TERMINAL VELOCITY EQUATION FOR A TWO-PHASE BUBBLE IN AN IMMISCIBLE LIQUID MEDIUM

An analytical expression for the instantaneous terminal velocity of a two-phase bubble evaporating or collapsing in a less viscous, immiscible liquid at large Reynolds numbers is derived. The predicted results are compared with the experimental data of Sideman and Taitel [1]. There is good agreement between experiment and theory     

Evolution of bubble size distribution,number density,and shape in semi-batch vertical gas–liquid Taylor vortex flow

Bubble size distribution and bubble ellipticity were measured as a function of axial position in a vertically oriented semi-batch gas–liquid Taylor vortex reactor with varying gas flow rate and inner cylinder rotation speed producing axial Reynolds numbers in the range 23.8–119 and azimuthal Reynolds numbers up to 4.2 × 10⁴. The mean bubble size increases monotonically with axial distance from the bottom of the reactor at the location of gas injection. The functional form of the growth of the mean bubble size with axial position depends upon the azimuthal Reynolds number. Specifically, when the azimuthal Reynolds number is less than 1.3 × 10⁴, the mean bubble size increases linearly with axial distance from the bubble injection point. In contrast, for azimuthal Reynolds numbers greater than this critical value, the mean bubble size increases with axial distance in a sigmoidal manner.     

Suspending a solid sphere in laminar inertial liquid flow—experiments and simulations

The critical conditions for the suspension of single, spherical solid particles by a liquid flow in a square container driven by a rotating disk have been determined. In the experiments, the motion of the sphere has been visualized quantitatively. The conditions are such that the flow in the container is laminar (Reynolds numbers based on the rotating disk characteristics are in the range 10–40). The Archimedes numbers of the spheres are of order 1. The suspension process has also been numerically simulated with full resolution of the liquid flow, including the flow around the sphere, and the translational and rotational motion of the sphere. The simulations recover the critical conditions to within 3% in terms of the rotational speed of the disk. Also the sphere's trajectory in the container is reproduced well by the simulations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1455–1469, 2015     

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.     

A comparison of drag reduction for flows in circular tubes with flow between parallel planes

Drag reduction in the turbulent flow of aqueous solutions of polyacrylamide and poly(ethylene oxide) was studied in tubes and parallel plates. Friction factors were determined at Reynolds numbers up to 20,000 for polymer concentrations of 0.10 to 400g/m³ in glass tubes run in a constant-head, gravity flow system in which the velocity was determined from the horizontal distance traveled by the effluent stream while falling a set vertical distance; and in Plexiglas parallel plates run in a constant-velocity, machine-driven system in which the pressure drop between two points on the plates was measured with a differential pressure transducer. A general method of correlating fraction laminarization or drag reduction effectiveness with polymer concentration for Reynolds numbers above 6000 was developed in which two master curves, one for very low concentrations which was the same for both tubes and parallel plates, and one for higher concentrations which differed for tubes and parallel plates, were found to represent the data very well for both polymers and all conduit sizes and Reynolds numbers. Additionally, relationships were found between conduit size and maximum fraction laminarization and optimum polymer concentration.     

Transient three-dimensional heat transfer from rotating spheres with surface blowing

Transient heat transfer and thermal patterns around a rotating spherical particle with surface blowing are studied numerically for Reynolds numbers in the range 10?Re?300 and non-dimensional angular velocities up to Ω=1. This range of Reynolds number includes three distinct wake regimes: steady and axisymmetrical, steady but non-symmetrical, and unsteady with vortex shedding. The Navier-Stokes and energy equations for an incompressible viscous flow are solved numerically by a finite-volume method in a three-dimensional and time-accurate manner. The transient aspects of the thermal wakes associated with the aforementioned wake regimes have been explored. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that an unsteady three-dimensional flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects, and thus, the temperature distributions around the particle are significantly affected. Despite the fact that particle rotation brings about major changes locally, the surface-averaged heat transfer rates are not influenced appreciably even at high rotational speeds; consequently, it is shown that the total heat transfer rates associated with rotating spheres with surface blowing can be calculated from heat transfer correlations developed for flow over evaporating droplets.     

