulence intensity of the suspension flow comparable with that of the particle‐free flow. At high electrolyte concentration, increased particle‐particle interaction leads to the formation of particle aggregates which support turbulence augmentation over a critical Reynolds number range. The range of Reynolds numbers over which this turbulence enhancement is observed is limited by both fluid dynamic effects at low Reynolds numbers (Re ≈ 5500) and aggregate breakup at high Reynolds numbers (Re ≈ 8000). © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

MATHEMATICAL MODELING OF THROUGH-HOLE-PLATING IN ELECTROCHEMICAL MICROFABRICATION I. AXISYMMETRIC TWO-DIMENSIONAL FLUID FLOW

A mathematical model to simulate the current distribution in a through-hole plating process is developed to account for fluid mechanics, mass transfer mechanism and electrochemical kinetics. The first phase of the study involved the calculation of the flow pattern of a viscous fluid in an axisymmetric through-hole geometry. Numerical calculations were conducted for various degrees of contraction and expansion and for several values of Reynolds numbers. Results indicated that the extend of fluid separation depends linearly on the Reynolds number. The expected adverse pressure gradient during separation was evaluated quantitatively. It was also demonstrated that the axial velocity profile could be approximated satisfactorily by a modified Hagen-Poiseuille distribution with one parameter.     

Non-Newtonian thin films: Theory and experiment

The flow of thin films of Newtonian and non-Newtonian, Power law fluids down a vertical plate was studied in the laminar and wavy flow regimes. A theoretical development based on the existence of a steady, periodic solution to the equations describing film flow was used to predict the flow characteristics of the film. Double logarithmic plots of film thickness versus Reynolds number (Re_{P. L.}) were linear, as predicted, up to a Re_{P. L.} = 100. The ratio of surface to average velocity was found to be approximately independent of the Reynolds number at values predicted by a laminar velocity profile. The wavelength of stable waves was found to be independent of the Reynolds number for a given fluid.     

管内垂直下降液膜速度与厚度分布特性

对洗涤冷却管内垂直降膜的流动特性进行研究,采用超声波多普勒测速仪对管内不同周向以及轴向位置的液膜厚度和速度进行了无接触式的测量,液膜Reynolds数范围为1.0×10⁴~3.1×10⁴。结果表明:在0°周向位置上液膜厚度与速度均达到最大值,导致该位置局部液膜厚度过大而不能保持稳定,部分液体脱离液膜表面,此外还造成了8°和16°位置的液膜厚度激增。在轴向上,当Reynolds数小于2.0×10⁴时,液膜速度在重力作用下随流动距离增加而增加,反之,液膜速度因为流动阻力会随距离增加而减小。随着Reynolds数的增大,液膜平均厚度和速度呈增大趋势。此外,Reynolds数的增大还会使得液膜更加不稳定。