Laminar,transitional and turbulent annular flow of drag-reducing polymer solutions

Mean and rms axial velocity-profile data obtained using laser Doppler anemometry are presented together with pressure-drop data for the flow through a concentric annulus (radius ratio κ = 0.506) of a Newtonian (a glycerine–water mixture) and non-Newtonian fluids—a semi-rigid shear-thinning polymer (a xanthan gum) and a polymer known to exhibit a yield stress (carbopol). A wider range of Reynolds numbers for the transitional flow regime is observed for the more shear-thinning fluids. In marked contrast to the Newtonian fluid, the higher shear stress on the inner wall compared to the outer wall does not lead to earlier transition for the non-Newtonian fluids where more turbulent activity is observed in the outer wall region. The mean axial velocity profiles show a slight shift (～5%) of the location of the maximum velocity towards the outer pipe wall within the transitional regime only for the Newtonian fluid.     

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight (M_w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ～4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.     

Non-Newtonian flow in microporous structures under the electroviscous effect

Single phase non-Newtonian microporous flow combined with the electroviscous effect is investigated in the pore-scale under conditions of various rheological properties and electrokinetic parameters. The lattice Boltzmann method is employed to solve both the electric potential field and flow velocity field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends on both the fluid rheological behavior and pore surface area ratio significantly. For the shear thinning fluid with power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electrovicous effect plays a more important role compared to the Newtonian fluid and shear thickening fluid. The high pore surface area ratio in the porous structure increases the electroviscous force and the induced flow resistance becomes important even to the flow of Newtonian and shear thickening fluids.     

Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.     

Electroviscous effect on non-Newtonian fluid flow in microchannels

Understanding non-Newtonian flow in microchannels is of both fundamental and practical significance for various microfluidic devices. A numerical study of non-Newtonian flow in microchannels combined with electroviscous effect has been conducted. The electric potential in the electroviscous force term is calculated by solving a lattice Boltzmann equation. And another lattice Boltzmann equation without derivations of the velocity when calculating the shear is employed to obtain flow field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends significantly on the fluid rheological behavior. For the shear thinning fluid of the power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electroviscous effect plays a more important role. And its effect on the flow increases as the ratio of the Debye length to the channel height increases and the exponent n decreases. While the shear thickening fluid of n > 1 is less affected by the electroviscous force, it can be neglected in practical applications.     

Some exact solutions for rotating flows of a generalized Burgers’ fluid in cylindrical domains

The velocity field and the adequate shear stress corresponding to the flow of a generalized Burgers’ fluid model, between two infinite co-axial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions J₁( ? ), J₂( ? ), Y₁( ? ) and Y₂( ? ), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers’, Oldroyd-B, Maxwell, second grade, Newtonian fluids and large-time transient solutions for generalized Burgers’ fluid are also obtained as special cases of the present general solutions. The effect of various parameters on large-time and transient solutions of generalized Burgers’ fluid is also discussed. Furthermore, for small values of the material parameters, λ₂ and λ₄ or λ₁, λ₂, λ₃ and λ₄, the general solutions corresponding to generalized Burgers’ fluids are going to those for Oldroyd-B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

Soret and Dufour effect on double diffusion mixed convection from a vertical surface in a porous medium saturated with a non-Newtonian fluid

A non-similar boundary layer analysis is presented to study the flow, heat and mass transfer characteristics of non-Darcian mixed convection of a non-Newtonian fluid from a vertical isothermal plate embedded in a homogeneous porous medium with the effect of Soret and Dufour and in the presence of either surface injection or suction. The value of the mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The numerical solution of the problem is derived using a Runge–Kutta integration scheme with Newton–Raphson shooting technique. Distributions for velocity, temperature and concentration, as well as for the rate of wall heat and mass transfer, have been obtained and discussed for various physical parametric values.     

