Numerical Analysis of Isothermal Gaseous Flows in Microchannel

Two‐dimensional compressible momentum equations were solved by a perturbation analysis and the PISO algorithm to investigate the effects of compressibility and rarefaction on the local flow resistance of isothermal gas flow in circular microchannels. The computations were performed for a wide range of Reynolds numbers and inlet Mach numbers. The explicit expression of the normalized local Fanning friction factor along the microchannel was derived in the present paper. The results reveal that the local Fanning friction factor is a function of the inlet Mach number, the Reynolds number and the length‐diameter ratio of the channel. For larger Reynolds and inlet Mach numbers, the friction coefficient in the microchannel is higher than the value in a macrotube, and the gas flow in the microchannel is dominated only by compressibility. For smaller Reynolds and inlet Mach numbers, the Fanning friction factor of gas flow in the microchannel is lower than that in a circular tube of conventional size due to slip flow at the wall and thus, rarefaction has a significant effect on the fluid flow characteristics in a microchannel.     

Wall factor for acceleration and terminal velocity of falling spheres at high reynolds numbers

The wall factor for spheres in the acceleration and terminal velocity ranges was determined experimentally for very high Reynolds numbers (13 500 < Re < 70 000). Experiments were performed with 12, 15, 18, 21, 25 and 31.75 mm spheres, falling in water inside cylinders 3.4, 4.9, 7, 10, 14 and 19 cm in diameter. A published empirical equation was found to yield good results for the terminal velocity wall factor in the range of studied Reynolds numbers.     

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.     

Influence of Impaction Plate Diameter and Particle Density on the Collection Efficiency of Round-Nozzle Inertial Impactors

This study has investigated the influence of impaction plate diameter ( Dc ) and particle density on the particle collection efficiency of single round-nozzle inertial impactors numerically assuming incompressible flow. The study shows that computed St 50 values range from 0.473 to 0.485, which are nearly independent of W/Dc ( W is the nozzle diameter) for the nozzle Reynolds number, Re > 1500, and when W/Dc < 0.32. St 50 values agree quite well with the theoretical values of Rader and Marple (1985), 0.49, and Marple and Liu (1974), 0.477. For a smaller impactor plate diameter such that W/D c > 0.32, St 50 will increase slightly. It increases from 0.483 to 0.507 (Re = 3000) or from 0.479 to 0.495 (Re = 1500) when W/Dc is increased from 0.32 to 0.48. When the nozzle Reynolds number is smaller than 1500, the influence of W/Dc on St 50 is found to be much more pronounced. The effect of particle density on the collection efficiency has also been investigated. When particle gravity is included, the results show that St 50 is not affected by particle density ranging from 0.5 to 10 g/cm 3 , although the particle collection efficiency increases slightly with increasing particle density at high ends of the collection efficiency curves at high nozzle Reynolds number due to an ultra-Stokesian effect. The particle interception effect does not affect the collection efficiency curves at high Reynolds numbers at all, and the effect is negligibly small at low Reynolds numbers.     

A new expression for spherical aerosol drag in slip flow regime

A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier–Stokes equations were solved and the velocity jump at the gas–particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed. The particle total drag coefficient was also correlated against Re and Kn over the range of gas–particle relative speeds yielding the incompressible slip flow from the Stokesian regime up to the threshold of compressibility. Inclusion of gas slip on the particle surface enhances the accuracy of particle drag force prediction up to 40.9% in the range of 0.01<Kn<0.1 and 0.125<Re<20 compared to the no-slip continuum drag values.     

Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Experimental results were obtained on the steady settling of spheres in quiescent media in a range of cylindrical tubes to ascertain the wall effects over a relatively wide range of Reynolds number values. For practical considerations, the retardation effect is important when the ratio of the particle diameter to the tube diameter (λ) is higher than about 0.05. A new empirical correlation is presented which covers a Reynolds number range Re = 53-15,100 and a particle to tube diameter ratio λ < 0.88. The absolute mean deviation between the experimental data and the presented correlation was 1.9%. The well-known correlations of Newton, Munroe and Di Felice agree with the presented data reasonably well. For steady settling of spheres in a counter-current water flow, the slip velocity remains practically the same as in quiescent media. However, for rising spheres in a co-current water flow, the slip velocity decreases with increasing co-current water velocity, i.e., the wall factor decreases with increasing co-current water velocity. Consequently, the drag coefficient for rising particles in co-current water flow increases with increasing water velocity.     

Axial Equilibrium Distance and Positioning of Particles in a Laminar Tube Flow

Particle transport in a laminar tube flow at low Reynolds numbers leads to accumulation of particles at specific equilibrium radii. The equilibrium radius depends on the particle size. Small particles find their equilibrium radius near the wall and large particles near the tube axis. During their radial migration to the equilibrium position, the particles move in axial direction with the flow. In an experimental setup, the axial equilibrium distance is measurement for several tube Reynolds numbers. The axial equilibrium distance is the distance a particle migrates in the flow direction, until it reaches its radial equilibrium position. The results are compared with CFD‐simulations of single particle movement in a laminar tube flow.     

