A new model of mass flow characteristics in electronic expansion valves considering metastability

This paper presents an experimental study on the mass flow characteristics of electronic expansion valves in a wide operating condition range. It was found that flow choking always occurs under common operating conditions in refrigeration systems. Based on metastability in EEVs, a new model predicting mass flow rate was proposed under flow choking conditions. Different from the conventional models using Bernoulli equation which employed downstream pressure at the EEV exit and a corrected mass flow coefficient, the present model considered metastable liquid flow caused by rapid depressurization, and employed single-phase incompressible flow coefficient and metastable pressure at the throat. An empirical correlation of the metastable pressure, based on the experimental data for R22 and its substitutes, R407C and R410A, was developed in a power law form of dimensionless parameters including upstream operating parameters and refrigerant thermophysical properties and throat area. The predictions of the present model were found to be in good agreement with the measured data, and approximately 95% of the measured data fall within a relative deviation of ±7.0%. The comparison with a prior model shows that, in terms of flashing mechanism application and predicting accuracy, the present model is better than the conventional model without considering metastability.     

Mechanical nonequilibrium considerations in homogeneous bubble nucleation for unsteady-state boiling

With thermal and mechanical nonequilbrium taken into consideration, the classical kinetic theory of boiling is modified to study unsteady-state homogeneous nucleation processes. Based on this newly developed model, the degree of superheat and the maximum nucleation rate corresponding to different rates of temperature rise in water are calculated and presented. For the first time, the initial nonequilibrium vapor pressure and the initial growth rate of bubble nuclei with different initial embryo sizes and different rates of temperature rise are accurately modeled. The resulting algorithm provides a method by which the details of bubble nucleation in a superheated liquid can be predicted, leading to a better understanding of the kinetics of boiling. Model validation, accuracy and application are also presented and discussed.     

Flow boiling of liquid nitrogen in micro-tubes: Part I – The onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop

This paper is the first portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents mainly include the onset of nucleate boiling (ONB), two-phase flow instability and two-phase flow pressure drop. At ONB, mass flux drops suddenly while pressure drop increases, and apparent wall temperature hysteresis in the range of 1.0–5.0 K occurs. Modified Thom model can predict the wall superheat and heat flux at ONB. Moreover, stable long-period (50–60 s) and large-amplitude oscillations of mass flux, pressure drop and wall temperatures are observed at ONB for the 1.042 and 1.931 mm micro-tubes. Block phenomenon at ONB is also observed in the cases of high mass flux. The regions for the oscillations, block and stable flow boiling are classified. A physical model of vapor patch coalesced at the outlet is proposed to explain the ONB oscillations and block. Vapor generation caused by the flash evaporation is so large that it should be taken into account to precisely depict the variation of mass quality along the micro-tube. The adiabatic and diabatic two-phase flow pressure drop characteristics in micro-tubes are investigated and compared with four models including homogeneous model and three classical separated flow models. Contrary to the conventional channels, homogeneous model yields better prediction than three separated flow models. It can be explained by the fact that the density ratio of liquid to vapor for nitrogen is comparatively small, and the liquid and vapor phases may mix well in micro-tube at high mass flux due to small viscosity of liquid nitrogen, which leads to a more homogeneous flow. Part II of this study will focus on the heat transfer characteristics and critical heat flux (CHF) of flow boiling of liquid nitrogen in micro-tubes.     

Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels

A model based on the augmented Young–Laplace equation and the Clausius–Clapeyron equation was developed to describe the extended evaporating meniscus in a microchannel. The effects of the adsorbed film thickness, channel height and temperature-dependent thermophysical properties of the fluid are included in the model at wall superheats up to 50 K. The liquid flow is coupled with the vapor flow to obtain the mass transport across the liquid–vapor interface. The results show that the constant thermophysical property model greatly overestimates the liquid pressure difference and the total thin film heat transfer rate at higher superheats compared with the variable thermophysical property model. The adsorbed film thickness, which is controlled by the disjoining pressure limit, reaches a minimum near about 20 K superheat for water. The maximum film curvature and liquid pressure difference then decrease at superheats larger than 20 K. The effects of the capillary pressure limit produced by the channel height can be reduced by increasing the superheat.     