Positive frictional pressure gradient in vertical gas-high viscosity oil slug flow

The present study describes the wall shear stress and the falling liquid film behavior in upward vertical slug flow of air and high viscosity oil. The frictional pressure gradient is directly related to the wall shear stress, and it is usually negative (opposite to the overall flow direction). However, in vertical slug flow, the average total wall shear stress of a slug unit may be negative (in the same direction of the overall flow), resulting in a positive frictional pressure gradient. However, this does not mean, by any way, generation of additional energy or violation of the second law of thermodynamics.The positive frictional pressure gradient phenomenon, reasons and required conditions were explained in this paper. A simplified model was developed and validated against recent experimental data of air-high viscosity oil slug flow in a 50.8 mm ID vertical pipe. The oil viscosity was in the range of 127 mPa s to 580 mPa s. Positive frictional pressure gradient appears when the liquid film wall shear stress supersede the wall shear stress in the slug body. The rate of increase of both wall shear stresses (with respect to the mixture Reynolds number) depend, not only, on the mixture Reynolds number but also, highly, on the liquid viscosity.     

The effect of mixed convection on the structure of channel flow at low Reynolds numbers

An experimental study was conducted to investigate the effect of bottom wall heating on the flow structure inside a horizontal square channel at low Reynolds numbers (Re) and high Grashof numbers (Gr). The flow field was found to be complex and three-dimensional due to the interactions of buoyancy-induced rising plumes of warm fluid, falling parcels of cold fluid and the shear flow. The mean streamwise velocity profiles were altered by bottom wall heating; and back flow was induced in the upper half of the channel when Gr/Re² > 55. The bottom wall temperatures were found to have more significant influence on the turbulent velocity magnitudes than the flow rate. The Reynolds stress became negative in the channel core region indicating the momentum transfer from the turbulent velocity field to the buoyancy field. The POD analysis revealed the presence of convective cells primarily in the lower half of the channel.     

Combined electroosmotically and pressure driven flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in the presence of pressure gradient through a slit is analyzed. After numerically solving the Poisson–Boltzmann equation, the momentum equation with electroosmotic body force is solved through an iterative numerical procedure for both favorable and adverse pressure gradients. The results reveal that, in case of pressure assisted flow, shear-thinning fluids reach higher velocity magnitudes compared with shear-thickening fluids, whereas the opposite is true when an adverse pressure gradient is applied. The Poiseuille number is found to be an increasing function of the dimensionless Debye–Hückel parameter, the wall zeta potential, and the flow behavior index. Comparison between the exact and the results based on the Debye–Hückel linearization reveals that the simplified solution leads to large errors in evaluating the velocity profile for zeta potentials higher than 25 mV, except for shear-thickening fluids in the presence of favorable pressure gradient.     

Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow

The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1–36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253–277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.     

Computational study of steady streaming from oscillating microbubbles with uniform and wavy wall motions

Steady streaming flow fields of a 5 μm bubble oscillating with uniform radial wall motion and a 500 μm bubble oscillating with wavy wall motion were simulated using a computational fluid dynamics method that incorporated fluid–structure interactions. The steady streaming flow fields for both bubbles were calculated, and they exhibited upward jet flow with two symmetrical counter-rotating vortices. The maximum streaming velocity ranged from a few to tens of millimeters per second. The simulated flow fields were compared with the theory and experimental measurements using particle image velocimetry. The simulation results agreed well with the theoretical and experimental data. Therefore, the proposed computational method would provide a useful tool to predict steady streaming flow fields of oscillating bubbles.     

New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions

The steady flow of generalized Newtonian fluid in a two-dimensional 1:3 sudden expansion was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of Reynolds number and Power law index values. The values of generalized Reynolds number, based on physical and rheological properties, upstream channel height and bulk velocity, were varied between 0.0001 ≤ Re_gen ≤ 10, while the Power law index values mapped the 0.60 ≤ n ≤ 1.40 range, allowing for the investigation of both shear-thinning and shear-thickening effects at creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on most important characteristics of recirculating fluid flow in the downstream section of sudden expansion geometry. It is shown that for the creeping flow regime there exist finite sized redevelopment length, extra pressure drop (Couette correction) and recirculation zones (also called as Moffatt vortices) that are influenced by the non-Newtonian viscous behaviour.     

