Mass Flux Research Articles

A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the external pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.

Roles of vaporization and thermal decomposition in the dynamic evolution of laser-induced bubble on the surface of a submerged metal plate

This paper aims to explain when the vaporization or thermal decomposition prevails during laser-induced bubble growth and how they influence bubble morphology. Bubbles were generated by irradiating a 304 stainless steel plate submerged in degassed water using millisecond lasers with a pulse width of 0.4 ms and powers of 1.6 kW and 3.2 kW, respectively. The dynamic evolution of bubbles was recorded by a high-speed camera. Moreover, the numerical models were developed to obtain a vaporization model and a decomposition model by incorporating the source terms due to the vaporization and decomposition mass fluxes into the governing equations, respectively. The simulated dynamic bubble evolution is consistent with the experimental results. When the laser power is 1.6 kW, a thin-layer bubble is formed, which gradually shrinks and eventually disappears after the laser stops irradiating. When the laser power is 3.2 kW, a spherical bubble is formed, and its volume decreases significantly after the laser stops irradiating. Subsequently, it remains relatively stable during the observation period. The fundamental reason for the difference between the bubble morphologies obtained from the vaporization model and the decomposition model lies in the presence of a condensation zone in the gas phase. When water vaporization or thermal decomposition dominates, the temperatures obtained from the models align with the decomposition ratios at varying temperatures reported in the literature. Our findings are significant for understanding the dynamic behavior of bubbles, with implications for various laser processing underwater.

Impacts of stochastic coalescence variability on warm rain initiation using Lagrangian microphysics in box and large-eddy simulations

Abstract Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing super-droplet method (SDM) and a version of SDM (dSDM) that applies a fractional approach similar to the average impact method. In LES, variabilities driven by microphysics and by flow realizations are separated using the “piggybacking” technique. Rain initiation averaged over many realizations of the box model is delayed and rain variability increases as the number of super-drops per collision volume (NSD) is decreased using SDM. In contrast, rain initiation time using SDM in LES is insensitive to NSD for 32 ≤ NSD ≤ 512. This is explained through the interaction between LES grid boxes, each acting as a separate collision volume. Variability across the ensemble of LES collision volumes using SDM results in rain quickly initiating in some of the LES grid cells at low NSD and leading to a similar overall timing of rain initiation from the cloud compared to simulations with high NSD. There is a ∼20% decrease in the total rain mass and mean rain flux as NSD is increased from 32 to 256, with little additional change as NSD is increased from 256 to 512. The fractional coalescence approach in dSDM leads to reduced microphysical variability and a 15-18 min delay in rain initiation compared to SDM. An additional LES ensemble with microphysical variability feeding back to the dynamics shows that flow variability dominates the impact of microphysical variability on rain properties. Thus, flow variability must be constrained to isolate impacts of microphysical variability.

Subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math. 49 (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity.

An experimental study of the effects of porosity and ratio of fin to channel width on water flow boiling in copper foam fin microchannels

Flow boiling in copper foam fin microchannels (FFMC) has demonstrated better heat transfer performance and flow stability. In this work, systematic experiments are conducted to investigate the effects of structural parameters on flow boiling in five FFMCs with porosities ranging from 0.78 to 0.82 and ratios of fin width to channel width ranging from 0.5 to 2. Five mass fluxes ranging from 68 kg/(m2s) to 408 kg/(m2s) and effective heat fluxes ranging from 2 W/cm2 to 297 W/cm2 are tested. The heat transfer, pressure drop, and flow instability characteristics are analyzed. Generally, the heat transfer in FFMCs follows the “three-zone” model. The heat transfer coefficient first increases with increasing heat flux and then decreases. A “synchronous backflow” phenomenon is observed in FFMCs, which is the direct cause of heat transfer deterioration. Due to the interaction of heat transfer area and the transverse flow resistance through the fins, the heat transfer coefficient increases with decreasing porosity in the low-quality region, while the opposite trend is observed in the high-quality region. The utilization efficiency of the fin area decreases as the fin width increases. An optimal ratio of fin width to channel width exists corresponding to the best heat transfer performance, which equals one in this work. A correlation is developed based on 583 data points considering heat transfer mechanisms in channels and fins. The new correlation predicts the experimental values with a mean absolute percentage error of 9 %, and over 99 % of the data are predicted within a 30 % deviation. A performance evaluation criterion is defined to comprehensively compare the FFMCs, and the FFMC with the porosity of 0.78 demonstrates the best flow boiling performance due to higher heat transfer coefficients and lower pumping powers when the ratio of fin to channel width is equal to one.

Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy

The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes.

Theoretical study on pressure oscillation dominant frequency of bubbles submerged jet under rolling condition

Steam direct contact condensation is a highly efficient heat and mass transfer phenomenon, usually accompanied by strong mass, momentum and energy exchanges at the water-steam interface, which can rapidly realize cooling and pressure relief, but also accompanied by pressure oscillations. When the relevant equipment is used in offshore nuclear power plants and naval non-energetic systems, the additional inertial force field caused by ocean motion may cause greater harm to the safe operation of the relevant devices. Therefore, a theoretical study is conducted to investigate the effect of rolling motion on dominant frequency of steam submerged jets pressure oscillation with low mass fluxes. Firstly, based on bubble dynamics theory, a theoretical model of bubble condensation oscillations under rolling motion with low mass flux is established. Then, the mechanism of the rolling conditions on the dominant frequency of pressure oscillation is analyzed from the aspect of theoretical derivation. Finally, on the basis of the potential flow function theory and small perturbation theory, the predicted correlation of pressure oscillation dominant frequency under the rolling motion with low mass flux is derived, and compared with the numerical simulation results, the prediction deviation is within ±10%.

Influence of Subcooling and pressure on flow boiling in a vertical mini-channel: Heat transfer analysis using inverse method

The background of this study is the problem of thermal runaway in the battery cells of electric vehicles. Increasingly powerful and compact battery packs require highly efficient thermal management. One potential solution is the direct liquid cooling of lithium-ion battery cells using a dielectric liquid which boils over a safety limit temperature. This approach intends to prevent in a first step the cell thermal runaway and if it fails in a second step its propagation to its neighbors: the liquid boiling helps to mitigate the cell temperature rise and to transport and spread the heat. The arrangement of the cells in the pack and their close spacing induce a scientific problem of convective boiling in a mini-channel. To enhance designs using this solution, a comprehensive understanding of flow boiling and a precise local heat transfer quantification is essential. The HFE-7100 has been selected as a working fluid for its attractive thermophysical properties and a suitable saturation temperature.The present paper introduces new experimental results of flow boiling dielectric fluid, the HFE-7100, in a vertical rectangular mini-channel. Measurements are carried out from start of boiling to dry-out. Boiling curves are obtained for a mass flux of 391 kg/(m².s), at different pressures (0.7, 1, 1.5 bar) and at different subcoolings (ΔTsub=0;15;30;45∘C). The test section is an aluminum block instrumented with three lines of five K-type thermocouples located all along the flow. The visualization of the flow is achieved through a glass pane with a high-speed camera to identify different flow patterns. The local heat transfer coefficient is calculated by a resolution of a 2D inverse heat conduction method.The experiment mainly aims at determining the heat transfer coefficient, the critical heat flux (CHF) and the pressure drop and at characterizing both the flow regimes and the dry-out phenomenon. The influence of subcooling and pressure on flow boiling is analyzed. An increase in subcooling enhances the CHF and the heat transfer coefficient, and delays the dry-out. Subcooling has an impact on the flow pattern and modifies the type of CHF. In the operating conditions tested, a decrease in pressure enhances CHF and delays dry-out. On the other hand, the heat transfer coefficient increases with rising pressure. Similarly, pressure drops are lower with higher pressure.

