Vapor Mass Flux Research Articles

The temperature and pressure jumps at the vapor–liquid interface: Application to a two-phase cooling system

The temperature and pressure jump boundary conditions at the liquid–vapor interfaces, obtained from the kinetic theory, are implemented for the numerical simulation of two-surfaces problem of evaporation and condensation. For a small temperature difference between two interfaces the system of the Navier–Stokes equations (NS) together with the energy conservation equation and the linear approximation of these equations with the same jump boundary conditions are considered in the vapor phase. The numerical and analytical solutions are compared with that obtained previously from the linearized kinetic equation. The analytical temperature profiles derived from the both linearized systems are very close to each other, while the temperature distribution obtained from the full NS and energy equations has an absolutely different character. The velocity and pressure in the vapor phase are found to be constant, though the full NS and energy equations solution gives abrupt change of velocity near the condensation interface. The inverse temperature gradient phenomenon occurs for the considered small temperature difference. The solution in the vapor phase is then applied to a coupled two-phase system problem, which can be realized in a heat-transfer device combining the principles of both thermal conductivity and phase transition. The coupled two-sided (liquid and vapor) model with jump boundary conditions proposed here allows us to estimate the values of the evaporative mass flux and the heat flux, which can be removed from a heat source.

A research on water desalination using membrane distillation

This research work aimed to investigate the performance of direct contact membrane distillation (MD) unit under different conditions. A mathematical model was developed to evaluate the experimental values of the membrane water mass flux, heat transfer coefficients, the membrane/liquid interface temperatures, the temperature polarization coefficient (TPC) and the evaporation efficiency. This model was solved numerically using MATLAB® software, and its results were used to predict the actual performance of the membrane unit. The MD coefficient was evaluated from the computer model data and was subsequently used to estimate water fluxes. Experimental tests were performed using 0.0572 m2 of poly-tetra-fluoro-ethylene membrane manufactured by membrane solution (85% porosity, 45-µm thickness, 0.22-µm nominal pore size). Feed solutions were aqueous NaCl solutions with 1,000–200,000 mg/L (0.1–20%) in concentration, its temperatures were 40–80°C and feed flow rate was 2 l/min. The temperature and flow rate of permeate water was fixed at 20°C and 3 l/min, respectively. The experimental observation showed that the vapour mass flux through the membrane pores increased with feed temperature, but decreased with feed concentration. It was found that the predicted mass fluxes agreed reasonably with the experimental data, except at a high feed concentration. The temperature polarization coefficients increased with concentration and decreased with increasing temperature. The membrane heat transfer rates and the permeate flux have been discussed in this paper.

Evaluating climate model performance in the tropics with retrievals of water isotopic composition from Aura TES

AbstractWe evaluate the NASA Goddard Institute for Space Studies ModelE2 general circulation model over the tropics against water isotope (HDO/H2O) retrievals from the Aura Tropospheric Emission Spectrometer. Observed isotopic distributions are distinct from other observable quantities and can therefore act as an independent constraint. We perform a small ensemble of simulations with physics perturbations to the cumulus and planetary boundary layer schemes. We examine the degree to which model‐data agreement could be used to constrain a select group of internal processes in the model, namely, condensate evaporation, entrainment strength, and updraft mass flux. All are difficult to parameterize but exert strong influence over model performance. We find that the water isotope composition is more sensitive to physics changes than precipitation, temperature, or relative humidity in the lower and upper tropical tropospheres. Among the processes considered, this is most closely, and fairly exclusively, related to midtropospheric entrainment strength. Our study indicates that water isotope observations could provide useful constraints on model parameterizations.

Effect of disjoining pressure (Π) on multi-scale modeling for evaporative liquid metal (Na) capillary

This work presents a new multiscale model of an evaporating liquid metal capillary meniscus under nonequilibrium evaporation sustaining a nonisothermal interface. The primary investigation is elaborated on to examine the critical role of the disjoining pressure, which consists of both the traditional van der Waals component and a new electronic pressure component, for the case of liquid metals. The fully extended dispersion force is modeled along with an electronic disjoining pressure component that is unique to liquid metals attributing to their abundant free electrons. For liquid sodium (Na), as a favorable coolant for high temperature two-phase devices, the extended meniscus thin film model (sub-microscale) is coupled to a CFD model of the evaporating bulk meniscus (sub-millimeter scale). Two extreme cases are compared, i.e. with or without incorporation of the electronic disjoining pressure component. It is shown that the existence of electronic component of the disjoining pressure leads towards larger total capillary meniscus surface areas and larger net evaporative mass flow rates. Furthermore, the net evaporative mass flux in the bulk meniscus region is needed to be accounted for to obtain a true picture of the total capillary evaporation transport.

