关于动量守恒律和动量矩守恒律 --理论力学札记之二

介绍质点系对任意动轴的动量守恒律和动量矩守恒律，并举例说明对完整和非完整系统的应用．     

Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases

This paper presents results of a large eddy simulation (LES) combined with Lagrangian particle tracking and a point-force approximation for the feedback effect of particles on the downward turbulent gaseous flow in a vertical channel. The LES predictions are compared with the results obtained by direct numerical simulation (DNS) of a finer computational mesh. A parametric study is conducted for particles with two response times in simulations with and without streamwise gravitational settling and elastic, binary interparticle collisions. It is shown that the classical and the dynamic Smagorinsky turbulence models adequately predict the particle-induced changes in the mean streamwise velocity and the Reynolds stresses of the carrier phase for the range of parameters studied. However, the largest discrepancies between the LES and DNS results are found in the cases of particle-laden flows. Conditional sampling of the instantaneous resolved flow fields indicates that the mechanisms by which particles directly oppose the production of momentum and vorticity of the organized fluid motions are also observed in the LES results. However, the geometric features of the near-wall quasistreamwise vortices are overestimated by the use of both turbulence models compared to the DNS predictions.     

On the momentum of Eulerian phonons

For a one-dimensional dispersive medium the linear momentum of a phonon is discussed in both the Lagrangian and the Eulerian picture, i.e. with the use of substantial (material) and local coordinates, respectively. As phonons are usually considered as solutions of the linearized equations of motion, in the Eulerian picture the linear momentum of a phonon is only defined up to linear terms in the fields. To obtain results relevant towards higher order in the fields, one has to solve the nonlinear equations of motion. This is done to obtain expressions for the linear momentum up to terms quadratic in the fields.     

A numerical study of heat and momentum transfer for tube bundles in crossflow

A numerical scheme is developed to predict the heat transfer and pressure drop coefficients in flow through rigid tube bundles. The scheme uses the Galerkin finite element technique. The conservation equations for laminar steady-state flow are cast in the form of streamfunction and vorticity equations. A Picard iteration method is used for the solution of the resulting system of non-linear algebraic equations. Results for the heat transfer and pressure drop coefficients are obtained for tube arrays of pitch ratios of 1·5 and 2·0. Very good agreement of the present results and experimental data obtained in the past is observed up to Reynolds numbers of 1000. It is also observed that the results of the present method show better agreement with the experimental data and that they are applicable for higher Reynolds numbers than results of other studies.     

Smoothed‐profile method for momentum and heat transfer in particulate flows

The smoothed‐profile method for the motion of solid bodies suspended in a fluid phase is investigated when combined with a high‐order spatial discretization. The performance of the combined method is tested for a wide range of flow and geometry parameters as well as for static and for moving particles. Moreover, a sensitivity analysis is conducted with respect to the smoothed‐profile function. The algorithm is extended to include thermal effects in Boussinesq approximation. Several benchmark problems are considered to demonstrate the potential of the technique. The implementation of the energy equation is verified by dedicated tests. All simulations are compared with either theoretical, numerical, or experimental data. The results demonstrate the accuracy and efficiency of the smoothed‐profile method for non‐isothermal problems in combination with a discontinuous finite‐element solver for the fluid flow, which allows for a flexible handling of the grid and the order of spectral approximation in each element. Copyright © 2016 John Wiley & Sons, Ltd.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Characteristics of turbulence transport for momentum and heat in particle-laden turbulent vertical channel flows

The dynamic and thermal performance of particle-laden turbulent flow is investigated via direction numerical simulation combined with the Lagrangian point-particle tracking under the condition of two-way coupling, with a focus on the contributions of particle feedback effect to momentum and heat transfer of turbulence. We take into account the effects of particles on flow drag and Nusselt number and explore the possibility of drag reduction in con-junction with heat transfer enhancement in particle-laden turbulent flows.The effects of particles on momentum and heat transfer are analyzed,and the possibility of drag reduc-tion in conjunction with heat transfer enhancement for the prototypical case of particle-laden turbulent channel flows is addressed.We present results of turbulence modification and heat transfer in turbulent particle-laden channel flow,which shows the heat transfer reduction when large inertial parti-cles with low specific heat capacity are added to the flow. However,we also found an enhancement of the heat transfer and a small reduction of the flow drag when particles with high specific heat capacity are involved.The present results show that particles,which are active agents,interact not only with the velocity field,but also the temperature field and can cause a dissimilarity in momentum and heat transport.This demonstrates that the possibility to increase heat transfer and suppress friction drag can be achieved with addition of par-ticles with different thermal properties.     

