Dean Number De Research Articles

Characterization of liquid film distribution and sub-flow regimes of annular flow in helically coiled tubes using ring island array sensor

The distribution of liquid film thickness in helically coiled tubes (HCTs) directly affects the heat transfer performance of the annular flow region. However, due to the limitation of measurement technology, accurate measurement data of liquid film thickness in HCTs is very rare. In this paper, a non-invasive contact liquid film thickness sensor (ring island array sensor) is successfully developed to obtain the refined three-dimensional spatial-temporal distribution data of liquid film thickness in HCTs. According to the results, four typical liquid film flow regimes are defined based on the circumferential position of the thicker liquid film appearing in the tube wall, i.e., the bottom distribution (BD) dominated by liquid phase gravity force, the outside distribution (OD) dominated by liquid phase centrifugal force, the inside distribution (ID) dominated by gas centrifugal force and the inside-outside distribution (IOD) dominated by the secondary flow. These circumferential distributions of liquid film thickness are mainly affected by the HCT structure (e.g., coil diameter and coil pitch) and superficial gas-liquid velocities. Based on the modified Dean number De* and the modified Lockhart-Martinelli parameter X*, which consider the influence of HCT structures, fluid properties and operating parameters, a general sub-flow regime map of annular flow is proposed. The prediction models of transition boundaries of different liquid film flow regimes are also established and verified with present and available data in the literature.

Particle Behavior in Curved Microchannels: Aspect Ratio Effects

The sorting devices of microfluidic systems operate by both passive and active mechanisms. The microchannels of these systems are often curved to cope with secondary flows, which allow sorting or mixing. Therefore, it is essential to characterize the secondary flows in microfluidic systems. In this study, we investigate the particle behavior in a spiral rectangular microchannel and clarify the effects of the aspect ratio and Dean number De on particle sorting by comparing experimental and numerical results. We fabricated Archimedean spiral microchannel models with the rectangular cross-section of millimeter-scale dimensions. Particle sorting in the microchannels was observed by the particle-tracking velocimetry (PTV) method. In addition, the particle-sorting mechanism was analyzed by the particle-tracking method in three-dimensional numerical simulations. When particle density exceeded water density, good sorting was observed when 20 < De < 40. The numerical particle-sorting behaviors agreed well with the experimental results.

The effect of Dean, Reynolds, and Womersley number on the flow in a spherical cavity on a curved round pipe. Part 1. Fluid mechanics in the cavity as a canonical flow representing intracranial aneurysms.

Flow in side-wall cerebral aneurysms can be ideally modelled as the combination of flow over a spherical cavity and flow in a curved circular pipe, two canonical flows. Flow in a curved pipe is known to depend on the Dean number De, combining the effects of Reynolds number, Re, and of the curvature along the pipe centreline, κ. Pulsatility in the flow introduces a dependency on the Womersley number Wo. Using stereo PIV measurements, this study investigated the effect of these three key non-dimensional parameters, by modifying pipe curvature (De), flow-rate (Re), and pulsatility frequency (Wo), on the flow patterns in a spherical cavity. A single counter-rotating vortex was observed in the cavity for all values of pipe curvature κ and Re, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted both the flow patterns in the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate into the cavity. The circulation in the cavity was found to collapse well with only the Dean number, for both steady and pulsatile inflows. For pulsatile inflow, the counter-rotating vortex was unstable and the location of its centre over time was impacted by the curvature of the pipe, as well as the Re and the Wo in the freestream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds and Dean number pulsatile inflow, with very limited impact of the Womersley in the range studied.