Twenty first century cooling solution: Microchannel heat sinks

Due to rapid evolution in a wide range of technologies in twentieth century, heat dissipation requirement has increased very rapidly especially from compact systems. There is an urgent need for high-performance heat sinks to ensure the integrity and long life of these petite systems. Use of forced convection cooling has been limited by the requirement of the excessively high flow velocity and associated noise and vibration problems. Microchannel heat sink seems to be most reliable cooling technology due to its superior command over heat carrying capability. Understanding the flow boiling phenomena in microchannel heat sink experimentally and analytically has been topic of intense research in twenty first century. In this review paper, the experimental studies on flow visualization, pressure drop and heat transfer characteristics of microchannels presented by different researchers are summarized. Some different flow patterns observed in microchannel geometry such as bubble nucleation in thin film, periodic variation of flow pattern, flow circulation, bubble suppression and cross-channel flow are explained briefly. The influence of vapour quality, heat flux, mass flux and channel geometry on pressure drop and heat transfer characteristics of microchannel are reported. Different correlations reported for single and two phase heat transfer characteristics are compared. The comparative analysis showed that available single phase and two phase correlations are inconsistence and large variation is observed among these correlations for same channel geometry, fluid and operating condition. Different instabilities associated with microchannels are also briefly presented.

Significant heat transfer enhancement for R123 condensation by micromembrane cylinder

Renewable energy or low grade energy utilizations need high performance of phase change heat exchangers. Suspending micromembrane cylinder in tube (called modulated heat transfer tube) increases the void fractions or vapor qualities near the tube wall to significantly enhance heat transfer. The R123 condensation heat transfer with horizontal position was investigated. The results for the bare tube and modulated heat transfer tube were tested case by case. It is found that the modulated heat transfer tube significantly enhance the condensation heat transfer, with the heat transfer enhancement factors (EF) covering the range of 1.118–2.124. The comprehensive performance evaluation criteria (PEC) had the range of 0.71–1.66, with most of runs behaving PEC larger than 1.0. For the two-phase outlet conditions, the EF values are increased with increases in the vapor mass fluxes, Gxin, where G is the mass flux and xin is the inlet vapor mass quality. The EF values are inversely related to Gxin for the subcooled liquid outlet cases. The enhanced heat transfer mechanisms are analyzed with the observed images together with the discussion of pressure and velocity distributions.

Flow boiling heat transfer and pressure drop of water in a plate heat exchanger with corrugated channels at low mass flux conditions

The plate heat exchanger (PHX) has been widely used as a heat exchanger in fresh water generators (FWGs) at low mass flux conditions. In this study, the flow boiling heat transfer and pressure drop characteristics of water in a PHX for the FWG were measured by varying mass flux from 14.5 to 33.6kgm−2s−1, heat flux from 15.0 to 30.0kWm−2, and mean vapor quality from 0.09 to 0.6 in the pressure range of 112–121kPa. The flow boiling heat transfer of water in the PHX was in the convective boiling region. The flow boiling heat transfer coefficient decreased with increasing mean vapor quality and decreasing mass flux. However, the effect of the heat flux on the flow boiling heat transfer coefficient was almost negligible. In addition, the two-phase frictional pressure drop increased with increasing mean vapor quality and mass flux, but it remained nearly constant according to the heat flux. Two-phase heat transfer and pressure drop correlations for water in PHXs were developed based on the measured data. The proposed heat transfer and pressure drop correlations showed mean absolute deviations of 4.4% and 10.4%, respectively, compared with the measured data.

Study on two-phase pressure drop of LNG during flow boiling in a 8 mm horizontal smooth tube

Two-phase pressure drop of LNG (liquefied natural gas) during flow boiling has been measured in a horizontal smooth tube with an inner diameter of 8mm at 0.3–0.7MPa. And the experiments was conducted with the mass flux of 50–200kgm−2s−1, heat flux of 8–32kWm−2, and vapor quality of 0.16–0.83. The effects of vapor quality, heat flux and mass flux, inlet pressure on the frictional pressure drop of LNG are discussed. The comparisons of the experimental data with the predicted value by existing six correlations are analyzed. Müller-Steinhagen and Heck [8] and Friedel [21] can provide acceptable predictions for two-phase pressure drop of LNG at inlet pressure of 0.3–0.7MPa among them.

