Dynamics of dual-particles settling under gravity

As a first step towards understanding particle–particle interaction in fluid flows, the motion of two spherical particles settling in close proximity under gravity in Newtonian fluids was investigated experimentally for particle Reynolds numbers ranging from 0.01 to 2000. It was observed that particles repel each other for Re>0.1 and that the separation distance of settling particles is Reynolds number dependent. At lower Reynolds numbers, i.e. for Re<0.1, particles settling under gravity do not separate.The orientation preference of two spherical particles was found to be Reynolds number dependent. At higher Reynolds numbers, the line connecting the centres of the two particles is always horizontal, regardless of the way the two particles are launched. At lower Reynolds numbers, however, the particle centreline tends to tilt to an arbitrary angle, even of the two particles are launched in the horizontal plane. Because of the tilt, a side migration of the two particles was found to exist. A linear theory was developed to estimate the side migration velocity. It was found that the maximum side migration velocity is approximately 6% of the vertical settling velocity, in good agreement with the experimental results.Counter-rotating spinning of the two particles was observed and measured in the range of Re=0–10. Using the linear model, it is possible to estimate the influence of the tilt angle on the rate of rotation at low Reynolds numbers. Dual particles settle faster than a single particle at small Reynolds numbers but not at higher Reynolds numbers, because of particle separation. The variation of particle settling velocity with Reynolds number is presented. An equation which can be used to estimate the influence of tilt angle on particle settling velocity at low Reynolds number is also derived.     

Secondary flow patterns and mixing in laminar pulsating flow through a curved pipe

Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r ₀/r _c  = 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced. To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe. Experiments are carried out for the Reynolds numbers range 420 ≤ Re_st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U _max,osc/U _m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters 8.37 < (α = r ₀(ω/ν)^0.5) < 24.5, where α² is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing. The effects of each parameter (Re_st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ _P |/|ζ _S |) and dimensionless transverse strain rates (|ε _P |/|ε _S |) during a complete oscillation period.     

Two-phase flow laden with spherical particles in a microcapillary

Solid–liquid two-phase flow in a finite Reynolds number range (2 < Re < 12), transporting neutrally-buoyant microspheres with diameters of 6, 10, and 16 μm through a 260-μm microcapillary, is investigated. A standard microparticle-tracking velocimetry (μ-PTV) that consists of a double-pulsed Nd:YAG laser, an epi-fluorescent microscope, and a cooled-CCD camera is used to examine the flow. The solid particles are visualized in view of their spatial distributions. We observe a strong radial migration of the particles across the flow streamlines at substantially small Re. The degree of particle migration is presented in terms of probability density function. Some applications based on this radial migration phenomena are discussed in conjunction with particle separation/concentration in microfluidic devices, where the spatial distribution of particles is of great importance. In doing so, we propose a particle-trajectory function to empirically construct the spatial distribution of solid particles, which is well correlated with our experimental data. It is believed that this function provides a simple method for estimating the spatial distribution of particles undergoing radial migration in solid–liquid two-phase flows.     

Local measurements of turbulent angular momentum transport in circular Couette flow

We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent circular Couette flow. Our apparatus is short (cylinder height to gap width ratio Γ ~ 2) and of relatively high wall curvature (ratio of cylinder radii η ~ 0.35). Fluctuation levels and the mean specific angular momentum are found to be roughly constant over radius, in accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used to directly measure the r − θ Reynolds stress component as a function of Reynolds number (Re), revealing approximate scalings in the non-dimensional angular momentum transport that confirm previous measurements of torque in similar flows. 2D LDV further allows for a decomposition of the turbulent transport to assess the relative roles of fluctuation intensity and r − θ cross-correlation. We find that the increasing angular momentum transport with Re is due to intensifying absolute fluctuation levels accompanied by a slightly weakening cross-correlation.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 2. Validation and application at Reynolds numbers up to <Emphasis Type="Italic">Re</Emphasis> ≤ 10<Superscript>4</Superscript>

Hybrid unsteady-flow simulation combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) is introduced in the series of two papers. Particle velocities on a laser-light sheet acquired with time-resolved PTV in a water tunnel are supplied to two-dimensional DNS with time intervals corresponding to the frame rate of the PTV. Hybrid velocity fields then approach those representing the PTV data in the course of time, and the reconstructed velocity fields satisfy the governing equations with the resolution comparable to numerical simulation. In part 2, by extending the capabilities of the hybrid simulation to higher Reynolds numbers, we simulate flows past the NACA0012 airfoil over ranges of Reynolds numbers (Re ≤ 10⁴) and angles of attack (−5° ≤ α ≤ 20°) and validate the proposed technique by comparing with experimental results in terms of the lift and drag coefficients. We also compare the results with unsteady Reynolds-averaged Navier–Stokes (URANS) simulation in two-dimensions and show the advantages of the hybrid simulation against two-dimensional URANS.     