Modeling the turbulent heat and momentum transfer in flows under different thermal conditions

Two-equation turbulence models for velocity and temperature (scalar) fields are developed to calculate wall shear flows under various flow conditions and related turbulent heat transfer under various wall thermal conditions. In the present models, we make the modified dissipation rates of both turbulent energy and temperature variance zero at a wall, though the wall limiting behavior of velocity and temperature fluctuations is reproduced exactly. Thus, the models assure computational expediency and convergence. Also, the present k- model is construted using a new type of expression for the Reynolds stress proposed by Abe et al. [Trans. JSME B 61 (1995) 1714–1721], whose essential feature lies in introducing the explicit algebraic stress model concept into the nonlinear k- formulation, and the present two-equation heat transfer model is constructed to properly take into account the effects of wall thermal conditions on the eddy diffusivity for heat. The models are tested with five typical velocity fields and four typical thermal fields. Agreement with experiment and direct simulation data is quite satisfactory.     

Large eddy simulation and self-similarity analysis of the momentum spreading in the near field region of turbulent submerged round jets

Self-Similarity in turbulent round jets has been the object of investigation from several decades. The evolution of turbulent submerged jets is characterized by the presence of two regions: the region of flow establishment, or near field region (NFR) and the fully developed region (FDR), or far-field region (FFR). The momentum spreading in the FDR is known to be self-similar and few mathematical models have been presented in the past to describe it. The flow evolution in the NFR has been rarely studied since there is a certain consensus on the idea that the flow in the NFR is not self-similar. In this work, we study the flow evolution of a turbulent submerged round jet by means of large eddy simulation (LES) at several Reynolds numbers ranging from 2492 to 19,988. Three new self-similar laws are proposed to describe the flow evolution in the NFR, one for the initial region, called Undisturbed Region of Flow, (URF), and two for the final region, the potential core region (PCR). The numerical results presented in this work are also validated with the self-similar laws for the FDR proposed by Tollmien (1926) and Görtler (1942), and the experimental data of Hussein et al. (1994), and Panchapakesan and Lumley (1993), in the FDR; those of Davies et al. (1963), in the PCR; and van Hout et al. (2018), in the URF. The conclusion is that previous inability to find the self-similarity law in the NFR is due to the attempt to find a unique self-similar variable to describe the momentum spreading in both the URF and the PCR.     

On the momentum equations in dispersed two-phase systems

For so-called dispersed two-phase flow systems the equations of motion are derived for each phase separately. The equations are developed using a minimum of mathematics by applying mass and momentum balances respectively over a small cubic volume element. Special attention is paid to those particles which are cut by the boundaries of this control volume element. In fact these particles are treated by means of two methods, both methods giving the same final result.     

Approximate solutions of heat and momentum transfer in laminar plane wall jet

In the present paper approximate solutions for the fluid and thermal boundary layers in an incompressible laminar plane wall jet with isothermal and adiabatic walls have been studied respectively, and comparisons with the known exact solutions have been made wherever possible. It is found that the present method is simple and straightforward, and gives results being in good agreement with the exact solutions. For moderate values of the Prandtl number the method may be used for calculating the heat transfer from an isothermal wall and temperature recovery factor for an adiabatic wall respectively.Nomenclature a* dimensionless temperature gradient at the wall - c _p specific heat at constant pressure - K momentum flux through a cross-section of the jet - Q volume flux through a cross-section of the jet - r* temperature recovery factor - T temperature of the fluid in the boundary layer - T _r adiabatic wall temperature - T temperature of the fluid at rest - u, v velocity components along and normal to the plane wall respectively - x, y rectangular coordinates along and normal to the plane wall respectively - z Greek symbols fluid boundary layer thickness - _t, _T thermal boundary layer thickness for an isothermal and an adiabatic wall respectively - dimensionless y-coordinate - dimensionless temperature difference (T–T )/T - coefficient of thermal conductivity - coefficient of viscosity - coefficient of kinematic viscosity - Prandtl number - _w shearing stress on the plane wall     

