non-Darcian Effects Research Articles

Non-Darcian Effects on Natural Convection in a Porous Square Cavity Heated Periodically On Both Sidewalls

Non-Darcian Effects on Natural Convection in a Porous Square Cavity Heated Periodically On Both Sidewalls

Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer

Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer

A Semianalytical Solution for Transient Confined–Unconfined Flow with Non-Darcian Effect

A Semianalytical Solution for Transient Confined–Unconfined Flow with Non-Darcian Effect

Semi-empirical models for predicting stable water inflow and influence radius of a tunnel considering non-Darcian effect

How to accurately predict water inflow and relevant groundwater influence of a tunnel are classical scientific issues in the field of hydrogeology, which are also of great significance to the construction and operation of underground engineering. This issue is usually investigated based on the assumption of the linear Darcy's law. However, the tunnel inflow is usually featured by high velocities or high pressures, especially in karst regions, which allows the flow regime to easily develop into non-Darcian flow regime. The impact of the non-Darcian effect on predicting water inflow and influence radius of a tunnel has not yet been systematically examined. Here, we numerically investigated the prediction of stable water inflow and influence radius under non-Darcian flow regime. By numerically solving the continuity equation of seepage flow incorporating the nonlinear Forchheimer law, a series of numerical simulations were conducted for stable water inflow into a tunnel by varying key controlling parameters. The quantitative dependencies of stable water inflow on these parameters were figured out, based on which a semi-empirical stable water inflow model was developed considering the non-Darcian effect. Meanwhile, the magnitude of the influence radius was investigated by statistical analysis of 59 actual engineering cases and estimated using existing empirical formulas. Based on these preliminary explorations, a semi-empirical model for estimating influence radius was concluded from massive simulations. The validities of our proposed semi-empirical models for stable water inflow and influence radius were further numerically verified. Comparative study and application in a real engineering case showed that compared with our proposed models, most existing empirical methods predicted a larger stable water inflow and a smaller influence range of groundwater. Besides, comparative results of proposed models with omitting non-Darcian term indicated that neglecting non-Darcian effect would overestimate both the stable water inflow and influence radius. These findings and established models would be useful for assessing stable water inflow and influence radius of a tunnel under non-Darcian flow regime.

Non-Darcian effect on a sinusoidal pumping test in a leaky confined aquifer

Non-Darcian effect on a sinusoidal pumping test in a leaky confined aquifer

Chemical reaction and non-Darcian effects on MHD generalized Newtonian nanofluid motion

Chemical reaction and non-Darcian effects on MHD generalized Newtonian nanofluid motion

Mixed convection phenomenon in packed beds: A comprehensive review

This review summarises first the studies that have been performed to date for establishing a suitable model for mixed convection phenomenon in packed beds with working fluids include some simplifying assumptions such as local thermal equilibrium ( L T E ) condition, neglect of channelling effect, and neglect of thermal dispersion effect. It was found that most of these studies are based on Darcy’s model for the flow and on an averaged single equation model ( L T E ) for the energy equation with using the Boussinesq approximation to represent the variation in fluid density. Theoretical, numerical, or experimental studies, or studies which combine these approaches, are reviewed and for various 2- or 3-dimensional geometries such as horizontal, vertical or inclined parallel plate channels, ducts, cylinders, annuli, etc. In addition, the literature showed that there has been resealable efforts exerted to report works on the non-Darcian mixed convection, in which the effects of boundary, inertia, porosity variation, and inclusion of thermal dispersion under local thermal equilibrium condition ( L T E ) or under thermal non-equilibrium condition ( L T N E ). • This article reviews firstly the studies done about mixed convection phenomenon in packed beds using Darcy and (LTE) energy models. • Studies that include non-Darcian effects such as boundary, inertia, and thermal dispersion, are then summarised. • Works about utilising (LTNE) energy model are lastly reported.

Transient behaviour of heat transfer with complete evaporation process in Porous Channel with localised heating using non-Darcian flow and LTNE model

This study numerically presents the transient behaviour of complete evaporation process inside porous channel. Based on the modified enthalpy formulation under non-Darcy flow and Local Thermal Non-Equilibrium (LTNE) conditions, solutions have been obtained utilizing the finite volume method for various relevant parameters. The results have been validated with the experiments and they show good agreement between them. The results demonstrate that LTNE model should be employed while modelling the transient complete evaporation process in porous media. The non-Darcy effects have considerable influences on the locations of the initiation and termination of the phase change processes as compared to Darcy flow model. Therefore, the behaviours of the two-phase and the superheated vapour zones, when the steady-state solutions is reached, are substantially changed for non-Darcy flow as compared to Darcy model due this assumption provides an additional mechanism for heat transfer that represented by the heat exchange between the solid and fluid phases. It has been observed that the two-phase zone is considerably extended in the axial direction and this zone has not been occupied a large size towards transverse direction due to the axial velocity is noticeably higher than the transverse velocity, caused by reducing the diffusive energy through the two-phase region. The results indicate that non-Darcian effects leads to considerably extend the size of superheated region towards the outlet of the channel, which is not the case for Darcy model. The non-Darican effects become more pronounced for high Reynolds number and heat flux. The influences of varying in Reynolds number, heat flux, porosity, and solid thermal conductivity are substantial near the heated surface, whereas Darcy number has a minor impact on the solution of complete evaporation process. It can be emphasised from the present predictions that the non-Darcy flow along with LTNE condition is indispensable model for the complete evaporation process, especially under high mass flowrate as well heat flux.