Generally-valid optimal Reynolds and Dean numbers for efficient liquid-liquid mixing in helical pipes

This work documents optimal flow conditions in terms of Reynolds number Re (and Dean number De) for mixing of two miscible liquids in helical pipes. Extending our previous investigations (Mansour et al., 2017, 2018), many more configurations have been considered with widely different dimensions; as a consequence, generally-valid values for Reopt and Deopt have been obtained. A full-factorial design of experiment (DOE) has been carried out by considering all possible combinations of geometrical parameters studied in Mansour et al. (2018). This leads to a total of 27 different coiled configurations with a wide variety of curvature ratio (0.033–0.214) and dimensionless pitch (0.034–0.273). Additionally, 47 different values of the Reynolds number have been considered within the laminar range of 5–4000, which corresponds to a Dean number range of De = 2–1850. This study involves at the end 1269 distinct numerical simulations. The results reveal that the mixing efficiency as function of the Reynolds number always exhibits two peaks at nearly similar Reynolds numbers. Average values of the two optimal ranges of Reynolds number and Dean number have been deduced from all simulations, leading to Reopt,1≈35 (Deopt,1≈10), and Reopt,2≈650 (Deopt,2≈185). Those can be used to get excellent mixing within any coiled configuration. The first optimal value leads to a much lower pressure drop and a slightly better mixing efficiency, and is therefore recommended to get optimal mixing and power consumption.

Numerical study of Unsteady Fluid Flow and Heat Transfer Through a Rotating Curved Rectangular Channel

Numerical study of unsteady fluid flow and heat transfer through a rotating curved rectangular channel with aspect ratio 2 and curvature ratio 0.05 has been performed by using a spectral-based numerical method, and covering a wide range of the rotational parameter, the Taylor number Ta, for both the positive and negative rotation of the channel. In this paper, unsteady flow characteristics are investigated under combined action of the centrifugal, Coriolis and buoyancy forces for the Dean number De = 1000. For positive rotation, we investigated unsteady solutions for 0 ≤Ta ≤500, and it is found that the chaotic flow turns into steady-state flow through periodic or multi-periodic flows. For negative rotation, on the other hand, unsteady solutions are investigated for –500 ≤Ta≤0, and it is found that the unsteady flow undergoes through various flow instabilities. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Ta, and it is found that the unsteady flow consists of asymmetric two- to eightvortex solutions. The present study shows that convective heat transfer is significantly enhanced as the secondary flow becomes stronger and the chaotic flow enhances heat transfer more effectively than the steady-state or periodic solutions.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 73-92

Characterisation of the steady, laminar incompressible flow in toroidal pipes covering the entire curvature range

This work is concerned with a detailed investigation of the steady (laminar), incompressible flow inside bent pipes. In particular, a toroidal pipe is considered in an effort to isolate the effect of the curvature, δ, on the flow features, and to compare the present results to available correlations in the literature. More than 110 000 numerical solutions are computed, without any approximation, spanning the entire curvature range, 0 ≤ δ ≤ 1, and for bulk Reynolds numbers Re up to 7 000, where the flow is known to be unsteady. Results show that the Dean number De provides a meaningful non-dimensional group only below very strict limits on the curvature and the Dean number itself. For δ>10−6 and De > 10, in fact, not a single flow feature is found to scale well with the Dean number. These considerations are also valid for quantities, such as the Fanning friction factor, that were previously considered Dean-number dependent only. The flow is therefore studied as a function of two equally important, independent parameters: the curvature of the pipe and the Reynolds number. The analysis shows that by increasing the curvature the flow is fundamentally changed. Moderate to high curvatures are not only quantitatively, but also qualitatively different from low δ cases. A complete description of some of the most relevant flow quantities is provided. Most notably the friction factor f for laminar flow in curved pipes by Ito [J. Basic Eng. 81:123–134 (1959)] is reproduced, the influence of the curvature on f is quantified and the scaling is discussed. A complete database including all the computed solutions is available at www.flow.kth.se.

GS52 テイラー・ディーン流れを利用したマイクロミキサの数値的研究 : 流路のアスペクト比の効果

Chaotic mixing in a curved-rectangular channel flow is studied numerically. One wall of the channel (inner wall) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flow. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing fluid mixing and velocity field. It is found that good mixing performance is obtained in the case of De/Tr &le; 1/6. This tendency appears more strongly if aspect ratio is large.

