Line Sink Research Articles

Unsteady free surface flow due to a line sink at an arbitrary location with surface tension

The unsteady flow generated when a line sink is located at an arbitrary location beneath the free surface of a fluid of finite depth is considered. Interest is in the evolution to a steady state flow, splashing flows and the drawdown of the surface. The location of the sink away from, but near to, a vertical barrier leads to some interesting new surface flows due to interactions and reflection, some of which have a profound impact on the nature of the critical drawdown flow parameters. Interesting new solutions with a delayed drawdown that are initiated by a reflected wave are presented. A linearized solution and a fully nonlinear solution are presented and the results discussed. Regions of steady, unsteady and supercritical flow are identified.

Power-saving system designs for hexagonal cell based wireless sensor networks with directional transmission

This paper examines the lifetimes of alternative system configurations for a wireless sensor network (WSN) in a circular region. The coverage region is divided into hexagonal cells, and the information from each cell is combined and transmitted to the sink or to other cells. Sensors are equipped with directional antennas that improve transmit/receive power efficiency and potentially reduce interference. Simultaneous transmission to multiple cells is permitted, and the power level of different transmissions can be controlled to different levels. Under the assumptions of uniform information density and uniform sensor distribution, we show that for larger systems (with 800 cells or more) lifetime can be prolonged by more than 10 times by introducing a limited number of transmission lines or line sinks to facilitate information transfer to the main sink. Alternatively, introducing up to six secondary sinks can increase the system lifetime by a factor of about 4.5 for the same size region. Our results imply that incorporating line or secondary sinks may provide simple, low-cost solutions for extending system lifetime for larger WSN’s.

Profiling ponded soil surface in saturated seepage into drain-line sink: Kalashnikov’s method of lateral leaching revisited

Two boundary value problems are solved for potential steady-state 2D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled. The aim of this shaping is ‘uniformisation’ of the velocity and travel time between this surface and a horizontal drain modelled by a line sink. The complex potential domain is a half-strip, which is mapped onto a reference plane. Either the velocity magnitude or a vertical coordinate along the land surface are control variables. Either a complexified velocity or complex physical coordinate is reconstructed by solving mixed boundary-value problems with the help of the Keldysh-Sedov formula via singular integrals, the kernel of which are the control functions. The flow nets, isotachs and breakthrough curves are found by computer algebra routines. A designed soil hump above the drain ameliorates an unwanted ‘preferential flow’ (shortcut) and improves leaching of salinised soil of a cropfield during a pre-cultivation season.

Flow induced by a line sink near a vertical wall in a fluid with a free surface, Part II: finite depth

Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink.

Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

The two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, x_mathrm{{s}} < 1, there is only one stagnation point on the surface, at the wall. However, if the horizontal location x_{mathrm{s}} > 1, a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.

Selective withdrawal of a three-layer viscous fluid

Two dimensional, selective withdrawal of a three-layer fluid in a rectangular tank is considered. Each fluid is viscous, weakly compressible and miscible. The lowermost, heaviest fluid flows with constant speed out through line sinks located on the base and lower side walls of the tank. The uppermost and lightest fluid recharges the tank via line sources located along the top and on the upper side walls at a rate that matches the outward flux. If the line sinks are turned on suddenly, the interfaces between the fluids are drawn downward at different rates; this disparity arises due to the fact that the wave configurations that propagate along the two interfaces are not the same. Density and vorticity contours are presented and used to determine the time at which the middle transition layer of fluid begins to be withdrawn from the tank; at this point the rate of extraction of the most dense fluid is its greatest. Inviscid linearised interfaces are calculated which serve as checks on the early stage evolution of the full nonlinear model.

A hydraulic resistance model for interstitial fluid flow in the brain.

Metabolic wastes may be cleared from the brain by the flow of interstitial fluid (ISF) through extracellular spaces in the parenchyma, as proposed in the glymphatic model. Owing to the difficulty of obtaining experimental measurements, fluid-dynamic models are employed to better understand parenchymal flow. Here we use an analytical solution for Darcy flow in a porous medium with line sources (representing penetrating arterioles) and line sinks (representing ascending venules) to model the flow and calculate the hydraulic resistance as a function of parenchymal permeability and ISF viscosity for various arrangements of the vessels. We calculate how the resistance varies with experimentally determined arrangements of arterioles and venules in mouse and primate brains. Based on experimental measurements of the relative numbers of arterioles and venules and their spacing, we propose idealized configurations for mouse and primate brains, consisting of regularly repeating patterns of arterioles and venules with even spacing. We explore how the number of vessels, vessel density, arteriole-to-venule ratio, and arteriole and venule distribution affect the hydraulic resistance. Quantifying how the geometry affects the resistance of brain parenchyma could help future modelling efforts characterize and predict brain waste clearance, with relevance to diseases such as Alzheimer's and Parkinson's.