Magnetized water-based hybrid nanofluid flow over an exponentially stretching sheet with thermal convective and mass flux conditions: HAM solution

Abstract The boundary-layer flow on a shrinking/contracting sheet has abundant industrial applications, which include continuous glass casting, metal or polymer extrusions, and wire drawing. In this regard, the present analysis focuses the hybrid nanofluid flow on an exponentially extending sheet. The water-based hybrid nanofluid flow contains CoFe2O4 and TiO2 nanoparticles. Heat transfer rate analysis involves the utilization of the Cattaneo–Christov heat flux model. Moreover, the Brownian motion and thermophoresis effects are used in this novel work. The mathematical model is presented in the form of system of partial differential equations, which is then transformed into system of ordinary differential equations (ODEs) using the similarity variables. The system of ODEs is evaluated by homotopy analysis method. The variation in the flow profiles has been investigated using figures and tables. The conclusions demonstrate that the effect of magnetic parameter is 52% better for hybrid nanofluid flow than for the pure water. Conversely, the increasing magnetic parameter diminishes the thermal transfer rates for water, TiO2–H2O, CoFe2O4–H2O, and TiO2–CoFe2O4/H2O. The increasing thermophoresis parameter upsurges the thermal flow rate of nanofluids and hybrid nanofluid, while the increasing Brownian motion parameter lessens the thermal transfer rates of nanofluids and hybrid nanofluid. The increasing effect of thermophoresis parameter is 39% better for hybrid nanofluid than for the base fluid. However, the declining impression of Brownian motion factor is 48% greater for hybrid nanofluid related to pure water.

Mass Transfer Mechanism Within Commercial PTFE Membranes In Spacer-Filled Direct Contact Membrane Distillation

The mass transfer mechanism within commercial PTFE membrane with various nominal pore sizes in spacer-filled direct contact membrane distillation (DCMD) was determined. Mass fluxes and membrane permeability (MP) values for each commercial PTFE membrane were experimentally measured. The MP values increased insignificantly with 2.3% and 4% when the inlet temperature at feed side rose from 400C to 500C in different membrane pore sizes. All investigated mass transfer models except from Dusty Gas model were good enough to simulate the mass transfer inside smaller membrane pore sizes (0.22 µm, and 0.45 µm). Compared to combined diffusion model, the predicted mass fluxes using the overall mass transfer model including the contribution of Poiseuille flow obtained better agreement with experimental results for larger membrane pore size (1 µm). The mean absolute percentage error (MAPE) values for combined diffusion model were up to 16.5% compared with the Ding et al. model or Schofield et al. model (under 3%). Regarding the root mean square error (RMSE), the combined diffusion model obtains larger values than the mass transfer model considering the Poiseuille flow contribution. Consequently, the contribution of Poiseuille flow in mass transfer mechanism within smaller PTFE membrane pores (0.22 µm, and 0.45 µm) could be ignored, however, the contribution of Poiseuille flow to the overall mass transfer should be included in case of larger membrane pores (1 µm), or the case of applied transmembrane hydrostatic pressure.

Mathematical modelling of biodigestion in an Indian biodigester and its stability analysis via Lyapunov technique

Biodigesters are vessels in which a microbiological consortium converts an organic residue into biogas and biofertilizer. This bioprocess, anaerobic biodigestion, plays an important environmental role since the residue at the end of the reaction has a reduced organic load, in addition to lower toxicity, and can therefore be disposed of with less impact on the environment. Moreover, biodigestion produces biogas, which is of great interest in view of the current shortage of fossil fuels. In this sense, this work proposes a nonlinear mathematical model based on the mass flux balance of an Indian biodigester and it also analyses its properties, in particular the Lyapunov stability of its equilibrium solutions, and verifies the non-negativity of its solutions to be consistent with the biology of the issue. The proposed model represents an important tool to describe anaerobic biodigestion in an Indian biodigester, providing information for further planning, scenario prediction and control of the bioprocess. Simulations of the model in different scenarios showed that lower initial bacteria/substrate concentration ratios (≈0.14) can promote better biogas production performance.

