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.     

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.     

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.     

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     

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.     

Natural convection momentum and heat transfer in saturated highly porous media — An asymptotic approach —

Starting from a clear flow situation with no porous matrix a regular perturbation analysis is applied to account for the influence of a highly porous matrix. The perturbation parameter is 1 –n,n being the porosity. By means of asymptotic formulae thex-dependence of the problem under consideration as well as most parameters of the problem can be separated. Thus only ordinary differential equations with the Prandtl number as a parameter have to be solved. Skin friction and heat transfer formulae are given asymptotically which compare well with literature data for highly porous media.Ausgehend von der Strömungssituation ohne poröse Matrix wird eine reguläre Störungsrechnung durchgeführt, die den Einfluß einer hoch porösen Matrix erfaßt. Der Störparameter ist 1 –n, wobein die Porosität ist. Mit Hilfe der asymptotischen Formulierung können diex-Abhängigkeit sowie eine Reihe von Parameterabbängigkeiten in dem Problem separiert werden. Auf diese Weise müssen nur gewöhnliche Differentialgleichungen gelöst werden, die als einzigen Lösungsparameter die Prandtl-Zahl besitzen. Die asymptotischen Ergebnisse für Impuls- und Wärmeübergang stimmen gut mit Literaturdaten zu hoch porösen Medien überein.     

The effect of free stream turbulence on the momentum,heat and mass transfer during flow around a sphere

On the basis of our own experimental investigations of the effect of the fluid stream turbulence on the mean heat transfer, a possibility of significant (up to about 60 per cent) intensification of the process was shown. In the second part of this work, the authors attempted to analyze phenomena which result in heat layer. The significant role of three-dimensional disturbances of the Goertler type in the process of formation of “pseudo-laminar” boundary layer, was emphasized.     

Simultaneous solution of 1D momentum and canonical momentum equations

A variational equation containing the weak forms of the momentum and the canonical momentum equation is derived. Based on this, a joint finite element formulation of momentum and canonical momentum equation is established that actually solves them simultaneously. The relation of the proposed formulation with the corresponding Arbitrary Lagrangian Eulerian is examined and some numerical examples from one-dimensional, linear and non-linear elasticity are provided.     

Similarity and decay laws of wakes with zero momentum and angular momentum

In [1–4] the laws of decay of the average and fluctuating velocities in momentumless turbulent wakes were experimentally investigated with and without swirl. In [5, 6] unswirled momentumless wakes and in [7] wakes with a nonzero angular momentum were theoretically investigated. However, turbulent wakes with zero momentum and angular momentum were not covered by these investigations. This class of flows is the subject of the present study.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 35–41, September–October, 1993.