Silvio L. M. Junqueira

Numerical Investigation of Natural Convection in Heterogeneous Rectangular Enclosures

The aim of this study is to investigate numerically the steady natural convection resulting from horizontally heating a rectangular enclosure filled with a fluid and containing uniformly distributed, conducting, fixed and disconnected solid blocks (i.e., not touching each other). In particular, the effects of solid volume fraction, solid–fluid thermal conductivity ratio, and total number of blocks on the heat transfer process are determined by solving the mass, momentum, and energy conservation equations using the finite-volume method. The enclosure aspect ratio is varied from 0.25 to 4, the Rayleigh number from 105 to 108, and the Prandtl number is set as unity. Results of the numerical simulations are presented in terms of the surface-averaged Nusselt number, streamfunction, and streamline and isotherm distributions. The interference phenomenon caused by the solid blocks on the natural convection process is considered in detail and used to explain and predict the surprising and complex behavior of surface-averaged Nusselt number.

A Simplified Model with a Hybrid Analytical-Numerical Solution for Predicting the Unsteady Conjugate Heat Transfer Process in Pipelines

This work presents a new, simplified and yet efficient model for studying the transient conjugate heat transfer process in pipelines. The simplified model consists of assuming the thermal transport by fluid flow in bulk form and the pipe–wall heat conduction as two-dimensional. The scale analysis of the dimensionless equations resulting from the simplified model allows for the identification of two predicting parameters useful in determining when axial diffusion in the pipe wall is important, ψ = Pe Γ/ξ < 1 and λ = 4 Nu E 2/ξ < 1, and when radial diffusion is important, ψ > 1 and λ > 1. When these criteria are satisfied, in which case the existing analytical solution becomes invalid, the simplified model proposed here becomes an efficient alternative to the full-scale numerical simulations required for solving the problem. The scale analysis predictions and the hybrid analytical-numerical solutions of the simplified model, involving the Laplace transform and the finite-volume method, are validated first by comparison against the existing analytical solution, and then by comparison against experimental results of turbulent flow, showing excellent agreement in both cases.

Measurement of Mass Flow Rate by Employing Thermometry

Sudden changes of flow temperature along a tube are common in industrial applications. One may suggest those changes can be related to the flow rate. The current work presents a feasibility analysis to evaluate the mass flow rate by measuring changes of temperature at two positions along a tube wall separated by a known distance. The ratio of the distance and the time to change the temperature at the two points may be related to the average flow speed. This is a convectionconduction heat transfer phenomenon at the flow and tube wall. This conjugated heat transfer is modeled by the energy conservation equation that is solved numerically. The study identifies the ranges of parameters, such as, Reynolds and Biot numbers, wall thickness, etc., on which the technique can be applied. The model results are compared to an analytical solution and preliminary experimental results.

SIMULAÇÃO NUMÉRICA DE ESCOAMENTO PARTICULADO APLICADO AO PREENCHIMENTO DE CANAL FRATURADO

RESUMO No presente trabalho, uma analise numerica do preenchimento de um canal vertical com fratura transversal e apresentada. A abordagem escolhida para o preenchimento consiste em adicionar material particulado ao escoamento para promover a deposicao de particula no interior da fratura, reduzindo a fuga de fluido nessa regiao. A analise e realizada atraves de uma abordagem euleriana para o fluido e lagrangiana para as particulas. Para efetuar o acoplamento entre as fases e realizar o calculo das colisoes entre as particulas os modelos DDPM (Dense Discrete Phase Model) e DEM (Discrete Element Method) sao combinados. O resultado do processo de preenchimento, estudado atraves da variacao da quantidade de particulas injetadas no canal, e analisado atraves das caracteristicas geometricas do leito de particulas formado no interior da fratura, da vazao de fluido sendo perdido pela fratura e atraves do monitoramento da pressao na entrada do canal devido ao processo de injecao. Os resultados mostram que a influencia da quantidade de particulas injetadas exerce maior influencia sobre o tempo necessario para realizar o preenchimento. Assim, a concentracao reduz o tempo de preenchimento, porem implica no aumento da pressao na regiao de entrada do canal.

