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Unsteady detonation with thermodynamic nonequilibrium effect based on the kinetic theory

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Communications in Theoretical Physics 2023年第7期75卷 132-144页

作者： Xianli Su Chuandong Lin Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen UniversityZhuhai 519082China

In this paper,unsteady detonation is simulated and investigated from the viewpoint of kinetic theory.The deviations of the velocity distribution function from the equilibrium state are studied in the evolution of detonation.It has been discovered that the characteristics of the deviation around the detonation wave are significantly different from those in the post-wave region.Besides,the kinetic moments of the reaction term have been simulated,verified and analyzed in detail.In addition,the reaction manifestation is defined to describe the global effects of kinetic moments due to chemical reactions.It is interesting to find that there are three types of periodic oscillations of the reaction manifestation during the evolution of the unsteady detonation.Via the fast Fourier transform,it can be seen that the reaction manifestation is mainly composed of several signal frequencies.Moreover,the impact of rate constants of the two-step reaction scheme on the reaction manifestation is studied,and the influence of chemical heat is investigated as well.

关键词： unsteady detonation chemical reaction kinetic theory discrete Boltzmann method

A 2-D kinetic theory for Flows of Monodomain Polymer-Rod Nanocomposites

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Communications in Computational Physics 2010年第2期7卷 250-282页

作者： M.Gregory Forest Qingqing Liao Qi Wang Department of Mathematics University of North Carolina at Chapel HillChapel HillNC 27599USA Department of Mathematics University of South CarolinaColumbiaSC 29208USA Department of Mathematics and NanoCenter at USC University of South CarolinaColumbiaSC 29208USA

We merge classical kinetic theories [M. Doi and S. F. Edwards, The theoryof Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rodcomposites (PNCs). A mean-field potential for the polymer-rod interface provides thekey coupling between the two phases. We restrict this first study to two-dimensionalconformational space. We solve the coupled set of Smoluchowski equations for threebenchmark experiments. First we explore how rod semi-flexibility and the polymer-rod interface alter the Onsager equilibrium phase diagram. Then we determine mon-odomain phase behavior of PNCs for imposed simple elongation and shear, respec-tively. These results inform the effects that each phase has on the other as parametricstrengths of the interactions are varied in the context of the most basic rheological ex-periments.

关键词： kinetic theory polymer nanorod nanocomposites monodomains equilibrium elon-gation shear

THE SETTING UP OF THE EQUATIONS FOR TWO-PHASE FLOWS BY THE kinetic theory METHOD

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Acta Mechanica Sinica 1986年第3期2卷 220-231页

作者： Liu Dayou(Institute of Mechanics,Academia Sinica) 中科院力学所，100080

The fundamental equations for two-phase flows are deduced from the Boltzmann’sequation.The collision terms are treated with a method similar to what is used in the classical kinetictheory for handling the transport properties of dense gases.It is shown that collision pressure andcollision thermal flux exist in gas-particle flows in addition to the general partial pressure and partialthermal flux.Their physical natures are quite different from those of the general partial pressure andpartial thermal flux.The applicability of the binary collision assumption and the molecular chaosassumption to gas-particle flows is also discussed.Finally,the equations for two-phase flowsobtained by the method of the kinetic theory are compared with those obtained by averagecontinuum models and by the model of particle clouds.The results from the kinetic theory showclearly the physical significance of various parameters and clarify some confusing concepts.

关键词： two-phase flow kinetic theory collision term in Boltzmann’s equation collision pressure

Tunable Thermal Rectification and Negative Differential Thermal Resistance in Gas-Filled Nanostructure with Mechanically-Controllable Nanopillars

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Journal of Thermal Science 2022年第4期31卷 1084-1093页

作者： LI Fan LI Haiyang WANG Jun XIA Guodong HWANG Gisuk MOE Key Laboratory of Enhanced Heat Transfer and Energy Conservation Beijing Key Laboratory of Heat Transfer and Energy ConversionBeijing University of TechnologyBeijing 100124China Department of Mechanical Engineering Wichita State University Wichita KS 67260USA

In this study,by using the nonequilibrium molecular dynamics and the kinetic theory,we examine the tailored nanoscale thermal transport via a gas-filled nanogap structure with mechanically-controllable nanopillars in one surface only,i.e.,changing nanopillar height.It is found that both the thermal rectification and negative differential thermal resistance(NDTR)effects can be substantially enhanced by controlling the nanopillar height.The maximum thermal rectification ratio can reach 340%and the△T range with NDTR can be significantly enlarged,which can be attributed to the tailored asymmetric thermal resistance via controlled adsorption in height-changing nanopillars,especially at a large temperature difference.These tunable thermal rectification and NDTR mechanisms provide insights for the design of thermal management systems.

