Heat,Water, and Solution Transfer in Unsaturated Porous Media: I -- Theory Development and Transport Coefficient Evaluation

A detailed theory describing the simultaneous transfer of heat, water, and solute in unsaturated porous mediais developed. The theory includes three fully-coupledpartial differential equations. Heat, water, andsolute move in the presence of temperature, T; matricpressure head, _m ; solution osmotic pressure head _o ; and solute concentration C gradients. Thetheory can be applied to describe the mass and energyin radioactive waste repositories, food processing,underground energy storage sites, buried electriccables positions, waste disposal sites, and inagricultural soil. Several transport coefficients forheat, water, and solute are included in the theory. The coefficients are evaluated for a silty clay loamsoil to clarify their dependence on water content (),T, and C. The thermal vapor diffusivity D _Tv first increased as increased to0.22 m³/m³ then decreased with furtherincreases in . D _Tv was 3 orders of magnitudegreater than either isothermal vapor D _mv orosmotic vapor D _ov , diffusivities at of0.20~m³/m³, T of 50°C, and C of 0.001mol/kg. All of the liquid and vapor water transport coefficients increased with increasing T. D _Tv decreased with increasing C to a greater extent thanD _mv and D _ov . The effective thermalconductivity decreased slightly with increasing C. Thesolute diffusion coefficient D _d was 6 to 7orders of magnitude greater than the thermal soluteand salt sieving diffusion coefficients at of0.20~m³/m³, T of 50°C, and C of 0.001 mol/kg.     

A Study of Magma Flows in the Case of Non-Equilibrium Diffusion of Water in the Melt

All volcanic eruptions are accompanied by the degasification of the magma, which results in the growth of gas bubbles in the silicate melt. The number and growth rate of the bubbles determine the character of the eruption. When the free-gas concentration is low, the eruption is weak and takes a short time. At high concentrations, the melt is fragmented and a gas-particle mixture is formed. This results in the catastrophic intensification of the eruption. In this study, for describing the magma flow in a volcano conduit with account for the mass transfer between the bubbles and the melt, we construct models in which the conduit magma flow is considered simultaneously with the dynamics of gas-bubble growth in the melt. The models describe the magma eruptions with equilibrium or weak growth of the bubbles and also with a moderate rate of bubble growth, which is more typical of volcanic systems. Using the models constructed, an intense steady-state eruption and the problem of the evolution of the eruption to the steady-state regime after the rupture of a plug near the top of the conduit are considered. The effect of gas diffusion on the intensity and duration of the eruption is indicated.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Modeling Floodplain Filtration for the Improvement of River Water Quality

A mathematical model was developed to describe a treatment method of floodplain filtration for the improvement of river water quality. The process consists of spraying poor quality river water onto the river floodplains and thus allowing soil filtration to treat water before it gets back again into the main river stream. This technique can be readily employed in Korea because it exploits the characteristics of the climate and rivers in the country, as described in an experimental study of Chung et al. The model was analyzed by numerical methods and validated by comparing the simulated values with experimental data. A scenario analysis of the model was also performed in order to have a better understanding of the floodplain filtration process. Our results show that the model was able to predict the reduction in organic matter and NO₃^– in river water through the floodplain filtration. Furthermore, it was found that only a few decimeters of top soil profile were enough to degrade most of the organic matter under wider operational conditions than those reported in the literature. Also, it was found that significant infiltration of atmospheric oxygen took place near the soil surface. The N₂O emission and the NO₃^– leaching increased with the increase in the influent NO₃^– concentration. However, the N₂O emission due to floodplain filtration was not expected to exceed 0.1 mL/m²-day.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

空投鱼雷倾斜姿态落水冲击研究

利用轴长体假设和Ｔａｙｌｏｒ关于圆柱在不同浸深时的附加质量表达式，运用切片理论建立了空投鱼雷在其纵向平面内以倾斜姿态落水时的运动微分方程组，通过实例计算得到了空投鱼雷入水冲击时作用在其上的弯矩和剪力分布的规律，为理论预测空投鱼雷入水冲击时的强度破坏建立了基础。     