Numerical Investigation of the Onset of Steady Natural Convection in a Square Cavity Partially Filled With a Single Porous Block

The critical Rayleigh number at the onset of natural convection within a square cavity filled with a centralized porous block was investigated. The porous medium is modeled by using the heterogeneous model and the governing equations are solved for each phase separately. The thermal gradient is applied from the bottom to the top horizontal walls while the vertical walls are kept adiabatic. The amount of solid within the cavity was kept constant by fixing both external and internal porosity in 36% and 40%, respectively. The equations are solved using the Finite Volume Method and the interpolation scheme for the convective terms is the Hybrid Scheme. For the pressure-velocity coupling, the SIMPLEC method is used. The effects on the conductive-convective regime transition, reads critical Rayleigh Number, characterized by the average Nusselt number and the heatlines contour plot, was investigated by varying the Rayleigh number and the porous block permeability. The results show that the so called critical Rayleigh number is affected by the block permeability. As the permeability decreases, the flow tends to recirculate around the block being squeezed against the cavity walls and therefore, more susceptible to viscous effects. A correlation to the critical Rayleigh number is presented as a function of the agglomerate permeability showing that the higher the permeability the lower the amount of energy required to trigger the convection.Copyright

Periodic Horizontal Heating of Enclosed Disconnected Solid Bodies Saturated With a Fluid

In the present study, the ensuing natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under time-periodic heating in the horizontal direction is investigated numerically. This configuration is akin to several practical engineering applications, such as in the food (baking) industry, metal parts (heat treating) industry, and containerization (storage and transportation) of discrete solid goods. Because of the relative large size of the solid bodies placed inside the enclosure, a porous medium approach is not appropriate in the present case. Hence, the solid and fluid constituents within the enclosure are viewed individually and modeled using continuum balance equations, with suitable compatibility conditions imposed at their interfaces. The periodic heating is simulated by imposing a sinusoidal time-function on the hot wall temperature, while maintaining the cold wall temperature constant. Results are presented in terms of surface-averaged (hot and cold) Nusselt numbers, time-varying energy capacity (equal to the thermal energy stored inside the enclosure), isotherms and streamlines, for Ra varying from 103 to 107, Pr = 1 and 36 uniformly distributed, conducting and disconnected solid square blocks. The results, focusing on the time-periodic regime, indicate the effect of varying Ra on the convection process. As Ra increases, the dynamic capacitor performance of the enclosure tends to be enhanced.© 2014 ASME

Preliminary Numerical Study of Natural Convection in a Heterogeneous Horizontal Layer Heated From Below

In the present preliminary study the natural convection in a horizontal fluid layer heated isothermally from below and cooled from above, and having disconnected and conducting square solid blocks uniformly distributed in a square array within it, is numerically investigated. Nondimensional steady balance equations are presented, for a Newtonian fluid, with fluid and solid properties being considered constant and uniform. Among the nondimensional parameters ruling the phenomenon, the layer Rayleigh number is set as 105 and 106, the aspect ratio of the layer varies from 1 to 8, and the fluid Prandtl number and the solid-to-fluid thermal conductivity ratio are set as unity. The focus is on the effect of increasing the number of blocks in the layer, the blocks having progressively smaller size as to maintain the solid volume-fraction inside the layer constant and equal to 26% — this is equivalent to dispersing a fixed amount of solid material in smaller and large number of solid blocks within the layer. In general, the increase in the layer aspect ratio, with all other parameters kept constant, affects the results more as Ra increases — as expected because large Ra yields stronger convection effects. The increase in the number of blocks per unit of square cell in the layer affects the flow as to hinder convection; i.e., the finer the dispersion of solid material within the layer is (as the number of blocks increases) the weaker the resulting flow.Copyright