Characterization of fluid flow patterns and heat transfer in horizontal channel mixed convection

Two mechanisms of roll initiation are highlighted in a horizontal channel flow, uniformly heated from below, at constant heat flux (Γ = 10, Pr = 7, 50 ≤ Re ≤ 100, 0 ≤ Ra ≤ 10⁶). The first mechanism is the classical one, it occurs for low Rayleigh numbers and is initiated by the lateral wall effect. The second occurs for higher Rayleigh numbers and combines the previous effect with a supercritical vertical temperature gradient in the lower boundary layer, which simultaneously triggers pairs of rolls in the whole zone in between the two lateral rolls. We have found that in the present configuration, the transition between the two roll initiation mechanisms occurs for Ra/Re ² ≈ 18. Consequently, the heat transfer is significantly enhanced compared to the pure forced convection case owing to the flow pattern responsible of the continuous flooding the heated wall with cold fluid.     

Buoyancy and cross flow effects on heat transfer of multiple impinging slot air jets cooling a flat plate at different orientations

The present article reports on heat transfer characteristics associated with multiple laminar impinging air jet cooling a hot flat plat at different orientations. The work aims to study the interactions of the effects of cross flow, buoyancy induced flow, orientation of the hot surface with respect to gravity, Reynolds numbers and Rayleigh numbers on heat transfer characteristics. Experiments have been carried out for different values of jet Reynolds number, Rayleigh number and cross flow strength and at different orientations of the air jet with respect to the target hot plate. In general, the effective cooling of the plate has been observed to be increased with increasing Reynolds number and Rayleigh number. The results concluded that the hot surface orientation is important for optimum performance in practical applications. It was found that for Re ≥ 400 and Ra ≥ 10,000 (these ranges give 0.0142 ≤ Ri ≤ 1.59 the Nusselt number is independent on the hot surface orientation. However, for Re ≤ 300 and Ra ≥ 100,000 (these ranges give 1.59 ≤ Ri ≤ 42.85): (i) the Nusselt number for horizontal orientation with hot surface facing down is less that that of vertical orientation and that of horizontal orientation with hot surface facing up, and (ii) the Nusselt number of vertical orientation is approximately the same as that of horizontal orientation with hot surface facing up. For all surfaces orientations and for the entire ranges of Re and Ra, it was found that increasing the cross flow strength decreases the effective cooling of the surface.     

Lateral migration mechanisms in capillary hydrodynamic chromatography

In all chromatographic systems that achieve separation of colloidal particles based on the particles' hydrodynamic behavior, there are partitioning mechanisms that promote lateral migration of particles across solvent streamlines. In this work, solvent inertia and particle electrostatics are incorporated in Brenner & Gaydos' general diffusive transport theory for particles and solvent flowing in a capillary, yielding the mean axial velocity of particles as a function of particle size. A comparison is made with capillary hydrodynamic chromatography results. The lateral migration of small particles is primarily due to diffusion, while large particles are focused by the inertial force at one equilibrium radial position, as observed in “tubular pinch” experiments. The transition from diffusion- to inertia-controlled lateral migration can be tuned to specific particle size ranges through variation of solvent ionic strength, flowrate and capillary radius. Poor prediction of the separation behavior of large particles is attributed to inaccuracy in the calculation of the inertial radial velocity, suggesting the need for further theoretical analysis and experimental study of inertial migration.     

An experimental investigation of moderate reynolds number flow in a T-Channel

An experimental investigation of water flow in a T-shaped channel with rectangular cross section (20 × 20 mm inlet ID and 20 × 40 mm outlet ID) has been conducted for a Reynolds number Re range of 56–422, based on inlet diameter. Dynamical conditions and the T-channel geometry of the current study are applicable to the microscale. 2-D planar particle imaging velocimetry (PIV) and laser-induced fluorescence (LIF) were used in multiple locations of the T-channel to investigate local dynamical behaviors. Steady symmetric and asymmetric flow regimes predicted in the literature, which is largely numerical, are experimentally verified. Unsteady flow regimes, which are numerically predicted to occur at higher Re but have not yet been experimentally characterized, are also examined, and real-time LIF results illuminate the evolution of unsteady structure. Experimental data of the present resolution and scope are not presently available for unsteady flow regimes. Time scales are presented for unsteady flow regimes, which are found to exhibit periodic behavior and to occur for Re  ≥ 195. An unsteady symmetrical regime is identified for Re ≥ 350 that is detrimental to mixing. Momentum fields and dynamical behaviors of all flow regimes are characterized in detail, such that published mixing trends may be better understood. Results of all experimental trials were used to construct a regime map. A symmetric topology is found to be dominant for Re from 56 to 116, when flow is steady, and 350 to 422, when flow is characterized by unsteady stagnation-point oscillation in the T-channel junction. Asymmetric flow, which is positively indicated for mixing, is dominant for Re between 142 and 298, and the fluid interface exhibits both steady (two standing vortices) and unsteady (shear-layer type roll-up) behaviors. This result is based on multiple experiments and suggests a practical operating range of 142  ≤ Re ≤ 298 where asymmetric flow is highly likely to experimentally occur. The identification of an upper limit on Re,  beyond which mixing appears negatively impacted by a more symmetrical momentum field, is practically important as pressure drops on the microscale are significant.     