Two-dimensional numerical pore-scale investigation of oxygen evolution in proton exchange membrane electrolysis cells

Oxygen blocking the porous transport layer (PTL) increases the mass transport loss, and then limits the high current density condition of proton exchange membrane electrolysis cells (PEMEC). In this paper, a two-dimensional transient mathematical model of anode two-phase flow in PEMEC is established by the fluid volume method (VOF) method. The transport mechanism of oxygen in porous layer is analyzed in details. The effects of liquid water flow velocity, porosity, fiber diameter and contact angle on oxygen pressure and saturation are studied. The results show that the oxygen bubble transport in the porous layer is mainly affected by capillary pressure and follows the transport mechanism of ‘pressurization breakthrough depressurization’. The oxygen bubble goes through three stages of growth, migration and separation in the channel, and then be carried out of the electrolysis cell by liquid water. When oxygen breaks through the porous layer and enters the flow channel, there is a phenomenon that the branch flow is merged into the main stream, and the last limiting throat affects the maximum pressure and oxygen saturation during stable condition. In addition, increasing the liquid water velocity is helpful to bubble separation; changing the porosity and fiber diameter directly affects the width of pore throat and the correlative capillary pressure; increasing porosity, reducing fiber diameter and contact angle can promote oxygen breakthrough and reduce the stable saturation of oxygen.     

Subcooled water critical pressure and critical flow rate in a safety valve

Subcooled water critical flow phenomena in a safety valve are investigated experimentally at various subcoolings between 10 and 125 K, and about 1 MPa of the inlet pressure with three different disk lifts, 1, 2, and 3 mm. The purpose of this experiment is to find the effects of subcooling and disk lift and to visualize flow patterns in a safety valve when the critical condition is established. All of the experiments show the critical characteristics such as constant throat pressure and constant flow rate when the back pressure is sufficiently decreased. Two correlations, critical pressure ratio and non-equilibrium factor, are developed by using the present experimental data represented in the form of non-dimensional disk lift, subcooling, and pressure. Critical pressure ratios and non-equilibrium factors are considerably affected by different subcoolings while the effect of disk lifts on them is relatively small. A non-equilibrium critical mass flow correlation for the safety valve is also developed based on Fauske's non-equilibrium model and the presented experimental data. The predictions of the correlation are within ±11% of the experimental data.     

Effects of wall slip and temperature jump on heat and mass transfer characteristics of an evaporating thin film

A new mathematical model is developed to predict heat and mass transport characteristics of the evaporating thin film. The model considers effects of velocity slip and temperature jump at the solid-liquid interface, disjoining pressure, and surface tension. Three-dimensional nonequilibrium molecular dynamics simulations for coupling between the momentum and heat transfer at the nanoscale solid-liquid interface are performed to obtain the slip length and interfacial thermal resistance length. It is found that both slip length and interfacial thermal resistance length decrease significantly with the decreasing interface wettability of the liquid to the wall. Velocity slip and temperature jump at the solid-liquid interface intend to reduce the superheat degree of the evaporating thin film, and thus result in a sharp decrease of the heat and mass transport characteristics of the evaporating thin film. It is also noted that velocity slip and temperature jump at the solid-liquid interface show a more pronounced effect as the superheat degree increases.     

分层对液化石油气储罐热响应的影响

由于液化气热分层的存在，LPG储罐内的压力增长加快。同时，还可能影响到蒸汽爆炸。液化石油气温度越高，泄压时产生的气泡量就越大。当温度接近过热极限时变化更加剧烈。所以研究蒸汽爆炸，不可能不考虑分层。对液化石油气储罐内的热分层现象进行了数值模拟，并分析了分层现象对蒸汽爆炸等响应过程的影响。     

Experimental study on static flash evaporation of aqueous NaCl solution

Experimental study on static flash of aqueous NaCl solution was present. Initial waterfilm concentration and superheat ranged between 0 and 0.15 (mass fraction), between 1.7 and 53.9 K respectively. Influence of factors, such as initial waterfilm concentration, initial waterfilm height and superheat on thermo-properties during flash, such as waterfilm temperature, non-equilibrium fraction (NEF), and volumetric heat transfer coefficient were analyzed and compared with that on flash of pure water. Results suggested that higher initial waterfilm concentration suppressed liquid–vapor phase change, reduced the rate of flash evaporating and weakened the intensity of boiling heat transfer. But the influences of superheat and initial waterfilm height on flash of aqueous NaCl solution were same as that on pure water. At last, NEF was fitted with relative error between ?49.30% and 55.2%, upon which volumetric heat transfer coefficient could be calculated with relative error varying between ?12.6% and 18.8%.     

