Evaporation Front Research Articles

THE STABILITY OF EVAPORATING FRONTS IN POROUS MEDIA

Evaporating fronts in porous media occur during drying processes, underground coal gasification, geothermal energy production from hot, dry rock, and around nuclear waste repositories. The stability of such fronts is pertinent to understanding the heat and mass transfer at the front. This article reports the results of linear stability analyses of evaporating fronts in infinite and semi-infinite domains. For the case of an infinite domain, subcooled or saturated liquid flows toward hot matrix rock above the saturation temperature, resulting in a moving evaporation front. For the semi-infinite domain, subcooled or saturated liquid flows toward a surface maintained at a temperature above the saturation temperature. For the infinite domain and an evaporating front normal to the gravitational vector, the front can be destabilized by gravity when a dense liquid overlies a less dense vapor. Whether the flow is vertical or horizontal, the front can be destabilized by mobility. It is demonstrated that evaporation, as characterized by the vapor phase Jakob number, has a destabilizing effect on mobility, however, this is countered by a stabilizing effect due to heat transfer at the interface. The stabilizing effect of heat transfer can dominate destabilizing effects of mobility and gravity at large wave numbers. For the semi-infinite domain, a stationary front can be shown to exist under certain conditions, and in this case, the stabilizing effect of heat transfer is always greater than the destabilizing effect of mobility for a fluid having the properties of water over a wide range of pressures. © 2010 Begell House, Inc.

THREE-DIMENSIONAL MODELING OF THE EVAPORATIONOFVOLATILE HYDROCARBONS FROM ANISOTROPIC POROUS MEDIA

Lean gas injection has been considered as a process to improve the recovery of residual volatile hydrocarbons from fractured petroleum reservoirs. The characterization and modeling of flow and mass transfer in fractured reservoirs are challenging tasks due to the complexity of the pore space, the anisotropy in the permeability of the rock, as well as the complex interplay between capillary, viscous, and buoyancy forces. In this contribution we develop a three-dimensional pore-network model that accounts for evaporation and diffusion of volatile liquids trapped in anisotropic pore networks. We investigate the effect of permeability gradients on the saturation profiles, the recovery rates, the evaporation patterns, and the stability of the receding evaporation fronts. It is shown that permeability gradients affect the stability of the evaporation front. When the permeability decreases in the direction of the receding evaporation front, then the front is stable and recedes in a piston-like manner, where a two-phase region of finite size develops early in the drying process. The size of this region depends on a permeability-based bond number defined in this paper. In the opposite case, where the permeability increases in the direction of the receding evaporation front, the liquid-gas interface becomes unstable and produces finger-like patterns. The thickness of these fingers is a function of the permeability-based bond number.

Fundamental characterization of evaporative water removal from fuel cell diffusion media

In polymer electrolyte fuel cell systems, a gas purge commonly is applied to remove excess water and achieve high performance and durability. The porous diffusion media (DM) typically store a significant fraction of the total liquid water during operation, but quantitative fundamental research examining water removal behavior from DM is not yet available in literature. The objective of this study is to investigate the fundamental behavior of evaporative water removal from fuel cell diffusion media with a special test rig developed to minimize in-plane gradients so that through-plane evaporative behavior can be analyzed. Evaporative water removal was characterized by a surface evaporation region, a constant evaporation rate region characterized by capillary flow to the evaporation front, and a falling rate region characterized by separated evaporating droplets. A semi-empirical correlation for the characteristic water removal, a generic plot of purge efficiency which describes the effectiveness of purge parameters, and a potential scheme for a more durable and less parasitic purge which describes characteristic water removal of each fuel cell component were developed. The results of this study can be used to predict and understand water removal from diffusion media and help develop a less parasitic purge protocol than presently utilized.