Measurements of heat transfer coefficients between turbulent liquid jets and a radially finned heated disk placed at the bottom of an open vertical circular cavity

 Experiments have been performed to assess the impact of an extended surface on the heat transfer enhancement for axisymmetric, turbulent liquid jet impingement on a heated round disk. The disk, with an array of integral radial fins mounted on its surface, is placed at the bottom of an open vertical circular cavity. Hydrodynamic and heat transfer data were obtained for a dielectric fluorocarbon liquid FC-77. For a fixed circular heater of diameter D=22.23 mm, several geometric parameters were tested: the nozzle diameter (4.42≤d≤9.27 mm), the confining wall diameter of the vertical cavity (22.23≤D _c≤30.16 mm), and the nozzle-to-heater spacing (0.5≤S/d≤5.0). The FC-77 flow rates varied from =0.2 to 11.0 l/min producing Reynolds numbers in the wide interval 700≤Re _d ≤44,000. For d=4.42 mm, the heat transfer response to the separation distance S/d was small but increased gradually with increasing nozzle diameter up to d=9.27 mm. The thermal resistance R _th increased with the confining wall diameter D _c and also with the nozzle diameter d. A minimum value of the thermal resistance of R _th,min=0.4 cm² K/W was attained for a combination of d=4.42 mm, D _c=22.23 mm, S/d=1, and =7.5 l/min. Based on a simplified heat transfer model, reasonable agreement was obtained between measured values of the thermal resistance and the R _th-predictions. The total fin effectiveness ɛ_f was shown to increase with increasing nozzle diameter, but was invariant with the flow rate (or the jet exit velocity). More than a three-fold heat transfer enhancement was realized through the addition of the array of integral radial fins on the heated round disk. Received on 30 August 2000 / Published online: 29 November 2001     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

Numerical investigation of particle lateral migration in straight channel flows using a direct-forcing immersed boundary method

Inertia-induced cross-stream migration has been recently exploited for precise position of particles in confined channel flows. In this work, a three-dimensional finite volume based immersed boundary method has been developed to study the lateral migration and hydrodynamic self-assembly of neutrally-buoyant particles in pressure-driven flows. Simulation results show that, in 2D channel flows, the equilibrium position for a circular particle is closer to the centreline for larger particle Reynolds number due to the increasing flow rate, while in 3D square duct flow, the equilibrium position for a spherical particle is near a face centre and is closer to the wall for larger particle Reynolds number. Self-assembly of a pair of particles is observed in 3D square duct flows but not in 2D channel flows. Mechanisms for the self-assembly are discussed.     

Reynolds number dependence of gas-phase turbulence in gas–particle flows

A downward flow of glass bead particles in a vertical pipe is investigated using a two-component LDV/PDPA for a range of Re (6400 < Re < 24,000) and a constant particle loading (m = 0.7). Two particle sizes of 70 and 200 μm are considered in the present work. For the 70 μm particles, the presence of the particles dampens the gas-phase turbulence intensity at the lowest value of Re investigated (8300) compared with the single-phase flow at the same Re. As Re increases, the gas turbulence increases, and for Re > 13,800 the gas turbulence is enhanced compared with the single-phase flow at the same Re. For the 200 μm particles, the intensity also increases with Re and is enhanced for all values of Re investigated, except at the lowest value of Re investigated (6400). At this value, the gas turbulence is equal to that of single-phase flow at the same Re. The observed trend in the gas-phase turbulence modulation with Re is proposed to be due to the change in the segregation patterns and in the average volume fractions of the particles with increasing Re. More importantly, the present experimental results suggest that, consideration of either the gas and particle characteristic length scales or the particle Reynolds number solely is insufficient to predict gas-phase turbulence modulation in gas–particle flows.     

