forchheimer equation
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Author(s):  
Francisco Fernando Hernandez ◽  
Federico Mendez ◽  
Jose Joaquin Lizardi ◽  
Ian Guillermo Monsivais

Abstract This work presents the numerical solution for different velocity profiles and friction factors on a rectangular porous microchannel fully saturated by the flow of a nanofluid introducing different viscosity models, including one nanofluid density model. The Darcy-Brinkman-Forchheimer equation was used to solve the momentum equation in the porous medium. The results show that the relative density of the fluid, the nanoparticle diameters and their volumetric concentration have a direct influence on the velocity profiles only when the inertial effects caused by the presence of the porous matrix are important. Finally, it was found that only viscosity models that depend on temperature and nanoparticle diameter reduce the friction factor by seventy percent compared to a base fluid without nanoparticles; furthermore, these models show a velocity reduction of even ten percent along the symmetry axis of the microchannel.


2021 ◽  
Author(s):  
Zhongxia Li ◽  
Junwei Wan ◽  
Tao Xiong ◽  
Hongbin Zhan ◽  
Linqing He ◽  
...  

Abstract. This study provides experimental evidence of Forchheimer flow and transition between different flow regimes from the perspective of pore size of permeable stone. We have firstly carried out the seepage experiments of permeable stones with four different mesh sizes, including 24 mesh size, 46 mesh size, 60 mesh size, and 80 mesh size, which corresponding to mean particle sizes (50 % by weight) of 0.71 mm, 0.36 mm, 0.25 mm, and 0.18 mm. The seepage experiments show that obvious deviation from Darcian flow regime is visible. In addition, the critical specific discharge corresponding to the transition of flow regimes (from pre-Darcian to post-Darcian) increases with the increase of particle sizes. When the “pseudo” hydraulic conductivity (K) (which is computed by the ratio of specific discharge and the hydraulic gradient) increases with the increase of specific discharge (q), the flow regime is denoted as the pre-Darcian flow. After the specific discharge increases to a certain value, the “pseudo” hydraulic conductivity begins to decrease, and this regime is called the post-Darcian flow. In addition, we use the mercury injection experiment to measure the pore size distribution of four permeable stones with different particle sizes, and the mercury injection curve is divided into three stages. The beginning and end segments of the mercury injection curve are very gentle with relatively small slopes, while the intermediate mercury injection curve is steep, indicating that the pore size in permeable stones is relatively uniform. The porosity decreases as the mean particle sizes increases, and the mean pore size can faithfully reflect the influence of particle diameter, sorting degree and arrangement mode of porous medium on seepage parameters. This study shows that the size of pores is an essential factor for determining the flow regimes. In addition, the Forchheimer coefficients are also discussed in which the coefficient A (which is related to the linear term of the Forchheimer equation) is linearly related to 1/d 2 as A = 0.0025 (1/d 2) + 0.003; while the coefficient B (which is related to the quadratic term of the Forchheimer equation) is a quadratic function of 1/d as B =1.14E-06 (1/d)2 − 1.26E-06 (1/d). The porosity (n) can be used to reveal the effect of sorting degree and arrangement on seepage coefficient. The larger porosity leads to smaller coefficients A and B under the condition of the same particle size.


Author(s):  
Xinguang Yang ◽  
Yong Yang ◽  
Wenjing Liu ◽  
Junzhao Zhang

This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the averaged state, the well-posedness of 3D functional Brinkman-Forchheimer flow model and its steady state equation have been obtained rstly, then the asymptotic stability of global solutions also derived via the convergence of trajectories for the corresponding systems.


