Asymmetric Velocity Profiles Research Articles

Extrudate shape of three-dimensional viscoelastic, non-isothermal extrusion flows

A 3D transient non-isothermal finite element code is developed to predict the extrudate shape of viscoelastic fluids emerging from an asymmetric keyhole shaped die. The corner-line method is employed to model the movement of the free surfaces. The code is tested using two benchmark problems. First the corner-line method is tested employing a trumpet shaped object during a 3D uniaxial extensional flow. Secondly, the implementation of the energy balance and therefore the viscoelastic material behaviour is tested employing a non-isothermal pipeflow. For both benchmark problems convergence was obtained, giving confidence that the 3D non-isothermal swell problem is correctly implemented. The influence of shear-thinning, elasticity and temperature on the form of the extrudate is systematically studied. Results are shown for isothermal flows also as for non-isothermal flows, with isothermal and non-isothermal die walls. Results for isothermal die walls show increasing extrudate swelling with increasing elasticity which the swelling opposes extrudate bending. Shear-thinning on the opposite hand, opposes swelling, which initially promotes bending, but also flattens the asymmetric velocity profile, resulting in less extrudate bending for top amounts of shear-thinning. Furthermore, extrudate bending was observed even for purely viscous, isothermal extrudates, suggesting that bending is caused by asymmetry within the viscous stresses. Extrudate swelling are often influenced by the wall temperature of the die and non-isothermal die walls can cause a change in bending direction. Extrusion is widely utilized in the polymer processing industry. Common requirement on the extrudate is dimensional accuracy. However, the size of the extrudate are highly influenced by a phenomenon called extrudate swell. For Newtonian fluids, having a continuing viscosity, extruded from cylindrical dies, the swell ratio is about 13% when physical phenomenon, inertia and gravitational forces are often neglected. For viscoelastic fluids, the swelling is far larger and therefore the final diameter of the extrudate are often several times the diameter of the die. This effect is attributed to normal stresses within the material.

Computational analysis of the extrudate shape of three-dimensional viscoelastic, non-isothermal extrusion flows

A 3D transient non-isothermal finite element code is developed to predict the extrudate shape of viscoelastic fluids emerging from an asymmetric keyhole shaped die. The corner-line method is used to model the movement of the free surfaces. The code is tested using two benchmark problems. First the corner-line method is tested using a trumpet shaped object in a 3D uniaxial extensional flow. Secondly, the implementation of the energy balance and the viscoelastic material behaviour is tested using a non-isothermal pipeflow. For both benchmark problems convergence was obtained, giving confidence that the 3D non-isothermal swell problem is correctly implemented. The influence of shear-thinning, elasticity and temperature on the shape of the extrudate is systematically studied. Results are shown for isothermal flows as well as for non-isothermal flows, with isothermal and non-isothermal die walls. Results for isothermal die walls show increasing extrudate swelling with increasing elasticity and that the swelling opposes extrudate bending. Shear-thinning on the other hand, opposes swelling, which initially promotes bending, but also flattens the asymmetric velocity profile, leading to less extrudate bending for high amounts of shear-thinning. Furthermore, extrudate bending was observed even for purely viscous, isothermal extrudates, suggesting that bending is caused by asymmetry in the viscous stresses. Extrudate swelling can be influenced by the wall temperature of the die and non-isothermal die walls can lead to a change in bending direction.

Wall Effects on Hydrodynamic Drag and the Corresponding Accuracy of Charge Measurement in Droplet Contact Charge Electrophoresis.

Droplet size dependent wall effects on hydrodynamic drag and the corresponding droplet contact charge estimations were experimentally and theoretically investigated. The consistent reduction in the dimensionless droplet contact charges proportional to droplet size was reported and explained by the parallel and approaching wall effects on the drag coefficient. Extrapolation of the size dependent droplet charge data showed that the droplet charge follows the perfect conductor theory when the droplet radius approaches zero. The proposed model was applied to the drag calculation to estimate and compare dimensionless charges before and after consideration of the wall effects. The droplet free fall test concluded that the droplets in the current experimental setup follow Stokes' law. The theoretical velocity profile of the droplet approaching the wall perpendicularly is proposed considering the approaching wall effect on hydrodynamic drag and verified by comparison with the experiment. The droplet size dependent velocity profile shape change was also explained by this approaching wall effect. The shape of the asymmetric velocity profile along the direction of droplet movement was explained by the effect of the image charge through direct numerical calculation of the electric force. The direct calculation of the electric force also showed that the electric correction at the center of the cuvette is negligible; thus, it is sufficient to consider only hydrodynamic correction for accurate charge measurement in this experimental system. The present study will contribute to the accurate measurement of the droplet charges under contact charge electrophoresis. It also provides the basis for precise control of droplet movement in lab-on-a-chip devices.