Numerical Simulations of Natural Convection With Radiation in an Open Cavity Containing a Conducting and Centered Solid Body

Although of relevance to a variety of engineering applications, the study of natural convection within an open cavity containing a conducting solid body is rarely found in the literature. Moreover, previous studies have pointed out that radiation heat transfer rates are at least of the same order of the laminar natural convection rates in cavities, making the inclusion of radiation effects and important step toward obtaining more realistic and practical results. The present study considers then a square cavity, with one wall heated and the other opened to an adjacent fluid reservoir, having a square conducting solid block centered in it and accounting for natural convection and radiation effects. Notice, for a large block size, the geometric configuration of the resulting flow channel is similar to that of a fracture along a reservoir wall. The resulting natural convection flow is simulated numerically for performing a nondimensional parametric study seeking to unveil the effects of block dimension, surface emissivity and Rayleigh number into the heat transfer process. The cavity filling fluid is assumed to have constant and uniform properties, as is the solid block, and the fluid-to-solid conductivity ratio is set as unity in the present study. The screening (radiation) effect caused by the presence of the solid block is discussed, as well as the convective and radiative drop phenomena. The convection and radiation Nusselt numbers are evaluated and compared for each simulated case.Copyright

Berkovsky-Polevikov Correlations for Natural Convection in a Nonhomogeneous Enclosure Filled With a Fluid and Disconnected-Conducting Solid Particles

This study investigates the suitability of the known Berkovsky-Polevikov correlations, used for predicting the wall-averaged Nusselt number, Nuav, of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection, to predict the heat transfer coefficient inside a nonhomogeneous enclosure heated from the side, filled with uniformly distributed, disconnected and conducting solid objects also saturated with a fluid undergoing natural convection. Hence, defining γ = RaHPr/(0.2+Pr), a correlation in the form of Nuav = AγB is investigated for curve fitting numerical simulation results. The numerical results are obtained by simulating the heat transfer process of the two distinct constituents, namely the fluid and the solid, within the enclosure using the finite-volume method with appropriate conservation equations and compatibility conditions at their interfaces. The right wall of the enclosure is maintained at temperature lower than that of the left wall, with the horizontal top and bottom surfaces of the enclosure assumed to be adiabatic. Results for 1, 4, 9, 16, and 36, evenly distributed square solid blocks are presented. Appropriate numerical values for coefficients A and B are determined and presented for the utilization of the corresponding Berkovsky-Polevikov correlations. Good correlation is obtained when the Rayleigh number is high (≥107), as to yield distinct boundary layers inside the enclosure.Copyright

The Effects of Solid Thermal Conductivity and Volume-Fraction in the Natural Convection Inside a Heterogeneous Enclosure

In this study, the natural convection inside a fluid filled enclosure containing several solid obstructions and heated from the side is simulated numerically as to determine the effects of the solid thermal conductivity and volume-fraction. The solid obstructions are conducting, disconnected square blocks, uniformly distributed inside the enclosure. The mathematical model follows a continuum approach, with balance equations of mass, momentum and energy presented for each one of the constituents (i.e., fluid and solid) inside the enclosure. The equations are then solved numerically via the finite-volume method. The effects of varying the solid-fluid thermal conductivity ratio (K), the fluid volume-fraction or porosity (φ), the number of solid blocks (N) and the heating strength (represented by the Rayleigh number, Ra) on the natural convection process inside the enclosure are investigated parametrically. The Nusselt number based on the surface-averaged heat transfer coefficient along the heated wall is chosen to characterize the convection strength inside the enclosure. The results indicate a competing effect caused by the proximity of the solid blocks to the heated and cooled walls of the enclosures, vis-a-vis hindering the boundary layer growth, hence reducing the heat transfer effectiveness, and at the same time enhancing the heat transfer when K is large. An analytical estimate of the minimum number of blocks beyond which the convection hindrance becomes predominant is presented and validated by the numerical results.Copyright