Jianzhong Lin

A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion

A new numerical approach for solving coagulation equation, TEMOM model, is first presented. In this model, the closure of the moment equations is approached using the Taylor-series expansion technique. Through constructing a system of three first-order ordinary differential equations, the most important indexes for describing aerosol dynamics, including particle number density, particle mass and geometric standard deviation, are easily obtained. This approach has no prior requirement for particle size spectrum, and the limitation existing in the log-normal distribution theory automatically disappears. This new approach is tested by comparing it with known accurate solutions both in the free molecular and the continuum regime. The results show that this new approach can be used to solve the particle general dynamic equation undergoing Brownian coagulation with sufficient accuracy, while less computational cost is needed.

Research on the Transport and Deposition of Nanoparticles in a Rotating Curved Pipe

A finite-volume code and the SIMPLE scheme are used to study the transport and deposition of nanoparticles in a rotating curved pipe for different angular velocities, Dean numbers, and Schmidt numbers. The results show that when the Schmidt number is small, the nanoparticle distributions are mostly determined by the axial velocity. When the Schmidt number is many orders of magnitude larger than 1, the secondary flow will dominate the nanoparticle distribution. When the pipe corotates, the distribution of nanoparticle mass fraction is similar to that for the stationary case. There is a “hot spot” deposition region near the outside edge of bend. When the pipe counter-rotates, the Coriolis force pushes the region with high value of nanoparticle mass fraction toward inside edge of the bend. The hot spot deposition region appears inside the edge. The particle deposition over the whole edge of the bend becomes uniform as the Dean number increases. The corotation of pipe makes the particle deposition efficiency ...

Research on reducing erosion by adding ribs on the wall in particulate two-phase flows

Abstract In the particulate two-phase flow with smooth wall and rib-welding wall, improved κ-ϵ turbulence model and one-way coupling method are employed to compute particle velocities and trajectories, and wall wastage caused by particle impacts. In order to verify the computational results, an apparatus is designed and corresponding experiment is made. Both computational and experimental results show that adding ribs on the wall can reduce wall erosion caused by particle impacts in the particulate two-phase flow. The wall wastage does not vary linearly as rib height. Under a definite rib height, it is most beneficial to reduce erosion when rib width is equal to gap between ribs. For a definite flow, in the region with relative small particle size, the variety of wastage rate changes steeply, whereas particle size exceeds a criterion, the wastage rate changes smoothly. The initial angle of motion direction between particles and gas affects the wall wastage.

Solution of the agglomerate Brownian coagulation using Taylor-expansion moment method

The newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation in the free-molecule regime and in the continuum regime, respectively. The moment equations with respect to fractal dimension are derived based on 3rd Taylor-series expansion technique. The validation of this method is done by comparing its result with the published data at each limited size regime. By comparing with analytical method, sectional method (SM) and quadrature method of moments (QMOMs), this new approach is shown to produce the most efficiency without losing much accuracy. At each limited size regime, the effect of fractal dimension on the decay of particle number and particle size growth is mainly investigated, and especially in the continuum regime the relation of mean diameters of size distributions with different fractal dimensions is first proposed. The agglomerate size distribution is found to be sensitive to the fractal dimension and the initial geometric mean deviation before the self-preserving size distribution is achieved in the continuum regime.

Experimental study on the flow field characteristics in the mixing region of twin jets

Twin jets flow, generated by two identical parallel axisymmetric nozzles, has been experimentally investigated. The dimensionless spacing (B) between two nozzles were set at 1.89, 1.75 and 1.5. Measurements have been carried out at several free-stream velocities ranging from 10 m/s to 25 m/s or Reynolds numbers (based on the nozzle diameter of 44 mm) ranging from 3.33×104 to 8.33×104. The results show that the twin jets attract each other. With the increasing Reynolds number, the turbulence energy grows, which indicates that the twin jets attract acutely. The jet flow field and the merging process of two jets vary with B. The width of the twin jets flow spreads linearly downstream and grows with B. The merging between two jets occurs at the location closer to the nozzle exit for the cases with smaller spacing between nozzles and higher Reynolds number.