Visual observations of steam–air submerged horizontal jets at low mass flux

Steam jet condensation at low mass flux is important especially in start-up, shutdown or accident conditions of various applications. Visual experiments of steam–air submerged jets through horizontal pipe were conducted in the ranges of mass flux 0–––20 kg/m2s, air mass fraction 0–––0.02, and water temperature 20 − 80℃. In pure steam jets, three condensation regimes of no bubbling, intermittent bubbling, and continuous bubbling were identified in steam jets. In no bubbling regime, rolling up and billows of plane shear flow were observed. In intermittent bubbling regime, large bubble was generated, detached and collapsed intermittently, accompanied by fluid oscillations. The bubble forming frequency increased with the rise of water temperature. Condensation heat transfer coefficients tends to decrease as the steam mass flux increases. In continuous bubbling, fluid oscillation no longer occurred. The bubble forming frequency decreased with the rise of water temperature. Condensation heat transfer coefficients increase as the steam mass flux increases. In the cases with shallow submerged depth, air-entrained vortex, surface water jets, and splash were observed after bubble condensation. In steam–air jets, condensation became stable and small bubbles increased. The condensation regime transitioned from intermittent bubbling to continuous bubbling earlier.

Spatial Dispersion and Statistical Description of Organized Cumulus Cloud Ensembles in Radiative Convective Equilibrium

AbstractDescriptions of cloud ensembles in radiative convective equilibrium (RCE) rely mostly on the assumption that clouds are randomly distributed in space, a hypothesis that obviously fails in presence of strong organization. In this work, idealized RCE simulations at horizontal grid spacings ranging from 2 km to 125 m are analyzed, displaying a transition between complete randomness at coarse resolution to a high degree of cold pool driven organization at high resolution. The objective is then twofold: (a) characterizing the spatial cloud patterns focusing on correlation scales and association with covariates; (b) providing a statistical description of organized cloud ensembles to generalize existing theories based on complete randomness. It is demonstrated that organized cloud ensembles may be treated as heterogeneous point processes where individual clouds do not interact substantially with their neighbors. In other words, clouds may be considered as randomly distributed if we restrict the space to regions of high cloud density. In addition, it is shown that in highly organized situations local cloud counts may be modeled using negative binomial distributions, while cloud mass fluxes follow lognormal distributions. The total mass flux within regions of varying sizes can then be predicted by compounding the two aforementioned distributions. The total mass flux variability at scales ≲5 km is dominated by the heavy‐tails of the mass flux distributions, whereas at scales ≳5 km, it is entirely controlled by the spatial cloud count variability (the spatial cloud pattern). These results have important implications for the parameterization of organized convection in quasi‐equilibrium.

Supercritical heat transfer of Novec 649 refrigerant in a minichannel with various inclination angles: Horizontal to vertically downward flows

The study of organic fluids under supercritical conditions has been less extensive than that of supercritical carbon dioxide and water. In addition, most studies on supercritical heat transfer have focused on horizontal or vertical channels, with limited research on inclination angles. Therefore, the focus of this study was to investigate the supercritical heat transfer of organic fluid (Novec 649) in a miniaturized channel across various inclination angles. The experimental findings reveal that the heat transfer coefficient (HTC) increases with an increase in the fluid's bulk temperature at a given mass flux and with an increase in the mass flux at a given bulk temperature. Notably, the HTC in horizontal flow channels marginally surpasses that in non-horizontal channels. The buoyancy effect, found to be non-dominant in a studied channel, does not lead to heat transfer deterioration. In vertical flow channels, under the experimental conditions, the acceleration parameters exceeded the threshold values, suggesting a potential significance of the acceleration effect. Particularly at higher mass fluxes, the acceleration parameter peaked as the film temperature approached the fluid's pseudocritical value. We further developed the supercritical heat transfer correlation by introducing an inclination angle parameter, achieving a mean absolute error of 12.7%.

