Numerical computation of macroscopic turbulence quantities in representative elementary volumes of the porous medium
01 Nov 2010-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 53, Iss: 23, pp 5190-5198
TL;DR: In this paper, the macroscopic turbulence quantities for porous media were computed and analyzed for different Reynolds numbers as well as for different porosity levels, and the results showed that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities.
Abstract: In this study, fully developed macroscopic turbulence quantities—based on their definitions in some existing turbulence models for porous media as well as those based on definitions introduced in a recently developed model [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009)]—are computed and analyzed for different Reynolds numbers as well as for different porosity levels. When computed based on the definition introduced in the new model, these numerically computed, pore-level turbulent quantities provide closure to the formulation. A large set of microscopic turbulent flow simulations of the REV of a porous medium, formed by staggered square cylinders, is carried out to achieve these tasks. For each Reynolds number selected, ten different porosities are simulated in the 5–95% range. The Reynolds number is varied from Re = 103 to Re = 105, covering four different cases of the turbulence flow regime. Numerical results obtained for the macroscopic turbulent kinetic energy based on the new definition show that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities. Additionally, it is found that for high porosities, the spatial average of the turbulent kinetic energy is the main contributor but the spatial dispersion of the mean flow cannot be neglected. The new definition of the macroscopic dissipation rate is found to asymptotically approach the volume average of this quantity at high Reynolds numbers. It is confirmed that microscopic numerical simulations are consistent with the macroscopic law that states that the macroscopic dissipation rate is determined by the pressure-drop through the REV.
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01 Jan 2013
TL;DR: In this paper, a porous medium is defined as a material consisting of a solid matrix with an interconnected void, and the interconnectedness of the void allows the flow of one or more fluids through the material.
Abstract: By a porous medium we mean a material consisting of a solid matrix with an interconnected void. We suppose that the solid matrix is either rigid (the usual situation) or it undergoes small deformation. The interconnectedness of the void (the pores) allows the flow of one or more fluids through the material. In the simplest situation (“single-phase flow”) the void is saturated by a single fluid. In “two-phase flow” a liquid and a gas share the void space.
46 citations
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published in 2010 and 2011 has been conducted as mentioned in this paper, which can be used as a starting point for future work.
Abstract: Here a comprehensive survey of the literature in the area of numerical heat transfer (NHT) published in 2010 and 2011 has been conducted. Due to the immenseness of the literature volume, journals s...
30 citations
TL;DR: In this paper, the interfacial heat transfer coefficient (h sf ) is analyzed by comparing results found in literature with those reported in this paper, and it is concluded that single REV simulations are, in general, not sufficient to compute the parameter.
Abstract: Numerical experiments in multiple representative elementary volumes (REVs) were conducted to validate calculations of macroscopic parameters for porous media models carried out employing a unit periodic cell (single REV). The simulation of a microscopic flow that develops through a porous medium formed by staggered square cylinders is presented to that purpose. A laminar steady flow regime is considered together with Peclet numbers in the 1–10 3 range and porosities between 55 and 95%. In particular, the interfacial heat transfer coefficient ( h sf ) is analyzed by comparing results found in literature with those reported here. First, the outlet boundary condition that is generally employed in single REV simulations for the case of constant wall temperature was tested by comparing the values it imposes in the flow with those obtained far away from the outlet (unperturbed). It was found that this outlet boundary condition is adequate and moreover, that the flow rapidly develops to satisfy it (one or two REVs in simulated cases). Additionally, two definitions found in the literature to calculate the h sf were compared, and it was shown that both calculations differ in approximately 20% for the 55% porosity case and still present significant differences (>5%) for greater porosities. The h sf coefficient was also calculated as a function of the REV’s positions in the porous structure to show that it is position dependent or, in other words, it shows pore scale fluctuations. Therefore, it is concluded that single REV simulations are, in general, not sufficient to compute the parameter. A double average that filters pore scale fluctuations was employed and differences between this quantity and those obtained in a single REV were quantified. The results show these differences are small ( Pe > 100 but differences can be up to 15% for Pe = 10 or larger, for lower Pe numbers. Finally, a method that allows capturing the pore scale fluctuation of the parameter by employing single REV values was proposed. This method can be employed to calculate the double average of the h sf coefficient for other boundary conditions, or to calculate other macroscopic parameters, such as the thermal dispersion coefficients.
23 citations
TL;DR: In this article, various turbulence models are compared to determine which models are most accurate in simulating two-phase fluid flow and heat transfer in steam surface condensers, based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for noncondensable gases.