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

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

Residence time distribution of a purely viscous non-Newtonian fluid in helically coiled or spatially chaotic flows

This work is dedicated to an experimental study of residence time distributions (RTD) of a pseudoplastic fluid in different configurations of helically coiled or chaotic systems. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean cells. Fluid particle trajectories become chaotic through a geometrical perturbation obtained by rotating the curvature plane of each bend of ±90° with respect to the neighboring ones (alternated or twisted curved ducts). Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the device. The experimental RTD is modeled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for generalized Reynolds numbers varying from 30 to 270. The Péclet number based on the diameter of the pipe is found to increase with the Reynolds number whatever the number of bends in the system. This reduction in axial dispersion is due to both the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction, which is one of the characteristic parameters of the model, increases with the Reynolds number, whatever the number of bends, to reach a maximum value ranging from 90% to 100%. For Reynolds numbers less than 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube center. Results have been compared with those previously obtained using Newtonian fluids. The values of the Péclet number are greater for the pseudoplastic fluid, the local change of apparent viscosity affecting the secondary flow. For pseudoplastic fluids, the apparent viscosity is lower near the wall and higher at the center of the cross section. The maximum axial velocity is flattened as the flow behavior index is reduced, inducing a decrease of the secondary flow in the central part of the pipe and an acceleration of it near the wall, which reduces the axial dispersion. These results are encouraging for the use of this system as continuous mixer for complex fluids in laminar regime, particularly for small Reynolds numbers.     

Analysis of non‐Brownian particle deposition from turbulent liquid‐flow

The deposition of non‐Brownian particles from turbulent liquid‐flow onto channel walls is numerically analyzed. The approach combines Lagrangian particle tracking with a kinematic model of the near‐wall shear layer. For nonbuoyant particles, direct interception is the main deposition mechanism and the deposition velocity scales as the particle diameter (in wall units) to the power of 1.7. When wall/particle hydrodynamic interactions are taken into account, the deposition velocity is significantly reduced and the correction factor scales as the cubic root of the wall roughness to particle diameter ratio. For buoyant particles, sedimentation is usually the predominant deposition mechanism and the hydrodynamic interactions significantly affect the deposition velocity when the drainage characteristic time driven by buoyancy is of the order of the particle residence time close to the wall. Last, a wall‐function for the suspended particles is proposed. © 2015 American Institute of Chemical Engineers AIChE J, 62: 891–904, 2016     

Particle motion and separation in a laminar tube flow with downstream enlargement

Particle classification becomes difficult when the difference in density between particle and fluid is low or negligible and the fluid is viscous. For such applications, a process capable of separating the particles according to their size is needed. Such applications are, e.g. found in biological systems for cell separation or in the removal of gel particles from polymer melts. Particle transport in laminar tube flows at low but non zero Reynolds numbers leads to accumulation of large particles near the tube center and forms a particle free zone near the wall. Small particles find their position on their equilibrium radius. Downstream widening of the flow enhances segregation between large and small particles. Large particles can be collected in a centered collector tube downstream, whereas small particles follow their streamlines around the collector tube and can be removed with the remaining flow. The said particle migration is observed when the ratio of particle to tube diameter is 0.2<d/D<0.51 and the tube Reynolds number is in between 0.2<Re<40. CFD simulations reveal the shape of the streamlines in the downstream enlargement with different tube Reynolds number. The efficiency of the classification process is characterized. Particles need a sufficient transportation length in the tube for proper demixing. This effect is analyzed by a laser sheet illuminated system within an acrylic glass tube.     

Direct numerical simulation of moderate-Reynolds-number flow past arrays of ellipsoids

Through particle-resolved direct numerical simulations of flow past arrays of ellipsoids, the hydrodynamic force on ellipsoids depends on the particle orientation, aspect ratio, particle Reynolds number, and solid volume fraction is revealed at moderate Reynolds numbers. The results show that the mean drag force on arrays of prolate/oblate ellipsoids decreases/increases as the Hermans orientation factor increases when flows are in the reference direction defined by the average symmetric axis of particles. The individual drag force on a prolate/oblate ellipsoid increases/decreases with the increase of incidence angle, and it is also affected by the orientation of surrounding particles. The individual lift force is also significant when the aspect ratio is away from unity at large particle Reynolds numbers. Based on simulation results, correlations for the hydrodynamic force on ellipsoids at arbitrary particle Reynolds numbers, solid volume fractions, Hermans orientation factors, incidence angles, and aspect ratios are formulated.     

CFD‐Modellrechnungen zum Auftreffgrad von Partikeln auf Tropfen

For wet scrubber simulation the knowledge of collision efficiencies of particles with droplets is needed with high resolution and in a wide range of droplet Reynolds numbers. CDF simulations enabled the calculation of collision efficiencies as a function of droplet Reynolds numbers in high resolution. For every droplet Reynolds number between 0.1 and 100 the Stokes‐Number was varied via the particle diameter, whose ratio to the droplet diameter was always smaller than 0.15. The calculated collision efficiencies presented here to some extend differ distinctively from the results known from the literature.     

