Numerical simulation of convective flows in a soil during the evaporation of water containing a dissolved admixture

The concentration profile is investigated for a solution that saturates a low-permeability soil. The simulation results showed the presence of three flow regimes. The salt accumulated near the phase transition boundary increases the solution density and may lead to the development of natural concentration-induced convection which interacts with the rising flow (forced convection). The stability threshold of the forced flow and the effect on it of natural convection that arises are determined. It is shown that at intense flow to the evaporation surface the admixture concentration increases at this boundary rapidly and reaches the saturation concentration. In this case, the admixture precipitates. In the slow evaporation regime the admixture diffuses from the high-concentration region, which prevents the development of convective flow.     

Accumulation and Precipitation of Salts during Groundwater Evaporation and Flow

A mathematical model for the precipitation of dissolved salts during groundwater evaporation is proposed. An asymptotic solution of the problem is obtained for a specified flow law. It is shown that there are two different regimes of solute precipitation which are determined by the evaporation front velocity and the groundwater flow rate. The dependence of the precipitated salt mass on the soil surface temperature, the atmospheric humidity, the initial solute concentration and the filtration rate is illustrated.     

Effect of Efflorescence Formation on Drying Kinetics of Porous Media

We study experimentally the evaporation of an aqueous NaCl solution with efflorescence formation in hydrophilic or hydrophobic two-dimensional model porous media. The efflorescence formation only marginally affects the invasion patterns but greatly modifies the drying kinetics compared to pure water. Two mechanisms are identified for explaining the impact of efflorescence formation on drying kinetics. It is shown that the efflorescence contributes to increase the evaporation rate compared to drying with pure water, a surprising result since the water activity is reduced in the presence of dissolved salt. This effect is explained by the efflorescence liquid capillary pumping effect associated with the porous nature of the efflorescence. Then, we identify a second phase where the efflorescence dries out and acts as a vapour diffusion barrier, leading to a dramatic reduction of evaporation rate.     

Effect of Rainfall-Induced Soil Seals on the Soil Water Regime: Drying Interval and Subsequent Wetting

The effects of rainfall-induced soil seals on drying processes and on infiltration following drying intervals are simulated for two different soils, a loam and a sandy loam. The simulated drying processes include water content redistribution without evaporation and under a constant evaporation rate of 5 mm day^–1. During evaporation, the water content at the seal surface decreases rapidly. A high water content gradient develops within the seal, which increases along the drying interval. It indicates that, at least during the first hours of drying, the seal layer fulfilled all the evaporation demand and therefore dries faster that an unsealed soil where the evaporation is supplied by a much deeper zone of the soil profile. This phenomenon is more accentuated in the loam than in the sandy loam soil. Considering the subsequent infiltration curves during rainfall following different drying intervals, the ponding time and the post-ponding infiltration rates increase when the antecedent drying period is longer, but no significant effect on the final infiltration is found following drying intervals of few days. Also, the water content at the sealed soil surface before rainfall seems to play a major role on infiltration. Very close infiltration curves were obtained after different drying intervals that ended with similar surface water content.     

在蒸发条件下土壤水盐运动的数值模拟

本研究对土壤中水盐运动对流扩散方程进行了数值计算。利用省时的一阶精度的特征-分步法及使对流项作保留迎风特性的二阶精度的差分法,对在蒸发条件下土壤盐分向上运动积盐过程进行模拟,两个方法的计算结果与实验结果总体上都重合较好。     

Heterogeneity Effects on Evaporation-Induced Halite and Gypsum Co-precipitation in Porous Media

Understanding evaporation from porous media in the presence of soluble salts plays a key role in describing many environmental processes. Several studies done in this field led to a wide acceptance that the prediction of soil salinization driven by evaporation from the unsaturated zone and mainly encountered in arid and semiarid regions is a challenging task because of the temporal and spatial variabilities of soil rocks combined with different interactions between the porous medium and the atmosphere. In this work, we present a reactive transport model developed with the aim of describing the processes of evaporation, salt accumulation and precipitation. We took the model presented in our previous paper (Jambhekar et al. in Transp Porous Media 114:341–369, 2016) as the basis and developed it with the required geochemical model to account for evaporative salt co-precipitation. The salts considered in this work are halite (NaCl) and gypsum (CaSO\(_{4}\cdot 2\mathrm{H}_{2}\)O). We focus particularly on the influence of spatial heterogeneities in the porous medium on the dynamics of the physical processes. In the numerical simulations performed in this work, we distinguished different heterogeneity configurations. The results show that the drying from heterogeneous porous media initially affects the coarser pores, where the salt crystals first appear.     