Experimental detection of bubble-wall interactions in a vertical gas-liquid flow

Bubble motions and bubble-wall interactions in stagnant liquid were experimentally investigated by high-speed CCD and PIV technique with the main feature parameters such as E(o)tv(o)s numbers Eo =0.98-1.10,Morton number Mo =3.21 × 10-9 and Reynolds numbers Re =180 ～ 190.The effect of bubble injecting frequency and the distance S between the gas injection nozzle and the wall on the statistical trajectory of bubbles,average velocity distribution of flow field and Reynolds shear stress were studied in detail.It was shown that the combination of bubble injecting frequency and the distance S caused different bubble motion forms and hydrodynamic characteristics.When the normalized initial distance was very little,like S* ≈ 1.2 (here S* =2S/de,and de is the bubble equivalent diameter),bubbles ascended in a zigzag trajectory with alternant structure of high and low speed flow field around the bubbles,and the distribution of positive and negative Reynolds shear stress looked like a blob.With the increase of distance S*,bubbles' trajectory would tend to be smooth and straight from the zigzag curve.Meanwhile,with the increase of bubble injecting frequency,the camber of bubble trajectory at 20 ＜ y ＜ 60 mm had a slight increase due to the inhibitory effect from the vertical wall.Under larger spacing,such as S* ≈ 3.6,the low-frequency bubbles gradually moved away from the vertical plane wall in a straight trajectory and the high-frequency bubbles gradually moved close to the vertical wall in a similar straight trajectory after an unstable camber motion.Under the circumstances,high-speed fluid was mainly distributed in the region between the wall and the bubbles,while the relative large Reynolds shear stress mainly existed in the region far away from the wall.     

离心式分子蒸馏设备在发酵L-乳酸精制工艺中的应用

以发酵液中的乳酸为原料,采用离心式分子蒸馏设备进行精制。研究了离心式分子蒸馏设备的蒸发面温度、蒸发面转速、冷热面间距、冷热面温差对L-乳酸纯度和收率的影响,试验结果表明利用离心式分子蒸馏设备精制发酵L-乳酸的最适工艺条件为：压力0.1Pa,进料温度50～70℃,蒸发面温度60～75℃,蒸发面转速700～900 r/min,冷热面间距20～30 mm,冷热面温差40～45℃,在此条件下操作L-乳酸的纯度由80%提高到95%,收率为70%。     

Emission studies of impinging premixed flames

This paper reports the results of an experimental investigation of emissions from an impinging flame to a flat cold surface. This study pertains to the fuel rich premixed flame issuing from a 8-mm diameter nozzle burner. The effects of burner to plate spacing, equivalence ratio and Reynolds numbers on the flame structure and emission are investigated. The flame structure is characterized by temperature measurement. The axial temperature profiles show that it is strongly dependent on the distance between the burner and cold surface. The temperature in the radial direction declines sharply after certain distance from the center of the plate which is also seen to depend on the separation distance. It has been found out that the CO level increases for separation distance greater than 12 nozzle diameter for all Reynolds number which may be attributed to the excess entrainment of air leading to the dilution of mixture. However, the CO level also increases with increase in equivalence ratio for same separation distance. The NO level decreases with increase in equivalence ratio and Reynolds number. The separation distance of 12 nozzle diameter case gives higher NO level for all Reynolds number. The CO₂ level increases with equivalence ratio for all Reynolds number. It is believed that these experimental data will be useful for designing and developing rapid heating devices.     

MASS TRANSFER FROM AN AEROSOL DROPLET AT INTERMEDIATE PECLET NUMBERS

A new experimental technique involving the use of optical resonances observed in an evaporating aerosol droplet suspended in an electrodynamic balance is developed in order to study mass transfer from a sphere. Previous theoretical and experimental results are compared with new data for the slow evaporation of dodecanol in nitrogen flowing at Reynolds numbers in the range 0.001 to 1.25. Mass transfer data for dodecanol and for hexadecane obtained with the “picobalance” are shown to be in good agreement with the singular perturbation expansion of Rimmer for Pe≤1.1, while the interpolation formula of Zhang and Davis best represents the results for Pe up to 4.     