Flow in a Circular Pipe Filled with Porous Medium in The Non-Darcian Effects.(Dept.M)

Flow in a Circular Pipe Filled with Porous Medium in The Non-Darcian Effects.(Dept.M)

Forced Convection Heat Transfer In a Cylindrical Porous Media exposed to Constant Wall Heat Flux.(Dept.M)

Forced convection heat flow in a cylindrical packed bed is examined numerically. The bed is filled with saturated spherical beads porous media and is exposed to a constant wall heat flux. Besides the energy equation, the generalized from. of the momentum equation including the non-Darcian effects such as the variable porosity, flow inertia, and viscous friction is considered, and the finite difference method is used. The results have been obtained numerically for sphere beads (3≤ d ≤8 mm diameter), ratio of the particle diameter to the pipe radius 0.05 ≤ D ≤0.5, and nondimensional pressure gradient B up to 108. The non-Darcian effects have a significant influence on the behavior of the temperature, thermal entry length. and Nusselt number across and at the channel wall. The channeling phenomenon near the walls enhanced the thermal communication between the fluid/solid matrix. composite and the walls. This fact yielded an overall 21 percent increase in the value of the Nu in the fully developed region, compared to the value predicted when the Darcy model was used. The results gives complete information about the flow structure and heat transfer for the expressed ranges of parameters. Also, useful correlations reporting the dependence of the thermal entry length on the problem parameters (d, D, B) were reported. A direct dependence of the thermal entry length on Re exists and gives the same correlation that obtained for the pure fluid flow case: XE = 0.1 Re To verifY the numerical results a comparison have been done with the numerical results obtained by Poulikakos and Renken [11], Kays and Crawford [26] and Petukhov [27]. The comparison shows a very good agreement for the presented results and proves the validity of the model.

A generalized non-Darcian model for packer tests considering groundwater level and borehole inclination

Packer test is a tool that has been long developed and widely used for characterizing the permeability of formation. The flow in the tested formation tends to transition from laminar to non-Darcian regime with increasing flow velocity and hydraulic gradient. But as the non-Darcian effect becomes important, how the borehole inclination and groundwater level influence the interpretation of packer test data remains unclear. In this study, a Forchheimer's law-based analytical model incorporating the effects of groundwater level and borehole inclination was presented by image method and velocity integration, which can be immediately reduced to Zangar's (1953) equation for vertical borehole under laminar flow condition and approximately reduced to Chen's (2015b) model when the test interval is at a moderate depth below the groundwater level. The proposed model was validated by numerical simulations. Parametric and error analyses indicate that the hydraulic conductivity will be overestimated while the non-Darcy coefficient will be underestimated if the effects of groundwater level and borehole inclination are neglected. The proposed model was applied to data interpretation of packer tests performed in fractured sedimentary rocks in Hainan Province, China. The results show that significant non-Darcian flow occurred in the tests. The borehole inclination has little influence on the estimation of hydraulic parameters, but demonstrates the anisotropy and heterogeneity of the rocks. • A generalized non-Darcian model was proposed for packer test data interpretation. • The influences of groundwater level and borehole inclination were evaluated. • Previous models overestimate permeability but underestimate non-Darcian coefficient. • Chen et al.'s (2015b) model applies as the depth becomes moderate from groundwater level.

A semi-empirical model for water inflow into a tunnel in fractured-rock aquifers considering non-Darcian flow