A spectral modelling approach for fluid flow into a line sink in a confined aquifer

A spectral method is developed to study the steady and unsteady flow of fluid into a line sink from a horizontally confined aquifer, and the results are compared to solutions obtained implementing the finite element package COMSOLTM. The aquifer or drain is considered to be confined below so that the solutions are fundamentally unsteady. Comparison is made between the two methods in determining the drawdown of the surface.

General analytical solutions of groundwater flow toward multi-dimensional sources/sinks in a confined aquifer with leakage and distributed recharge

A variety of hydrogeologic conditions and parameters play roles in obtaining analytical solutions for groundwater flow in aquifers. Changes of these influencing conditions typically require finding a new solution. Therefore, it is very useful if a general approach and solution can be provided to conveniently construct the solutions corresponding to the condition changes. In this study, two general analytical solutions for multi-dimensional groundwater flow in homogeneous, confined aquifers are derived using Green’s function method for instantaneous and continuous sources/sinks. A library of analytical solutions can be readily obtained by combining the general solutions with directional solutions for a variety of hydrogeologic and geometric conditions. The aquifer can be one-, two-, or three-dimensional and vertically and horizontally finite, semi-infinite, or infinite. The geometry of sources/sinks can be point, line, areal, and volumetric. Leakage from adjacent aquifers and distributed precipitation recharge are also included. The general solutions are validated by reported analytical solutions. A series of typical solutions for one-, two-, and three-dimensional groundwater flow are presented. A computational example is provided to compare the drawdown distributions caused by point, vertical line, vertical areal, and volumetric sinks. A field investigation and design at a groundwater-contaminated site using the derived analytical solution suggests that drainage slots (vertical areal sinks) can be an effective alternative to pumping wells (vertical line sinks) in lowering the groundwater level for a shallow aquifer.

Infiltration-induced phreatic surface flow to periodic drains: Vedernikov–Engelund–Vasil’ev’s legacy revisited

An explicit analytical solution is obtained to an old problem of a potential steady-state 2-D saturated Darcian flow in a homogeneous isotropic soil towards systematic drains modeled as line sinks (submerged drains under an overhanging of a phreatic surface), placed on a horizontal impervious substratum, with a constant-rate infiltration from the vadose zone. The corresponding boundary-value problem brings about a quarter-plane with a circular cut. A mathematical clue to solving the Hilbert problem for a two-dimensional holomorphic vector-function is found by engaging a hexagon, which has been earlier used in analytical solution to the problem of phreatic flow towards Zhukovsky’s drains (slits) on a horizontal bedrock. A hodograph domain is mapped on this hexagon, which is mapped onto a reference plane where derivatives of two holomorphic functions are interrelated via a Polubarinova-Kochina type analysis. HYDRUS2D numerical simulations, based on solution of initial and boundary value problems to the Richards equation involving capillarity of the soil, concur with the analytical results. The position of the water table, isobars, isotachs, and streamlines are analyzed for various infiltration rates, sizes of the drains, boundary conditions imposed on them (empty drains are seepage face boundaries; full drains are constant piezometric head contours with various backpressures).

Numerical and analytical predictions of nuclear steam generator secondary side flow field during blowdown due to a feedwater line break

For the structural integrity evaluation of pressurized water reactor (PWR) steam generator (SG) tubes subjected to transient hydraulic loading, determination of the tube-to-tube gap velocity and static pressure distributions along the tubes is prerequisite. This paper addresses both computational fluid dynamics (CFD) and analytical approaches for predicting the tube-to-tube gap velocity and static pressure distributions during blowdown following a feedwater line break (FWLB) accident at a PWR SG. First of all, a comparative study on CFD calculations of the transient velocity and pressure distributions in the SG secondary sides for two different models having 30 or no tubes is performed. The result shows that the velocities of sub-cooled water flowing between any adjacent two tubes of a tubed SG model during blowdown can be roughly estimated by applying the specified SG secondary side porosity to those of the no-tubed SG model. Secondly, simplified analytical approximate solutions for the steady two-dimensional SG secondary flow velocity and pressure distributions under a given discharge flowrate are derived using a line sink model. The simplified analytical solutions are validated by comparing them to the CFD calculations.