Author(s):  
Eric V. Mueller ◽  
Michael R. Gallagher ◽  
Nicholas Skowronski ◽  
Rory M. Hadden

AbstractModeling flow in vegetative fuel beds is a key component in any detailed physics-based tool for simulating wildland fire dynamics. Current approaches for drag modeling, particularly those employed in multiphase computational fluid dynamics (CFD) models, tend to take a relatively simple form and have been applied to a wide range of fuel structures. The suitability of these approaches has not been rigorously tested for conditions which may be encountered in a wildland fire context. Here, we focus on beds of Pinus rigida needle litter and undertake a two-part study to quantify the drag and evaluate the capabilities of a multiphase large eddy simulation CFD model, the NIST Fire Dynamics Simulator. In the first part, bed drag was measured in a wind tunnel under a range of conditions. The results were fit to a Forchheimer model, and the bed permeability was quantified. A traditional approach employed in the multiphase formulation was compared to the parameterized Forchheimer equation and was found to over-predict the drag by a factor of 1.2–2.5. In the second part, the development of a velocity profile above and within a discrete fuel layer was measured. Using the Forchheimer equation obtained in the first part of the study, the CFD model was able to replicate a qualitatively consistent velocity profile development. Within the fuel bed, the model appeared to under-predict the velocity magnitudes, which may be the result of unresolved pore-scale flow dynamics.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wenjing Liu ◽  
Rong Yang ◽  
Xin-Guang Yang

Author(s):  
Hoden A. Farah ◽  
Frank K. Lu ◽  
Jim L. Griffin

Abstract A detail numerical study of detonation propagation and interaction with a flame arrestor product was conducted. The simulation domain was based on the detonation flame arrestor validation test setup. The flame arrestor element was modeled as a porous zone using the Forchheimer equation. The coefficients of the Forchheimer equation were determined using experimental data. The Forchheimer equation was incorporated into the governing equations for axisymmetric reactive turbulent flow as a momentum sink. A 21-step elementary reaction mechanism with 10 species was used to model the stoichiometric oxyhydrogen detonation. Different cases of detonation propagation including inviscid, viscous adiabatic, and viscous with heat transfer and a porous zone were studied. A detail discussion of the detonation propagation and effect of the arrestor geometry, the heat transfer and the porous zone are presented. The inviscid numerical model solutions of the detonation propagation parameters are compared to one-dimensional analytical solution for verification. The viscous solutions are qualitatively compared to historical experimental data which shows very similar trend. The effect of the porous media parameters on shock transmission and re-initiation of detonation is presented.


Author(s):  
Hoden A. Farah ◽  
Frank K. Lu ◽  
Jim L. Griffin

Abstract A numerical study of the flow characteristics of a crimped flame arrestor element was conducted using a porous media model. The porous zone was modeled using the Forchheimer equation. The Forchheimer equation was incorporated into the governing conservation equations as a momentum sink. A small-scale crimped flame arrestor element was tested to determine the empirical coefficients in the Forchheimer equation. The numerical simulation result using this porous media model was verified using experimental data. The flow characteristics of a four-inch detonation flame arrestor with the same crimp design as the small-scale sample, was simulated using the porous media model. The numerical simulation flow data were compared against experimental values and agreed to within five percent. The method used to determine the Forchheimer coefficients and the experimental test setup are described in detail. The application of the Forchheimer equation into the governing flow equations is presented. The challenges and limitation of numerical studies in flame arrestors applications are discussed. The simplification gained by using the porous media model in flame arrestor numerical studies is presented.


Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2712
Author(s):  
Sung-Hoon Ji ◽  
Byeong-Hak Park ◽  
Kyung-Woo Park

In this study, we discussed distortion of the estimated hydraulic conductivity from a hydraulic test due to excessive injection or extraction of groundwater by evaluating the influence of nonlinear flow. Pulse, slug, and constant head withdrawal tests with various head displacements were conducted in fractured granite rock, and the changes of representative Reynolds numbers (Re) during the tests were calculated. The Forchheimer equation and cubic law were used to evaluate the influence of nonlinear flow on the hydraulic tests, and thus the possibility of distortion of the estimated hydraulic conductivity. Our results showed that there was little possibility that nonlinear flow occurred during the pulse tests in the test zones. In the slug tests at several test zones, however, the estimated hydraulic conductivities were likely to be distorted due to nonlinear flow. Except for the test zones with low permeability, the scale effects of the estimated hydraulic conductivities from different types of tests were observed. These results indicated that the scale effect and distortion of the hydraulic parameters can be evaluated by conducting various types of hydraulic tests.


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