Eulerian and Lagrangian approaches for predicting the behaviour of discrete particles in turbulent flows

A review of the work carried out during the last two decades by a group in Rouen, on Eulerian and Lagrangian approaches for predicting the behaviour of discrete particles in turbulent flows, is presented. The opportunity of this review is taken to direct the reader to a much larger literature and to point out unsolved problems.     

A diffusion-inertia model for predicting dispersion and deposition of low-inertia particles in turbulent flows

The objective of the paper is twofold: (i) to present a model (the so-called diffusion-inertia model) for predicting dispersion and deposition of aerosol particles in two-phase turbulent flows and (ii) to examine the performance of this model as applied to the flows in straight ducts and circular bends. The model predictions compare reasonable well with both experimental data and Lagrangian tracking simulations coupled with fluid DNS or LES.     

Eulerian approach for multiphase flow simulation in a glass melter

A glass furnace, consisting of a combustion space and a glass melter, uses combustion heat to melt sand and cullet into liquid glass to make products. Glass quality is mainly dependent on the temperature, glass composition, and the level of impurities in a glass melter, which include solid batch/cullet particles, liquid glass, and gas bubbles. A comprehensive computational model using an Eulerian approach has been developed to simulate multiphase flows in a glass melter. It includes all the phases, divides solid particles or gas bubbles into various size groups, and treats each group as a continuum. The derived mass, momentum, and energy conservation equations of the flow are solved for local properties for each phase. The simulation considers the heating and melting of the batch (mainly from the radiative heat from combustion and from the convective heat from the molten glass), the formation and transport of bubbles, and the heating and mixing of the liquid glass. The approach was incorporated into a multiphase reacting flow computational fluid dynamics code that simulates overall glass furnace flows to evaluate the glass quality and furnace efficiency.     

Combined effect of magnetic field and thermal dispersion on a non-darcy mixed convection

This paper is devoted to investigate the influences of thermal dispersion and magnetic field on a hot semi-infinite vertical porous plate embedded in a saturated Darcy-Forchheimer-Brinkman porous medium. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The effects of transverse magnetic field parameter (Hartmann number Ha), Reynolds number Re (different velocities), Prandtl number Pr (different types of fluids) and dispersion parameter on the wall shear stress and the heat transfer rate are discussed.     

LES of a turbulent premixed swirl burner using the Eulerian stochastic field method

A turbulent premixed swirl burner is simulated using the sgs-pdf evolution equation approach in conjunction with the Eulerian stochastic field solution method in the context of Large Eddy Simulation. Simple gradient diffusion models are adopted for the sub-grid stresses and eight stochastic fields were utilised to characterise the influence of the sub-grid fluctuations. The chemistry was represented by an augmented reduced mechanism derived from GRI 3.0 with 15 reaction steps and 19 species. Statistical means and instantaneous quantities show overall good agreement with the experimental data and demonstrate the capability of the pdf method in LES to simulate premixed combustion in complex flame configurations.     

A combined approach for determining the thermal performance of radiant barriers under field conditions

This paper deals with a combined approach for assessing the thermal performance of radiant barriers under field conditions, based both on dynamic simulations and field measurements. The methodology involves the combination of model predictions and experimental results of a complex roof including a radiant barrier installed on a dedicated test cell. During the empirical validation of the building thermal model and more particularly thanks to the results of sensitivity analysis, simplifications of the model were made. These considerations lead to successive simplified versions of the model and finally a very simplified one, which is used to determine the thermal resistance of the complex roof. We first present the detailed thermal model, elaborated with a prototype of building simulation code. We then describe the experimental test cell and put the emphasis on the details of the roof. The simplification of the detailed model is then explained and the results presented. A value of the thermal resistance is finally obtained and confirms the potential of radiant barriers for a tropical climate.     

Formulation for predicting deposition velocity of particles in turbulence

Relationships for the particle concentration and convection velocity profile has been obtained by the adaptation of the random surface renewal model [1], [2], [3], [4], [5] to the particle continuity and momentum equations of the nonisothermal turbulence boundary-layer flows; particle transport mechanisms of Brownian and turbulent diffusion, eddy impaction, particle inertia, and thermophoresis are included. This proposed model provides a useful framework for coupling these modeling parameters with analytical equation of the particle deposition velocity. The predictions obtained on the basis of this equation have been found to be in good agreement with experimental values of deposition velocity for fully-developed turbulent pipe flow.     