A Micromixer Using the Taylor-Dean Flow: Effects of Aspect Ratio and Inflow Condition on the Mixing

Chaotic mixing in three different types of curved-rectangular channels flow has been studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient are imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flow. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In this paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental results and numerical ones. We produced three micromixer models of the curved channel, several centimeters long, with rectangular cross-section of a few millimeters side. The secondary flow is measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. Also we performed three-dimensional numerical simulations with the open source CFD solver, OpenFOAM, for the same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is obtained in the case of De ≤ 0.1 Tr, and it becomes more remarkable when the aspect ratio tends to large. And it is found that the mixing efficiency changes according to the aspect ratio and inflow condition.

A Micromixer Using the Taylor-Dean Flow: Effect of Inflow Conditions on the Mixing

Chaotic mixing in a curved-square channel flow is studied experimentally and numerically. Two walls of the channel (inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction toward the exit of the channel. This flow is a kind of Taylor-Dean flows. There are two parameters dominating the flow, the Dean number De (∝ the pressure gradient or the Reynolds number) and the Taylor number Tr (∝ the angular velocity of the wall rotation). In the present paper, we analyze the physical mechanism of chaotic mixing in the Taylor-Dean flow by comparing experimental and numerical results. We produced a micromixer model of the curved channel several centimeters long with square cross section of a few millimeters side. The secondary flow was measured using laser induced fluorescence (LIF) method to examine secondary flow characteristics. We also performed three-dimensional numerical simulations for the exactly same configuration as the experimental system to study the mechanism of chaotic mixing. It is found that good mixing performance is achieved for the case of De ≤ 0.1Tr, and that mixing efficiency changes according to the difference in inflow conditions. The flow is studied both experimentally and numerically, and both results agree with each other very well.

GS09 テイラー・ディーン流れを利用したマイクロミキサの実験的研究 : 混合過程に及ぼすアスペクト比の効果

The micromixer, which has a rotor with a curved channel, is studied experimentally. The Taylor-Dean flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional parameters concerned are the Dean number De and the Taylor number Tr. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De &le; 0.1Tr. This tendency appears more strongly if aspect ratio is large. And we have confirmed the effect of aspect ratio on the mixing process.

G0503 テイラー・ディーン流れを利用したマイクロミキサの実験的研究 (混合に及ぼす流路の回転効果)(GS5 混合・物質伝達)

The micromixer, which has a rotor with a curved channel, is studied experimentally. The Taylor-Dean flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional parameters concerned are the Dean number De and the Taylor number Tr. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De ? 0.1Tr. This tendency appears more strongly if aspect ratio is large. And then we have confirmed the occurrence of reversal of the mean axial flow.

S055013 テイラー・ディーン流れを利用したマイクロミキサ : 流路の回転効果([S055-01]内部流れ(1))

The micromixer, which has a rotor with a curved channel, is studied experimentally. The Taylor-Dean flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature δ=α/R is taken to be about 0.1, where 2α is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number De=Reδ^<1/2>, where Re=qd_h/v is the Reynolds number, q the mean flow velocity in the channel axis direction, d_h the hydraulic diameter of the channel, v the kinematic viscosity, and the Taylor number Tr=2α^2Ω(2δ)^<1/2>/(δv), where Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De %le; 0.1|Tr|. This tendency appears more strongly if aspect ratio is large. And then we have confirmed the occurrence of reversal of the mean axial flow.

A Micromixer Using the Chaos of Secondary Flow: Rotation Effect of Channel on the Chaos of Secondary Flow

The micromixer, which has a rotor with a curved channel, is studied experimentally. The secondary flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature δ=a/R is taken to be about 0.1, where 2a is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number De=Reδ1/2, the Reynolds number Re=qdh/v, where q is the mean flow velocity in the channel axis direction, ν the kinematic viscosity, dh the hydraulic diameter of the channel, and the Taylor number Tr=2(2δ)1/2Ωa2/(δv), where Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De≤0.1|Tr| and for that case secondary flows show chaotic behaviors. And then we have confirmed the occurrence of reversal of the mean axial flow.