管内垂直下降液膜速度与厚度分布特性

对洗涤冷却管内垂直降膜的流动特性进行研究,采用超声波多普勒测速仪对管内不同周向以及轴向位置的液膜厚度和速度进行了无接触式的测量,液膜Reynolds数范围为1.0×10⁴~3.1×10⁴。结果表明:在0°周向位置上液膜厚度与速度均达到最大值,导致该位置局部液膜厚度过大而不能保持稳定,部分液体脱离液膜表面,此外还造成了8°和16°位置的液膜厚度激增。在轴向上,当Reynolds数小于2.0×10⁴时,液膜速度在重力作用下随流动距离增加而增加,反之,液膜速度因为流动阻力会随距离增加而减小。随着Reynolds数的增大,液膜平均厚度和速度呈增大趋势。此外,Reynolds数的增大还会使得液膜更加不稳定。     

Aerosol Deposition Efficiencies and Upstream Release Positions for Different Inhalation Modes in an Upper Bronchial Airway Model

Accurate predictions of micron-particle deposition patterns and surface concentrations in lung airways are most desirable for researchers assessing health effects of toxic particles or those concerned with inhalation delivery of therapeutic aerosols. Focusing on a rigid, symmetric triple bifurcation lung airway model, i.e., Weibel's generations G3-G6, a user-enhanced and experimentally validated finite volume program has been employed to simulate the airflow and particle transport under transient laminar three-dimensional flow conditions. Specifically, the effects of 3 inhalation modes, i.e., resting and light and moderate activities, were analyzed for typical ranges of Stokes numbers (St h 0.2) and Reynolds numbers (0 h Re h 2100). The detailed results show particle deposition patterns and efficiencies in the triple bifurcation under cyclic as well as steady-state inhalation conditions. Cyclic inhalation generates higher local and segmentally-averaged deposition rates when compared to steady mean Reynolds number inhalation; however, matching Stokes and Reynolds numbers, i.e., the average between mean and peak values, were found to provide fully equivalent results for all inhalation modes and bifurcations. In addition, particle maps were developed that show the release positions of deposited aerosols.     

Settling length for turbulent flow of air in an annulus

The settling length, or distance downstream from the entrance required for the development of the velocity profile, has been determined for four square entrance sectioned annuli, with diameter ratios of 0.2, 0.3, 0.5 and 0.7. Using air, a Reynolds number range of 5,000 to 50,000 was covered, and correlations have been obtained relating the settling length, equivalent diameter, Reynolds number and diameter ratio. The expression L/De = 0.795 R_e³⁷⁴(D₁/D₂)^?0.60 correlated the data for Reynolds numbers lower than 22,000 and for Reynolds numbers greater than this the relation was L/D_e = 15.96 R_e^.077(D₁/D₂)^?624.     

Laminar‐forced convection mass transfer to ordered and disordered single layer arrays of spheres

Laminar forced convection mass transfer to single layers of equidistantly and nonequidistantly spaced spheres perpendicular to the flow direction is studied. Average Sherwood numbers are reported as a function of geometric configurations and flow conditions, for open frontal area fractions between 0.25 and 0.95, Schmidt numbers between 0.7 and 10, and Reynolds numbers (based on the sphere diameter and the free stream velocity) between 0.1 and 100. For equidistantly spaced arrays of spheres, a general analytical expression is proposed for the average Sherwood number as a function of the Reynolds number, Schmidt number and the open frontal area fraction, as well as asymptotic scaling rules for small and large Reynolds. For all studied Schmidt numbers, equidistant arrays exhibit decreasing average Sherwood numbers for decreasing open frontal area fractions at low Reynolds numbers. For high Reynolds numbers, the Sherwood number approaches that of a single sphere, independent of the open frontal area fraction. For equal open frontal area fractions, the Sherwood number in nonequidistant arrays is lower than in equidistant arrays for intermediate Reynolds numbers. For very low and high Reynolds numbers, nonuniformity does not influence mass transfer. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1400–1408, 2013     

Mass transfer in a turbulent radial wall jet

Experimental and theoretical coefficients are reported for mass transfer in a turbulent radial wall jet initiated by an impinging free jet. The hydrodynamic solution was obtained by the momentum integral technique, and mass transfer was predicted by analogy. Point mass transfer data were obtained for air-naphthalene and cinnamic acid-water systems. At low Schmidt numbers, experimental coefficients were slightly above the theoretical prediction, and followed the theoretical trend with radial distance and nozzle Reynolds number from 10,000 to 60,000. Coefficients at high Schmidt numbers showed large positive deviations from theory, which decreased with radial distance and increased with Schmidt number. These discrepancies were attributed to surface roughness effects.     