Flow boiling heat transfer of R454B in a 24-port microchannel tube

R454B is a relatively low Global Warming Potential refrigerant, and it has emerged as a promising substitute for traditional refrigerants. Understanding the heat transfer and fluid dynamics characteristics of R454B becomes important for applying it. An experimental setup was built for measuring heat transfer coefficient (HTC) and pressure gradient (dP/dz) in a 24-port microchannel tube. The test condition covers mass fluxes of 100–250 kg-m-2s−1, heat fluxes of 2–8 kW-m−2, and saturation temperatures of 10–30 °C. The mass flux had a significant impact on the HTC, particularly at higher vapor quality. Additionally, the heat flux also played a crucial role in determining the HTC, with a stronger influence observed at lower vapor quality. The saturation condition had a relatively minor effect on HTC, showing a positive impact at low vapor quality but a negative impact at moderate and high vapor quality. The dP/dz tended to increase with vapor quality. Both the mass flux and saturation condition exhibited strong effects on dP/dz. However, the heat flux had a negligible impact on the dP/dz. The study also compared the performance of R454B with R32, R1234yf, and three R32/R1234yf mixtures (85/15, 50/50, and 15/85 by mass). The results showed that R454B had a HTC close to R1234yf and the 85/15 mixture. However, it had the lowest dP/dz compared among the compared fluids. The results were compared to existing correlations and those with less error were recommended. This study pioneered the examination of R454B flow boiling in microchannel tubes, and employed Pearson correlation coefficient analysis which presents a first-of-its-kind quantitative analysis of the impact of operational conditions on HTC and dP/dz, marking a significant advancement in thermal systems optimization.

An Evaluation of Correlations for Predicting the Heat Transfer Coefficient during the Condensation of Saturated and Superheated Vapors Inside Channels

Condensation heat transfer is involved in many industrial applications. Therefore, it is important to know the relative accuracy of the available methods for predicting heat transfer. Condensation can occur with saturated as well as superheated vapors. Predictive methods for both conditions were evaluated using a wide range of data. Twelve well-known correlations for the condensation of saturated vapor, including the most recent ones, were compared with data for 51 pure fluids and mixtures from 132 sources in horizontal and vertical channels of many shapes. Channel hydraulic diameters were 0.08–49 mm, the mass flux was 1.1–1400 kg/m2s, and the reduced pressure range was 0.0006–0.949. The fluids included water, CO2, ammonia, hydrocarbons, halocarbon refrigerants, various chemicals, and heat transfer fluids. The best predictive technique was identified. The three most commonly used models for heat transfer during the condensation of superheated vapors were studied. They were first compared with test data using measured saturated condensation and forced convection heat transfer coefficients to select the best model. The selected model was then compared with test data using various correlations for heat transfer coefficients needed in the model. The best correlations to use in the model were identified. The results of this research are presented, as are recommendations for use in design.

An Experimental investigation of void fraction characteristics of Flow Boiling in a 5×5 rod bundle channel

Flow boiling in the rod bundle channel is an important phenomenon in nuclear reactors. The local inhomogeneous void fraction distribution in the flow channel will affect the flow and heat transfer in two phase flow. A 5×5 rod bundle test section is designed and conductivity probe is utilized in the paper. A remote-control stepping driving assembly is designed to drive the void probe. The local void fraction characteristics at the outlet of a 5×5 rod bundle channel during subcooled boiling and saturated boiling are experimentally studied when the system pressure is 2∼3 MPa. The outlet subcooling ranges from 0 oC to 18 oC. The mass flux is 2000 kg/m2s and the heat flux ranges from 186.3 kW/m2 to 320.8 kW/m2.The effects of thermal parameters on local phase interfacial parameters in subcooled boiling and saturated boiling are obtained. The research results are important for revealing the two phase flow mechanisms in rod bundle channels.