A Micromixer Using the Chaos of Secondary Flow: Rotation Effect of Channel on the Chaos of Secondary Flow

The micromixer, which has a rotor with a curved channel, is studied experimentally. The secondary flow in a curved channel of rectangular cross-section is investigated using PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) methods. Two walls of the channel (the inner and top walls) rotate around the center of curvature and a pressure gradient is imposed in the direction of the exit of the channel. The non-dimensional channel curvature δ=a/R is taken to be about 0.1, where 2a is the width of the channel, R the curvature radius of the channel. Other non-dimensional parameters concerned are the Dean number De=Reδ1/2, the Reynolds number Re=qdh/v, where q is the mean flow velocity in the channel axis direction, ν the kinematic viscosity, dh the hydraulic diameter of the channel, and the Taylor number Tr=2(2δ)1/2Ωa2/(δv), where Ω is the angular velocity of the rotor. Photographs of the flow in a cross-section at 180° downstream from the curved channel entrance are taken by changing the flux (De) at a constant rotational speed (Tr) of the channel walls. It is found that good mixing performance is obtained in the case of De≤0.1|Tr| and for that case secondary flows show chaotic behaviors. And then we have confirmed the occurrence of reversal of the mean axial flow.

Stochastic modelling of aerosol deposition for LES of 90° bend turbulent flow

Aerosols deposition in turbulent bend flows is a major concern that is critical to many industrial, environmental and biomedical applications. In this work, a well-resolved LES was performed to compute the deposition efficiency of aerosols in turbulent circular cross-section bend flow of Dean number De = 4 , 225 . The numerical predictions were compared to the experimental work of Pui et al. [Pui, D.Y.H., Romay-Novas, F., Liu, B.Y.H., 1987. Experimental study of particle deposition in bend of circular cross-section. Aerosol Sci. Technol. 7, 301–315] and the fully-resolved LES of Breuer et al. [Breuer, M., Baytekin, H.T., Matida, E.A., 2006. Prediction of aerosol deposition in 90° bends using LES and an efficient Lagrangian tracking method. J. Aerosol Sci. 37, 1407–1428]. In the present LES, a slightly coarser but unstructured-grid numerical description was adopted, entailing that a portion of the small scales’ contribution to particle dispersion to be discarded. Thus, a Langevin-type stochastic model was used to model the effect of the discarded sub-grid motion on aerosol deposition. This stochastic model was shown to perform well in previous studies [Berrouk, A.S., Laurence, D., Riley, J.J., Stock, D.E., 2007. Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow. J. Turbulence, 8, 50]. Good care was taken to ensure that the main dynamical features of the continuous phase were captured by the present LES. An estimation of the filtered-out kinetic energy was provided. Results of the present LES with SGS model for particles were found to compare well with the experimental work and the fully-resolved LES (near-wall DNS) of Breuer for all the range of the Stokes number considered, 0.001 < St < 1.5 . Influence of the SGS model for particles was visible for the deposition efficiency of aerosols with Stokes number St < 0.3 .

Continuous particle separation in spiral microchannels using dean flows and differential migration

Microparticle separation and concentration based on size has become indispensable in many biomedical and environmental applications. In this paper we describe a passive microfluidic device with spiral microchannel geometry for complete separation of particles. The design takes advantage of the inertial lift and viscous drag forces acting on particles of various sizes to achieve differential migration, and hence separation, of microparticles. The dominant inertial forces and the Dean rotation force due to the spiral microchannel geometry cause the larger particles to occupy a single equilibrium position near the inner microchannel wall. The smaller particles migrate to the outer half of the channel under the influence of Dean forces resulting in the formation of two distinct particle streams which are collected in two separate outputs. This is the first demonstration that takes advantage of the dual role of Dean forces for focusing larger particles in a single equilibrium position and transposing the smaller particles from the inner half to the outer half of the microchannel cross-section. The 5-loop spiral microchannel 100 microm wide and 50 microm high was used to successfully demonstrate a complete separation of 7.32 microm and 1.9 microm particles at Dean number De = 0.47. Analytical analysis supporting the experiments and models is also presented. The simple planar structure of the separator offers simple fabrication and makes it ideal for integration with on-chip microfluidic systems, such as micro total analysis systems (muTAS) or lab-on-a-chip (LOC) for continuous filtration and separation applications.