关键词： thermal rectification negative differential thermal resistance kinetic theory nanopillars

STABLE BOUNDARY CONDITIONS AND DISCRETIZATION FOR P_(N) EQUATIONS

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Journal of Computational Mathematics 2022年第6期40卷 977-1003页

作者： Jonas Bunger Neeraj Sarna Manuel Torrilhon Applied and Computational Mathematics(ACoM) Department of MathematicsRWTH Aachen UniversitySchinkelstr 252062 AachenGermany

A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over time.In this paper,we present boundary conditions(BCs)for the spherical harmonic(P_(N))approximation,which ensure that this fundamental energy bound is satisfied by the P_(N) approximation.Our BCs are compatible with the characteristic waves of P_(N) equations and determine the incoming waves uniquely.Both,energy bound and compatibility,are shown on abstract formulations of P_(N) equations and BCs to isolate the necessary structures and properties.The BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step,which is similar to the truncation of the series expansion in the P_(N) method.We show that summation by parts(SBP)finite differences on staggered grids in space and the method of simultaneous approximation terms(SAT)allows to maintain the energy bound also on the semi-discrete level.

关键词： Boundary conditions Energy stability Spherical harmonic(P_(N))approximation kinetic theory Moment method Boltzmann Linear transport

Equal-time kinetic equations in a rotational field

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Chinese Physics C 2022年第2期46卷 149-159页

作者：陈诗乐王梓岳庄鹏飞 Physics Department Tsinghua UniversityBeijing 100084China

We investigate quantum kinetic theory for a massive fermion system under a rotational field.From theDirac equation in rotating frame we derive the complete set of kinetic equations for the spin components of the 8-and 7-dimensional Wigner functions.While the particles are no longer on a mass shell in the general case due to therotation-spin coupling,there are always only two independent components,which can be taken as the number andspin densities.With help from the off-shell constraint we obtain the closed transport equations for the two independent components in the classical limit and at the quantum level.The classical rotation-orbital coupling controls thedynamical evolution of the number density,but the quantum rotation-spin coupling explicitly changes the spin density.

关键词： equal-time transport rotation field kinetic theory

A kinetic description of the impact of agent competence and psychological factors on investment decision-making

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Chinese Physics B 2023年第8期32卷 520-530页

作者：胡春华陈弘婧 School of Economics Southwest Minzu UniversityChengdu 610041China School of Statistics Chengdu University of Information TechnologyChengdu 610103China

The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agents set their own investment strategies.The herding behavior is considered when analyzing the impact of an agent's psychological factors on investment decision-making.A nonlinear Boltzmann model containing herding behavior,agent competence and irrational behavior is employed to investigate investment decision-making.To characterize the agent's irrational behavior,we utilize a value function which includes current and ideal-investment decisions to describe the agent's irrational behavior.Employing the asymptotic procedure,we obtain the Fokker-Planck equation from the Boltzmann equation.Numerical results and the stationary solution of the obtained Fokker-Planck equation illustrate how herding behavior,agent competence,psychological factors,and irrational behavior affect investment decision-making,i.e.,herding behavior has both advantages and disadvantages for investment decision-making,and the agent's competence to invest helps the agent to increase income and to reduce loss.

关键词： kinetic theory investment decisions Fokker-Planck equation value function

A THEORETICAL AND NUMERICAL STUDY FOR THE ROD-LIKE MODEL OF A POLYMERIC FLUID

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Journal of Computational Mathematics 2004年第2期22卷 319-330页

作者： HuiZhang Ping-wenZhang LMAMandSchoolofMathematicalSciences PekingUniversityBeijing100871China

The first part of this paper is concerned with the well-posedness for the rigid rod-like model in shear flow of a polymeric fluid. The constitutive relations considered in this work are motivated by the kinetic theory. The stress tensor is given by an integral which involves the solution of the Fokker-Planck equation. A novel numerical scheme for the Fokker-Planck equation is proposed, which preserves the positivity of the distribution function.Another part of this work establishes the convergence theory of the fully discretized schemes for a simple micro-macro simulation of a polymeric flow.

关键词： Polymeric fluid Rod-like model kinetic theory Convergence

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

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Acta Mechanica Sinica 2004年第4期20卷 354-365页

作者：唐学林钱忠东吴玉林 Department of Hydraulic and Hydropower Engineering Tsinghua UniversityBeijing 100084China Department of Thermal Engineering Tsinghua UniversityBeijing 100084China

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

关键词： kinetic theory turbulent two-phase flow dynamic sub-grid-scale model conduit