A parametric study of refrigerant flow in non-adiabatic capillary tubes

This paper presents a parametric analysis of refrigerant flow through capillary tube–suction line heat exchangers, used in domestic refrigeration systems. The analysis is based on a homogeneous model developed by the authors. The model is based on the numerical solution of fundamental equations of conservation of mass, momentum and energy of refrigerant flow. The refrigerant flow characteristics are investigated by varying thermodynamic (e.g. condensing temperature, evaporating temperature, inlet sub-cooling, suction line superheat) and geometric parameters (e.g. inlet adiabatic length, heat exchanger length and internal diameter of the capillary tube) of the capillary flow. The source of divergence in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the capillary heat exchanger.     

Release and dispersion modeling of cryogenic under-expanded hydrogen jets

In the present work performed within the framework of the SUSANA EC-project, we address the release and dispersion modeling of hydrogen stored at cryogenic temperatures and high pressures. Due to the high storage pressures the resulting jets are under-expanded. Due to the low temperatures the choked conditions can be two-phase. For the release modeling the homogeneous equilibrium model (HEM) was used combined with NIST equation of state for hydrogen. For the dispersion modeling the 3d CFD methodology was used combined with a) a notional nozzle approach to bridge the expansion to atmospheric pressure region that exists near the nozzle, b) the ideal gas assumption for hydrogen and air and c) the standard (buoyancy included) k–ε turbulence model. Predicted release choked mass fluxes are compared against 37 experiments from literature. Predicted steady state hydrogen concentrations along the jet axis are compared against five dispersion experiments from literature as well as the Chen and Rodi correlation and the behavior of the proposed release and dispersion modeling approaches is assessed.     

A homogeneous non-equilibrium two-phase critical flow model

A non-equilibrium two-phase single-component critical (choked) flow model for cryogenic fluids is developed from first principle thermodynamics. Modern equations-of-state (EOS) based upon the Helmholtz free energy concepts are incorporated into the methodology. Extensive validation of the model is provided with the NASA cryogenic data tabulated for hydrogen, methane, nitrogen, and oxygen critical flow experiments performed with four different nozzles. The model is used to develop a hydrogen critical flow map for stagnation states in the liquid and supercritical regions.     

Numerical predictions of cryogenic hydrogen vertical jets

Comparison of Computational Fluid Dynamics (CFD) predictions with measurements is presented for cryo-compressed hydrogen vertical jets. The stagnation conditions of the experiments are characteristic of unintended leaks from pipe systems that connect cryogenic hydrogen storage tanks and could be encountered at a fuel cell refueling station. Jets with pressure up to 5 bar and temperatures just above the saturation liquid temperature were examined. Comparisons are made to the centerline mass fraction and temperature decay rates, the radial profiles of mass fraction and the contours of volume fraction. Two notional nozzle approaches are tested to model the under-expanded jet that was formed in the tests with pressures above 2 bar. In both approaches the mass and momentum balance from the throat to the notional nozzle are solved, while the temperature at the notional nozzle was assumed equal to the nozzle temperature in the first approach and was calculated by an energy balance in the second approach. The two approaches gave identical results. Satisfactory agreement with the measurements was found in terms of centerline mass fraction and temperature. However, for test with 3 and 4 bar release the concentration was overpredicted. Furthermore, a wider radial spread was observed in the predictions possibly revealing higher degree of diffusion using the k-ε turbulence model. An integral model for cryogenic jets was also developed and provided good results. Finally, a test simulation was performed with an ambient temperature jet and compared to the cold jet showing that warm jets decay faster than cold jets.     

Theoretical simulation of explosive boiling

The purpose of this paper is to describe the complex thermal and mass transfer processes taking place in a liquid as the limit of superheat is approached and to develop a set of criteria for estimating the limit of superheat in practical cases relevant to some MEMS applications, where an extremely small liquid volume may be heated non-uniformly. A mechanistic model is presented for estimating the spatial location and time for reaching the limit of superheat in a non-uniformly heated volume of liquid.     

Efficiency analysis of depressurization process and pressure control strategies for liquid hydrogen storage system in microgravity

In order to investigate dynamic characteristics of pressure fluctuation and thermal efficiency of a liquid hydrogen (LH₂) storage system during depressurization process under microgravity condition, a transient CFD model of LH₂ tank is established. Based on the assumption of lumped vapor, a UDF code is developed to solve phase change and heat transfer between liquid phase and vapor one. The thermal efficiency is provided for assessing the performance of different pressure control methods. Results show that raising the injection velocity and decreasing the temperature of the injection liquid can enhance the effect of fluid mixing and shorten the depressurization time. Increasing the pressure lower limit can also improve the efficiency of depressurization process. The model can predict the tendency of pressure changes in the tank, and provide theoretical guide to design LH₂ tank and optimize its parameters for space application.     