Flow Past Two Rotating Circular Cylinders in a Side-by-side Arrangement

Measurements were performed using Particle Image Velocimetry (PIV) to analyze the modification of flow by the combined effects of the rotation and the Reynolds number on the flow past two rotating circular cylinders in a side-by-side-arrangement at a range of 425 ≤ Re ≤ 1130, 0 ≤ α ≤ 4 (α is the rotational speed) at one gap spacing of T/d = 1.11 (T and d are the distance between the centers of two cylinders and the cylinder diameter, respectively). A new Immersed-Lattice Boltzmann Method (ILBM) scheme was used to study the effect of the gap spacing on the flow. The results show that the vortex shedding is suppressed as rotational speed increases. The flow reaches a steady state when the vortex shedding for both cylinders is completely suppressed at critical rotational speed. As the rotational speed further increases, the separation phenomenon in the boundary layers disappears at the attachment rotational speed. The critical rotational speed and attachment rotational speed become small as Reynolds number increases. The absolute rotational speed of cylinders should be large at same critical rotational speed and attachment rotational speed in the case of large Reynolds number. The gap spacing has an important role in changing the pattern of vortex shedding. It is very different in the mechanism of vortex shedding suppression for the flows around two rotating cylinders and single rotating cylinder.

Numerical Simulation For Nucleated Vehicle Exhaust Particulate Matters Via The Temom/Les Method

The combination of large eddy simulation (LES) and newly proposed Taylor-series expansion method of moments (TEMOM) is performed for simulating particulate matters emitted from vehicle engine tailpipe. The momentum, heat and mass transfer, binary homogeneous nucleation, Brownian coagulation, Brownian and turbulent diffusion, condensation and thermophoresis are simultaneously taken into account. Good agreements between the experimental and simulated results with respect to the pollutant dispersion are obtained. Compared to other published methods, the present TEMOM requires the least computational time with much accuracy for predicting nanoparticle dynamics. The instantaneous results show that large eddies dominate the evolution of particulate dynamics as exhaust develops, while binary homogeneous sulfuric-water nucleation mainly appears at the interface between the exhaust and ambient cool gases. The increasing of fuel sulfur content and relative humidity or the decreasing of environment temperature leads to an increase in particulate product rate, while volume-averaged particle diameter increases with increasing fuel sulfur content and environment temperature. The variation of geometric standard deviation suggests the nucleated particles eventually approach the asymptotic distribution in the dilution atmosphere, and this distribution is independent of the fuel sulfur content. The variance of upstream turbulence intensity significantly affects the evolution of particulate matters inside the plume.

Generalized TEMOM Scheme for Solving the Population Balance Equation

This article proposes a novel generalized Taylor expansion method of moments (TEMOM) scheme for solving the population balance equation. The proposed scheme can completely overcome the shortcoming of the existing TEMOM and substantially improve the accuracy for both integer and fractional moments. In the generalized TEMOM, the optimal number of equations is 2+1, where is an integer greater than zero. The existing TEMOM is a special case of the generalized TEMOM when is 1. The generalized TEMOM was tested for aerosols undergoing Brownian coagulation in the continuum regime, and it was verified to achieve nearly the same accuracy as the quadrature method of moments (QMOM) with a fractional moment sequence, and higher accuracy than the QMOM with an integer moment sequence. Regarding accuracy and efficiency, the generalized TEMOM scheme was verified to be a competitive method for solving the population balance equation. Copyright 2015 American Association for Aerosol Research

Effect of fibers on the flow property of turbulent fiber suspensions in a contraction

In the flow of turbulent fiber suspensions flowing through a contraction with rectangular cross-section, the Reynolds averaged Navier-Stokes equation with the term of additional stress resulting from fibers was solved with the Reynolds stress model to get distributions of the mean velocity, mean pressure, turbulent kinetic energy and turbulent dissipation. It is found that the mean velocities at exit are small around the center and large near the wall for higher concentration. Fibers reduce turbulent intensity and turbulent dissipation at central line, but enhance them over the cross section at exit. Fibers have no effect of restraint on the turbulence in the contraction flow. The additional stress resulting from fibers plays a role in the increase of drag.

Orientation distribution of cylindrical particles suspended in a turbulent pipe flow

A model of turbulent cylindrical particle suspensions is proposed to predict the orientation distribution of particles. The fluctuating equation for the orientation distribution function (ODF) of cylindrical particles is theoretically solved using the method of characteristics. The orientation-correlated terms in the mean equation for the ODF due to the random motion of cylindrical particles are related to the correlations of the mean ODF and the fluid velocity gradient. Thus, the evolution of the mean ODF is described by a modified convection-dispersion equation. The model and modified equation are used to calculate the ODF in a pipe flow numerically. The results compare qualitatively with the experimental data and show that the turbulent dispersion makes cylindrical particles have a broad orientation distribution, while the velocity gradient plays an opposite role. The increase of the particle aspect ratio leads to a less aligned distribution in the vicinity of the axis and a narrower orientation distri...