Modeling the effect of diffusion of the ambient medium on the long-term strength of a hollow cylinder under uniaxial tension

The problem of the long-term strength of an extended thick-walled tube containing a corrosive medium in the internal cavity is solved. The diffusion of this medium into the tube material is analyzed. The diffusion equation is solved approximately by introducing the diffusion front, and the error of the solution is estimated. The dependence of the time of fracture of the tube on the variable tensile stress and the concentration of the medium filling the cavity is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 88–93, July–August, 2007.     

Experimental determination of the diffusion coefficients of wood in isothermal conditions

The diffusion coefficients of frake (Terminalia superba) were determined in the radial, tangential, and longitudinal directions at tree different temperatures: 30°C, 35°C an 40°C. The longitudinal diffusion coefficient is larger than the transverse diffusion coefficient. In addition the radial coefficient is larger than the tangential coefficient.     

Freezing of Water in a Differentially Heated Cubic Cavity

An experimental and numerical study has been made of transient natural convection of water freezing in a cube-shaped cavity. The effect of the heat transfer through the side walls is studied in two configurations: with the cavity surrounded by air and with the cavity immersed in an external water bath of constant temperature. The experimental data for the velocity and temperature fields are obtained using liquid crystal tracers. The transient development of the ice/water interface is measured. The collected data are used as an experimental benchmark and compared with numerical results obtained from a Finite-difference code with boundary fitted grid generation. The computational model has been adopted to simulate as closely as possible the physical experiment. Hence, fully variable fluid properties are implemented in the code, and, to improve modelling of the thermal boundary conditions, the energy equation is also solved inside the bounding walls. Although the general behaviour of the calculated ice front and its volume matches observations, several details of the flow structure do not. Observed discrepancies between experimental and numerical results indicate the necessity of verifying and improving the usual assumptions for modelling ice formation.     

Unsteady theory of the hydrofoil of finite span

A three-dimensional unsteady flow around the hydrofoil has been dealt with in this paper. Under the assumption of infinitesimal wave and thin hydrofoil, analytic solution of perturbation velocity potential induced by the unsteady flow of a hydrofoil which is simplified as a series of rectangular vortex rings is achieved and then the unsteady forces can be evaluated. The paper had been accepted by the X VI th International Congress of IUTAM, Lyngby, Denmark, Aug. 19–25, 1985.     

Role of NAPL Thermal Properties in the Effectiveness of Hot Water Flooding

Hot water flooding is a thermal nonaqueous phase liquid (NAPL) recovery technology originally developed in the petroleum industry that has recently been proposed for enhanced recovery of NAPLs in the contaminated subsurface. This technology, however, has received relatively little laboratory or numerical modeling investigation in the contaminant hydrology community. In this study the utility of flooding NAPL contaminated source zones at elevated water temperatures was investigated. Simulations were conducted using 16 different geostatistical representations of an actual field site. Two NAPLs were selected for this study—a light NAPL with hydraulic properties that have moderate temperature dependencies and a dense NAPL with significant viscosity temperature dependency. For these two NAPLs, flooding the source zone with water at elevated temperatures resulted in enhanced NAPL recovery. However, injection of hot water also resulted in accelerated downward movement of coal tar DNAPL due to the reduced viscosity at elevated temperatures. NAPL recovery was also dependent on the source zone architecture with greater NAPL mass recovery when the NAPL was localized in a small volume at high saturations. These results suggest that hot water flooding can significantly speed up the recovery of viscous NAPLs and, as such, is a powerful technique for the remediation of viscous NAPLs.     