Flashing phenomena of depressurized liquid nitrogen in a pressure vessel. Part 2: Mist formation and behavior of the liquid surface in the early depressurization process

Flashing of liquid nitrogen in a pressure vessel (cryostat) was observed at depressurization rates from 0.01 to 4.0 MPa/s. The explosive boiling behavior was observed by using a video camera. Pressure and temperature changes in the pressure vessel were measured. In the case of high depressurization rates, mist formation was observed in the vapor phase near the vapor—liquid interface in the early stages of the depressurization process. The mist layer became more dense as the depressurization rate increased. Observations of mist formation and the estimated temperature drop of the vapor under an adiabatic expansion process show that mist formation depends on the vapor expansion and boiling near the liquid surface. Mist formation in flashing phenomena plays an important role in the relaxation of thermal nonequilibrium states between the subcooled vapor and the superheated liquid generated by depressurization. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 327–335, 1998     

A novel interphase mass transfer model toward the VOF simulation of subcooled flow boiling

In this study, a novel interphase mass transfer model has been developed to predict mass and energy exchange in the vicinity of the phase interface. The proposed model involves the new time relaxation parameter which takes into account the effect of the subcooling, the wall superheat, and Reynolds number, and is obtained from simulation results by the method of trial and error. Transient simulations of subcooled flow boiling in Hua’s experimental horizontal rectangular channel are performed. The Volume of Fluid (VOF) method is used to track the vapor–liquid interface using OpenFOAM software package. The constant coefficients of new time relaxation parameter are determined using fitted method. The predicted results show that the deviation between the predicted and experimental wall superheats using the proposed model, which is within 20%, is smaller than that of Lee model. As a further step, the novel interphase mass transfer model has been validated in other experimental data under similar condition. These results indicate that the novel interphase mass transfer model is quite accurate and robust.     

Experimental study on static/circulatory flash evaporation

Comparative study on heat and mass transfer properties of static/circulatory flash evaporation, i.e., non-equilibrium fraction (NEF), evaporated mass and heat transfer coefficient, was presented based on two experimental systems. NEF evolution in static flash was newly fitted by error function equation, based on which a unified calculating model for heat and mass transfer properties of both flashes was set up initially. At last, heat transfer coefficient was redefined as average heat flux released from unit volume of waterfilm under unit superheat. Results suggested that this coefficient was a time-depended function and a peak value existed in its evolution versus time.     

1 kWe sodium borohydride hydrogen generation system: Part II: Reactor modeling

Sodium borohydride (NaBH₄) hydrogen storage systems offer many advantages for hydrogen storage applications. The physical processes inside a NaBH₄ packed bed reactor involve multi-component and multi-phase flow and multi-mode heat and mass transfer. These processes are also coupled with reaction kinetics. To guide reactor design and optimization, a reactor model involving all of these processes is desired. A one-dimensional numerical model in conjunction with the assumption of homogeneous catalysis is developed in this study. Two submodels have been created to simulate non-isothermal water evaporation processes and pressure drop of two-phase flow through the porous medium. The diffusion coefficient of liquid inside the porous catalyst pellets and the mass transfer coefficient of water vapor are estimated by fitting experimental data at one specified condition and have been verified at other conditions. The predicted temperature profiles, fuel conversion, relative humidity and pressure drops match experimental data reasonably well.     

THERMODYNAMIC ANALYSIS OF THE INTRINSIC STABILITY OF SUPERHEATED LIQUID IN A MICROMECHANICAL ACTUATOR WITH ELASTIC WALLS

The rise in internal pressure and or the increase in volume that results from heating of a liquid in a closed chamber can be used as a thermally driven actuator mechanism in MEMS components. The conditions at which phase instability and subsequent homogeneous nucleation occur in such systems is often of central importance, either because bubble formation is undesirable or because bubble formation is a desired part of the design behavior. This article examines the thermophysics of the onset of nucleation in a superheated liquid in a chamber with an elastic wall. Classical limits of thermodynamic intrinsic stability, which are usually derived for a system held at constant pressure, are not directly applicable to a system of this type. A model analysis is developed from the results of statistical thermodynamics theory and a Redlich-Kwong equation of state that can be used to predict the onset of nucleation in a liquid chamber with an elastic wall. The model predicts that the elastic modulus of the wall material together with the thermodynamic properties of the fluid dictate whether the thermodynamic limit of superheat will be reached during heating of liquid in the actuator chamber.