Experimental and numerical studies on the flow characteristics and separation properties of dispersed liquid-liquid flows

The local dynamics of spatially developing liquid-liquid dispersed flows at low superficial velocities, ranging from 0.2 to 0.8 m s−1, are investigated. The dispersions are generated with an in-line static mixer. Detailed measurements with laser-based diagnostic tools are conducted at two axial pipe locations downstream of the mixer, namely, at 15 and 135 equivalent pipe diameters. Different flow patterns are recorded, and their development along the streamwise direction is shown to depend on the initial size and concentration of the drops as well as the mixture velocity. The drop size is accurately predicted by an empirical formula. The variations in drop concentration over the pipe cross-section along the pipe result in local changes of the physical properties of the mixture and consequently in asymmetrical velocity profiles, with the maxima of the velocity located in the drop-free region. Computational fluid dynamics simulations based on a mixture approach predict the experimental results close to the experimental uncertainties for the majority of the cases. The simulation results reveal that gravity and lift forces, as well as shear-induced diffusion are the most important mechanisms affecting the drop migration. It is found that the drops behave as suspensions of rigid spheres for the conditions investigated, despite the deformation effects, which are found experimentally to be stronger at the densely packed region.

Flow rate measurement in flows with asymmetric velocity profiles by means of distributed thermal anemometry

Flow rate in closed conduits is one of the most frequently measured parameters in industrial processes and in gas and water supply. For an accurate measurement, flow meters typically require a fully developed symmetric flow profile with preferably no radial or tangential velocity components. This is commonly secured by mounting flow meters in a pipe at a sufficiently long distance downstream any change in cross-section or pipe direction. In this paper, we introduce a new approach for flow rate measurement of gases or liquids that employs a novel spatially resolving fluid velocity sensor basing on thermal anemometry. The new principle allows accurate flow rate measurements for non-axisymmetric velocity profiles, even directly after pipe bends, T-junctions or other alterations in the pipe geometry. This is exemplified for air flow in three different pipe bend configurations.

Measurements of local droplet velocities in horizontal gas-liquid pipe flow with low liquid loading

New data on streamwise droplet velocity profiles for low liquid loading pipe flows are reported. The fluids used in the experiments are SF6 (gas-phase) and Exxsol D60 (oil-phase). Experiments are conducted in a 10 cm pipe diameter high-pressure (∼780 kPa, absolute) flow loop to reproduce gas-condensate field conditions. Instantaneous streamwise velocity data, obtained using the non-intrusive Laser Doppler Anemometry (LDA) technique, are used to calculate mean and root-mean-squared (RMS) local velocities. Asymmetric droplet velocity profiles with respect to the pipe center-line are observed especially for the stratified low atomization flow conditions. However, as the flow momentum increases, the droplet velocity profiles seem to become more symmetric. Also, these data suggest that, irrespective of the conditions studied, the single-phase gas flow characteristics are preserved closer to the top pipe wall. The data from the LDA imply that the bottom pipe half region is highly influenced by the gas-liquid interfacial characteristics. This results in high streamwise turbulence intensity in the region influenced by the interfacial waves (interfacial turbulence). An isokinetic sampling instrument is also used to measure the local instantaneous dynamic pressure. The dynamic pressure and the locally extracted liquid (droplets) volume rate under isokinetic conditions are used to calculate local fluid velocity. Excellent agreement has been obtained when comparing this calculated local velocity from the isokinetic instrument to the LDA data.

Influences of trailing boundary layer velocity profiles on wake vortex formation in a high-subsonic-turbine cascade

In this paper, delayed detached eddy simulations are performed to study wake flows of a turbine blade at a high subsonic exit Mach number, [Formula: see text], and high Reynolds number, [Formula: see text], based on the chord length and outlet velocity. It is found that a slight change in the trailing suction profile would have a big influence on the formation of wake vortex street, which is believed to be caused by the change in the boundary layer state near the trailing edge, and suction boundary layer with a fuller velocity profile tends to destabilize the wake flow, promoting the generation of wake vortex and enhancing the unsteady effect. Local spatial-temporal stability analyses of the wake velocity profiles suggest that wake flows with asymmetric velocity profiles might have a stabilizing effect. It is suggested that the vortex formation and its strength can be controlled by making some slight modifications on the rear blade suction surface, and the mixing loss in the wake can be reduced due to a weaker unsteady effect.