Fine particle turbulence modulation

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

Inertial migration and multiple equilibrium positions of a neutrally buoyant spherical particle in Poiseuille flow

The radial migration of a single neutrally buoyant particle in Poiseuille flow is numerically investigated by direct numerical simulations. The simulation results show that the Segré and Silberberg equilibrium position moves towards the wall as the Reynolds number increases and as the particle size decreases. At high Reynolds numbers, inner equilibrium positions are found at positions closer to the centerline and move towards the centerline as the Reynolds number increases. At higher Reynolds numbers, the Segré and Silberberg equilibrium position disappears and only the inner equilibrium position exists. We prove that the inner annuluses in the measurements of Matas, Morris & Guazzelli (J. Fluid Mech. 515, 171–195, 2004) are not transient radial positions, but are real equilibrium positions. The results on the inner equilibrium positions and unstable equilibrium positions are new and convince us of the existence of multiple equilibrium radial positions for neutrally buoyant particles.     

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

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

A Micro-layer Model for the Lubrication Effect Near Collisions of Immersed Particles

A micro-layer model is proposed to account for the lubrication effect of liquid layer near collisions of immersed particles at moderate particle Reynolds number. This new model is to allow determination of the pressure profile within the micro-layer including the fluid inertia and viscosity. Then a correction based on the micro-layer model is applied to unsteady 3-D direct simulation of a particle approaching another one. The simulation is based on a modified immersed boundary method with direct force scheme. The quantitative agreement between numerical and experimental results validates the model presented in the study. The simulation results show that the fluid is squeezed prior to contact. When a particle approaches a flat wall or another particle, the lubrication force, obtained by integrating the pressure profile over the particle surface, is increased and prevents the particle from approaching. The model predicts that the velocity of approaching particle starts to decrease when separation distance of particles is less than 0.1dp, where dp is the particle diameter.     

Numerical study of particle–particle collision in swirling jets: A DEM–DNS coupling simulation

The particle–particle collisions in swirling jets are studied by a coupling method of discrete element method (DEM, a hard-sphere approach) and direct numerical simulation (DNS). The characteristics of distribution of collision in configuration and velocity spaces are investigated in detail through probability density functions (PDFs) in the generalized coordinates. The dependency of particle–particle collision on turbulence characteristics, such as turbulent kinetic energy (TKE), dissipation rate (TDR), fluctuation, and correlated fluctuations, is studied by exploring the PDFs and the correlations between them. The results show that the spatial distribution of particle–particle collision in swirling jets is highly dependent on the Stokes numbers. For small particles, collision is dominated by the enclosure of bubble vortices whereas for large particles it is mainly determined by the configuration of the flow domain. The distribution of collision in velocity space has corresponding features of dependency on the particle property. Small particles are most probable to collide with each other near zero streamwise velocity within the recirculation zone, whereas large particles are most probable to take collision with their axial velocities close to the inflow velocity of fluid. The dependency of collision on TKE and TDR is fairly complicated. For example, for Stokes number slightly less than unity and far larger than unity, collision is relatively well-correlated to TKE, resulting in an augmented effect of turbulence modulation. It is investigated in detail and the physical mechanisms are well interpreted. Finally, the correlation between the PDF of collision and fluctuations of turbulence indicates that collision probability is positively correlated to the normal components of Reynolds stress tensor, but negatively correlated to the shearing components of Reynolds stress tensor.     

Rear surface deposition of fine particles on spheres — eddy deposition or electrostatic effects?

The aim of this investigation is to show the demarcation of two possible mechanisms for surface deposition of fine particles on the rear surface of single spheres. By means of single particle trajectory computation, based on numerically determined flow fields (Re_max = 10³), it is shown that the mere existence of a wake is not in itself sufficient to produce eddy deposition. In addition, the particle's motion must undergo a lateral transfer promoted by fluid trubulence, in order to effect eddy deposition commencing at a Reynolds number of about 100. On the other hand, rear deposition, influenced by electrostatic forces, especially by the Coulomb force, is possible at any Reynolds number. Consequently, for Reynolds numbers of less than 100, only electrostatic effects can produce rear surface deposition. In the range of high Reynolds numbers, the coexistence of both mechanisms is possible. Very high Reynolds numbers (Re > 10³) and low Stokes numbers indicated the predominance of the electrostatic effect over eddy deposition, whereas at very high Reynolds numbers and medium to high Stokes numbers the electrostatic effect is only predominant in presence of high electrostatic charges.     

不同翼片扰流特性的PIV对比实验

利用粒子成像测速（PIV）技术对圆管内置梯形翼片后方流场进行了测量,分析了翼片迎流（UFW）和顺流（DFW）两种放置方式对流场的扰动特性。结果表明,迎流翼片形成的涡沿周向延展范围较大,持续性好,涡偶内侧为向壁流;顺流翼片形成的涡沿径向延展范围较大,在较短距离内扰动较为明显,涡偶内侧为背壁流。两种流动结构都能有效提高壁面附近的速度分量,促进主流和壁面附近流体的质量交换。随着Reynolds数增大,纵向涡的稳定性减弱,在Re=3000时,翼片的扰流效果均较好。