Water inflow into a tunnel is usually estimated by assuming that the flow follows the linear Darcy’s law. However, fluid flow in fractured-rock aquifers is prone to deviation from Darcy’s law and gives rise to nonlinear flow phenomena due to significant inertial losses. This non-Darcian effect is seldom considered when evaluating water inflow into the tunnel in a fractured-rock aquifer. In this study, we investigated an analytical method for predicting water inflow into a tunnel considering the non-Darcian effect. A series of numerical simulations for water inflow into a tunnel were conducted with different combinations of parameters, where non-Darcian flow was considered and characterized by the Forchheimer’s law. Based on the numerical results and an ingenious parameter integration method, a semi-empirical model was developed to analytically predict water inflow into a tunnel where the flow is under non-Darcian flow regime. The semi-empirical model includes the classic theoretical formula for predicting water inflow and the Forchheimer equation for describing non-Darcian flow. In this context, the non-Darcian effect on water inflow into a tunnel can be quantitatively estimated. This developed model has a concise expression satisfying dimensional consistency with the parameters having sound physical meanings, and it can be successfully reduced to the classic formula under the Darcy flow regime. The validity of this semi-empirical model was confirmed by numerical results, showing a high fidelity in predicting water inflow into a tunnel. By means of this proposed model, the error induced by neglecting non-Darcian effect was estimated for a large number of real engineering cases, which rapidly increased as a power function with the magnitude of water inflow into the tunnel. The necessity of considering the non-Darcian effect when calculating water inflow was thus proven, especially for massive tunnel gushing. The proposed model and the method used in this study can provide guidance for accurately predicting water inflow into a tunnel under a complex non-Darcian flow regime.

Forced Convective Laminar flow In Elliptic Pipes of Different Aspect Ratios.(Dept.M)

The present analysis investigates non-Darcy forced convective heat transfer in a cylindrical pipe filled with spherical beads saturated with non-Newtonian drag reducing fluid. The cylindrical pipe is subjected to either a uniform heat flux (UHF) or a constant wall temperature (CWT). In modeling the flow, both the energy equation and a modified momentum (Darcy-Forschheimer-Brinkman) equation are used , in which the variable porosity, flow inertia, Brinkman viscous friction (non-Darcian effects) besides the elongational viscosity of drag reducing fluids are taken into consideration and the finite difference technique is used. The results are obtained for a non-Newtonian drag parameter range of 0≤up≤5000, and nondimensional pressure gradient B up to 108. The results show that the non-Newtonian character of drag reducing fluids have a significant influence on the entrance length, beat transfer characteristics and the temperature profiles. Important results documenting and analyzing the behavior of the entrance length and the heat characteristics and its dependence on the non-Newtonian drag parameter are also reported. To examine the adequacy of the present heat transfer model. The governing equations were solved under conditions corresponding to those in Poulikakos and Renken [20]. The comparison of the calculated Nuf with that of Poulikakos and Renken[20]for d=3 and 5mm,up=0.0.05≤D≤0.15 and 104≤B≤106 shows good agreement and validates the presented heat transfer model.

Non-Newtonian Drag Reducing Fluid Flow in a Circular Pipe Filled with Porous Medium in The Non-Darcian Effects.(Dept.M)

This work presents an analysis of a non-Newtonian drag reducing fluid (dilute polymer solutions) in a circular pipe filled with porous media. The flow is developed by modifying the momentum equation for the flow in porous media to account for the elougational viscosity of drag reducing fluids. The modified Darcy-Forschheimer-Brinkman's equation is solved using the finite difference method. The results are obtained for flow Reynolds number up to 105, a non-Newtonian drag parameter range of 0≤ up < /strong>≤5000, and nondimensional pressure gradient B up to 1010. The results show that the non-Newtonian effect of drag reducing fluids have a significant influence on the velocity and signifies relative increase in the maguitude of the velocity in the region adjacent to the wall which in turns signifies the channeling effect. This phenomena is reflected in the great influence on the fluid flow characteristics such as the boundary frictional drag, the elongational viscous drag, and in turns in the total drag. Important results documenting and analyzing the behavior of the velocity and the fluid flow characteristics and its dependence on the non-Newtonian drag parameter are also reported in the course of the study. An experimental investigation was carried out for the flow of water and a dilute polymer solutions with concentrations C = 1, 5, 20, 50 and 100 wppm of the polyacryiamide in a circular rube of 20mm diameter filled with 3.2 mm diameter stainless-steel spheres. Comparison of the numerical results with the experimental results show good agreement of the presented results and prove the validity of the model.

Non-Darcian effect on double-diffusive natural convection inside aninclined square Dupuit-Darcy porous cavity under a magnetic field

This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, ?, about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy, and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, Hartmann number, Lewis number, the buoyancy ratio, inclination angle, and tilting angle of the magnetic field. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer.

Electromagnetic and non-Darcian effects on a micropolar non-Newtonian fluid boundary-layer flow with heat and mass transfer

The purpose of this paper is to investogate the ectromagnetic and micropolar properties on biviscosity fluid flow with heat and mass transfer through a non-Darcy porous medium. Morever, The heat source, viscous dissipation, thermal diffusion and chemical reaction are taken into consideration. The system of non linear equations which govern the motion is transformed into ordinary differential equations by using a suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the velocity, microtation velocity, temperature and concentration are obtained as a functions of the physical parameters of the problem. Moreover the effects of these parameters on these solutions are discussed numerically and depicted graphically. It is found that the microtation velocity increases or deceases as the electric parameter, Hartman parameter and the microrotation parameter increase. Morever, the temperature increases as Forschheimer number, Eckert number increase.

