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Nanoparticle nucleation and coagulation in a mixing layer

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Acta Mechanica Sinica 2010年第4期26卷 521-529页

作者： jian-zhong lin Yan-Hua Liu China Jiliang University 310018 Hangzhou China Department of Mechanics Zhejiang University310027 Hangzhou China

Numerical simulation of nanoparticle nucleation and coagulation in a mixing layer with sulfuric acid vapor binary system is performed using the large eddy simulation and the direct quadrature method of moment. The distributions of number concentration, volume concentration, and average diameter of nanoparticles are obtained. The results show that the coherent structures have an important effect on the distributions of number concentration, volume concentration and average diameter of nanoparticles via continuously transporting and diffusing the nanoparticles to the area of low particle concentration. In the streamwise direction, the number concentration of nanoparticles decreases, while the volume concentration and the average diameter increase. The distributions of number concentration, volume concentration and average diameter of nanoparticles are spatially inhomogeneous. The characteristic time of nucleation is shorter than that of coagulation. The nucleation takes place more easily in the area of low temperature because where the number concentration of nanoparticles is high, while the intensity of coagulation is mainly affected by the number concentration. Both nucleation and coagulation result in the variation of average diameter of nanoparticles.

关键词： Nanoparticles Nucleation - Coagulation Mixing layer Direct quadrature method of moment

Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

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Acta Mechanica Sinica 2012年第5期28卷 1227-1237页

作者： jian-zhong lin Fu-Jun Gan China Jiliang University Department of Mechanics Zhejiang University

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.

关键词： Nanoparticles - Brownian coagulation. Bimodalsize distribution Moment method

Motion and orientation of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第5期9卷 664-671页

作者： Xiao-ke KU jian-zhong lin Department of Mechanics Zhejiang University Hangzhou 310027 China College of Metrology Technology and Engineering China Jiliang University Hangzhou 310018 China

Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The transient impulse model of 3D collisions between particles and between particle and wall is proposed. The numerical results are qualitatively in agreement with and quantitatively comparable to the experiment data. The results show that the increases of both the cylindrical particle to pipe size ratio and the particle aspect ratio decrease the rotation about all axes. All rotations of cubic particles decrease with increasing the particle concentration. The cubic particles, rotating more drastically in the flow with large Reynolds number, rotate faster than the cylindrical particles with the same size. The cylindrical particles align with the flow direction more obviously with decreasing Reynolds numbers. However, the orientations of cubic particles are spread all over the range with no significant difference in magnitude, and the Reynolds numbers have no obvious effect on the orientations of cubic particles.

关键词： Particulate flow Angular velocity Orientation Lattice Boltzmann method

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

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Acta Mechanica Sinica 2008年第3期24卷 243-250页

作者： jian zhong lin Ke Sun Weifeng Zhang China Jiliang University Hangzhou 310018 China Department of Mechanics Zhejiang UniversityHangzhou 310027 China Institute of Marine and Coastal Sciences Rutgers UniversityNew Brunswick N J USA

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.

关键词： Turbulent fiber suspensions Fiber orientation Rheological property Boundary layer Numericalsimulation

The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity

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Applied Mathematics(A Journal of Chinese Universities) 2011年第4期26卷 493-502页

作者： SHI jian-guo WU zhong-lin Department of Mathematics Huanghuai University Zhumadian 463000 China

Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.

关键词： Infinite Prandtl number limitl Rayleigh-Benard convection Boussinesq system asymptotic expansions singular perturbation classical energy methods.

Friction factor and heat transfer of nanofluid in the turbulent flow through a 90°bend

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Journal of Hydrodynamics 2021年第6期33卷 1105-1118页

作者： Pei-jie Zhang jian-zhong lin Xiao-ke Ku Department of Mechanics State Key Laboratory of Fluid Power and Mechatronic SystemZhejiang UniversityHangzhou 310027China