Seepage to ditches and topographic depressions in saturated and unsaturated soils

An isobar generated by a line or point sink draining a confined semi-infinite aquifer is an analytic curve, to which a steady 2-D plane or axisymmetric Darcian flow converges. This sink may represent an excavation, ditch, or wadi on Earth, or a channel on Mars. The strength of the sink controls the form of the ditch depression: for 2-D flow, the shape of the isobar varies from a zero-depth channel to a semicircle; for axisymmetric flow, depressions as flat as a disk or as deep as a hemisphere are reconstructed. In the model of axisymmetric flow, a fictitious J.R. Philip's point sink is mirrored by an infinite array of sinks and sources placed along a vertical line perpendicular to a horizontal water table. A topographic depression is kept at constant capillary pressure (water content, Kirchhoff potential). None of these singularities belongs to the real flow domain, evaporating unsaturated Gardnerian soil. Saturated flow towards a triangular, empty or partially-filled ditch is tackled by conformal mappings and the solution of Riemann's problem in a reference plane. The obtained seepage flow rate is used as a right-hand side in an ODE of a Cauchy problem, the solution of which gives the draw-up curves, i.e., the rise of the water level in an initially empty trench. HYDRUS-2D computations for flows in saturated and unsaturated soils match well the analytical solutions. The modeling results are applied to assessments of real hydrological fluxes on Earth and paleo-reconstructions of Martian hydrology-geomorphology.

Anti-Tumor Effects of Astaxanthin by Inhibition of the Expression of STAT3 in Prostate Cancer.

Astaxanthin is a natural product gaining increasing attention due to its safety and anti-cancer properties. In this study, we investigated the mechanisms of the anti-cancer effects of astaxanthin on prostate cancer (PCa) cell lines using aggressive PCa DU145 cells. Also an instantaneous silenced cell line (si-STAT3) derived from DU145 and a control cell line (si-NK) were used for the MTT and colony formation assays to determine the role of astaxanthin in proliferation and colony formation abilities. Flow cytometry assays were used to detect the apoptosis of tumor cells. Migration and invasion assays detected the weakening of the respective abilities. Western blot and RT-PCR tests detected the levels of STAT3 protein and mRNA. Astaxanthin resulted in suppression of the proliferation of DU145 cells and the level of STAT3. The treatment of DU145 cells with astaxanthin decreased the cloning ability, increased the apoptosis percentage and weakened the abilities of migration and invasion of the cells. Furthermore, astaxanthin reduced the expression of STAT3 at protein and mRNA levels. The effects were enhanced when astaxanthin and si-STAT3 were combined. The results of animal experiments were consistent with the results in cells. Thus, astaxanthin inhibits the proliferation of DU145 cells by reducing the expression of STAT3.

Extraction of density-layered fluid from a porous medium

We consider axisymmetric flow towards a point sink from a stratified fluid in a vertically confined aquifer. We present two approaches to solve the equations of flow for the linear density gradient case. Firstly, a series method results in an eigenfunction expansion in Whittaker functions. The second method is a simple finite difference method. Comparison of the two methods verifies the finite difference method is accurate, so that more complicated nonlinear, density stratification can be considered. Such nonlinear profiles cannot be considered with the eigenfunction approach. Interesting results for the case where the density stratification changes from linear to almost two-layer are presented, showing that in the nonlinear case there are certain values of flow rate for which a steady solution does not occur.

Medical Image Intelligent Recognition Predicts the Recessivity Variation of Human Tissue

By analyzing and predicting the latent variation of human tissues, the concept of iterative programming of heavy kernel clustering is introduced to solve the problem of intelligent recognition of medical images of inflammation and cancer. Inflammatory cells modify the accumulation of cancer cells and leap to the early stage of cancer, which is called image entropy. The hypercomplex symmetric structure of the edge sliding kernel of the entropy kernel of high-dimensional <i>s</i>≥ 6 image. As well as the fusion of image entropy nucleus dumbbell double sphere complex sphere, the exchangeability of the central source extreme compression line sink; the central source superstring sink compresses to the critical point, and the unconstrained <i>2N + 1</i> laminated incision will cause the high-dimensional superstring sink to break up and release the exfoliated cells. Non analytic exploitation is the inverse kernel factor of aidicom that can judge the entropy of latent tissue variation image from inflammation to early cancer. It is a foundation of revealing (predicting) system recognition data array, and can carry the first-order and second-order partial differential carriers of kernel core area. In the medical image, the identification of inflammation and cancer often troubles doctors. Based on the inherent logic between cell modification fluctuation and image, aidicom system gives the concept of image entropy, and uses the dieg algorithm to complete the classification of focus detection and recognition, as well as the prediction of future development.

