Three-dimensional numerical simulation of fluid flow with phase change heat transfer in an asymmetrically heated porous channel

Fluid flow with phase change heat transfer in a three-dimensional porous channel with asymmetrically heating from one side is numerically studied in this paper. The “modified” Kirchhoff method is used to deal with the spatial discontinuity in the thermal diffusion coefficient in the energy equation. The velocity and temperature fields, as well as the liquid saturation field on the heated section of the wall with different Peclet and Rayleigh numbers are investigated. The results show that the liquid flow bypasses the two-phase zone, while the vapor flows primarily to the interface between the sub-cooled liquid zone and the two-phase zone. An increase in the Peclet number decreases the two-phase region while an increase in the Rayleigh number helps to spread the heat to a larger region of the domain. The distribution of the liquid saturation on the heated section of the wall indicates that the minimum liquid saturation increases with the increase of both the Peclet and Rayleigh numbers.     

Fluid inclusions in minerals from the geothermal fields of Tuscany,Italy

A reconnaissance study on fluid inclusions from the geothermal fields of Tuscany indicates that the hydrothermal minerals were formed by fluids which were, at least in part, boiling. Four types of aqueous inclusions were recognized: (A) two-phase (liquid + vapor) liquid rich, (B) two-phase (vapor + liquid) vapor rich, (C) polyphase hypersaline liquid rich and (D) three phase—H₂O liquid + CO₂ liquid + CO₂-rich vapor. Freezing and heating microthermometric determinations are reported for 230 inclusions from samples from six wells. It is suggested that boiling of an originally homogeneous, moderately saline, CO₂-bearing liquid phase produced a residual hypersaline brine and a CO₂-rich vapor phase. There are indications of a temperature decrease in the geothermal field of Larderello, especially in its peripheral zones.     

Supercritical phases of hydrogen

Using experimental data from literature [1], hydrogen density-pressure (ρ-P) and density-temperature (ρ-T) phase diagrams were drawn and evaluated for various pressure and temperature intervals. Solid, liquid, vapor, gas, supercritical liquid, supercritical gas and supercritical fluid regions were identified on the obtained diagrams. There are exact equilibrium boundaries between subcritical phases. On the contrary, it is concluded that there are no such exact boundaries for supercritical phases. Formation of the supercritical fluid between liquid and gas phases explained thermodynamically with first and second order partial derivatives of chemical potential relative to pressure at constant temperature.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

Two-dimensional flow modelling of a thin slice kettle reboiler

The two-fluid model is applied to a thin sliced kettle reboiler. The tube bundle is treated as a porous medium in which the drag coefficient and tube-wall force are deduced from the empirically-based, one-dimensional model. Methods available in the open literature are used in the two-phase pool surrounding the tube bundle. The predictions are verified by comparing them with experimental data and models available in the open literature.The boundary condition applied at the free surface of the pool is found to be crucial in determining the flow pattern within it. When only liquid re-enters through the boundary an all-liquid pool results. Comparison with the experimental evidence suggests that this boundary condition corresponds to bubbly flow within the tube bundle. Allowing a predominantly vapour re-entry produces a two-phase pool that is consistent with intermittent flow in the tube bundle. When the appropriate boundary condition is applied, the two-fluid model predictions are shown to reproduce the visual records and pressure drop measurements reasonably accurately.     

Modeling and experimental investigation of looped separate heat pipe as waste heat recovery facility

A looped separate heat pipe as waste heat recovery facility for the air-conditioning exhaust system has been developed in this work. A one-dimensional steady-state model is presented for determining the upper and lower operating boundaries of the initial filling ratio of the working fluid, as a function of the separate heat pipe geometry, vapor temperature of working fluid and power throughput, combined with two-phase heat exchange characteristics and distribution of the liquid film velocity along with the liquid film thickness direction. A parametric analysis is performed to investigate the effects of the length of the evaporator, vapor temperature, and power throughput on the critical values of the upper and lower boundaries. Simulation results show that the length of the evaporator makes almost no influence on the upper boundary, but great effect on the lower boundary. An increase of the vapor temperature leads to the easier arriving of the lower boundary. Moreover, operation ranges of the separate heat pipe vary with the working fluids. Water and methanol were used separately. An experiment was implemented to validate the simulated results. The numerical predictions compare favorably with experimental results.     

Laminar film condensation on an elliptical tube embedded in porous media

Laminar film condensation of saturated vapor flowing over an isothermal elliptical tube embedded in a porous medium is analyzed for conditions of free and forced convection. The flow field in the porous medium is described by the Darcy–Brinkman–Forchheimer model. The effect of vapor shear on condensation is determined by simultaneous solution of the two phase vapor boundary layer and condensate film momentum equations. The numerical results, which are presented in the form of local film thickness and local Nusselt number, show a dependence of these physical parameters on practical dimensionless parameters such as Reynolds number, Darcy number, Bond number and eccentricity.     