Design of a small thermochemical receiver for solar thermal power

Capture of solar thermal energy by means of chemical conversion provides an attractive means for collection of solar energy. A converter has been designed for operation at the focus of a 7 m diameter paraboloid. The converter is constructed from a multi-passage ceramic extrusion, which is wound into a spiral form prior to firing. The innermost wrap is designed to operate with a cavity-facing surface heated to 1000°C. In the passages adjacent to this surface SO₃ is catalytically dissociated into SO₂ and O₂. The eight outer wraps are used for heat exchange between an inflowing SO₃ rich gas stream and an outflowing SO₂ rich gas stream.     

Equilibrium thermal characteristics of a building integrated photovoltaic tiled roof

Photovoltaic (PV) modules attain high temperatures when exposed to a combination of high radiation levels and elevated ambient temperatures. The temperature rise can be particularly problematic for fully building integrated PV (BIPV) roof tile systems if back ventilation is restricted. PV laminates could suffer yield degradation and accelerated aging in these conditions. This paper presents a laboratory based experimental investigation undertaken to determine the potential for high temperature operation in such a BIPV installation. This is achieved by ascertaining the dependence of the PV roof tile temperature on incident radiation and ambient temperature. A theory based correction was developed to account for the unrealistic sky temperature of the solar simulator used in the experiments. The particular PV roof tiles used are warranted up to an operational temperature of 85 °C, anything above this temperature will void the warranty because of potential damage to the integrity of the encapsulation. As a guide for installers, a map of southern Europe has been generated indicating locations where excessive module temperatures might be expected and thus where installation is inadvisable.     

On the modeling of turbulent evaporating sprays: Eulerian versus lagrangian approach

Recently developed mathematical models for turbulent evaporating sprays are described. The relative merits of Eulerian and Lagrangian approaches in handling the dispersed phase are discussed. These two approaches are evaluated vs reported data for evaporating dilute sprays (in the region z/D 50), produced by an air-atomizing injector in a still environment. Results show that both approaches are successful in predicting the main features of this type of flow; however, the Eulerian approach performs better. The ignorance of the turbulence effects on the droplet motion is found to lead to significant errors when the mean relative velocity becomes comparable to the carrier phase r.m.s. velocity fluctuation. The one-size Eulerian treatment yields very comparable results to that of the multi-size treatment when the droplet size range is not very wide. Finally, the cost analysis for the two approaches demonstrates that the use of the Monte Carlo technique in simulating droplet dispersion is even more expensive than the multisize Eulerian treatment.     

Artificial neural network models for predicting soil thermal resistivity

Thermal properties of soils are of great importance in view of the modern trends of utilizing the subsurface for transmission of either heated fluids or high power currents. For these situations, it is essential to estimate the resistance offered by the soil mass in dissipating the heat generated through it. Several investigators have tried to develop mathematical and theoretical models to estimate soil thermal resistivity. However, it is evident that these models are not efficient enough to predict accurate thermal resistivity of soils. This is mainly due to the fact that thermal resistivity of soils is a complex phenomenon that depends upon various parameters viz., type of the soil, particle size distribution and its compaction characteristics (i.e., dry density and moisture content). To overcome this, Artificial Neural Network (ANN) models, which are based on experimentally obtained thermal resistivity values for clay, silt, silty-sand, fine- and coarse-sands, have been developed. Incidentally, these soils are the most commonly encountered soils in nature and exhibit entirely different characteristics. The thermal resistivity of these soils, corresponding to their different compaction states, was obtained with the help of a laboratory thermal probe and compared vis-à-vis those obtained from the ANN model. The thermal resistivity of these soils obtained from ANN models and experimental investigations are found to match extremely well. The performance indices such as coefficient of determination, root mean square error, mean absolute error, and variance account for were used to control the performance of the prediction capacity of the models developed in this study. In addition to this, thermal resistivity of these soils obtained from ANN models were compared with those computed from the empirical relationships reported in the literature and were found to be superior. The study demonstrates the utility and efficiency of the ANN model for estimating thermal resistivity of soils.     

