The Experimental And Numerical Simulation Study Of Seepage Resistance In Porous Media

Darcy's law provides a theoretical basis for the study of seepage and is widely used in various engineering fields,and any seepage deviating from this linear relationship is considered as non-Darcian flow.Although many related studies about Darcian flow and non-Darcian flow have been carried out in porous media.However,the current research has the following problems:Firstly,the Reynolds number and moody chart are usually used to analyze the conduit flow,and it has been widely used in porous media flow by analogy to the theory of conduit flow,the Reynolds number was introduced to distinguish the Darcian flow and non-Darcian flow.However,the critical Reynolds numbers obtained by different scholars with seepage resistance experiments in different types of porous media are different.Therefore,using traditional Reynolds number as the criterion of non-Darcian flow is defective.Secondly,among the numerous experimental investigations on flow regimes,most studies were focused on the impact of mean particle sizes.It was partly because many of those experiments were conducted using relatively uniform and idealized spherical or cylindrical shapes of particles,which is inconsistent with the nature situation of inhomogeneous porous media.Therefore,it is not enough to take the mean particle size as the influencing factor to study the law of fluid mechanics in porous media.Recognizing the importance of particle heterogeneity in understanding the transition of flow regimes,some scholars have carried out the seepage resistance experiments in heterogeneous porous media,which are mainly focusing on the effects of particle size distribution on the Forchheimer equation coefficients.However,they did not investigate the transition between different flow regimes.At last,the inertial force gradually increases with the increases of the specific discharge,which leads to a significant deviation from the linear law.And the particle size and pore structure are two main factors that influence the inertia term and flow regimes.And the streamline deflects when obstructed by particles,which results in additional energy loss.However,a quantitative analysis from an energy?or hydraulic head?loss perspective about the flow regimes has not been done yet.Furthermore,the difference between the laws of energy loss in porous media flow and conduit flow needs to be explained from a more fundamental physical perspective.In view of the above problems in the current research,this paper carried out a series of seepage resistance experiments and numerical simulation,including the seepage resistance experiment with single particle size,the seepage resistance experiment with mixed particle sizes,the numerical simulation of rough conduit with different relative roughnesses and the numerical simulation of homogeneous porous media.We first carried out the seepage resistance experiment of homogeneous porous media?quartz sand with a single particle size?to explore the influence of mean particle size on the seepage law.The experimental results show that the permeability coefficient increases to a peak and then decreases in the first phase rather than a constant with the increase of the specific discharge.In order to distinguish it from the traditional definition of the permeability coefficient,the permeability coefficient is defined as the"pseudo permeability coefficient"in this paper.In addition,the permeability coefficient increases with the increase of the specific discharge,which is defined as pre-Darcian flow.On the contrary,the permeability coefficient decreases with the increase of the specific discharge,which is defined as post-Darcian flow.And the experimental results show that the seepage law deviated from Darcy's law with the increase of specific discharge.The critical Reynolds number for the deviation point increases as the particle size increases.When the mean particle size is small?1.075mm,1.475mm,1.85mm,2.5mm?,the obvious pre-Darcian flow and post-Darcian flow can be observed,with the mean particle size reached 3.17mm,only the post-Darcian flow was observed.Moreover,the transition between different flow regimes is smooth,and no obvious Darcian flow was observed.In order to explore the influence of heterogeneous porous medium on the seepage law,we further carried out the seepage resistance experiments of heterogeneous porous medium.To meet the objectives,we have firstly conducted flow experiments in sand columns with two kinds of particle sizes of quartz sands.After that,we have carried out flow experiments using more heterogeneous porous media consisting of five different sizes of quartz sands.The experimental results of flow in mixtures of two different particle sizes show that the relationship between hydraulic gradient and specific discharge also deviates from Darcy's law.And the critical Reynolds number corresponding to the change of flow regime increases with the increase of the proportion of coarse quartz sand.However,the experimental results of flow in mixtures of five different particle sizes show that only the post-Darcian flow can be observed.Comparing the heterogeneous media?or mixtures of five different particle sizes?experimental results with homogeneous media?or single-particle sizes?we can find that the heterogeneous media leads to greater permeability coefficient,which leads to the flow regime transfers to post-Darcian flow earlier.We defined the ratio of inertial force and viscous force as the new Reynolds number for judging non-Darcian flow through a series of seepage resistance experiments.The new critical Reynolds number value of 0.1 is identified as a quantitative criterion for the start of the non-Darcian flow regime by drawing a logarithmic curve of friction coefficient and new Reynolds number,which have been well verified both in homogeneous porous media and heterogeneous porous media when the Forchheimer equation is valid.In order to quantitatively analyze the law of seepage in porous media and conduit,three different types of numerical simulation are carried out in this paper including rough conduits with different relative roughnesses,rough conduits with maximum roughness and homogeneous porous medium.The numerical simulation results are verified by the experimental results.The numerical simulation results of rough conduits with different relative roughnesses show that different flow regimes have different effects on energy loss.The relationship between specific discharge and energy loss is linear in the laminar flow regime.The linear relationship between fitting coefficient m?the slope of energy loss with respect to specific discharge?and different relative roughnesses is obtained as follows:m=2.63E-06??35?/d?-4.64E-07.The relationship between energy loss and specific discharge becomes quadratic in the fully developed turbulent flow regime,the coefficients in front of the linear?A?and quadratic?B?terms can be predicted as:A=-4.57E-06??35?/d?+8.83E-07,B=2.6E-03??35?/d?2-1.1E-03??35?/d?+1.0E-04.We used the local head loss coefficient???serving as an evaluation indicator to reflect the energy dissipation influenced by relative roughness,and find that the local head loss coefficient???decreases gradually with the increase of specific discharge,finally tends to be stable.A larger relative roughness leads to a larger local head loss coefficient when the specific discharge is the same.When the flow through a rough conduit with the maximum relative roughness of1/2.4?which can be regarded as a simple porous media model as the roughness asperities on opposite sides of the conduit contact each other?,the numerical simulation results show that the curvature and variable cross-section of flow channels would cause frequent changes and acceleration in flow directions because of the rough elements even if the specific discharge is very small?v=0.001m/s?.The relationship between energy loss and specific discharge is obtained as follows:?35?h?28?1.60E-04v²?10?3.97E-06v.In addition,the local head loss coefficient also decreases with the increase of specific discharge and finally tends to be stable.From conduit flow to porous media seepage,we further carried out the numerical simulation of homogeneous porous media in this paper.This simulation is still based on the basic assumption of seepage,and the streamlines pass through the porous medium region horizontally.The results of numerical simulation show that the relationship between specific discharge and energy loss is quadratic in homogeneous porous medium.The relationship between fitting coefficient A1 and B1?the slope of energy loss with respect to specific discharge?and different mean particle sizes are obtained as follows:A1=-5.09E-04(d₅₀)²-2.76E-03(d₅₀)+4.6E-03,B1=0.0238(d₅₀)²-0.1146(d₅₀)+0.1488.In this paper,the influence of mean particle size and particle size distribution of porous media on the seepage law is discussed through a series of seepage resistance experiments,and the energy loss under different flow regimes is quantitatively discussed through numerical simulation.In the future experimental research,we can carry out more experiments with abundant particle size and particle sizes distribution.In terms of numerical simulation,random or irregular roughness elements?instead of the identical roughness elements used in this study?should be utilized to make the problem more relevant to the actual setting.In a word,we can combine the theoretical analysis,laboratory experiments and numerical simulation to enrich and improve the theory of porous media seepage.