Classification of Pulsating Flow Patterns in Curved Pipes

The fully developed periodic laminar flow of incompressible Newtonian fluids through a pipe of circular cross section, which is coiled in a circle, was simulated numerically. The flow patterns are characterized by three parameters: the Womersley number Wo, the Dean number De, and the amplitude ratio beta. The effect of these parameters on the flow was studied in the range 2.19 < or = Wo < or = 50.00, 15.07 < or = De < or = 265.49 and 0.50 < or = beta < or = 2.00, with the curvature ratio delta fixed to be 0.05. The way the secondary flow evolved with increasing Womersley number and Dean number is explained. The secondary flow patterns are classified into three main groups: the viscosity-dominated type, the inertia-dominated type, and the convection-dominated type. It was found that when the amplitude ratio of the volumetric flow rate is equal to 1.0, four to six vortices of the secondary flow appear at high Dean numbers, and the Lyne-type flow patterns disappear at beta > or = 0.50.

Effects of Bingham Viscosity on Flow in Curved Pipes.

Bingham plastic fluid flows through coiled pipes of circular cross section were experimentally studied. In the investigations, kaolin clay slurries were used as the Bingham plastic fluid. The effects of the Reynolds number Re or the Dean number De on the friction factor λc in the laminar steady flow of the Bingham plastic fluid flowing through coiled pipes were clarified. The apparent Reynolds number Reap, expected to play the equivalent role of Re in Newtonian fluids, was introduced using the similarity law of energy dissipation which was derived from a generalized equation of non-Newtonian fluid. It was clarified that the effects of the curvature of the pipes are greater in the case of greater concentration of the slurry, and that there exists a good correlation between the friction factor and the apparent Dean number Deap(defined according to Reap).

Characteristics of a Pulsating Bingham Plastic Fluid Flow in a Curved Pipe. Experimental and Numerical Study.

The fully developed pulsating laminar flows of an incompressible Bingham plastic fluid through a pipe of circular cross section coiled in a circle were investigated experimentaly and numerically. The flow fields were characterized by the Dean number De, Hedstrom number He, the Womersley number Wo and the curvature ratio δ. The friction factors were measured experimentaly for various volumetric ratio in the case of Wo=4. The calculations were carried out for a fixed He. The flow patterns and the axial velocity profiles were required in the calculations. It was clarified that the effects of the curvature of the pipes appeared easily for Newtonians compared with the plastic fluids. That is, the values of the amplitudes of the friction factor λac of the plastic fluid were smaller than that of Newtonians for a range of high Dean number, especially in the case of lower curvature ratio. In the calculations, it was found in the case of a plastic fluids that, in the axial velocity distributions a typical plug flow area appeared near the outer side of the vent in all of a period, and that the strength of the secondary flows were greater than that of Newtonians especially within the period the volumetric rates increased.

Transport Phenomena of Pulsatile Flow in a Curved Pipe.

Pulsatile flow in a curved pipe enhances gas or substance transport because of the existence of secondary flows, and provides more mixing in the liquid phase than do steady flows. In this study, numerical analysis was performed on fully developed pulsating flow in a curved pipe under flow conditions similar to those characteristic of the blood flow in an aortic arch or in a booster lung. The calculations were performed over a wide range of Dean numbers De and Womersley numbers Wo for a fixed curvature ratio δ=0.05, and Schmidt number Sc=2900. The isodensity contour of the axial direction having a thin boundary layer near the wall was shown. Furthermore, it was revealed that the time- averaged Sherwood number (Sh)^^- increased by about 10 times due to the convection effect of secondary flows in the case of high Dean number flows compared with low Dean number flows, and that in the case of pulsatile flows, the time- averaged Sherwood number approached the values that of steady flows when the volumetric flow rate β equaled 10.