Intense fracturing and fracture sealing induced by mineral growth in porous rocks

Mineral precipitation in the pores of a rock may exert a force, which is called crystallization pressure. This process has been studied experimentally and results bring a new look on the way fractures may develop and seal in natural systems. Cylindrical core samples of porous limestone and sandstone were left for several weeks in contact with an aqueous solution saturated with sodium chloride, at 30 or 45 °C, under axial normal stress in the range 0.02–0.26 MPa. The fluid was allowed to rise in the core samples by capillary forces, up to a controlled height where evaporation and precipitation occurred. The uniaxial deformation of the samples was measured using high-resolution displacement sensors. The samples were characterized using computed X-ray tomography, allowing therefore imaging in 3D the intensity and localization of the damage. Two kinds of damage could be observed. Firstly, small rock fragments were peeled from the sample surface. Secondly, and more interestingly, fracture networks developed, by nucleation of microcracks at the interface where evaporation occurred, and propagation to the free surface. Two families of fractures could be identified. A first set of sealed fracture parallel to the evaporation front is directly induced by crystallization pressure. A second fracture network, perpendicular to the evaporation front, accommodates the first set of fractures. An analytical model where fluid flow is coupled to evaporation, vapour transport, and localization of mineral precipitation explains the shape of this fracture network.

COMBINED MODELING OF ACCELERATION, TRANSPORT, AND HYDRODYNAMIC RESPONSE IN SOLAR FLARES. I. THE NUMERICAL MODEL

Acceleration and transport of high-energy particles and fluid dynamics of atmospheric plasma are interrelated aspects of solar flares, but for convenience and simplicity they were artificially separated in the past. We present here self-consistently combined Fokker-Planck modeling of particles and hydrodynamic simulation of flare plasma. Energetic electrons are modeled with the Stanford unified code of acceleration, transport, and radiation, while plasma is modeled with the Naval Research Laboratory flux tube code. We calculated the collisional heating rate directly from the particle transport code, which is more accurate than those in previous studies based on approximate analytical solutions. We repeated the simulation of Mariska et al. with an injection of power law, downward-beamed electrons using the new heating rate. For this case, a ~10% difference was found from their old result. We also used a more realistic spectrum of injected electrons provided by the stochastic acceleration model, which has a smooth transition from a quasi-thermal background at low energies to a nonthermal tail at high energies. The inclusion of low-energy electrons results in relatively more heating in the corona (versus chromosphere) and thus a larger downward heat conduction flux. The interplay of electron heating, conduction, and radiative loss leads to stronger chromospheric evaporation than obtained in previous studies, which had a deficit in low-energy electrons due to an arbitrarily assumed low-energy cutoff. The energy and spatial distributions of energetic electrons and bremsstrahlung photons bear signatures of the changing density distribution caused by chromospheric evaporation. In particular, the density jump at the evaporation front gives rise to enhanced emission, which, in principle, can be imaged by X-ray telescopes. This model can be applied to investigate a variety of high-energy processes in solar, space, and astrophysical plasmas.

Chemodynamical evolution of gas near an expanding HII region

A self-consistent model for the chemical-dynamical evolution of a region of ionized hydrogen around a massive young star and of the surrounding molecular gas is presented. The model includes all main chemical and physical processes, namely the photoionization of atomic hydrogen, photodissociation of molecular hydrogen and other molecules, and the evaporation of molecules from the mantles of dust particles. Heating and cooling processes are taken into account in the temperature calculations, including cooling in molecular and atomic lines. The hydrodynamical equations were solved using the Zeus2D hydrodynamical software package. This model is used to analyze the expansion of a region of ionized hydrogen around massive stars (effective temperature of 30 000 and 40 000 K) in a medium with various initial density distributions. The competition between evaporation from dust mantles and the photodissociation of molecules results in the formation of a transition layer between the hot HII region and cool quiescent medium, characterized by high abundances of molecules in the gas phase. The thickness of the transition layer is different for different molecules. Since there is a velocity gradient along the transition layer, and the maxima in the distributions of different molecules are at different distances from the star, observations of molecular emission lines should reveal distinction in shifts of lines of different molecules relative to the velocity of the quiescent gas. Such shifts have indeed been detected during molecular observations of the region of ionized hydrogen Sh2-235. For an initial gas density of 103 cm−3, the increase in the abundances of H2O and H2CO in the transition layer after desorption from dust occurs gradually rather than in a jump-like fashion; therefore, the concept of a “evaporation front” can be used only formally. In addition, the distances between the evaporation fronts for different molecules are significant. At higher initial gas densities (104 cm−3), sharp evaporation fronts are formed for the different molecules, which are close to each other and to the shock front. In this case, it is possible to speak of a single evaporation front for CO, H2O, and H2CO.