Viscous flow through particle assemblages at intermediate reynolds numbers — a cell model for transport in bubble swarms

The fluid mechanical behaviour of a bubble swarm was simulated using a cell model. The Navier-Stokes equations were solved numerically for the liquid flow in a uniform assemblage of circulating, spherical bubbles. Ranges of parameters studied included, Reynolds numbers, 0–1000 and porosities, 0.4–1. The numerical calculations show the effects of variations in Reynolds numbers and porosity on: surface vorticity and pressure distributions and form and friction drag coefficients. For all Reynolds numbers investigated a standing vortex ring was absent Predicted drag coefficients and Sherwood or Nusselt numbers agree with limiting analytical solutions for low and high Reynolds numbers. The theoretical results show good agreement with experimental data for porosity as a function of superficial gas velocity. Predicted and measured Sherwood and Nusselt Numbers were in substantial disagreement, making detailed comparison unwarranted The calculations should also be valid for dispersions of uniform, circulating, spherical droplets for the special case where the droplet viscosity is much less than the viscosity of the continuous fluid     

Drag coefficients of evaporating spheres in a turbulent air stream

A study was made to determine the effect of mass transfer on the drag coefficients of freely-moving aerodynamically smooth spheres, accelerating in a co-current turbulent air stream. The particles consisted of celite impregnated with liquid sulphur dioxide and varied in diameter from 0.184 to 0.989-inch. Accurate time-distance data were obtained with a new particle-tracking technique which allowed the quantitative measurement of drag coefficients for relative turbulence intensities varying from 5 to 30%. The range of Reynolds numbers studied was from 2100 to 29,800, which, because of the effect of free-stream turbulence, forms a part of the super-critical flow regime. The results have thus been compared with the previously reported drag data for solid non-evaporating spheres in a similar flow region. Mass transfer was found, in general, to decrease the super-critical drag on a sphere and to reduce the influence of relative turbulence intensity. This alteration in momentum transfer is probably due to a reduction in the skin friction and to a pressure increase in the wake of an evaporating sphere.     

Kenics型静态混合器内分散相液滴破碎和聚结过程的CFD-PBM数值模拟

采用CFD-PBM耦合方法对Kenics型静态混合器内分散相油滴破碎及聚并行为进行数值模拟研究,分析了雷诺数、混合元件数、元件长径比等参数对分散相液滴粒径的影响,揭示了分散相在Kenics静态混合器内流动过程中液滴粒径的演化规律.结果表明,随雷诺数增大,分散相液滴出口粒径不断减小,并出现临界趋势;静态混合器的前几个元件...     

环形通道内层流入口段换热及流体变物性的影响

采用SIMPLER算法对环形通道内二维定常轴对称入口段流动与换热进行了数值计算, 研究了两种边界条件下的层流流动与换热规律, 给出了不同Prandtl数以及半径比率下沿程Nusselt数的变化曲线,同时还给出了流体物性随温度变化对流动与换热的影响, 最后还拟合出了不同半径比率下平均Nusselt数的关联式.计算结果还表明,环形通道能强化传热,强化程度随半径比率减小而增大,且入口段的换热强化与其较高的径向速度有关.     

A drag correlation for a nonporous sphere steadily approaching an impermeable plane at finite Reynolds numbers

A particle experiences resistance while moving in a viscous fluid and this drag force increases in the vicinity of no-slip surfaces due to the wall effect. For a nonporous solid spherical particle steadily approaching an impermeable plane, Brenner analytically obtained the wall effect correction factor for the small Reynolds number (Brenner, 1961). For finite Reynolds numbers Wu and Lee calculated the correction factor from their numerical simulation (Wu, 1998). Unifying the results of these previous studies, we propose a compact form of the wall effect correction factor that is valid for Reynolds numbers less than 40.