REITERATED HOMOGENIZATION OF INTEGRAL FUNCTIONALS

2000 ◽  
Vol 10 (01) ◽  
pp. 47-71 ◽  
Author(s):  
ANDREA BRAIDES ◽  
DAG LUKKASSEN
Keyword(s):  
Energy Density ◽  
Quadratic Form ◽  
Phase Structure ◽  
Effective Properties ◽  
Effective Property ◽  
Integral Functionals ◽  
Effective Energy ◽  
Two Phase ◽  
Wide Range ◽  
Reiterated Homogenization

We consider the homogenization of sequences of integral functionals defined on media with several length-scales. Our general results connected to the corresponding homogenized functional are used to analyze new types of structures and to illustrate the wide range of effective properties achievable through reiteration. In particular, we consider a two-phase structure which is optimal when the integrand is a quadratic form and point out examples where the macroscopic behavior of this structure underlines an effective energy density which is lower than that of the best possible multirank laminate. We also present some results connected to a reiterated structure where the effective property is extremely sensitive of the growth of the integrand.

An Effective Property, LHF-Type Model for Spray Combustion

2000 ◽  
Vol 122 (2) ◽  
pp. 275-279 ◽  
Author(s):  
Marouan A. A. Nazha ◽  
Hobina Rajakaruna ◽  
Roy J. Crookes
Keyword(s):  
Gas Phase ◽  
Turbulent Mixing ◽  
Energy Transport ◽  
Effective Properties ◽  
Control Volume ◽  
Effective Property ◽  
Type Model ◽  
Two Phase ◽  
Wide Range ◽  
Property Changes

A mathematical model capable of describing the evaporation, mixing and burning characteristics of a confined reacting two-phase flow is presented. The flow field is described by solving the partial differential equations of continuity, momentum, and energy transport, together with the k-ε equations of turbulence. Evaporation is accounted for via a droplet evaporation sub-model which runs in parallel with the gas-phase solver exchanging data with it. Effective properties are calculated in each control volume and the property changes resulting from the evaporation are allowed to propagate according to the turbulent mixing model. Combustion follows the mixing process and is assumed to proceed to equilibrium. The model is validated against experimental results, and its applicability over a wide range of conditions is investigated. [S0742-4795(00)03002-7]

Mechanisms of Convective Heat Transfer of Nanofluids

2008 ◽  
Author(s):  
Dongsheng Wen
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Single Channel ◽  
Effective Properties ◽  
Effective Property ◽  
The Body ◽  
Two Phase ◽  
Continuous Equation

Research on nanofluids has progressed rapidly since its enhanced thermal conductivity was identified about a decade ago. Much evidence shows that the enhancement of convective heat transfer is much higher than that of thermal conductivity only. The mechanism of such enhancement, however, is still unclear. This work reviews the mechanisms of convective heat transfer of nanofluids in a single channel, and identifies two most likely mechanisms: the modification of effective properties and the migration of nanoparticles under flow conditions. A numerical simulation based on a combined Euler and Lagrange method is investigated in this work to illustrate the feature of nanoparticle migration and the drawback of the effective property approach. The motion of discrete nanoparticles is determined by the Lagrangian trajectory method based on the Newton’s second law that includes influence of the body force, various hydrodynamic forces, and the Brownian and thermophoresis forces. The coupling of discrete particles with continuous flow is realized through the modification of the source term of the continuous equation. It concludes that the two-phase flow nature of nanofluids, especially the nanoparticle migration and the resultant non-uniform particle and effective property profile, needs to be considered to properly model the convective heat transfer.

Bounds and estimates for the properties of nonlinear heterogeneous systems

1992 ◽  
Vol 340 (1659) ◽  
pp. 531-567 ◽  
Keyword(s):  
Variational Principle ◽  
Energy Density ◽  
Optimization Problem ◽  
Effective Properties ◽  
Heterogeneous Systems ◽  
Effective Energy ◽  
Central Idea ◽  
Nonlinear Composite ◽  
Order Bounds ◽  
Nonlinear Composites

A powerful and versatile variational principle, allowing the estimation of the effective properties of nonlinear heterogeneous systems, has been introduced recently by Ponte Castañeda (1992). The central idea is to express the effective energy-density function of a given nonlinear composite in terms of an optimization problem involving the effective energy-density functions of linear comparison composites with similar microstructure. This permits the computation of bounds and estimates for the effective properties of given classes of nonlinear heterogeneous systems directly from well-known bounds and estimates for the effective properties of corresponding classes of linear comparison composites. In this paper, we review the variational principle and apply it to determine bounds and estimates for the effective properties of certain classes of nonlinear composite dielectrics with homogeneous, isotropic phases. Thus, nonlinear bounds of the Hashin-Shtrikman and Beran types are obtained for composites with overall isotropy and prescribed volume fractions (of the phases). While nonlinear (second-order) bounds of the Hashin-Shtrikman type have been obtained previously, in different form, by other methods, the nonlinear (higher-order) Beran bounds are the first of their type. Finally, exact estimates are also obtained for nonlinear composites with ‘sequentially layered’ microstructures. These special composites, which have proved to be extremely useful in assessing the optimality of bounds for linear systems, are also useful, although to a lesser extent, in assessing the sharpness of the nonlinear bounds.

Time Domain Simulation of the Vibration of a Steam Generator Tube Subjected to Fluidelastic Forces Induced by Two-Phase Cross-Flow

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Téguewindé Sawadogo ◽  
Njuki Mureithi
Keyword(s):  
Steam Generator ◽  
Two Phase Flow ◽  
Work Rate ◽  
Fretting Wear ◽  
Phase Flow ◽  
Reference Case ◽  
Two Phase ◽  
Steam Generator Tube ◽  
Wide Range ◽  
Instability Regime

Having previously verified the quasi-steady model under two-phase flow laboratory conditions, the present work investigates the feasibility of practical application of the model to a prototypical steam generator (SG) tube subjected to a nonuniform two-phase flow. The SG tube vibration response and normal work-rate induced by tube-support interaction are computed for a range of flow conditions. Similar computations are performed using the Connors model as a reference case. In the quasi-steady model, the fluid forces are expressed in terms of the quasi-static drag and lift force coefficients and their derivatives. These forces have been measured in two-phase flow over a wide range of void fractions making it possible to model the effect of void fraction variation along the tube span. A full steam generator tube subjected to a nonuniform two-phase flow was considered in the simulations. The nonuniform flow distribution corresponds to that along a prototypical steam-generator tube based on thermal-hydraulic computations. Computation results show significant and important differences between the Connors model and the two-phase flow based quasi-steady model. While both models predict the occurrence of fluidelastic instability, the predicted pre-instability and post instability behavior is very different in the two models. The Connors model underestimates the flow-induced negative damping in the pre-instability regime and vastly overestimates it in the post instability velocity range. As a result the Connors model is found to underestimate the work-rate used in the fretting wear assessment at normal operating velocities, rendering the model potentially nonconservative under these practically important conditions. Above the critical velocity, this model largely overestimates the work-rate. The quasi-steady model on the other hand predicts a more moderately increasing work-rate with the flow velocity. The work-rates predicted by the model are found to be within the range of experimental results, giving further confidence to the predictive ability of the model. Finally, the two-phase flow based quasi-steady model shows that fluidelastic forces may reduce the effective tube damping in the pre-instability regime, leading to higher than expected work-rates at prototypical operating velocities.

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