Self-similar condensing flows in porous media

Similarity solutions are obtained for the propagation of a condensation wave into an initially dry porous matrix which receives an inflow of saturated vapor due to a step increase in temperature and pressure at the boundary. The generalized Darcy (low Reynolds number) formulation of two-phase flow leads to hyperbolic/parabolic equations in which capillarity and heat conduction are suppressed in order to emphasize the shock-like behavior. Application of the x/√t similarity transformation gives ordinary differential equations which are solved by shooting methods, using jump-balance (Rankine-Hugoniot) conditions to preserve discontinuities in saturation (quality), pressure gradient and sometimes temperature. The distribution of condensate (saturation) is wave-shaped, with a forward-facing shock on the leading side. For a small temperature difference, there is little condensate and it is nearly immobile; the saturation shock lies close to the boundary, and the outer region is described by a reduced system of equations. With increasing temperature difference, the shock moves forward into the flow and gains in strength until the medium is liquid-full behind the shock. Beyond this, the shock splits into a pair of back-to-back shocks separated by a subcooled liquid slug. The considered prototypic problem is representative of a broad class of two-phase flows which occur in energy-related and geologic applications.     

Effects of capillary forces on laminar filmwise condensation on horizontal disk in porous medium

This study investigates the problem of steady filmwise condensation on a horizontal disk embedded in a porous medium. The disk surface is cold and faces upwards into the porous medium, which is filled with a dry vapor. Due to the effects of capillary forces in the porous medium, a two-phase zone is formed between the liquid film and the vapor zone. As in the classical filmwise condensation problem, this study assumes that the inertia within the liquid film is negligible and that the properties of the porous medium, dry vapor, and condensate are constant. Darcy’s law is used to analyze the liquid flow in both the liquid film and the two-phase zone. A capillary parameter, Bo_c, is introduced to characterize the liquid flow caused by capillary forces in the porous medium. It is shown that the mean Nusselt number, , increases at higher values of the capillary parameter, Bo_c. Finally, this study derives a simple closed form correlation for the Nusselt number for the case where the capillary forces are neglected.     

Transient two-phase flow and heat transfer with localized heating in porous media

The transient behavior of two-phase flow and heat transfer in a channel filled with porous media was numerically studied in this paper. Based on the two-phase mixture model, numerical solutions were obtained using the Finite-Volume Method (FVM). Two methods to treat the discontinuous diffusion coefficient in the energy equation, i.e. the harmonic mean method and the “modified” Kirchhoff method were compared. It was found that the “modified” Kirchhoff method was better in dealing with the rapid change in the diffusion coefficient. Three different cases, with discrete heat flux applied at (1) the upper wall, (2) lower wall and (3) both the upper and lower walls were studied. The velocity and temperature fields for these cases were discussed. The results show that the liquid and vapor flow fields, as well as the temperature and liquid saturation fields have distinctly different features with the change in heating location. An analysis of the vapor volume fraction indicates that the largest amount of vapor with the highest vapor generation rate was for the case in which the heat flux is applied from the lower wall.     

A two-dimensional model of the kettle reboiler shell side thermal-hydraulics

A two-dimensional two-fluid numerical model is developed for the prediction of two-phase flow thermal-hydraulics on the shell side of the kettle reboiler. The two-phase flow around tubes in the bundle is modeled with the porous media approach. A closure law for the vapour–liquid interfacial friction is based on modified pipe two-phase flow correlations. The tube bundle flow resistance is calculated by applying to each phase stream the correlations for the pressure drop in a single phase flow across tube bundles and by taking into account the separate contribution of each phase to the total pressure drop. Physically based boundary conditions for the velocity field at the two-phase mixture swell level are stated. The system of governing equations is solved numerically with the finite volume approach for two-phase flow built in the commercial computer program. Simulations are performed for available conditions of performed physical experiments. In comparison to the previous kettle reboiler two-dimensional modeling approaches, here presented model is original regarding the applied closure laws for the interfacial friction and bundle flow resistance, as well as applied boundary conditions for the modeling of two-phase mixture free surface. Also, regarding the previous published results, here obtained numerical results are compared with the available measured data of void fraction within the tube bundle and acceptable agreement is shown.     

Numerical and experimental investigation of paper drying: Heat and mass transfer with phase change in porous media

The physics of paper drying combines heat and mass transfer with phase change in wet porous media. The drying processes can be modeled with the liquid and vapor mass conservation equation, the liquid–gas mixture mass conservation equation, and the energy conservation equation. The drying model of paper includes the convection and the capillary transport of liquid and the convection and the diffusion transport of gas and vapor. Numerical simulation and experimental investigation of whole paper drying are done on an actual paper machine. The drying parameters in boundary conditions including the temperature of outer surface of the cylinder, the temperature and the relative humidity of the air pocket were measured. The numerical results of paper sheet temperature of the first 26th cylinders and the final moisture content after 78 cylinders agree well with experimental data, which means the drying model is valid to predict the performance of paper drying.     

Investigation of the 3D model of coupled heat and liquid moisture transfer in hygroscopic porous fibrous media

This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory.     

