用12bit格子气自动机模型模拟静止流和Couette流的温度分布

为了理解格子气自动机的热性质,本文用12bit六方格子多重速度模型模拟了静止流和Couette流的流场分布和温度分布。模拟结果与理论结果进行了比较,得出了有益的结论。     

Heat transfer in lattice BGK modeled fluid

The thermal lattice BGK model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics. The quality of the lattice BGK simulation is checked in this paper by calculating temperature profiles in the Couette flow under different Eckert and Mach numbers. A revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect, especially in the flow regime with a higher Mach number.     

微尺度振荡Couette流的格子Boltzmann模拟

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响. 关键词： 格子Boltzmann方法 有效MRT模型 Knudsen层 振荡流     

Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

Generally speaking, rheological properties of materials are specified by their so-called constitutive equations. The simplest constitutive equation for a fluid is a Newtonian one, on which the classical Navier-Stokes theory is based. The mechanical behavior of many fluids is well described by this theory. However, there are many rheologically compli- cated fluids such as polymer solutions, blood and heavy oils which are inadequately de- scribed by a Newtonian constitutive equation that does …     

Atomistic hybrid DSMC/NEMD method for nonequilibrium multiscale simulations

A multiscale hybrid method for coupling the direct simulation Monte Carlo (DSMC) method to the nonequilibrium molecular dynamics (NEMD) method is introduced. The method addresses Knudsen layer type gas flows within a few mean free paths of an interface or about an object with dimensions of the order of a few mean free paths. It employs the NEMD method to resolve nanoscale phenomena closest to the interface along with coupled DSMC simulation of the remainder of the Knudsen layer. The hybrid DSMC/NEMD method is a particle based algorithm without a buffer zone. It incorporates a new, modified generalized soft sphere (MGSS) molecular collision model to improve the poor computational efficiency of the traditional generalized soft sphere GSS model and to achieve DSMC compatibility with Lennard-Jones NEMD molecular interactions. An equilibrium gas, a Fourier thermal flow, and an oscillatory Couette flow, are simulated to validate the method. The method shows good agreement with Maxwell–Boltzmann theory for the equilibrium system, Chapman–Enskog theory for Fourier flow, and pure DSMC simulations for oscillatory Couette flow. Speedup in CPU time of the hybrid solver is benchmarked against a pure NEMD solver baseline for different system sizes and solver domain partitions. Finally, the hybrid method is applied to investigate interaction of argon gas with solid surface molecules in a parametric study of the influence of wetting effects and solid molecular mass on energy transfer and thermal accommodation coefficients. It is determined that wetting effect strength and solid molecular mass have a significant impact on the energy transfer between gas and solid phases and thermal accommodation coefficient.     

高剪切率的Couette流下液氩流体热导率的分子动力学模拟

基于平衡分子动力学(EMD)模拟方法,对Lees-Edwards周期性边界条件作一修正并成功地应用其形成具有高恒定剪切率的Couette流动,最后通过Green-Kubo公式计算得到了剪切流下液氩流体的热导率。计算结果,表明在剪切流下液氩流体的热导率仍然表现为各向同性,同时还发现流动方向的热导率不随流动剪切率的增加而发生变化,并且该值跟静态下液氩的热导率(λ=0.132 Wm~(-1)K~(-1))基本一致。     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

Power spectra of nonlinearly coupled waves

Swinney et al. (1977) have found that turbulence in rotational Couette flow results from a small number of instabilities. They have raised the question of whether these instabilities conform with the ideas of Ruelle and Takens (1971). We show that a simple model of the Couette flow yields power spectra similar to those seen in the experiments. The model is consistent with the Ruelle and Takens picture.     

Couette流能量的演变

利用Green函数法解析求得Couette流流函数的精确解,通过定义Couette能量、相对能量和能量增长率讨论了初始场结构对Couette流能量演变的影响、能量达到最大值时对应的时间与初始场的关系、最有利于Couette流能量在有限时段快速增长的初始场结构,并对Farrell的研究结果进行了补充和完善.在此基础上,进一步探讨了初值扰动对Couette流能量演变的影响.     