Analytical solution of capture time to a partially penetrating well in a semi-infinite aquifer

Calculating the capture time of contaminant to a well is important in the context of both groundwater protection and aquifer remediation. Although partially penetrating wells are much more commonly used than fully penetrating wells, there is no analytical solution for capture time calculations, probably due to the challenges of mathematically modeling such types of wells. In this study, an analytical solution of capture time was developed, based on the assumption that a partially penetrating well was installed in a homogeneous and semi-infinite aquifer. For an example case, the capture time result by the analytical solution fitted well with result by a high-resolution particle tracking method established according to the fourth-order Runge-Kutta algorithm. The impacts of different parameters are analyzed, and results indicate that the effects of both screen length L and anisotropic ratio a2 on capture time T are spatially dependent. Such comparisons also demonstrate that the influence of the lower boundary is stronger as penetration increases. In the end we compare the analytical solution for a line sink with that for a point sink, and demonstrate that larger differences occur near the wellbore, however, at a sufficiently large distance from the wellbore, the capture time distributions become the same for both source types.

Critical surface coning due to a line sink in a vertical drain containing a porous medium

The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.&#x0D; &#x0D; doi:10.1017/S1446181119000099

CRITICAL SURFACE CONING DUE TO A LINE SINK IN A VERTICAL DRAIN CONTAINING A POROUS MEDIUM

The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.

Pressure performance of interlaced fracture networks in shale gas reservoirs with consideration of induced fractures

Multi-stage fracturing in shale gas reservoirs may create complex fracture network around horizontal wellbore, due to the widely-distributed natural fractures. However, little work has been done to investigate the effects of secondary fractures on well testing models for shale gas reservoirs. In this paper, a more comprehensive model was developed for interlaced fracture networks in shale gas reservoirs with consideration of multiple transport mechanisms and different flow states. By employing the source function and Laplace transformation, the line sink solutions for four kinds of flow states were unified. Based on the discretization method and unified line sink solution, the pressure responses for interlaced fracture networks with infinite conductivity were obtained. Type curves were plotted and typical flow regimes of this model were identified. In order to have a further understanding of the effect of induced fractures, the slope curves of pseudo-pressure derivative were introduced to analyze the interference between fractures. The influences of the angel and the length of induced fractures on the well testing curves were simulated by the semi-analytical model for the first time. Then, the flux distributions of interlaced fracture networks were simulated and discussed for achieving significant advice. Finally, the proposed model was verified by a simplified case and a field case. The presented model will be helpful for understanding the transient performance of multi-stage fractured horizontal wells with consideration of induced fractures.

Analytical solution for the soil freezing process induced by an infinite line sink

One-dimensional soil freezing process induced by an infinite line sink is investigated, a problem that is generally encountered during the application of the artificial ground freezing technique. The special feature of the freezing process of soil is that the amount of liquid water in the soil pores decreases gradually with the soil temperature decreasing, and thus latent heat is continuously released. After approximating the continuous phase change process of the soil with a multi-step phase change process of a polymorphous material, the original problem is transformed to a cylindrical multiphase Stefan problem. Using the similarity transformation technique, an analytical solution for the problem is developed, in which there are coefficients that need to be determined by a group of non-linear equations. A theoretical proof is presented showing that these coefficients can be appropriately determined by the non-linear equations. The computational results of the analytical solution are compared with those of the numerical solution, and the two solutions are in good agreement. The effects of the variation of different parameters on the movement of freezing front are studied. The results show that neglecting the existence of unfrozen water will underestimate the freezing front velocity. The relative error of this underestimation under different conditions is also investigated and discussed. In situations that the unfrozen water content is given as a discrete function of the temperature, the analytical solution can be applied directly, and an illustrative example is presented.