Heat transfer and energy performance of Al_(2)O_(3)/water nanofluid in a 90°bend with circular cross-section are investigated in the range of Reynolds number(Re)from 5000 to 30000,particle volume concentration(Φ)from 0.005%to 4%,Schmidt number(Sc)from 9870 to 296100,Dean number(De)from 6636 to *** momentum and energy equations of nanofluid together with the dynamic equation for nanoparticles are solved numerically with the particle convection,diffusion,coagulation and breakage taken into *** results are validated by comparing with the available experimental or numerical *** effect of Re,Φ,Sc and De on the friction factor and heat transfer of Al_(2)O_(3)/water nanofluidis *** results showed that the particle number decreases along the *** De,Sc leads to a decrease and increase ofΦ,*** mean particle diameter and particle polydispersity increase with increasing Debut with decreasing *** friction factor increases with increasingΦ,Sc De and Pr but with decreasing *** ratio of energy performance evaluation criterion(PEC)for the Al_(2)O_(3)/water nanofluid to the base fluid increases with increasing Re,Φand De,but with decreasing ***,the expression of ratio of energy PEC for the nanofluid to the base fluid as a function of Re,Φ,Sc and De is derived.

关键词： Al_(2)O_(3)/water nanofluid friction factor heat transfer energy performance evaluation turbulent pipe flow 90°bend numerical simulation

Wind induced deformation and vibration of a Platanus acerifolia leaf

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Acta Mechanica Sinica 2012年第3期28卷 583-594页

作者： Chuan-Ping Shao Ye-Jun Chen jian-zhong lin China Jiliang University 310018 HangzhouChina

Deformation and vibration of twig-connected sin- gle leaf in wind is investigated experimentally. Results show that the Reynolds number based on wind speed and length of leaf blade is a key parameter to the aerodynamic prob- lem. In case the front surface facing the wind and with an in- crease of Reynolds number, the leaf experiences static defor- mation, large amplitude and low frequency sway, reconfigu- ration to delta wing shape, flapping of tips, high frequency vibration of whole leaf blade, recovery of delta wing shape, and twig-leaf coupling vibration. Abrupt changes from one state to another occur at critical Reynolds numbers. In case the back surface facing the wind, the large amplitude and low frequency sway does not occur, the recovered delta wing shape is replaced by a conic shape, and the critical Reynolds numbers of vibrations are higher than the ones correspond- ing to the case with the front surface facing the wind. A pair of ram-horn vortex is observed behind the delta wing shaped leaf. A single vortex is found downstream of the conic shaped leaf. A lift is induced by the vortex, and this lift helps leaf to adjust position and posture, stabilize blade distortion and reduce drag and vibration.

关键词： Tree leaf. Wind. Deformation Vibration

Numerical computations of the flow in a finite diverging channel

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2010年第1期11卷 50-60页

作者： Zhao-sheng YU Xue-ming SHAO jian-zhong lin State Key Laboratory of Fluid Power Transmission and Control Department of Mechanics Zhejiang University Hangzhou 31002 7 China

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial condition,intersection angle,length of the wedge edges,and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow,then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow,the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°,a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow,although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability,the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment,providing a possible explanation for the hysteresis phenomenon in the experiment.

关键词： Diverging channel Flow structures Bifurcation Fictitious domain

Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow

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Chinese Physics B 2022年第8期31卷 266-272页

作者： Pei-Feng lin Xiao Hu jian-zhong lin Key Laboratory of Fluid Transmission Technology of Zhejiang Province Zhejiang Sci-Tech UniversityHangzhou 310018China Department of Mechanics State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhou 310027China

The lattice Boltzmann method is used to study the inertial focusing and rotating characteristics of two-dimensional elliptical particles and rectangular particles in channel flow. The results show that both elliptical particles and rectangular particles initially located on one side and two sides of channel centerline migrate first towards the equilibrium ***, the single-line particle train with an increasing spacing and the staggered particle train with stable spacing are formed. The axial spacing of the staggered particle pair increases with aspect ratio and Reynolds number increasing. The staggered elliptical or rectangular particle pairs form perpendicular orientation angles, which will be more obvious at larger aspect ratio and lower Reynolds number. The single-line particle trains with different shapes seldom form the perpendicular orientation angle.

关键词： lattice Boltzmann method particle trains self-organization inertial migration particle shape