Non-Darcian Effects on Nanoliquid Flow Past a Stretching Sheet with Temperature Jump Condition and Thermal Radiation

This article explores the influence of non-Darcy porous medium on nanoliquid flow past a stretching plane with thermal radiation and thermal slip on surface. The pedesis and thermophoresis effects have been included into the nanofluid model. The equations governing the momentum and energy are initially cast into dimensionless form using the suitable non-dimensional variables. The resultant system of equations is then solved employing variational Finite Element Method (FEM). The impact of pertinent parameters such as thermal radiation, temperature jump, non-Darcy on the flow, temperature and local skin friction coefficient, local Nusselt number are investigated and presented graphically. The Forchheimer number is found crucial to increase temperature and lower the local heat transfer rate in the boundary layer.

Non-Darcian effect on a variable-rate pumping test in a confined aquifer

Groundwater flow in an aquifer has frequently been found to be non-Darcian. In this study, a transient model of a variable-rate pumping test in a confined aquifer was established considering non-Darcian flow in the aquifer. A piecewise-linear function was adopted to reproduce the variability in pumping rate, and the classical Izbash equation was employed to describe the non-Darcian flow. The type-curve analysis suggested that a smaller quasi-conductivity will result in an earlier deviation and a smaller extent of the decreasing features in the drawdown under the condition of a linearly decreasing pumping rate compared to that under the condition of a constant pumping rate. The sensitivity analysis indicated that the variability in pumping rates under non-Darcian flow can increase the sensitivity of drawdown to the radius of the well casing at inflection times of the discrete linear stages, and drawdown closer to the pumping well is more sensitive to the change in the well casing. A type-curve method was proposed and employed to interpret the pumping test data, which were collected at a field site located in Wuxi city, Jiangsu Province, China. The parameter estimates indicate a high possibility of the occurrence of prelinear flow in the aquifer of interest.

Non-Darcian flow effect on discharge into a tunnel in karst aquifers

The groundwater flow in karst aquifers is prone to become non-Darcian due to the presence of karst conduits, and this effect may become more pronounced during tunnel construction. Prediction of discharge into tunnels in karst aquifers remains a challenging task because of the complex nature of non-Darcian flow and the uncertainty of aquifer's properties. This study aims to evaluate the effect of non-Darcian flow on the discharge into a tunnel in karst aquifers in Guizhou Province, China, where a large proportion (~86%) of borehole packer tests evidences the flow in non-Darcian regime. An integrated method combining packer test data interpretation, statistical correlation and inverse modelling is proposed to determine the non-Darcian flow properties of the aquifer system. Numerical simulations of steady-state flow show that the predicted discharge based on the Forchheimer's equation agrees better with measurements than that based on the Darcy's law by ~27%. The region with the most pronounced non-Darcian effect occurs at the intersection between the tunnel and a karstified fault connecting to an underground river, and the occurrence of non-Darcian flow leads to an increase in hydraulic gradient, but a reduction in discharge into the tunnel. This work presents a framework that combines aquifer properties estimation and numerical simulations for more accurately evaluating the discharge and seepage erosion risk induced by tunnel construction in karst aquifers.

Analysis of the Flow Dynamics of Blood Through Viscoelastic Constricted Artery

In this paper, we focused on the flow through an axisymmetric constricted artery of the pulmonary region to study the condition of stenosis. Theory of dust particles suspended in gas is applied on blood flow through the artery, where the “particles” represent “cells” suspended in plasma. The flow is governed by two dimensional Navier–Stokes’ equations by including Darcy–Forchheimer drag force caused by non-Darcian effect. The material of the artery is approximated as a linear elastic and simplest rheological equation that includes viscosity and elasticity (considered lung as a Voigt body) is used. Effect of various parameters, such as Reynolds number (Re), Forchheimer number ($$F_s$$), Darcy number (Da), aspect ratio ($$\beta $$), shape factor ($$S_f$$), porosity ($$\epsilon $$), aerodynamic diameter ($$d_p$$), bulk compression ($$\phi $$) of elasticity, shear ($$\eta $$) and bulk ($$\zeta $$) coefficients of parenchymal viscosity are obtained on the radial and axial velocities of blood and particles graphically. We found that the fluid (blood) and particle (cells suspended in plasma) velocities along both the axes (axial and radial) increase by increasing Reynolds number, the pulsating amplitude, aspect ratio, and porosity of walls. While by increasing Forchheimer number, velocities of blood and particles in both the axes decreases gradually. The present analysis is also indicate that the viscoelasticity of walls are affected by the amplitude of pulsatile flow of blood and for a large value of amplitude, the viscoelastic effect decreases.