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution α, so that the only free parameter is the (reduced) thermal gradient ϵ. It turns out that the reduced moments of order k are polynomials of degree k−2 in ϵ, with coefficients that are nonlinear functions of α. In particular, the rheological properties (k = 2) are independent of ϵ and coincide exactly with those of the simple shear flow. The heat flux (k = 3) is linear in the thermal gradient (generalized Fourier’s law), but with an effective thermal conductivity differing from the Navier–Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.     

Continuum modeling of micro-particle electrorotation in Couette and Poiseuille flows—The zero spin viscosity limit

A continuum mechanical model is presented to analyze the negative electrorheological responses of a particle-liquid mixture with the suspended micro-particles undergoing Quincke rotation for both Couette and Poiseuille flow geometries by combining particle electromechanics and continuum anti-symmetric/couple stress analyses in the zero spin viscosity limit. We propose a phenomenological polarization relaxation model to incorporate both the micro-particle rotation speed and macro-continuum spin velocity effects on the fluid polarization during non-equilibrium motion. Theoretical predictions of the Couette effective viscosity and Poiseuille flow rate obtained from the present continuum treatment are in good agreement with the experimental measurements reported in current literature.     

Nonlinear Couette Flow in a Low Density Granular Gas

A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution function are determined explicitly. The results apply for conditions such that viscous heating dominates collisional cooling, including large gradients far from the reference homogeneous cooling state. Explicit expressions for the generalized transport coefficients (e.g., viscosity and thermal conductivity) are obtained as nonlinear functions of the coefficient of normal restitution and the shear rate. These exact results for the model kinetic equation are also shown to be good approximations to the corresponding state for the Boltzmann equation via comparison with direct Monte Carlo simulation for the latter.     

表征体元尺度渗流的离散统一动理学格式

结合表征体元尺度的通用渗流模型,提出离散统一动理学格式（DUGKS）渗流方法,分别用均匀网格和非均匀网格计算二维Poiseuille、Couette、方腔流等经典渗流问题,检验DUGKS渗流方法的有效性和非均匀网格应用的优势,将DUGKS渗流方法应用到裂缝系统中.     

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field as well as uniform suction and injection applied perpendicular to the parallel plates. A numerical solution for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature-dependent viscosity and thermal conductivity on both velocity and temperature distributions is examined.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Light scattering from a nonequilibrium fluid undergoing a planar Poiseuille-Couette flow

We calculate the Rayleigh-Brillouin spectrum of a Newtonian fluid undergoing a planar Poiseuille-Couette flow using the fluctuating hydrodynamic approach of Landau and Lifshitz. Our results reduce to the corresponding results for pure Couette flow when the pressure gradient is made to vanish. The Brillouin spectrum is obtainable from that appropriate to Couette flow by a simple rescaling. There are very minute corrections which impart asymmetry to the Brillouin lines as well as the Rayleigh line, and these can be selectively picked up by suitable choice of the scattering geometry.     

Subcritical finite-amplitude solutions for plane Couette flow of viscoelastic fluids

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. The results suggest a scenario for weakly turbulent viscoelastic flow which is similar to the one for Newtonian fluids as a function of Reynolds number.     

The influence of viscous heating and wall thermal conditions on the thermal ignition of a poiseuille/couette reactive flow

This paper investigates the stationary thermal stability of an exothermic reactive viscous non-Newtonian fluid between two parallel walls in the plane Poiseuille and generalized Couette flow configurations for two different thermal conditions. Assuming the system is adiabatic with negligible reactant consumption, the closed-form solution obtained from the momentum equation was inserted into the energy equation due to the dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using a variational technique. The influence of the viscous heating parameter (Γ), wall dynamical (Λ) and the thermal conditions of the walls on the thermal ignition parameters were examined.     

Experimental investigation of thermal processes in the multi-ring Couette system with counter rotation of cylinders

The effect of parameters of the multi-ring Couette system with counter rotating coaxial cylinders on the process of thermal energy release in a viscous liquid filling this system is considered with regard to the problem of determining the possibility of creating the high-performance wind heat generator. The multi-cylinder rotor design allows directly conversion of the mechanical power of a device consisting of two “rotor” wind turbines with a common axis normal to the air flow into the thermal energy in a wide range of rotational speed of the cylinders. Experimental results on the measurement of thermal power released in the pilot heat generator at different relative angular speeds of cylinder rotation are presented.