Dynamics and scaling of internally cooled convection

Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with the bulk cooling in thermal equilibrium with the input heat flux. This simple model represents idealised dry convection in the atmospheric boundary layer, where the cooling mimics the radiative cooling to space notably through longwave radiation. We perform linear stability analysis of the model for different values of the mean stratification to derive the critical forcing above which the fluid is convectively unstable to small perturbations. The dynamic behaviour of the fluid system is described and the scaling of various important measured quantities such as the total vertical convective heat flux and the upward mass flux is measured. We introduce a lapse-rate dependent dimensionless Rayleigh-number Raγ that determines the behaviour of the system, finding that the convective heat-flux and mass-flux scale scale approximately as Raγ0.5 and Raγ0.7 respectively. The area-fraction of the domain that is occupied by upward and downward moving fluid and the skewness of the vertical velocity are studied to understand the asymmetry inherent in the system. We conclude with a short discussion on the relevance to atmospheric convection and the scope for further investigations of atmospheric convection using similar simplified approaches.

Quantifying Supraglacial Debris‐Related Melt‐Altering Effects on the Djankuat Glacier, Caucasus, Russian Federation

AbstractWe use a spatially distributed and physically based energy and mass balance model to derive the Østrem curve, which expresses the supraglacial debris‐related relative melt alteration versus the debris thickness, for the Djankuat Glacier, Caucasus, Russian Federation. The model is driven by meteorological data from two on‐glacier weather stations and ERA‐5 Land reanalysis data. A direct pixel‐by‐pixel comparison of the melt rates obtained from both a clean ice and debris‐covered ice mass balance model results in the quantification of debris‐related relative melt‐modification ratios, capturing the degree of melt enhancement or suppression as a function of the debris thickness. The main results show that the distinct surface features and different surface temperature/moisture and near‐surface wind regimes that persist over debris‐covered ice significantly alter the pattern of the energy and mass fluxes when compared to clean ice. Consequently, a maximum relative melt enhancement of 1.36 is modeled on the glacier for thin/patchy debris with a thickness of 0.03 m. However, insulating effects suppress sub‐debris melt under debris layers thicker than a critical debris thickness of 0.09 m. Sensitivity experiments show that especially within‐debris properties, such as the thermal conductivity and the vertical debris porosity gradient, highly impact the magnitude of the sub‐debris melt rates. Our results also highlight the scale‐dependency as well as the dynamic nature of the debris thickness‐melt relationship for changing climatic conditions, which may have significant implications for the climate change response of debris‐covered glaciers.

Effect of water film evaporation on the shale gas transmission in inorganic nanopores under viscosity.

Shale gas reservoirs generally have ultra-low water saturation, and the water in reservoirs is closely bound to the walls of inorganic nanopores, forming a water film structure on the hydrophilic surface. When shale gas enters the inorganic nanopores, the water films in the inorganic pores will be removed by evaporation instead of being driven away by the gas, which increases the difficulty of predicting production during shale gas extraction. Based on molecular dynamics simulations, a water film evaporation model is proposed, considering the evaporation of water films during shale gas transport and the influence of water film evaporation on the shale gas transport mechanism. The Green-Kubo method is employed to calculate the viscosity of the water film. The evaporation flux of the water film under the influence of viscosity is discussed in the evaporation model. The transport mechanisms of shale gas in nanopores and the effect of water film evaporation on shale gas transport mechanisms are analyzed in detail. The result indicates that the water films in the inorganic nanopores are constrained on the hydrophilic surface, and the viscosity normal to the surface of the water film of 4Å is 0.005 26 Pa⋅S, which is 6.12 times the reference value of viscosity at 298K. In the process of water film evaporation, the evaporation flux of the water film is influenced by viscosity. In the study of the shale gas transport mechanism, water films in inorganic nanopores can hinder the surface diffusion of the methane molecules adsorbed on boundary and significantly reduce the mass flux of shale gas.