Particle behavior in a turbulent pipe flow with a flat bed

Particle behavior in a turbulent flow in a circular pipe with a bed height h = 0.5R is studied at Re_b = 40,000 and for two sizes of particles (5 μm and 50 μm) using large eddy simulation, one-way coupled with a Lagrangian particle tracking technique. Turbulent secondary flows are found within the pipe, with the curved upper wall affecting the secondary flow formation giving rise to a pair of large upper vortices above two smaller vortices close to the pipe floor. The behavior of the two sizes of particle is found to be quite different. The 50 μm particles deposit forming irregular elongated particle streaks close to the pipe floor, particularly at the center of the flow and the pipe corners due to the impact of the secondary flows. The deposition and resuspension rate of the 5 μm particles is high near the center of the floor and at the pipe corners, while values for the 50 μm particles are greatest near the corners. Near the curved upper wall of the pipe, the deposition rate of the 5 μm particles increases in moving from the wall center to the corners, and is greater than that for the larger particles due to the effects of the secondary flow. The maximum resuspension rate of the smaller particles occurs above the pipe corners, with the 50 μm particles showing their highest resuspension rate above and at the corners of the pipe.     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

Effect of Schmidt number on the structure and propagation of density currents

The results of a numerical study of two- and three-dimensional Boussinesq density currents are described. They are aimed at exploring the role of the Schmidt number on the structure and dynamics of density driven currents. Two complementary approaches are used, namely a spectral method and a finite-volume interface capturing method. They allow for the first time to describe density currents in the whole range of Schmidt number 1 ≤ Sc ≤ ∞ and Reynolds number 10² ≤ Re ≤ 10⁴. The present results confirm that the Schmidt number only weakly influences the structure and dynamics of density currents provided the Reynolds number of the flow is large, say of O(10⁴) or more. On the contrary low- to moderate-Re density currents are dependant on Sc as the structure of the mixing region and the front velocities are modified by diffusion effects. The scaling of the characteristic density thickness of the interface has been confirmed to behave as (ScRe)^−1/2. Three-dimensional simulations suggest that the patterns of lobes and clefts are independent of Sc. In contrast the Schmidt number is found to affect dramatically (1) the shape of the current head as a depression is observed at high-Sc, (2) the formation of vortex structures generated by Kelvin–Helmholtz instabilities. A criterion is proposed for the stability of the interface along the body of the current based on the estimate of a bulk Richardson number. This criterion, derived for currents of arbitrary density ratio, is in agreement with present computed results as well as available experimental and numerical data.      

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Numerical investigation of natural convection of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanofluid in vertical annuli

This paper presents the numerical study of internal free convection of Al₂O₃ water nanofluid in vertical annuli. Vertical walls are maintained at constant temperatures and horizontal walls are adiabatic. Results are validated by experimental data. Effect of nanofluids on natural convection is investigated as a function of geometrical and physical parameters and particle fractions for aspect ratio of 1 ≤ H/L ≤ 5, Grashof number of 10³ ≤ Gr ≤ 10⁵ and concentration of 0 ≤ ϕ ≤ 0.06. More than 330 different numerical cases are investigated to develop a new correlation for the Nusselt number. This correlation is presented as a function of Nusselt number of base fluid and particle fraction which is a linear decreasing function of particle fraction. The developed correlation for annuli is also valid for the natural convection of Al₂O₃ water nanofluid in a square cavity. Furthermore, the effect of the viscosity and conductivity models on the Nusselt number of nanofluids in cylindrical cavities are discussed.     

Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel

Unsteady momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel is numerically investigated using FLUENT for the ranges of Reynolds numbers as 10≤Re≤500, of the blockage ratio as 0.1≤β≤0.4, and of the gap ratio as 0.125≤γ≤1 for a constant value of the Prandtl number of 0.744. The transition of the flow from steady to unsteady (characterized by critical Re) is determined as a function of γ and β. The effect of γ on the mean drag and lift coefficients, Strouhal number (St), and Nusselt number (Nu _w ) is studied. Critical Re was found to increase with decreasing γ for all values of β. and St were found to increase with decreasing values of γ for fixed β and Re. The effect of decrease in γ on was found to be negligible for all blockage ratios investigated.     

A note on wind-tunnel turbulence measurements with DPIV

At moderate Reynolds numbers (10⁴ ≤ Re ≤ 10⁵), the performance of lifting surfaces is strongly affected by the potential for laminar boundary layer separation and subsequent reattachment and the use of high-quality, low-turbulence wind tunnels is essential in characterising flight at comparatively small scales (where the wing chord may be from 1 to 5 cm in length) and low speeds (on the order of 10 m/s). Measurement of the existing turbulence levels in such facilities is hard and has not been achieved using DPIV methods due to the relatively small bandwidth of measurable velocities. A series of experiments is reported here where DPIV sampling parameters are driven beyond their normal range in an attempt to measure turbulence levels in a low turbulence wind tunnel. The results show that DPIV can measure the background turbulence, and therefore its instantaneous structure. The measurements also reveal certain challenges in investigating the aerodynamic performance of small-scale flying devices.