On configurational compatibility and multiscale energy momentum tensors

In this work the continuum theory of defects has been revised through the development of kinematic defect potentials. These defect potentials and their corresponding variational principles provide a basis for constructing a new class of conservation laws associated with the compatibility conditions of continua. These conservation laws represent configurational compatibility conditions which are independent of the constitutive behavior of the continuum. They lead to the development of a new concept termed configurational compatibility, dual to the concept of configurational force. The contour integral of the corresponding conserved quantity is path-independent, if the domain encompassed by the integral is defect-free. It is shown that the Peach-Koehler force can be recovered as one of these invariant integrals. Based on the proposed defect potentials and their corresponding defect energies, two-field multiscale mixed variational principles can be employed to construct multiscale energy momentum tensors. An application is outlined in the form of a mode III elasto-plastic crack problem for which the new configurational quantities are calculated.     

关于对动点的动量矩定理------理论力学札记之八

介绍质点系对动点的动量矩定理并讨论它的一些应用.     

Investigation of transitional and turbulent heat and momentum transport in a rotating cavity

The paper gives the results of the DNS/LES which was performed to investigate the transitional and turbulent non-isothermal flows within a rotor/stator cavity. Computations were performed for the cavity of aspect ratio L = 2–35, Rm = 1.8 and for rotational Reynolds numbers up to 290000. The main purpose of the investigations was to analyze the influence of aspect ratio and Reynolds number on the flow structure and heat transfer. The numerical solution is based on a pseudo-spectral Chebyshev–Fourier–Galerkin collocation approximation. The time scheme is semi-implicit second-order accurate, which combines an implicit treatment of the diffusive terms and an explicit Adams–Bashforth extrapolation for the non-linear convective terms. In the paper we analyze distributions of the Reynolds stress tensor components, the turbulent heat flux tensor components, Nusselt number distributions and the turbulent Prandtl number and other structural parameters, which can be useful for modeling purposes. Selected results are compared with the experimental data obtained for single heated rotating disk by Elkins and Eaton (2000).     

可压缩多介质粘性流体和湍流的大涡模拟

在可压缩多介质粘性流体动力学高精度计算方法MVPPM(multi-viscous-fluid piecewise parabolicmethod)基础上,引入Smagorinsky和Vreman亚格子湍流模型,采用大涡数值模拟方法求解可压缩粘性流体NS(Navier-Stokes)方程,给出适用于可压缩多介质流体界面不稳定性发展演化至湍流阶段的计算方法和二维计算程序MVFT(multi-viscosity-fluid and turbulence)。在2种亚格子湍流模型下计算了LANL(Los Ala-mos National Laboratory)激波管单气柱RM不稳定性实验,分析了气柱的形状、流场速度以及涡的特征,通过与LANL实验和计算结果的比较可知,Vreman模型略优于Smagorinsky模型,MVFT方法和计算程序可用于对界面不稳定性发展演化至湍流阶段的数值模拟。     

On the eddy viscosity model of periodic turbulent shear flows

Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation, it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity, do not take this effect into account. The project supported by the National Natural Science Foundation of China (19732005) and Liu Hui Center for Applied Mathematics of Nankai & Tianjin University     

关于广义动量守恒的物理意义－－理论力学札记之四

讨论Lagrange方程广义动量守恒的物理意义, 它可以是动量守恒, 可以是动量矩守恒,也可以既不是动量也不是动量矩守恒.     

Rotational and translational diffusivities of germanium nanowires

Understanding the rheological behavior of dilute dispersions of cylindrical nanomaterials in fluids is the first step towards the development of rheological models for these materials. Individual particle tracking was used to quantify the rotational and translational diffusivities of high-aspect-ratio germanium nanowires in alcohol solvents at room temperature. In spite of their long lengths and high aspect ratios, the rods were found to undergo Brownian motion. This work represents the first time that the effects of solvent viscosity and confinement have been directly measured and the results compared to proposed theoretical models. Using viscosity as a single adjustable parameter in the Kirkwood model for Brownian rods was found to be a facile and versatile way of predicting the diffusivities of nanowires across a broad range of length scales.