A fractal model for thermal conductivity in a disperse system of even particles

In this paper the geometrical structure of disperse system is described by fractal theory, which is based on the easily measurable parameters, such as the occupation probability, the diameters of disperse pellets, etc. A fractal model of thermal conductivity of a disperse system with even particles has been developed with the aid of the analogy between the heat conduction and percolation. The measurement of the thermal conductivity in the disperse system was carried out by the cutout hot wire method. The model's prediction as to the ratio of thermal conductivity for different particle sizes is reasonably in agreement with the experimental results. © 2000 Scripta Technica, Heat Trans Asian Res, 29(7): 535–544, 2000     

A new approach for predicting vertical global solar irradiance

Solar irradiance, particularly on vertical surfaces, plays a major role in determining the thermal and energy performance of a building. It is important to the design and analysis of both active solar systems and passive solar buildings. Many mathematical models are mainly developed to predict the sky-diffuse irradiance on inclined surfaces from the measured horizontal diffuse component. This paper presents an approach to estimate the vertical global irradiance based on direct beam and ground-reflected components which can be accurately determined. Hourly data recorded from January 1996 to December 1998 in Hong Kong were used for the model development. The performance of the proposed model and two well-known anisotropic inclined surface models (Muneer and Perez) was evaluated against data measured in 1999. Statistical analysis indicated that the proposed model gives reasonably good agreement with measured data for all vertical planes. Although the new model has been found less effective than the Perez model, its simplicity nature provides buildings designers a convenient and reliable alternative in the estimation of vertical solar irradiance.     

The dynamics of aerosol particles in a gradient acoustic field

An approach is suggested to obtain approximate analytical solutions for the problems of aerosol particle dynamics in an oscillating medium carrier. In the case considered, the oscillations of the medium are due to the action of the acoustic field on the two-phase system. The principal role of the oscillating amplitude gradient in the drift of particles toward a decreasing oscillating amplitude is revealed. The algorythm suggested can be applied to the analysis of similar models describing the transient dynamics of heterogeneous systems with low concentration and particularly to the study of particle transfer in turbulent flow.     

Estimation of the thermal dispersion in a porous medium of complex structures using a lattice Boltzmann method

The thermal dispersion in a porous medium of complex structure is investigated by using the lattice Boltzmann method. The media under consideration include two-dimensional arrays of uniformly distributed circular and square cylinders, and uniformly distributed spherical and cubical inclusions. Upon validating the procedure, calculations have been performed for flows of various Prandtl and Reynolds number combinations. The porosity and the fluid–solid diffusivity ratio have been varied to investigate their effects on the dispersivity. For both 2D and 3D cases, the dispersivity is found to increase with the Peclet number raised to the same constant exponent regardless of the medium structures. The in-line arrangement yields higher dispersivity than the staggered arrangement, however, the dispersivity is independent of the inclusion shape except for the 3D staggered cases. New correlations for dispersivity for 2D and 3D cases are then proposed in terms of Peclet number, porosity, and the fluid–solid diffusivity ratio.     

Analytical study of the thermal behaviour and stability of a small satellite

In this work the thermal analysis of a small satellite orbiting around the Earth has been approached by direct integration of the heat balance equations of a two-node reduced model, obtaining a linearized second order ODE problem, similar in form to the classical case of the forced vibration of a damped system. As the thermal loads (solar radiation, albedo, etc.) are harmonic, the problem is solved by means of Fourier analysis methods. Research on that field can be directly applied to the analysis of thermal problems and the results obtained are satisfactory. Working on the frequency domain streamlines the analysis, simplifies the study and facilitates the experimental testing. The transfer functions are obtained for the two-node case but the study can be extended to an n-node model.     

A thermal dispersion model for single phase flow in porous media

A new model for thermal dispersion is proposed based on the character of flow in porous media which relates the dispersion with the velocity and the tortuosity of fluid flow in the pores. Compared with former similar models, this one has fewer adjustable empirical constants, and therefore it is expected to be used more conveniently. The prediction by the present model can successfully reproduce the temperature distributions in the nearby wall region when a single phase fluid flows through a packed channel. The results of Nu versus Re agree well with the experimental results. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(6): 545–552, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10107