Effects of confinement, geometry, inlet velocity profile, and Reynolds number on the asymmetry of opposed-jet flows

The opposed-jet counterflow configuration is widely used to measure fundamental flame properties that are essential targets for validating chemical kinetic models. The main and key assumption of the counterflow configuration in laminar flame experiments is that the flow field is steady and quasi-one-dimensional. In this study, experiments and numerical simulations were carried out to investigate the behavior and controlling parameters of counterflowing isothermal air jets for various nozzle designs, Reynolds numbers, and surrounding geometries. The flow field in the jets’ impingement region was analyzed in search of instabilities, asymmetries, and two-dimensional effects that can introduce errors when the data are compared with results of quasi-one-dimensional simulations. The modeling involved transient axisymmetric numerical simulations along with bifurcation analysis, which revealed that when the flow field is confined between walls, local bifurcation occurs, which in turn results in asymmetry, deviation from the one-dimensional assumption, and sensitivity of the flow field structure to boundary conditions and surrounding geometry. Particle image velocimetry was utilized and results revealed that for jets of equal momenta at low Reynolds numbers of the order of 300, the flow field is asymmetric with respect to the middle plane between the nozzles even in the absence of confining walls. The asymmetry was traced to the asymmetric nozzle exit velocity profiles caused by unavoidable imperfections in the nozzle assembly. The asymmetry was not detectable at high Reynolds numbers of the order of 1000 due to the reduced sensitivity of the flow field to boundary conditions. The cases investigated computationally covered a wide range of Reynolds numbers to identify designs that are minimally affected by errors in the experimental procedures or manufacturing imperfections, and the simulations results were used to identify conditions that best conform to the assumptions of quasi-one-dimensional modeling.

Particle migration in planar Couette–Poiseuille flows of concentrated suspensions

Particle migration phenomena in parallel slit channel flows of concentrated suspensions with asymmetric velocity profiles, which are governed by planar Couette–Poiseuille (C-P) flow conditions, are numerically investigated employing the diffusive flux model (DFM) via the finite volume method. The particle distributions predicted by DFM are confirmed by comparing quantitatively with those by the reported experimental results and the lattice Boltzmann method. The main factors governing the migration dynamics in the DFM, such as particle size, concentration, and flow length from an inlet of the channel, are effectively unified into a nondimensional length element. The effects of the asymmetric C-P flow fields on particle dynamics are clarified by the evolution of the concentration distribution along the nondimensional length element under a different asymmetric velocity and initial concentration conditions. From scale analysis, this asymmetric distribution is analytically interpreted by adopting a concept of...

Determination of the Flow Rate of Coolant in Pipelines with Unstabilized Flow of Fluid in the Area Following a Bend

Questions related to the determination of the flow rate of coolant in the pipelines of electric plants are considered. Amethod of determining the flow of single-phase coolant for the case of an asymmetric unstabilized velocity profile that is present following a bend in a pipeline is proposed. Results from the use of the proposed method in novel experiments on the testing unit of the Elektrogorsk Scientific Research Center and in the steam pipelines of power unit No. 3 of the Balakovo nuclear power plant are presented.

Instantaneous sediment transport model for asymmetric oscillatory sheet flow.

On the basis of advanced concentration and velocity profiles above a mobile seabed, an instantaneous analytical model is derived for sediment transport in asymmetric oscillatory flow. The applied concentration profile is obtained from the classical exponential law based on mass conservation, and asymmetric velocity profile is developed following the turbulent boundary layer theory and the asymmetric wave theory. The proposed model includes two parts: the basic part that consists of erosion depth and free stream velocity, and can be simplified to the total Shields parameter power 3/2 in accordance with the classical empirical models, and the extra vital part that consists of phase-lead, boundary layer thickness and erosion depth. The effects of suspended sediment, phase-lag and asymmetric boundary layer development are considered particularly in the model. The observed instantaneous transport rate proportional to different velocity exponents due to phase-lag is unified and summarised by the proposed model. Both instantaneous and half period empirical formulas are compared with the developed model, using extensive data on a wide range of flow and sediment conditions. The synchronous variation in instantaneous transport rate with free stream velocity and its decrement caused by increased sediment size are predicted correctly. Net transport rates, especially offshore transport rates with large phase-lag under velocity skewed flows, which existing instantaneous type formulas failed to predict, are predicted correctly in both direction and magnitude by the proposed model. Net sediment transport rates are affected not only by suspended sediment and phase-lag, but also by the boundary layer difference between onshore and offshore.

