Thermophoretic deposition of aerosol particles in laminar tube flow with mixed convection

A model is developed to investigate the thermophoretic deposition of aerosol particles on the wall of a relatively cool cylindrical tube. A key aspect of the flow is the presence of mixed convection. Continuity, momentum, and energy equations are solved to determine the velocity and temperature profiles of the system. Additionally, an aerosol population balance that incorporates thermophoresis and Brownian diffusion is solved. The results indicate that more particles deposit at shorter axial distances in downward flow through a vertical pipe than in upward flow. This behavior is traced to the larger residence time associated with downward flow, despite the presence of a reduced radial temperature gradient relative to the upward configuration. Model predictions also indicate that a bulk Richardson number (Ri) of at least unity is necessary, but not sufficient for free convection effects to be important. The additional evaluation of a local Ri provides a more reliable indicator.     

Gravitational deposition of aerosol particles from a developing flow in a horizontal circular tube

Aerosol particle deposition due to gravitational settling in a horizontal circular duct is examined for steady laminar flow, which develops from a uniform velocity profile at the entrance to a parabolic velocity profile downstream. Numerical calculation methods, based on the analysis of the limiting trajectories of the particles, are used to determine the deposition efficiency as a function of the duct entrance length. The results show that the deposition for the limiting cases of very large or small settling approach the solutions for deposition in a slug or a Poiseuille flow, respectively. In addition, particle inertial effects were included and for relatively large inertia, the deposition rate was significantly affected.     

三角形螺旋流道充分发展层流流体的流动性能

基于角钢螺旋夹套,展开了对三角形螺旋流道层流流动性能的实验和数值研究。经对比,同一模型下的实验结果和模拟结果吻合良好。采用数值方法得到了充分发展状态下流体的主流速度、二次流速度、流函数及涡量的分布特点,分析了三角形边界上局部阻力系数的分布规律,并与半圆管螺旋流道进行了比较。结果表明：在所研究的Dean数及量纲1曲率（k）内,流道横截面上的二次流为稳定的两涡结构,内、外壁面局部阻力系数的分布明显不同,外壁面局部阻力系数的平均值约为内壁面阻力系数平均值的1.54～2.72倍;随着Dean数及k 的增大,二次流动增强,内、外壁面阻力系数均增大;对于量纲1挠率及Dean数均较小的三角形螺旋流道,挠率对流体流动的影响很小;通过对比,两种流道具有相同内壁面面积、曲率半径、螺距及Reynolds数时,三角形螺旋流道的流动阻力小于半圆管螺旋流道。     

Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows

An analysis of the two-fluid model in the case of vertical fully developed laminar bubbly flows is conducted. Firstly the phase distribution in the central region of the pipe (where wall effects vanish) is considered. From the model equations an intrinsic length scale L is deduced such that the scaled system reduces to a single equation without parameters. With the aid of this equation some generic properties of the solutions of the model for pipes with diameter greater than about 20L (the usual case, since L is of the order of the bubble radius) are found. We prove that in all physically meaningful solutions an (almost) exact compensation of the applied pressure gradient with the hydrostatic force occurs (with ρ_eff the effective density and the gravity). This compensation implies flat void fraction and velocity profiles in the central region not affected by the wall, even when no turbulence effects are accounted for.We then turn to consider the complete problem with a numerical approach, with the effect of the wall dealt via wall forces. The previous mathematical results are confirmed and the near-wall phase distributions and velocity profiles are found. With the numerical code it is also possible to investigate the regime in which the pressure gradient is greater than the weight of the pure liquid, in which case a region of strictly zero void fraction develops surrounding the axis of the pipe (in upward flow of bubbles).Finally, the same code is used to study the effect of reducing the gravity. As decreases, so does the relative velocity between the phases, making the lift force increasingly dominant. This produces, in upward bubbly flows, narrower and sharper void fraction peaks that also appear closer to the wall.     

Modeling of flow dynamics in laminar aerosol flow tubes

Flow behaviour in laminar aerosol flow tubes was investigated using a Computational Fluid Dynamics (CFD) model. Since these flow tubes are typically operated at low gas velocity, even small temperature gradients produce convection currents strong enough to interfere with laminar flow. This results in recirculation, causing the residence times of aerosol particles to be poorly defined. The situation is exacerbated when temperature inversions are present, or when the flow direction and temperature are changed simultaneously. We analyzed several characteristic flow tube configurations to define the range of experimental conditions that will ensure a laminar flow profile with minimal recirculation. For a laminar flow situation, we evaluated the extent of diffusion-controlled exchange between aerosol and the flow tube wall.     

