Microscopic Numerical Investigation Of Seepage Flow Through Porous Media Consisting Of Obstacles Of Different Sizes

Many available empirical expressions only can be used in seepage flowthrough porous media consisting of the same particles． Some experimentalinvestigations on the porous media consisting of obstacles of different sizes werepresented to the real porous media consisting of obstacles of different sizes for thediversity of porous media in nature， but the complexity in their analyticalexpression makes its practical use difficult．In this study， a series of exhaustivenumerical computations were carried out for a number of geometrical models,describing collections of obstacles of different sizes，exploiting periodic boundaryconditions．Two-dimensional and three-dimensional numerical simulations wereperformed to reveal the characteristics of seepage flow through porous mediaconsisting of obstacles of different sizes．An effective diameter concept has beenproposed to correlate the resulting macroscopic pressure gradients with theempirical formula．The main work and achievements of the dissertation are summedup as following：（1）two-dimensional numerical models consisting of square rods of differentsizes are constructed to represent porous media for the cases of collections ofobstacles of three-，four-and five-different sizes．The Carman-Kozeny type generalformula has been proposed along with a definition of an effective average size incondition of low Reynolds number，which，when substituted into the formula，yields a good approximation to the permeability of multi-sized obstacles．（2）As a sequel to the study in determining the permeability of the porousmedia composed of obstacles of different sizes，exhaustive numerical calculationswere conducted using the same two-dimensional numerical models of square rodsas in the previous study in condition of high Reynolds number．Computations werecarried out to reveal the details of Forchheimer Term and the influence about thepressure drop with different angles． There results are integrated to find themacroscopic pressure gradients for collections of multi-sized obstacles．The Ergun type general formula has been proposed along with a definition of an effectiveaverage size，which, when substituted into the formula, yields a reasonable estimatefor the macroscopic pressure drops in multi-sized obstacles．Hence， a generalformula can be used for porous media consisting of obstacles of different sizes．（3）three-dimensional numerical models of multi-sized structure which ismore close to the reality are proposed to describe porous media consisting ofspheres of different sizes. Numerical calculations are performed to find out themost appropriate definition of the effective diameter．The microscopic numericalresults are processed to determine the permeability for the given porosity．Thesevalues are examined to find out the appropriate definition of the effective diameterto be substituted in the Ergun formula．Then，the results are re-processed toevaluate the inertia effects, namely，the Forchheimer coefficient．Thus，the mostappropriate definition of the effective diameter is sought，such that it，whensubstituted in the Ergun formula，gives the most reasonable estimate on the pressuredrop for the given porosity and diameter distribution．A revised formula was whichis more close to reality are proposed to calculate seepage flow through porousmedia consisting of particles of different sizes．The research results above provide basic theory of design and seepagecalculation of porous material, and also provide technical support for analysis ofmechanics of the microcosmic structure impacting the seepage.