Electric field controlled transport of water in graphene nano-channels.

Motivated by electrowetting-based flow control in nano-systems, water transport in graphene nano-channels is investigated as a function of the applied electric field. Molecular dynamics simulations are performed for deionized water confined in graphene nano-channels subjected to opposing surface charges, creating an electric field across the channel. Water molecules respond to the electric field by reorientation of their dipoles. Oxygen and hydrogen atoms in water face the anode and cathode, respectively, and hydrogen atoms get closer to the cathode compared to the oxygen atoms near the anode. These effects create asymmetric density distributions that increase with the applied electric field. Force-driven water flows under electric fields exhibit asymmetric velocity profiles and unequal slip lengths. Apparent viscosity of water increases and the slip length decreases with increased electric field, reducing the flow rate. Increasing the electric field above a threshold value freezes water at room temperature.

The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel

In the present study, the effect of attack angle of triangular ribs, by using finite volume method, has been numerically studied in a two-dimensional microchannel. The cooling fluid is water/Ag nanofluid with volume fractions of 0–4% of nanoparticles, and nanoparticle diameters are 25, 50 and 75 nm. The nanofluid flow has been considered as laminar with Reynolds numbers of 5, 100 and 500. Also, the attack angles have been studied at the range of 30°–60°. In this study, the effects of variations in attack angles on triangular ribs, volume fraction of nanoparticles, nanoparticles diameter and Reynolds number have been investigated. The results indicate that using nanoparticles with smaller diameter improves heat transfer rate. Moreover, it is shown that the friction coefficient and pumping power are almost independent of nanoparticle diameter. However, increasing Reynolds number, pumping power enhancement becomes more important by increasing the volume fraction of nanoparticles. In low Reynolds numbers, the influence of ribs is approximately insignificant on the streamlines; it is very effective in high Reynolds numbers. The existence of rib on the direction of fluid motion causes asymmetrical velocity profile in the top section of the rib. Using triangular rib with higher attack angle can improve heat transfer significantly due to the high-velocity gradients and better mixing of fluid flow.

Erosion boundary effects due to fill fraction variation within quasi-2D granular tumblers

Simulations of granular flow assume a consistent flowing layer profile observed in circular tumblers that were half full. While the constant shear rate model predicts mixing kinematics adequately, the model has not been empirically tested in systems where the erosion from the solid body has inertial velocity components along the dynamic angle of repose. This paper explores experiments that analyze the relationship between tumbler fill fraction and the kinematics of the erosion boundary transition into the flowing layer. Tumblers greater than 50% full have inertial velocity along the angle of repose whereas fill conditions less than 50% enter with velocity opposite the free surface angle. Results confirm that flowing layer chord length alone properly scales flowing layer depth only when fill fraction is near 50% – otherwise fill fraction must be considered. This is due to the streamwise velocity of particles at the erosion boundary affecting the energy balance of the system. In addition, the asymmetric velocity profile derived from the non-dimensional momentum equation is confirmed for non-half full systems. Lastly, linear and exponential shear models are explored and shown to be qualitatively similar and variation is only exhibited at extreme fill and far ends of the flowing layer.

Role of centrifugal force on solid-liquid two-phase flow through rotating channel

The work reveals an interesting and contra-intuitive observation in numerically simulating the solid-liquid flow field through a straight rotating channel. A previous study (Gupta and Pagalthivarthi, 2007) showed that at moderate rotation rates, increase in rotational speed results in an asymmetric velocity profile, because the Coriolis acceleration tends to increase the level of turbulence on the pressure-side and decrease on the suction-side. The present work contra-intuitively shows that higher rotation rates enhance centrifugal acceleration that pushes the velocity maxima towards the pressure-side of the channel. Centrifugal acceleration is also seen to play a prominent role with increase in inlet concentration.

Initial information prior to movement onset influences kinematics of upward arm pointing movements.