Thin film evaporation of n-octane on silicon: Experiments and theory

Microscope-based reflectometry was used to measure the thickness profiles of thin films of n-octane on silicon wafer substrates. Thin films, created in an axisymmetric capillary feeder, were subjected to heat or a nitrogen flow to promote evaporation into a saturated gas phase. Steady state film profiles were established, with a non-evaporating adsorbed film transitioning to the intrinsic meniscus. The reflectometer was coupled with micro-positioning motorized stages to provide two-dimensional profiles of the film thickness. A numerical model was formulated to include lubrication theory of the liquid flow within the film, heat conduction across the film from the heated wall to the liquid–vapor interface, kinetic theory of evaporation from the interface to the vapor phase, and disjoining pressure based on a retarded van der Waals interaction. When combined, the governing equations form a fourth-order, nonlinear differential equation for the film thickness vs. distance, which is solved numerically and compared to the experimental data. Useful results of the model include the liquid–vapor interface temperature, the Hamaker coefficient, and the evaporative mass flux profile.

The phase separation concept condensation heat transfer in horizontal tubes for low-grade energy utilization

This paper reports condensation heat transfer in a horizontal tube with a 14.81 mm inside diameter and a 1200 mm heat transfer length, by using the phase separation concept. The hollow mesh cylinder was formed by packaging two layers of mesh screen surface. The outer layer had the pore size of 76 μm. This invention constructs a multiscale condenser tube. The modulation of stratified flow and annular flow was focused on. Liquid was held within the mesh cylinder to increase the vapor covered tube wall surface to enhance the heat transfer for stratified flows. For annular flows, liquid droplets in the vapor core were captured by the mesh screen surface to increase the vapor void fractions near the tube wall, enhancing the hat transfer. The measurements showed that the heat transfer coefficients could be more than two times of those in the bare tube. The total thermal resistance was decreased by 45.6%, maximally. The heat transfer enhancement ratios were increased with the vapor mass fluxes, Gxin, for the condensation flow along the whole tube length. A pressure analysis explained the increased heat transfer trend. The increment of heat transfer enhancement ratios was suppressed with a liquid flow part in the tube.

Using a WRF simulation to examine regions where convection impacts the Asian summer monsoon anticyclone

Abstract. The Asian summer monsoon is a prominent feature of the global circulation that is associated with an upper-level anticyclone (ULAC) that stands out vividly in satellite observations of trace gases. The ULAC also is an important region of troposphere-to-stratosphere transport. We ran the Weather Research and Forecasting (WRF) model at convective-permitting scales (4 km grid spacing) between 10 and 20 August 2012 to understand the role of convection in rapidly transporting boundary layer air into the ULAC. Such high-resolution modeling of the Asian ULAC previously has not been documented in the literature. Comparison of our WRF simulation with reanalysis and satellite observations showed that WRF simulated the atmosphere sufficiently well to be used to study convective transport into the ULAC. A back-trajectory analysis based on hourly WRF output showed that > 90% of convectively influenced parcels reaching the ULAC came from the Tibetan Plateau (TP) and the southern slope (SS) of the Himalayas. A distinct diurnal cycle is seen in the convective trajectories, with a majority of them crossing the boundary layer between 1600 and 2300 local solar time. This finding highlights the role of "everyday" diurnal convection in transporting boundary layer air into the ULAC. WRF output at 15 min intervals was produced for 16 August to examine the convection in greater detail. This high-temporal output revealed that the weakest convection in the study area occurred over the TP. However, because the TP is at 3000–5000 m a.m.s.l., its convection does not have to be as strong to reach the ULAC as in lower altitude regions. In addition, because the TP's elevated heat source is a major cause of the ULAC, we propose that convection over the TP and the neighboring SS is ideally situated geographically to impact the ULAC. The vertical mass flux of water vapor into the ULAC also was calculated. Results show that the TP and SS regions dominate other Asian regions in transporting moisture vertically into the ULAC. Because convection reaching the ULAC is more widespread over the TP than nearby, we propose that the abundant convection partially explains the TP's dominant water vapor fluxes. In addition, greater outgoing longwave radiation reaches the upper levels of the TP due to its elevated terrain. This creates a warmer ambient upper-level environment, allowing parcels with greater saturation mixing ratios to enter the ULAC. Lakes in the Tibetan Plateau are shown to provide favorable conditions for deep convection during the night.

Condensation heat transfer enhancement in a horizontal non-circular microchannel

Numerical investigation of steam condensation in a non-circular microchannel is conducted. The conservation equation of mass, momentum and energy have been solved in both phases for various microchannel hydraulic diameters. Different correlations established for condensation flow heat transfer are evaluated. It is found that the correlation of Dobson et al. and Koyama et al. are the closest to the calculated steam condensation average heat transfer. Results are given for different microchannels shapes, aspect ratio, and for various inlet vapor mass fluxes and contact angle. Reducing the microchannel hydraulic diameter from 250 to 80 μm reduces the condensate film thickness and increases the average heat transfer coefficient up to 39% for the same mass flux. The enhancement factor of the heat transfer coefficient reaches 100% by increasing the contact angle from 6 to 15°. The influence of the microchannel shape on the condensation heat transfer is highlighted too. Thus it is seen that the lowest average Nusselt numbers are obtained for the square microchannel.