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation. The model’s predictions are validated in multi-dimensions against experiments of high velocity projectile impact onto a liquid tank. Simulations are compared to experiments and reveal excellent quantitative agreement regarding shock and cavitation pocket dynamics as well as projectile deceleration versus time. Then model’s capabilities are illustrated for flow computations around underwater missiles.

MHD STABILITY OF INTERSTELLAR MEDIUM PHASE TRANSITION LAYERS. I. MAGNETIC FIELD ORTHOGONAL TO FRONT

We consider the scenario of a magnetic field orthogonal to a front separating two media of different temperatures and densities, such as cold and warm interstellar gas, in a 2-D plane-parallel geometry. A linear stability analysis is performed to assess the behavior of both evaporation and condensation fronts when subject to incompressible, corrugational perturbations with wavelengths larger than the thickness of the front. We discuss the behavior of fronts in both super-Alfvenic and sub-Alfvenic flows. Since the propagation speed of fronts is slow in the ISM, it is the sub-Alfvenic regime that is relevant, and magnetic fields are a significant influence on front dynamics. In this case we find that evaporation fronts, which are unstable in the hydrodynamic regime, are stabilized. Condensation fronts are unstable, but for parameters typical of the neutral ISM the growth rates are so slow that steady state fronts are effectively stable. However, the instability may become important if condensation proceeds at a sufficiently fast rate. This paper is the first in a series exploring the linear and nonlinear effects of magnetic field strength and orientation on the corrugational instability, with the ultimate goal of addressing outstanding questions about small-scale ISM structure.

Laminar premixed spray flame analysis with thermally sensitive intermediate kinetics

A new thermo-diffusive analysis of one-dimensional laminar lean or rich off-stoichiometric premixed spray flames has been performed using a chain branching/chain breaking chemical kinetic scheme and under the assumption that the fuel droplets evaporate in a sharp front. The sensitivity of the flame structure, speed and the location of the evaporation front to the initial droplet load have been demonstrated. A linear stability analysis reveals the way in which the spray's presence modifies the neutral stability curves.

Charge separation at evaporation and vapor growth of ice and water

A mathematical model of the interface charging at evaporation and growth of ice and water phases from vapor is proposed. This model takes into account the competition between the two mechanisms of charge separation, one of which is based on protons and the other involves orientational defects. The first mechanism leads to the accumulation of a positive charge by ice and water during evaporation, while the second one provides negative charge accumulation. The protonic mechanism dominates at low velocities of the evaporation front with respect to the condensed phase material (lower than 10−11–10−9 m/s). At high rates, the mechanism based on orientational defects is dominant. When vapor is condensed, and, correspondingly, the ice and water phases grow, the charge polarity is opposite to the polarity in the case of evaporation. The proposed model adequately describes the experimentally observed interface electric current and the signs of phase charges during evaporation and condensation.

Bread baking as a moving boundary problem. Part 2: Model validation and numerical simulation

A simultaneous heat and mass transfer model proposed to describe the bread baking process is validated. The mathematical model is based on a moving boundary problem formulation with equivalent thermophysical properties and includes the moving evaporation front, the evaporation–condensation mechanism and the development of the crust observed during bread baking. The problem is solved over an irregular three-dimensional geometry using the finite element method. Variation in temperature and water content of bread during baking is predicted with high accuracy by the model. Parameter estimation procedure and sensitivity analysis are performed for some thermophysical properties. The proposed formulation and analysis can be applied for other bakery products as well as for similar food engineering applications.

Bread baking as a moving boundary problem. Part 1: Mathematical modelling

A mathematical model for the bread baking process is developed in this work. Experimental data (temperature, water content, weight loss, crust thickness) obtained during baking is used to well understand the simultaneous heat and mass transfer occurring during the process. The evaporation–condensation mechanism is responsible for the rapid heating of the porous matrix and takes place either in a closed (dough) or open (crumb) structure. The existence of a moving evaporation front inside bread, which is a determining step of baking, is incorporated in a model applying a moving boundary formulation with equivalent thermophysical properties. The approach proposed here can be extended to other similar processes such as baking of other products (e.g. biscuit, cake), high-temperature drying, cooking and roasting.