Numerical Analysis of Laminar-Turbulent Transition in a Circular Pipe with Periodic Inflow Perturbations

The problem of the spatio-temporal evolution of perturbations introduced into the inlet cross-section of a circular pipe is solved numerically. The case of time-periodic inflow perturbations is considered for Re = 4000. It is shown that for relatively small inflow perturbations periodic flow regimes and for greater perturbations chaotic regimes are established.Periodic regimes the flow is a superposition of steady flow and a damped wave propagating downstream. The velocity profile of the steady component differs essentially from both the parabolic Poiseuille and developed turbulent flows and is strongly inhomogeneous in the angular direction. The angular distortion of the velocity profile is caused by longitudinal vortices developing as a result of the nonlinear interaction of inflow perturbations.Chaotic flow regimes develop when the amplitude of the inflow perturbations exceeds a certain threshold level. Stochastic high-frequency pulsations appear after the formation of longitudinal vortices in the regions of maximum angular gradient of the axial velocity. In the downstream part of the flow, remote from the transition region, the developed turbulent regime is formed. The distributions of all the statistical moments along the pipe level off and approach the values measured experimentally and calculated numerically for developed turbulent flows.     

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.     

Symmetry Solutions for Transient Solute Transport in Unsaturated Soils with Realistic Water Profile

We examine solutions for solute transport using the convection-dispersion equation (CDE) during steady evaporation from a water table. It is common, when solving the CDE, to first approximate the volumetric water content of the soil as a constant. Here, we assume a reasonable function for the water content profile and construct realistic nonlinear hydraulic transport properties. Both classical and nonclassical symmetry techniques are employed. Invariant solutions are obtained for the one dimensional CDE even with a nontrivial background profile for volumetric water content.     

Interaction of wetting fronts with an impervious surface — Longer time behaviour

The interaction of a wetting front with an impervious surface can be described very easily in the early stages of interaction by using a superposition principle. After the time when the superposition principle fails to describe the interaction properly, two flow regimes are analysed. For most of the interaction the profile is only affected by the impervious surface near that surface and in particular the inflow into the soil layer is unchanged. Then, only at the very end of the process is the inflow decreasing because of the impervious surface.     

Impact of Capillary-Driven Liquid Films on Salt Crystallization

Flow-through drying of ionic liquids in porous media can lead to super saturation and hence crystallization of salts. A model for the evolution of solid and liquid concentrations of salt, in porous media, due to evaporation by gas flow is presented. The model takes into account the impact of capillary-driven liquid film flow on the evaporation rates as well as the rate of transport of salt through those films. It is shown that at high capillary wicking numbers and high dimensionless pressure drops, supersaturation of brine takes place in the higher drying rate regions in the porous medium. This leads to solid salt crystallization and accumulation in the higher drying rate region. In the absence of wicking, there is no transport and accumulation of solid salt. Results from experiments of flow-through drying in rock cores are compared with model prediction of salt crystallization and accumulation.     

Injection of a salt solution into a geothermal reservoir saturated with superheated vapor

The injection of water containing a dissolved admixture into a high-temperature geothermal reservoir saturated with superheated vapor is considered. Behind the evaporation front on which the admixture precipitates a dissolution front separating regions with the initial concentration and with the concentration of the saturated solution coexisting with the solid salt phase is formed. It is found that the self-similar solution of the problem with two moving boundaries is two-valued. With variation of the parameters and the initial and boundary conditions the solutions may approach each other and at certain critical values merge. In the supercritical region the self-similar solution does not exist. The non-existence of a solution can be interpreted as the filling of the pores with precipitated salt and the cessation of the phase motion.     

An experimental investigation of combined turbulent free and forced evaporation

The wide variation in correlations available in the literature for predicting water evaporation rates in a moving air stream necessitated a new investigation to determine which correlations can be considered reliable. Water evaporation measurements were made from a heated pool (a class-A pan) into a low speed wind tunnel. The evaporation regime examined combined turbulent free and turbulent forced convection over the range 0.1 < Gr_m/Re² < 10.0. The data includes the range in which combined convection modes are important, as well as the limits where either free or forced convection effects may dominate. The data are compared to several evaporation correlations based on laboratory wind tunnel data. These historical correlations do not produce consistent estimates in predicting evaporation rates. It is believed that the apparent inconsistencies arise because many correlations do not adequately describe the appropriate evaporation regimes for which they are valid. A new correlation using the combined free/forced convection Sherwood number has been developed to predict evaporation rates for a moving air stream. This correlation allows the results of this study to be extended to other evaporating conditions (i.e. variation in surface geometry and air turbulence levels) than those described here. For a 95% confidence limit, the Sherwood number correlation matches the data within ±7.9%.     

On Ions Transport during Drying in a Porous Medium

Salt crystallisation at the surface or in a porous medium has been recognised as a major mechanism of deterioration of buildings and historical monuments. Often crystallisation occurs when the concentration of salt dissolved in the water contained in the porous medium reaches the saturation concentration as the result of evaporation. In order to predict the evolution of the ion distribution during drying, we develop a simple volume averaged model combining a semi-analytical model of drying with the numerical computation of the ions transport. The model is used to analyse the influence of the drying rate, size of the porous medium, average pore size and initial ion concentration on the ion distribution during drying and therefore the possible location of crystallisation.     