Two-phase heat transfer and pressure drop of LNG during saturated flow boiling in a horizontal tube

Two-phase heat transfer and pressure drop of LNG (liquefied natural gas) have been measured in a horizontal smooth tube with an inner diameter of 8mm. The experiments were conducted at inlet pressures from 0.3 to 0.7MPa with a heat flux of 8–36kWm−2, and mass flux of 49.2–201.8kgm−2s−1. The effect of vapor quality, inlet pressure, heat flux and mass flux on the heat transfer characteristic are discussed. The comparisons of the experimental data with the predicted value by existing correlations are analyzed. Zou et al. (2010) correlation shows the best accuracy with 24.1% RMS deviation among them. Moreover four frictional pressure drop methods are also chosen to compare with the experimental database.

The boiling heat transfer characteristics of the mixture HFO-1234yf/oil inside a micro-fin tube

The boiling heat transfer characteristics of refrigerant HFO-1234yf in a 7mm O.D. micro-fin tube were investigated. The local heat transfer coefficients and pressure drops were measured at the mass fluxes of 100, 200, 400kg/m2s, the heat fluxes of 4, 8, 12kW/m2, the saturation temperatures of 5, 15°C and the oil concentrations of 0%, 1.5%, 3.0% and 5.0%. The influences of vapor quality, mass flux, heat flux and saturation temperature on the heat transfer coefficients were analyzed. The effect of lubricant oil on the boiling heat transfer performance of HFO-1234fy in the micro-fin tube was also discussed. All researches provided a good basis for the application of HFO-1234fy.

Experimental investigations on flow boiling heat transfer in plate heat exchanger at low mass flux condition

In this paper, flow boiling heat transfer in a plate heat exchanger at the low mass flux condition was investigated for low temperature lift heat pump applications. The effects of vapor quality, heat flux, evaporation pressure, and mass flux were studied. The current study shows that the influence of convective boiling heat transfer is suppressed under given test conditions, and the effect of boiling heat transfer was dominant. This is evident from the insignificant effect of vapor quality on flow boiling heat transfer coefficient. It showed a dominant effect of nucleate boiling heat transfer. When heat flux was increased, the flow boiling heat transfer coefficient increased which is an indication of nucleate boiling heat transfer. Excess temperature was also studied, which closely relates to nucleate boiling regime. As evaporation pressure was decreased, it became easier for vapor bubbles to generate, which can be explained with a lower excess temperature. Furthermore, a more rigorous bubble movement at a low excess temperature range involved in this study enhanced heat transfer across the surface, so that flow boiling heat transfer coefficient increased. For the effect of mass flux, the flow boiling heat transfer coefficient increased slightly as the mass flux was increased. This means that convective boiling heat transfer is present, but it just played a minor role in the evaporation heat transfer because of a low fluid mass flux.

Condensation heat transfer on patterned surfaces

An experimental study of condensation heat transfer was carried out on a 25.4mm diameter surface using steam as the condensing fluid. Three surface conditions were studied: hydrophilic, hydrophobic, and a surface with patterns of distinct hydrophilic and hydrophobic regions. The effects of inlet vapor velocity, mass flux, and hydraulic diameter on the heat transfer coefficients were investigated. The inlet vapor velocity was varied from about 0.05m/s to about 5m/s and the hydraulic diameter was varied from 4.5mm to 32.5mm. Depending on the surface condition, the heat transfer coefficients showed different responses to the varying parameters of the experiments. For the hydrophilic surface, the heat transfer coefficient was observed to be up to 2.5 times lower than that for the hydrophobic surface with all other parameters unaltered. On the other hand, the surfacewith a pattern of distinct hydrophobic and hydrophilic regions showed heat transfer coefficients that were higher than that of the hydrophilic surface and lower than that of the hydrophobic surface. In both the patterned and the hydrophobic surfaces, the heat transfer coefficient was observed to increase significantly with mass flux, while for the hydrophilic surface, the heat transfer coefficient was observed to be affected much less by the mass flux. In all cases, the heat transfer coefficients increased with increasing heat flux and decreased with increasing wall sub-cooling. The effect of average quality of the steam showed little effect on the heat transfer coefficients.

