Structural stability for Forchheimer fluid in a semi-infinite pipe

In this paper, it is assumed that the Forchheimer flow goes through a semi-infinite cylinder. The nonlinear boundary condition is satisfied on the finite end of the cylinder, and the homogeneous boundary condition is satisfied on the side of the cylinder. Using the method of energy estimate, the structural stability of the solution in the semi-infinite cylinder is obtained

Relating porous media structure to the Darcy-Forchheimer model

Flow in porous media is an important aspect of many systems, such as fluid separation, heat exchange, underground fluid transport, filtration, and purification. Computational modeling is used in all of these systems to increase the understanding of the system and enable researchers to make optimal decisions regarding the processes within the system. Current tools for modeling flow in porous media require calibration of each system individually, which reduces the quantity and efficiency of the information that simulations can provide. The most common method for modeling flow in porous media, is the Darcy-Forchheimer model. Although this model is accurate and robust, it relies on two coefficients which can only be determined through physical experiments on each individual porous media. These coefficients can be expressed as a product of the fluid properties and the properties of porous media structure; however the variables representing the structure of the porous media are still unable to be determined without physical experiments. For many years determining the relationship between porous media structure and the Darcy-Forchheimer model has been considered impractical, because the scale of porous media made it difficult if not impossible to measure the geometric properties of the material. Additionally, naturally occurring porous media have random structures; thus even if it were feasible to measure the porous media, it would have been difficult to determine the characteristics that most affect flow. Now researchers can both measure and manufacture porous media for specific purposes; however the models have not been updated to allow researchers to take advantage of this technology. Although researchers have the ability to control the exact structure of porous media, the models still lack the ability to help researchers create optimal designs for their systems. This research focuses on understanding the fundamental dynamics of flow in porous media, to enable complex systems to be modeled and developed more easily. Here computational upscaling is used to develop a revised Darcy-Forchheimer equation which includes a relation to the parameters of the porous media. The revised model was developed by simulating several homogeneous structured porous media. The porous media were studied by simulating a periodic unit cell of each porous media to understand the geometric effects. A primary porous media, made of stacked screens was used for the initial analysis. This porous media could be described in as little as two parameters, allowing multiple analyses to be completed without consideration of previous knowledge regarding how flow should behave in porous media. This analysis supported the long held assumption that the Darcy-Forchheimer equation can be divided into a viscous loss term and an inertial loss term. After this primary analysis several less ideal porous media were modeled and analyzed similar to the primary case. A more general relationship that can be used for a wide variety of homogeneous porous media was developed

Symmetry in the Mathematical Inequalities

This Special Issue brings together original research papers, in all areas of mathematics, that are concerned with inequalities or the role of inequalities. The research results presented in this Special Issue are related to improvements in classical inequalities, highlighting their applications and promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities. This volume will be of interest to mathematicians specializing in inequality theory and beyond. Many of the studies presented here can be very useful in demonstrating new results. It is our great pleasure to publish this book. All contents were peer-reviewed by multiple referees and published as papers in our Special Issue in the journal Symmetry. These studies give new and interesting results in mathematical inequalities enabling readers to obtain the latest developments in the fields of mathematical inequalities. Finally, we would like to thank all the authors who have published their valuable work in this Special Issue. We would also like to thank the editors of the journal Symmetry for their help in making this volume, especially Mrs. Teresa Yu

Large Eddy Simulation of Wall-bounded Turbulent Flows at High Reynolds Numbers

In the simulation of turbulent flows, resolving flow motions near a solid surface requires a high resolution that is computationally expensive. The present research investigates reducing the computational cost of simulating wall-bounded flows through a technique, called wall-modeling, that introduces the effects of the near-wall flow dynamics as a wall shear stress to the outer layer. Turbulent wall bounded flows were studied using large eddy simulation at moderate to high Reynolds numbers to evaluate the performance of the wall-modeling. The results of wall-modeled turbulent channel flow at Re = 2000 were in good agreement with the experimental data. However, a log-layer mismatch was observed in the mean velocity profile below the matching point due to the inconsistency between the local grid resolution and that required by the subgrid scale model. Moving the matching point further from the wall mitigated the mismatch. The effects of time averaging and temporal filtering schemes on the performance of the wall model were also investigated. It was found that smaller time periods for time averaging result in a wall model that is more responsive to the flow structures in the outer layer. The results indicated that the temporal filtering scheme is strongly dependent on the location of the matching point. Next, the wall-modeling was implemented in the simulation of a turbulent boundary layer. Inflow generation methods were reviewed, and a recycling rescaling method was employed to generate realistic turbulence at the inlet boundary. Zero pressure gradient turbulent boundary layers over a wide range of Reynolds numbers up to Re = 25 523 were studied in terms of the mean velocity profile, Reynolds stress, and skin-friction coefficient. It was found that a wall-modeled turbulent boundary layer can be resolved using a much lower grid resolution in the wall layer. Finally, the wall stress model was implemented to introduce the effects of wall roughness into the wall-modeling via the eddy viscosity. The proposed wall model was examined for transitionally and fully rough channel flows and successful results were achieved. For high-Reynolds number wall-bounded flows, wall-modeling can effectively couple a large eddy simulation to the wall via the wall shear stress without the need to fully resolve the inner region

Proceedings of the First International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics

1st International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Kruger Park, 8-10 April 2002.This lecture is a principle-based review of a growing body of fundamental work stimulated by multiple opportunities to optimize geometric form (shape, structure, configuration, rhythm, topology, architecture, geography) in systems for heat and fluid flow. Currents flow against resistances, and by generating entropy (irreversibility) they force the system global performance to levels lower than the theoretical limit. The system design is destined to remain imperfect because of constraints (finite sizes, costs, times). Improvements can be achieved by properly balancing the resistances, i.e., by spreading the imperfections through the system. Optimal spreading means to endow the system with geometric form. The system construction springs out of the constrained maximization of global performance. This 'constructal' design principle is reviewed by highlighting applications from heat transfer engineering. Several examples illustrate the optimized internal structure of convection cooled packages of electronics. The origin of optimal geometric features lies in the global effort to use every volume element to the maximum, i.e., to pack the element not only with the most heat generating components, but also with the most flow, in such a way that every fluid packet is effectively engaged in cooling. In flows that connect a point to a volume or an area, the resulting structure is a tree with high conductivity branches and low-conductivity interstices.tm201

Bibliography of Lewis Research Center technical publications announced in 1992

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1992. All the publications were announced in the 1992 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Bibliography of Lewis Research Center technical publications announced in 1993

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1993. All the publications were announced in the 1993 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses