Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

Iterative Method on Well Bore Boundary in Numerical Modeling of Variably Saturated Flow

An iterative method was developed for incorporating the well bore boundary into the finite difference model of water flow in variably saturated porous media. Six cases were presented involving groundwater pumping or injection to demonstrate the advantages of the iterative method over the traditional method. For the iterative method, the total flux gradually approached the well discharge and the flux profile was non-uniform. And the iterative method took into account the variation of well bore water table. Compared to the traditional method, the iterative method can simulate the variably saturated flow caused by pumping or injection more realistically.

Integrated numerical model for vegetated surface and saturated subsurface flow interaction

The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional （Q3D） vegetated surface flow model with a two-dimensional （2D） saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations （SWEs） with the implicit finite difference solution of Navier-Stokes equations （NSEs） for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations （SGFEs）. The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

Methodology for expressing the flow coefficients of coupled throttling grooves in a proportional–directional valve

Calculating the flow coefficient of a spool-valve is complicated due to the coupling–throttling effect in the throttling grooves of a proportional–directional valve.In this paper,a methodology for expressing the flow coefficient of coupled throttling grooves is proposed to resolve that difficulty.With this purpose,an approach of a 3 D numerical simulation and an experimental bench were introduced based on the prototype of a commercial proportional valve.The results show consistency between the numerical simulation and the bench test.Based on that,the concept of‘saturation limit’is introduced to describe the value gap between the current and saturated flows,so that the flow-coefficient saturation limit of the prototype in the process can be deducted.Accordingly,an approximate flow coefficient suitable for coupled throttling grooves within finite variable space,which is based on three typical throttling structures(i.e.O-shape,U-shape,and C-shape)of the coupled throttling grooves,is obtained based on an orthogonal test.The model results are consistent with the numerical and experimental results,with maximum errors of less than 5.29%and 5.34%,respectively.This suggests that the proposed method is effective in approximating the flow coefficient.

AN ELLIPTIC-PARABOLIC SYSTEM ARISING FROM THE FLUID-SOLITE-HEAT FLOW THROUGH SATURATED POROUS MEDIA

In this paper an elliptic-parabolic coupled system arising from the fluid-solute-heat flowthrough a saturated porous medium is considerd.The uniqueness and the existence of classicalsolutions are proved.The asymptotic behavior of solutions for large time is shown,too.

Research on pumped two-phase single-sided cold plate of IGBT for rail transit applications

The use of pumped two-phase cooling to improve the thermal management of insulated gate bipolar transistor(IGBT)in rail transportation is a novel cooling technology.An experimental investigation on pumped two-phase cold plate of IGBT used in HXD1C locomotives was conducted at a mass flow rate of 0.1 kg/s–0.29 kg/s and a heat flux of 6.2 W/cm^(2),with R245fa as the working fluid.The experimental results showed that the base temperature nonuniformity can be controlled within 2.2℃ at flow rates of 0.14 kg/s and 0.19 kg/s,which is of great benefit to the reliability of IGBT.Based on well known correlations for saturated flow boiling in tubes,an analytical model was developed and compared with the experimental data.The model could predict the base temperature data within an error band of±3℃,as well as capture the trend of base temperature as a function of vapour quality and mass flow rate.The performance of the pumped two-phase cold plate of IGBT could be further improved with the aid of the developed model.