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Volume Averaging (volume + averaging)

Distribution by Scientific Domains
Engineering50%

Selected Abstracts

Real-scale miscible grout injection experiment and performance of advection,dispersion,filtration model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2001
F. Bouchelaghem
Abstract A model was developed, to describe miscible grout propagation in a saturated deformable porous medium, based on Bear's statistical model with spatial volume averaging. In a previous paper, the model was first successfully confronted to one-dimensional laboratory experiments. In the present paper, the numerical model is used to simulate practical grouting operation in a cylindrical injection model. The cylindrical injection model lends itself to study main flow and propagation character istics for a dispersed suspension-type grout, under axisymmetric conditions close to real scale conditions. Comparison between numerical solutions and experimental results is essential to confirm the validity and accuracy of the proposed model from a phenomenological standpoint. The numerical model performances show that the underlying mathematical model constitutes a realistic predictive model reproducing most prominent features during injection of a suspension-type grout into a deformable porous medium. The basic mechanism by which injected miscible grout permeates a soil mass is discussed in detail. Such a tool leads to quality control criteria for grouting on a theoretical basis, which complements existing criteria acquired through engineering practice. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A two-scale domain decomposition method for computing the flow through a porous layer limited by a perforated plate

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003
J. Dufręche
Abstract A two-scale domain decomposition method is developed in order to study situations where the macroscopic description of a given transport process in porous media does not represent a sufficiently good approximation near singularities (holes, wells, etc.). The method is based on a decomposition domain technique with overlapping. The governing equations at the scale of the microstructure are solved in the vicinity of the singularities whereas the volume averaged transport equations are solved at some distance of the singularities. The transfer of information from one domain to the other is performed using results of the method of volume averaging. The method is illustrated through the computation of the overall permeability of a porous layer limited by a perforated plate. As shown in the example treated, the method allows one to estimate the useful size of the microscopic region near the singularities. As illustrated in the paper, the method can lead to a considerable gain in memory requirement compared to a full direct simulation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A turbulence dissipation model for particle laden flow

AICHE JOURNAL, Issue 6 2009
John D. Schwarzkopf
Abstract A dissipation transport equation for the carrier phase turbulence in particle-laden flow is derived from fundamental principles. The equation is obtained by volume averaging, which inherently includes the effects of the particle surfaces. Three additional terms appear that reveal the effect of the particles; these terms are evaluated using Stokes drag law. Two of the terms reduce to zero and only one term remains which is identified as the production of dissipation due to the particles. The dissipation equation is then applied to cases where particles generate homogeneous turbulence, and experimental data are used to evaluate the empirical coefficients. The ratio of the coefficient of the production of dissipation (due to the presence of particles) to the coefficient of the dissipation of dissipation is found to correlate well with the relative Reynolds number. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

Role of nutrient supply on cell growth in bioreactor design for tissue engineering of hematopoietic cells

BIOTECHNOLOGY & BIOENGINEERING, Issue 7 2005
Pragyansri Pathi
Abstract In the present study, a dynamic mathematical model for the growth of granulocyte progenitor cells in the hematopoietic process is developed based on the principles of diffusion and chemical reaction. This model simulates granulocyte progenitor cell growth and oxygen consumption in a three-dimensional (3-D) perfusion bioreactor. Material balances on cells are coupled to the nutrient balances in 3-D matrices to determine the effects of transport limitations on cell growth. The method of volume averaging is used to formulate the material balances for the cells and the nutrients in the porous matrix containing the cells. All model parameters are obtained from the literature. The maximum cell volume fraction reached when oxygen is depleted in the cell layer at 15 days and is nearly 0.63, corresponding to a cell density of 2.25 × 108 cells/mL. The substrate inhibition kinetics for cell growth lead to complex effects with respect to the roles of oxygen concentration and supply by convection and diffusion on cell growth. Variation in the height of the liquid layer above the cell matrix where nutrient supply is introduced affected the relative and absolute amounts of oxygen supply by hydrodynamic flow and by diffusion across a gas permeable FEP membrane. Mass transfer restrictions of the FEP membrane are considerable, and the supply of oxygen by convection is essential to achieve higher levels of cell growth. A maximum growth rate occurs at a specific flow rate. For flow rates higher than this optimal, the high oxygen concentration led to growth inhibition and for lower flow rates growth limitations occur due to insufficient oxygen supply. Because of the nonlinear effects of the autocatalytic substrate inhibition growth kinetics coupled to the convective transport, the rate of growth at this optimal flow rate is higher than that in a corresponding well-mixed reactor where oxygen concentration is set at the maximum indicated by the inhibitory kinetics. ©2005 Wiley Periodicals, Inc. [source]