Abstract: In this paper, various turbulence models are compared to determine which models are most accurate in simulating two-phase fluid flow and heat transfer in steam surface condensers. The numerical method is based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for non-condensable gases. Modified standard k–e and RNG k–e models are proposed to account for the effects of tube bundles and two-phase interactions on the gas-phase turbulence. A quasi-three-dimensional approach is used to account for the effect of the temperature difference in the coolant flowing in the tubes. Finally, the numerical results are compared with the experimental data to assess the performance of the proposed turbulence models.
19 citations
TL;DR: In this article, the volume and time-averaged (macroscopic) turbulence, and non-equilibrium turbulent heat and mass transfer equations for randomly packed spheres, based on computational results of flow and heat transfer for a unique geometric model, were derived from pore-level information obtained from numerical simulations of turbulent heat.
Abstract: Turbulent heat and mass transfer in packed beds of spheres is widely encountered in industrial and food storage applications and, as such, modeling of such cases is of interest in design and development. Herein, we propose a closure of the volume- and time-averaged (macroscopic) turbulence, and non-equilibrium turbulent heat and mass transfer equations for randomly packed spheres, based on computational results of flow and heat transfer for a unique geometric model. In this respect, the closure results are derived from pore-level (microscopic) information obtained from numerical simulations of turbulent heat and fluid flow. Turbulence is incorporated at both levels using the k–ɛ model, and the dispersive effects of turbulence are also considered. For the momentum equation, the closure is sought for the Darcy and Forchheimer terms. For the non-equilibrium heat and mass transport equations, we obtain closures for the dispersion, turbulent flux, turbulent dispersion, and interfacial heat and mass transfer terms. The closure results are found to be dependent upon the porosity and Reynolds number. However, the mean sphere diameter and its local variation inside the representative elemental volumes only weakly affect the results. The closure results are presented as power law-based correlations, such that they can be easily implemented in a volume-time-averaged framework.
18 citations
References
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Book•
01 Jan 1980
TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.
Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.
21,858 citations
TL;DR: In this paper, a convective modeling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencings.
Abstract: A convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing. For combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream-pluscentral differencing - however, highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy, with obvious practical advantaged in terms of both speed and storage. The algorithm is based on a conservative control-volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node. This results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream-weighted schemes. The consistent treatment of diffusion terms is equivalent to central differencing. With careful modelling, numerical boundary conditions are not troublesome. Some idealized problems are studied, showing the practical advantages of the method over other schemes in comparison with exact solutions. An application to a complex unsteady two-dimensional flow is briefly discussed.
4,190 citations
TL;DR: In this paper, numerical simulations of fully developed turbulent channel flow at three Reynolds numbers up to Reτ=590 were reported, and it was noted that the higher Reynolds number simulations exhibit fewer low Reynolds number effects than previous simulations at Reτ = 180.
Abstract: Numerical simulations of fully developed turbulent channel flow at three Reynolds numbers up to Reτ=590 are reported. It is noted that the higher Reynolds number simulations exhibit fewer low Reynolds number effects than previous simulations at Reτ=180. A comprehensive set of statistics gathered from the simulations is available on the web at http://www.tam.uiuc.edu/Faculty/Moser/channel.
2,618 citations
Book•
01 Oct 1991
TL;DR: In this article, the authors identify the principles of transport in porous media and compare the available predicted results, based on theoretical treatments of various transport mechanisms, with the existing experimental results, and the theoretical treatment is based on the volume-averaging of the momentum and energy equations with the closure conditions necessary for obtaining solutions.
Abstract: Although the empirical treatment of fluid flow and heat transfer in porous media is over a century old, only in the last three decades has the transport in these heterogeneous systems been addressed in detail. So far, single-phase flows in porous media have been treated or at least formulated satisfactorily, while the subject of two-phase flow and the related heat-transfer in porous media is still in its infancy. This book identifies the principles of transport in porous media and compares the available predicted results, based on theoretical treatments of various transport mechanisms, with the existing experimental results. The theoretical treatment is based on the volume-averaging of the momentum and energy equations with the closure conditions necessary for obtaining solutions. While emphasizing a basic understanding of heat transfer in porous media, this book does not ignore the need for predictive tools; whenever a rigorous theoretical treatment of a phenomena is not available, semi-empirical and empirical treatments are given.
2,551 citations
01 Jan 1979
2,299 citations