Modeling of water transport through the membrane electrode assembly for direct methanol fuel cells

In this work, a one-dimensional, isothermal two-phase mass transport model is developed to investigate the water transport through the membrane electrode assembly (MEA) for liquid-feed direct methanol fuel cells (DMFCs). The liquid (methanol–water solution) and gas (carbon dioxide gas, methanol vapor and water vapor) two-phase mass transport in the porous anode and cathode is formulated based on classical multiphase flow theory in porous media. In the anode and cathode catalyst layers, the simultaneous three-phase (liquid and vapor in pores as well as dissolved phase in the electrolyte) water transport is considered and the phase exchange of water is modeled with finite-rate interfacial exchanges between different phases. This model enables quantification of the water flux corresponding to each of the three water transport mechanisms through the membrane for DMFCs, such as diffusion, electro-osmotic drag, and convection. Hence, with this model, the effects of MEA design parameters on water crossover and cell performance under various operating conditions can be numerically investigated.     

Analyses of heat and water transport interactions in a proton exchange membrane fuel cell

A two-phase non-isothermal model is developed to explore the interaction between heat and water transport phenomena in a PEM fuel cell. The numerical model is a two-dimensional simulation of the two-phase flow using multiphase mixture formulation in a single-domain approach. For this purpose, a comparison between non-isothermal and isothermal fuel cell models for inlet oxidant streams at different humidity levels is made. Numerical results reveal that the temperature distribution would affect the water transport through liquid saturation amount generated and its location, where at the voltage of 0.55 V, the maximum temperature difference is 3.7 °C. At low relative humidity of cathode, the average liquid saturation is higher and the liquid free space is smaller for the isothermal compared with the non-isothermal model. When the inlet cathode is fully humidified, the phase change will appear at the full face of cathode GDL layer, whereas the maximum liquid saturation is higher for the isothermal model. Also, heat release due to condensation of water vapor and vapor-phase diffusion which provide a mechanism for heat removal from the cell, affect the temperature distribution. Instead in the two-phase zone, water transport via vapor-phase diffusion due to the temperature gradient. The results are in good agreement with the previous theoretical works done, and validated by the available experimental data.     

Analysis of heat transfer for compressible flow in two-dimensional porous media

Gas from a reservoir at constant pressure and temperature is forced through a two-dimensional porous region. The surface through which the gas exits is at a specified uniform temperature and pressure. The local gas and solid matrix temperatures are assumed equal. General solutions for the local temperature and pressure in the porous medium are found as a function of a potential. This potential can be determined by solving Laplace's equation in the porous region for a simple set of boundary conditions, and the temperature and pressure will then be known functions of position. Because of the nature of the boundary conditions it is particularly convenient to solve Laplace's equation by conformai mapping. By using this technique some illustrative heat and mass flow results were calculated for a porous wall with a step in thickness, a wall supplied with gas through periodic slots, and an eccentric annular region.     

On the quasi-instantaneous aerodynamic load and pressure field measurements on turbines by non-intrusive PIV

An experimental technique is presented to non-intrusively measure the quasi-instantaneous aerodynamic loads and surrounding pressure field for a turbine by using particle image velocimetry (PIV). The PIV measurements provide the velocity flow field needed to calculate the pressure field around the turbine using three different methods. In the first method, the quasi-instantaneous and mean pressure fields are obtained by solving the Poisson equation and by calculating the boundary conditions from the Navier–Stokes equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradient. In the third method, the pressure is calculated using the Bernoulli equation. The experimental results are compared to aerodynamic load theoretical predictions from the Blade Element Momentum theory (BEM). An analysis of the experimental results showed the importance of the local acceleration, convective and pressure terms when calculating the forces and the pressure field in a stationary reference frame. Only the Poisson method includes all these terms, and had a small standard deviation between the calculated instantaneous forces. Furthermore, the Poisson method results are independent of the control volume size investigated while the other two experimental methods are affected. This experimental technique could be used to simultaneously replace instrumentation such as force balance and pressure taps while providing for the first time quasi-instantaneous information about the surrounding flow in any turbine immersed in an incompressible flow. In addition, it could be applied to evaluate unsteady wind loads and aerodynamic stall and also provide much needed information for validating computational studies.     

Thermofluid Characteristics in Microporous Structure With Different Flow Channels for Loop Heat Pipe

The use of two-phase heat transfer devices using capillary action in a microscale porous structure such as a loop heat pipe (LHP) is a promising heat transport technology. This is because they have characteristics of higher heat transfer power and longer heat transport distances with no electrical power compared with conventional heat pipes. The thermal performance of an LHP is governed by the thermofluid behavior in a microscale porous structure called the wick. In this research, high-performance wicks made of polymer have been developed, and their pore distribution and permeability were evaluated. The effects of the vapor channel's shape on the loop's thermal performance have been investigated by calculation and experiment to enhance evaporator performance. A mathematical model of the evaporator considering super heat in the channel, pressure drop across the wick, and two-phase pressure loss on the boundary face between the wick and the evaporator case was newly developed. The experiment was also conducted as a function of the groove shapes. From calculations and test results, it was found that in order to increase the maximum heat transport capability and decrease the operating temperature, the groove should be well distributed.