To elaborate a motor plan and perform online control in the gravity field, the brain relies on priors and multisensory integration of information. In particular, afferent and efferent inputs related to the initial state are thought to convey sensorimotor information to plan the upcoming action. Yet it is still unclear to what extent these cues impact motor planning. Here we examined the role of initial information on the planning and execution of arm movements. Participants performed upward arm movements around the shoulder at three speeds and in two arm conditions. In the first condition, the arm was outstretched horizontally and required a significant muscular command to compensate for the gravitational shoulder torque before movement onset. In contrast, in the second condition the arm was passively maintained in the same position with a cushioned support and did not require any muscle contraction before movement execution. We quantified differences in motor performance by comparing shoulder velocity profiles. Previous studies showed that asymmetric velocity profiles reflect an optimal integration of the effects of gravity on upward movements. Consistent with this, we found decreased acceleration durations in both arm conditions. However, early differences in kinematic asymmetries and EMG patterns between the two conditions signaled a change of the motor plan. This different behavior carried on through trials when the arm was at rest before movement onset and may reveal a distinct motor strategy chosen in the context of uncertainty. Altogether, we suggest that the information available online must be complemented by accurate initial information.

Joint effect of input asymmetrical velocity profile and initial turbulence intensity on hydraulics of a separated diffuser of GTE combustion chamber

This paper presents the regularities of effect of the input asymmetry of the velocity profile on the flow structure in a separated diffuser of the GTE annular combustion chamber. These regularities allow predicting the integral value of hydraulic resistance. We experimentally identified a kind of dependence between the hydraulic losses and Reynolds number in the case of asymmetric velocity profile in a prediffuser assessing the growth of pressure losses. Some updated dependencies are proposed that take into account the joint effect of the input parameters of the working fluid on the integral characteristics of its effectiveness.

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers. Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before. Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.

A comparison of wake measurements in motor-driven and flow-driven turbine experiments

We present experimental data to compare and contrast the wake characteristics of a turbine whose rotation is either driven by the oncoming flow or prescribed by a motor. Velocity measurements are collected using two-dimensional particle image velocimetry in the near-wake region of a lift-based, vertical-axis turbine. The wake of this turbine is characterized by a spanwise asymmetric velocity profile which is found to be strongly dependent on the turbine tip speed ratio (TSR), while only weakly dependent on Reynolds number (Re). For a given Re, the TSR is controlled either passively by a mechanical brake or actively by a DC motor. We find that there exists a finite region in TSR versus Re space where the wakes of the motor-driven turbine and flow-driven turbine are indistinguishable to within experimental precision. Outside of this region, the sign of the net circulation in the wake changes as TSR is increased by the motor. Shaft torque measurements show a corresponding sign change above this TSR threshold set by circulation, indicating a transition from net torque due to lift to net torque due to drag produced by the turbine blades, the latter of which can give wake measurements that are inconsistent with a flow-driven turbine. The results support the claim that the turbine kinematics and aerodynamic properties are the sole factors that govern the dynamics of its wake, irrespective of the means to move the turbine blades. This has significance for both experimental and computational studies where it may be necessary, or perhaps more economical, to prescribe the turbine kinematics in order to analyze its aerodynamic characteristics.

Characterization of the startup transient electrokinetic flow in rectangular channels of arbitrary dimensions, zeta potential distribution, and time-varying pressure gradient.

The solution to the startup transient EOF in an arbitrary rectangular microchannel is derived analytically and validated experimentally. This full 2D transient solution describes the evolution of the flow through five distinct periods until reaching a final steady state. The derived analytical velocity solution is validated experimentally for different channel sizes and aspect ratios under time-varying pressure gradients. The experiments used a time resolved micro particle image velocimetry technique to calculate the startup transient velocity profiles. The measurements captured the effect of time-varying pressure gradient fields derived in the analytical solutions. This is tested by using small reservoirs at both ends of the channel which allowed a time-varying pressure gradient to develop with a time scale on the order of the transient EOF. Results showed that under these common conditions, the effect of the pressure build up in the reservoirs on the temporal development of the transient startup EOF in the channels cannot be neglected. The measurements also captured the analytical predictions for channel walls made of different materials (i.e., zeta potentials). This was tested in channels that had three PDMS and one quartz wall, resulting in a flow with an asymmetric velocity profile due to variations in the zeta potential between the walls.