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.

Vapor bubble growth at the surface of flat and cylindrical heaters

The growth dynamics are investigated of a sole vapor bubble in a nonuniform temperature field. A two-zone model is developed of the bubble growth on the solid surface. The calculation results are in satisfactory agreement with the experimental data available for the flat and cylindrical heaters. The influence is considered of the evaporation front occurring under high overheating on the bubble growth dynamics.

Laser shock processing: modeling of evaporation and pressure field developed in the laser-produced cavity

Laser shock processing during high-intensity beam ablation of the metallic surface is examined. The phase change due to evaporation and melting is modeled using an energy method. The vapor front expansion and pressure build-up in the laser-produced cavity are obtained numerically using a control volume approach. Elasto-plastic response of the substrate material due to mechanical loading of pressure field developed in the cavity is modeled and predicted using a finite element method. It is found that a high-pressure region is developed in the vicinity of the cavity edge, which, in turn, results in excessive stresses and plastic strain in this region. The depth of the plastic region in the order of a few micrometers below the surface is predicted.

Modelling phase transition in metastable liquids: application to cavitating and flashing flows

A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

Planetesimal formation near the snow line in MRI-driven turbulent protoplanetary disks

The formation of planetesimals in protoplanetary disks due to collisional sticking of smaller dust aggregates has to face at least two severe obstacles, namely the rapid loss of material due to radial inward drift and particle fragmentation due to destructive collisions. We present a scenario to circumvent these two hurdles. Our dust evolution model involves two main mechanisms. First, we consider a disk with a dead zone. In an almost laminar region close to the midplane, the relative velocities of the turbulent particles are comparatively small, which decreases the probability of destructive particle collisions. Second, turbulence is not the only source of violent relative particle velocities, because high radial drift speeds can also lead to boulder fragmentation. For this reason, we focus additionally on the snow line. Evaporation fronts can be associated with gas pressure maxima in which radial drift basically vanishes. This implies that particle fragmentation becomes even less likely. Our simulation results suggest that particles can overcome the fragmentation barrier. We find that boulders of several 102 m can form within only a few thousand years.

Numerical and experimental investigation of heat and mass transfer in unsaturated porous media with low convective drying intensity

AbstractThe heat and mass transfer in an unsaturated wet cylindrical bed packed with quartz particles was investigated theoretically and experimentally for relatively low convective drying rates. The medium was dried by blowing dry air over the top of the porous bed which was insulated by impermeable, adiabatic material on the bottom and sides. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi‐phase flow in the unsaturated porous medium using the energy and mass conservation equations for heat and mass transfer during the drying. The drying model included convection and capillary transport of the moisture, and convection and diffusion of the gas. The wet and dry regions were coupled with a dynamic boundary condition at the evaporation front. The numerical results indicated that the drying process could be divided into three periods: the initial temperature rise period, the constant drying rate period, and the reduced drying rate period. The numerical results agreed well with the experimental data, verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. ©2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(5): 290–312, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20205

Distribution of the intensity absorbed by evaporative front in laser cutting nonmetallic material

The distribution of the intensity absorbed by the evaporative cutting front is investigated using ray-tracing method after the laser beam undergoes multiple reflections in an actual kerf photographed experimentally. The laser beam is characterized by focused Gauss beam. Fresnel absorption on the kerf is taken into account, while inverse bremsstrahlung absorption is negligible. The influences of the times of multiple reflections and laser beam's position on the absorbed intensity are also discussed. Results indicate front intensity absorption is mainly determined by the first three incident beams. The laser axis moves toward the front, which is affected by the cutting speed.

Third heat transfer crisis at subcooling

The effect of liquid subcooling below the saturation temperature on the third heat transfer crisis was studied experimentally at pool boiling. Experimental data on the threshold values of superheating and heat fluxes, above which the evaporation front and third heat transfer crisis for acetone at subcooling from 0.3 to 10 K are formed, were shown. Formation of evaporation fronts is the necessary, but not sufficient condition for the third heat transfer crisis at subcooling. It was found that formation of a stable vapor film after propagation of condensation fronts over the heater surface is possible at heat fluxes considerably lower than the first critical one.