Spectral Analysis of the Balance Equation of Ground Water Hydrology

The spectral analysis of the balance equation of ground water flow, associated to an asymptotic expansion of the conductivity (K) and head (h) fields, permits to show that the high wave number components of the source terms, F, and of the conductivity, K, are attenuated when h is computed as solution to the balance equation. This has important consequences on the inverse mapping (h, F) → K: in fact it is not possible to recover in a reliable way the high wave number components of K, because small errors on the corresponding components of h are amplified so that they can hidden the true signal.     

Perfecting a method of micro-analysis of water and acetic acid in a cocoa bean in the course of drying: applying to determine transportation coefficients

This article is about the study of the diffusion of water and acetic acid in a grain of cocoa in course of drying. The authors present a method of microanalysis which enables the analysis of each little slice of the grain : a precise measurement of each slice is realised in view of the analysis from the centre to the surface of the grain with the aid of a cutting apparatus, designed and realised to this effect. At each instant of the drying process, the profiles of water and acetic acid contents are then determined. A one dimensional diffusion model enables a shell by shell evaluation of the diffusion of water and acid in the cocoa grain. The results obtained show an augmentation of transport coefficients in course of drying. We however observe a decrease of the diffusion coefficient of water to the low moisture content : what makes us think of the appearance of crusting phenomenon.     

Effect of the Nonmonotonic Temperature Dependence of Water Density on the Decay of an Initial Density Discontinuity

The effect of the nonmonotonic temperature dependence of water density on gravity current flow after removal of the shield which separated warm and cold water was studied experimentally. If the temperature of water of maximum density was in the interval between the initial temperatures on the different sides of the shield, Rayleigh-Taylor instability developed along with shear instability under normal conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 66–73, January–February, 2006.     

A Numerical Study of the Distribution of Water in Partially Saturated Porous Rock

The distribution of water and air phases in small blocks of porous sandstone is examined by using a simulated annealing technique that finds the minimum interfacial energy distributions at different saturations. Simulations are based on existing sandstone microstructures that were determined by X-ray microtomography. At low saturations, some of the water is distributed in films along the walls of larger pore spaces, and connects to pendular structures in the crevices and smaller pores. As the amount of water in the pores increases the water films become thicker and pores fill from the pendular structures. The distribution of water voxels in the pore space is examined by calculating interfacial areas, by classifying water voxels as to whether they lie within films or clusters, and by determining the size and distribution of these film clusters. An exponential relationship is found between the fraction of water voxels in the films and the degree of saturation. In addition, the dependency of small-sample electrical conductivity on saturation is examined by using a random walk method.     

Effect of the Nonmonotonic Temperature Dependence of Water Density on the Propagation of a Vertical Plane Jet

This paper gives results of two experiments in which warmer water in the form of a vertical plane jet was let into colder water. In one experiment, the temperature of inflowing and initially quiescent water exceeded 4°C and warm water propagated only along the free surface. In the other experiment, the temperature of inflowing water was above 4°C and that of quiescent water was below 4°C. In this case, two jets — surface and bottom — first formed, and then the inflowing liquid was entirely concentrated in the bottom jet. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 23–29, March–April, 2006.     

Finite Element Analyses in Surface Water and Groundwater: An Overview of Investigations at the U.S. Army Engineer Waterways Experiment Station

This paper highlights the finite element hydrodynamic and transport modeling developments being conducted by the U.S. Army Engineer Waterways Experiment Station (WES) and its partnering organizations. The WES developments in support of surface water, groundwater, and watershed management are presented. A particular facet of these developments, the creation of integrated, comprehensive modeling systems which greatly increase the productive use of WES hydroenvironmental models, is discussed. Future development directions, including the use of scalable high performance computing resources, are also provided.     

Water Redistribution in Irrigated Soil Profiles: Invariant Solutions of the Governing Equation

Exact solutions for a class of nonlinear partial differential equations modelling soil water infiltration and redistribution in irrigation systems are studied. These solutions are invariant under two-parameter symmetry groups obtained by the group classification of the governing equation. A general procedure for constructing invariant solutions is presented in a way convenient for investigating numerous new exact solutions.     

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 24–36, March–April, 2009.