Numerical simulation of the fountain flow instability in injection molding

For the first time, the viscoelastic flow front instability is studied in the full non-linear regime by numerical simulation. A two-component viscoelastic numerical model is developed which can predict fountain flow behavior in a two-dimensional cavity. The eXtended Pom-Pom (XPP) viscoelastic model is used. The levelset method is used for modeling the two-component flow of polymer and gas. The difficulties arising from the three-phase contact point modeling are addressed, and solved by treating the wall as an interface and the gas as a compressible fluid with a low viscosity. The resulting set of equations is solved in a decoupled way using a finite element formulation. Since the model for the polymer does not contain a solvent viscosity, the time discretized evolution equation for the conformation tensor is substituted into the momentum balance in order to obtain a Stokes like equation for computing the velocity and pressure at the new time level. Weissenberg numbers range from 0.1 to 10. The simulations reveal a symmetric fountain flow for Wi = 0.1–5. For Wi = 10 however, an oscillating motion of the fountain flow is found with a spatial period of three times the channel height, which corresponds to experimental observations.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

Flow pattern and molecular visualization of DNA solutions through a 4:1 planar micro-contraction

The present work explores unusual flow behavior of entangled fluids in an abrupt contraction flow device. Fluorescent imaging was carried out on four different entangled DNA solutions with concentrations ranging from 0.1 to 1.0% (with a wide range of entanglements per chain Z = 7–55). For weakly entangled solutions (Z < 30), vortex flow was dominant at high flow rates. However, for well-entangled DNA solutions (Z ≥ 30), unusual time dependant shear banding was observed at the contraction entrance. Upon reducing the slip length by adding sucrose to the well-entangled DNA solution, vortex flow became dominant again. In vortex flow, most DNA chains remained coiled at the corner in regular recirculation. However, when jerky-shear-banding flow developed, significant stable stretching of DNA chains occurred at the center-line, with quasi-periodic switching between stretching and recoil at the corner.     

Experimental study on the direct contact condensation of the steam jet in subcooled water flow in a rectangular channel: Flow patterns and flow field

Direct contact condensation (DCC) of steam jet in subcooled water flow in a channel was experimentally studied. The main inlet parameters, including steam mass flux, water mass flux and water temperature were tested in the ranges of 200–600 kg/(m² s), 7–18 × 10³ kg/(m² s), 288–333 K, respectively. Two unstable flow patterns and two stable flow patterns were observed via visualization window by a high speed camera. The flow patterns were determined by steam mass flux, water mass flux and water temperature, and the relationship between flow patterns and flow field parameters was discussed. The results indicated that whether pressure or temperature distributions on the bottom wall of channel could represent different flow patterns. And the position of pressure peak on the bottom wall could almost represent the condensation length. The upper wall pressure distributions were mainly dependent on steam and water mass flux; and the upper wall temperature distributions were affected by the three main inlet parameters. Moreover, the bottom wall pressure and temperature distributions of different unstable flow patterns had similar characteristics while those of stable flow patterns were affected by shock and expansion waves. The underlying cause of transition between different flow patterns under different inlet parameters was reflected and discussed based on pressure distributions.     

Effect of magnetic field on 3D flow and heat transfer during solidification from a melt

We present the effect of a magnetic field on three-dimensional fluid flow and heat transfer during solidification from a melt in a cubic enclosure. The walls of the enclosure are considered perfectly electrically conducting and the magnetic field is applied separately in three directions. The finite-volume method with enthalpy formulation is used to solve the mathematical model in the solid and liquid phases. The results obtained by our computer code are compared with the numerical and experimental data found in the literature. For Gr = 5 × 10⁵ and Ha = 0, 25, 50, 75, and 100 (where Gr and Ha are the Grashof and Hartmann numbers, respectively), the effects of magnetic field on flow and thermal fields, and on solid/liquid interface shape are presented and discussed. The interface is localized with and without magnetic field. The results show a strong dependence between the interface shape and the intensity and orientation of magnetic field. When the magnetic field is applied along the X-direction, the magnetic stability diagrams (V_max–Ha) and (Nu_avg–Ha) show the strongest stabilization of the flow field and heat transfer.