Evaporation of Nanodroplets on Heated Substrates: A Molecular Dynamics Simulation Study

Molecular dynamics simulations of Lennard-Jones particles have been performed to study the evaporation behavior of nanodroplets on heated substrates. The influence of the liquid-substrate interaction strength on the evaporation properties was addressed. Our results show that, during the temperature-raising evaporation, the gas is always hotter than the droplet. In contrast to the usual experimental conditions, the droplet sizes in our simulations are in the nanometer scale range and the substrates are ideally smooth and chemically homogeneous. As a result, no pinning was observed in our simulations for substrates denoted either hydrophilic (contact angle θ < 90°) or hydrophobic (contact angle θ > 90°). The evaporative mass flux is stronger with increasing hydrophilicity of the substrate because the heat transfer from the substrate to the droplet is more efficient for stronger attraction between the solid and the droplet. Evaporation and heat transfer to the gas phase occur preferentially in the vicinity of the three-phase contact line in the hydrophilic system. However, in the case of a hydrophobic substrate, there is no preferential location for mass and heat fluxes. During the whole evaporation process, no pure behavior according to either the constant-angle or the constant-radius model was found; both the contact angle and contact radius decrease for the droplets on hydrophilic and hydrophobic substrates alike.

Modelling the formation of surface hoar layers and tracking post-burial changes for avalanche forecasting

Predicting the spatial distribution and persistence of buried surface hoar layers is important when evaluating avalanche hazard. This study used weather-based models to predict the formation of surface hoar and investigated how buried layers change over time. Seven years of study plot observations from the Columbia Mountains of British Columbia were used to calibrate models for surface hoar formation. The latent heat flux was modelled with weather station data and forecasted data from the Canadian numerical weather prediction model (GEM15). A linear relationship was found between vapour mass flux and observed surface hoar crystal size (r2 of 0.84 with weather station data and 0.70 with GEM15 data), and was used to predict crystal size over seven winters. Crystal size predictions had root mean square errors of 2.4 and 4.1mm with weather station and GEM15 data, respectively. The model was compared with other empirical weather-based models. Layers of buried surface hoar were tracked with shear frame tests, compression tests (CT) and propagation saw tests (PST). PSTs and fracture character in CTs indicated that the propensity for propagation in layers of surface hoar remained high for up to six weeks. Layers with large crystals were found to weakly indicate low stability. Results from this study could be used to improve the representation of surface hoar layers in snow cover models and make spatial predictions with NWP data.

Volume of fluid-based numerical modeling of condensation heat transfer and fluid flow characteristics in microchannels

The present work proposes a numerical model for the simulation of condensation heat transfer and fluid flow characteristics in a single microchannel. The model was based on the volume of fluid approach, which governed the hydrodynamics of the two-phase flow. The condensation characteristics were governed by the physics of the phenomena and did not include any empirical expressions in the formulation. The conventional governing equations for conservation of volume fraction and energy were modified to include source terms that accounted for the mass transfer at the liquid–vapor interface and the associated release of latent heat, respectively. A microchannel having characteristic dimension of 100μm was modeled using a two-dimensional computational domain. The working fluid was R134a and the vapor mass flux at the channel inlet ranged from 245 to 615kg/m2s. The channel wall was maintained at a constant heat flux ranging from 200 to 800kW/m2. The predictive accuracy of the numerical model was assessed by comparing the two-phase frictional pressure drop and Nusselt number with available empirical correlations in the literature. A reasonably good agreement was obtained for both parameters with a mean absolute error of 8.1% for two-phase frictional pressure drop against a recent universal predictive approach, and 16.6% for Nusselt number against an available correlation. Further, a qualitative comparison of various flow patterns against experimental visualization data also indicated a favorable agreement.

Condensation heat transfer characteristics of R-134a flowing inside the multiport minichannels

In this study, the condensation heat transfer characteristics of R-134a flowing inside multiport minichannels were investigated. The multiport minichannel-tested tubes have 14 channels with a 1.1mm hydraulic diameter, and eight channels with a 1.2mm hydraulic diameter were designed as a counterflow tube-in-tube heat exchanger. The experiment was performed with mass fluxes of refrigerant between 340 and 680kg/m2s, with 15, 20, and 25kW/m2 heat fluxes, and saturation temperatures of 35–45°C. The flow pattern for the experimental data was initially predicted using existing flow pattern maps. It could be noted that the annular flow pattern existed for most of the experimental data. Results showed that the average heat transfer coefficient increased with the increase of vapor quality, mass flux, and heat flux, but decreased as saturation temperature rose. When compared with two correlations obtained from condensation inside the multiport minichannels, the heat transfer coefficient could be predicted within an acceptable range.