A numerical study of the influence of ion–aerosol mixing on unipolar charging in a laminar flow tube

A theoretical investigation has been carried out to examine the effect of the initial ion–aerosol mixing state on the resulting charged fraction (extrinsic charging efficiency) of ultrafine particles in a circular tube under laminar flow conditions. Particle and ion loss to the walls by diffusion and electrostatic dispersion were taken into account in the calculations. Four different mixing states were considered at the inlet section of the charging tube: (I) uniform mixing of ions and neutral particles; (II) a core of ions surrounded by an envelope of neutral particles; (III) a core of neutral particles surrounded by an envelope of ions; and (IV) the inlet section split up into two circular segments, one containing neutral particles alone, the other only ions. The numerical results show that the extrinsic charging efficiency strongly depends on the initial mixing state, the maximum efficiency being attained for mixing state II, a state which can be easily realized in practice by injecting ions and particles into the charger through two coaxial cylinders. The worst case is that of mixing state III, the reverse of II, in which the neutral particles are injected through the inner cylinder, and the unipolar ions through the annular space between the injection tubes. The main reason underlying the observed behavior is the strong dependency of the ions loss rate to the wall on their initial spatial distribution.     

Air flow in a tube with a diverging inlet: II. Measurement and correlation of confirmed fully developed turbulent flow

Mean local velocities were measured in the section of a tube where turbulent flow was experimentally confirmed to be fully developed. Over Reynolds numbers from 9,000 to 56,0 00, the velocities correlated, using a logarithmic distribution, almost identically to those of Deissler. Because of the limited data for γ⁺< 26, no meaningful correlation near the wall was obtained. Using these data as a basis, a comparison of the various correlations for fully developed turbulent flow in the core region was performed. Although measurements in the laminar sublayers were limited, some discussion of correlations applicable over the entire cross-section of the tube is included. Pai's equation, valid from the wall to the center-line, was found to correlate all of the data best for the several approaches tested. In the turbulent core, the improved universal velocity distribution correlation suggested by Bogue but in simplified form, correlated the data equally well. Using the method of Wasan et al, this logarithmic distribution could be joined without a discontinuity to other suitable correlaions valid near the wall.     

Analysis of laminar flow forced convection heat transfer with uniform heating in the entrance region of a circular tube

A new integral or boundary-layer solution for laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux. The solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to hydrodynamically developing flow through a circular tube. Unlike available boundary-layer solutions, the new analysis provides results which join smoothly and asymptotically to the fully developed values. Results for the Nusselt number were found to agree favorably with available numerical solutions.     

内插不同形状涡产生器管内层流流动与传热特性的对比分析

内插扰流元件是一种可操作性强的管内强化传热方式,其强化传热机理主要是在管内诱导产生了二次流。在均匀壁温热边界条件下,对内插不同形状涡产生器管内层流流动与传热特性进行了数值分析。研究发现：在扭带基础上裁去部分面积相同的条件下,管内插等腰梯形涡产生器的换热能力最强,直角梯形涡产生器次之,矩形涡产生器的换热能力最差,管壁上的局部Nusselt数的峰值所在圆周位置及其大小与涡产生器形状有关,而不同形状的涡产生器对管内流动的阻力系数影响较小。插入涡产生器后,管内二次流强度参数Se和平均Nusselt数Nu均随Reynolds数Re的增大而增大,二者随Reynolds数Re的变化规律具有一致性。平均Nusselt数Nu与二次流强度参数Se呈幂函数相关,内插涡产生器管内的二次流强度决定了其对流换热强度。     

Two-phase laminar zero net flow in a circular inclined pipe

Steady countercurrent zero net flow of two immiscible fluids in an inclined circular tube has been studied under laminar flow conditions. Using appropriate dimensionalization, the interface position and viscosity ratio become the only two parameters that govern the flow. Velocity profiles and shear stresses were determined from numerical solutions of the equations of motion and are compared with the analytical solutions for flow between parallel plates. Such zero net flows are encountered at shutdown of long inclined slurry pipelines. The results of the present investigation are suitable for modelling these flows.     

Thresholds of secondary organic aerosol formation by ozonolysis of monoterpenes measured in a laminar flow aerosol reactor

The reactions of ozone with a series of monoterpenes (α-pinene, sabinene, limonene and myrcene) were investigated in a novel flow reactor dedicated to the investigation of secondary organic aerosol (SOA) formation. Rate constants for the gas phase reactions and nucleation thresholds were determined at T～296 K, P～764 Torr under dry conditions (dew point ≤?33 °C) and in absence of OH radicals scavenger and seed particles. Comparison with the literature as well as data from a simulation chamber showed good agreement. The experiments also show that the novel flow reactor improves the accuracy in evaluating the nucleation thresholds during the ozonolysis of monoterpenes and show that aerosol flow reactor is a useful tool to study the SOA nucleation step. Given as an upper limit, the nucleation thresholds obtained are (in molecule cm^?3/ppb): α-pinene, 3.9×10¹⁰/1.56; sabinene, 6.2×10⁹/0.26; limonene, 1.1×10¹⁰/0.43 and myrcene 2.1×10¹⁰/0.83.     

Molecular diffusion in the laminar sub-layer during turbulent flow in a smooth tube

A model is proposed that can predict the fully developed mass transfer coefficient for a turbulent flowing fluid in a smooth tube. Model results are compared to experimental data over a range of Reynolds number from 7750 to 50,200 and for Schmidt numbers of 850, 900, and 2400. Also, the model prediction is compared to an existing correlation that was derived from experimental data. In all cases the model prediction is in excellent agreement with the published experimental data and is an improvement over the existing correlation.