Calculation of channel flow with wall evaporation induced by radiative-conductive heat transfer

Below, a flow model and a method of calculating the flow in a narrow plane channel of finite length in the presence of evaporation or sublimation on one wall induced by radiative-conductive heat transfer from the other hot wall are proposed. The Prandtl approximation is employed. The pressure difference between the center and the exit section of the channel is of the order of the characteristic value of the pressure in it. Subcritical and critical vapor outflow regimes are considered. The effect of the problem parameters on the evaporation rate and pressure distributions in the channel is investigated numerically.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 27–34, September–October, 1993.     

Mathematical modeling of near-wall flows of two-phase mixture with evaporating droplets

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Evaluation of Model Concepts to Describe Water Transport in Shallow Subsurface Soil and Across the Soil–Air Interface

Soil water evaporation plays a critical role in mass and energy exchanges across the land–atmosphere interface. Although much is known about this process, there is no agreement on the best modeling approaches to determine soil water evaporation due to the complexity of the numerical modeling scenarios and lack of experimental data available to validate such models. Existing studies show numerical and experimental discrepancies in the evaporation behavior and soil water distribution in soils at various scales, driving us to revisit the key process representation in subsurface soil. Therefore, the goal of this work is to test different mathematical formulations used to estimate evaporation from bare soils to critically evaluate the model formulations, assumptions and surface boundary conditions. This comparison required the development of three numerical models at the REV scale that vary in their complexity in characterizing water flow and evaporation, using the same modeling platform. The performance of the models was evaluated by comparing with experimental data generated from a soil tank/boundary layer wind tunnel experimental apparatus equipped with a sensor network to continuously monitor water–temperature–humidity variables. A series of experiments were performed in which the soil tank was packed with different soil types. Results demonstrate that the approaches vary in their ability to capture different stages of evaporation and no one approach can be deemed most appropriate for every scenario. When a proper top boundary condition and space discretization are defined, the Richards equation-based models (Richards model and Richards vapor model) can generally capture the evaporation behaviors across the entire range of soil saturations, comparing well with the experimental data. The simulation results of the non-equilibrium two-component two-phase model which considers vapor transport as an independent process generally agree well with the observations in terms of evaporation behavior and soil water dynamics. Certain differences in simulation results can be observed between equilibrium and non-equilibrium approaches. Comparisons of the models and the boundary layer formulations highlight the need to revisit key assumptions that influence evaporation behavior, highlighting the need to further understand water and vapor transport processes in soil to improve model accuracy.

     

Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls

Particle migration in a horizontal flow of dilute suspension through a vertical slot with porous walls is studied using the two-continua approach. The lateral migration is induced by two opposite effects: an inertial lift force due to particle settling and directed toward the slot centre-line, and a drag due to leak-off entraining particles toward the walls. An expression for the inertial lift on a settling particle in a horizontal channel flow found recently is generalized to the case of a low leak-off velocity. The evolution of an initial uniform particle concentration profile is studied within the full Lagrangian approach. Four migration regimes are found differing by the direction of particle migration and numbers of equilibrium positions. Conditions of the regime change and a critical value of dimensionless leak-off velocity for particle deposition on the walls are obtained analytically. Suspension flows with zones where the particle concentration is zero or increases infinitely, are studied numerically.     

Modeling and Simulation of Effects of Turbulence on Vaporization, Mixing and Combustion of Liquid-Fuel Sprays

The objective of this work is twofold. Firstly, the effects of turbulence intensity variations on the turbulent droplet dispersion, vaporization and mixing for non-reacting sprays (with and without swirl) are pointed out. Secondly, the effects of the coupling of the turbulence modulation with external parameters, such as swirl intensity, on turbulent spray combustion are analyzed in configurations of engineering importance. This is achieved by using advanced models for turbulence, evaporation and turbulence modulation implemented into FASTEST-LAG3D-codes: (1) To highlight the influence of turbulence modulation on some spray properties, a thermodynamically consistent modulation model has been considered besides the standard assumption and the well known Crowe's model. For turbulent droplet dispersion, we rely on the Markov-sequence formulation. (2) In order to characterize phase transition processes ongoing on droplets surfaces, a non-equilibrium evaporation model shows better agreement with experiments in comparison with the quasi-equilibrium-based evaporation models often used. (3) The results of turbulence intensity variations reveal the existence of a limited range out of which the increase or decrease of the turbulence intensity affects no more the efficiency of the heat and mass transfer. A derived characteristic number, a vaporization Damkhöler number, possesses a critical value which separates two different behavior regimes with respect to the turbulence/droplet vaporization interactions. (4) Under reacting conditions, it is shown how the evaporation characteristics, mixing rate and combustion process are strongly influenced by swirl intensity and turbulence modulation. In particular, the turbulence modulation modifies the evaporation rate, which in turn influences the mixing and the species concentration distribution. In the case under investigation, it is demonstrated that this effect cannot be neglected for low swirl intensities (Sw.Nu. ≤ 1) in the region far from the nozzle, and close to the nozzle for high swirl number intensities. In providing these particular characteristics, a reliable control of the mixing of gaseous fuel and air in evaporating and reacting sprays, and a possible optimization of the mixing process can tentatively be achieved.