Modeling liquid hydrogen cavitating flow with the full cavitation model

Cavitation is the formation of vapor bubbles within a liquid where flow dynamics cause the local static pressure to drop below the vapor pressure. This paper strives towards developing an effective computational strategy to simulate liquid hydrogen cavitation relevant to liquid rocket propulsion applications. The aims are realized by performing a steady state computational fluid dynamic (CFD) study of liquid hydrogen flow over a 2D hydrofoil and an axisymmetric ogive in Hord's reports with a so-called full cavitation model. The thermodynamic effect was demonstrated with the assumption of thermal equilibrium between the gas phase and liquid phase. Temperature-dependent fluid thermodynamic properties were specified along the saturation line from the “Gaspak 3.2” databank. Justifiable agreement between the computed surface pressure, temperature and experimental data of Hord was obtained. Specifically, a global sensitivity analysis is performed to examine the sensitivity of the turbulent computations to the wall grid resolution, wall treatments and changes in model parameters. A proper near-wall model and grid resolution were suggested. The full cavitation model with default model parameters provided solutions with comparable accuracy to sheet cavitation in liquid hydrogen for the two geometries.     

Computational fluid dynamics simulations of direct contact heat and mass transfer of a multicomponent two-phase film flow in an inclined channel at sub-atmospheric pressure

A method for simultaneous heat and multicomponent mass transfer incorporated with the volume of fluid surface tracking method was developed in a two-dimensional inclined channel. The process in the channel includes direct contact condensation of hydrocarbon mixtures with and without noncondensable gas, and distillation effect is also considered. Interfacial transport was performed by a multicomponent phase change model in kinetic forms considering the assumption of thermodynamic equilibrium at the vapor–liquid or vapor/gas–liquid interface using Peng–Robinson equations. The shear-stress transport k–ω turbulence model damped near the vapor–liquid or vapor/gas–liquid interface was used. The hydrocarbon mixtures in both phases were described by five pseudo-components, and Stefan–Maxwell equations were used to describe diffusional interactions in the multicomponent system. Parametric studies were performed to investigate further the model with various boundary conditions. Simulations for a binary system were also performed for a preliminary validation. For the liquid phase, similar trends of the Sherwood numbers were found between the results by simulations and predicted by the Penetration Theory. For the vapor phase, good agreement was observed between the results by empirical correlation and simulations.     

Effect of gravity conditions on heat transfer and flow fluctuations of liquid hydrogen in a non-isothermal horizontal circular tube

Liquid hydrogen phase transition is a common phenomenon in space missions for space vehicles using low temperature liquid hydrogen as propellant. In this study, a numerical model with coupled RANS solver and VOF/Level-set method was used to simulate the liquid hydrogen phase transition in a non-isothermal horizontal circular tube under different gravity conditions (1g-10^?4 g). The gas phase hydrogen produced by evaporation of liquid hydrogen was calculated by Lee model. The statistics of the overall volume, heat flux, mass flow rate, mean velocity of gas phase hydrogen was carried out. The data results shown that the flow fluctuations were strongest under the gravity acceleration of 10^?1 g relative to other gravity conditions. The average bubble volume at 10^?1 g was the smallest, which was 11.58% smaller than that at 10^?3 g condition. The intermittent contact with the tube wall, which leaded to intermittent long bubble and flow resistance, was the main reason.     

Extended compressible thermal cavitation model for the numerical simulation of cryogenic cavitating flow

The compressibility of the vapour–liquid phase is indispensable in simulating liquid hydrogen or liquid nitrogen cavitating flow. In this paper, a numerical simulation method considering compressibility and combining the thermal effects of cryogenic fluids was developed. The method consisted of the compressible thermal cavitation model and RNG k–ε turbulence model with modified turbulent eddy viscosity. The cavitation model was based on the Zwart–Gerber–Belamri (ZGB) model and coupled the heat transfer and vapour–liquid two-phase state equations. The model was validated on cavitating hydrofoil and ogive, and the results agreed well with the experimental data of Hord in NASA. The compressibility and thermal effects were correlated during the phase change process and compressibility improved the accuracy of the numerical simulation of cryogenic cavitating flow based on thermal effects. Moreover, the thermal effects delayed or suppressed the occurrence and development of cavitation behaviour. The proposed modified compressible ZGB (MCZGB) model can predict compressible cryogenic cavitating flow at various conditions.     

富氧燃烧烟气加压脱硝的实验与模拟研究

为了解决富氧燃烧烟气中NOx对CO2资源化利用的影响问题,实验研究了加压条件下鼓泡与液膜反应器中液体对NOx的吸收作用。建立了高压下NOx吸收的传质及动力学耦合模型,利用该模型对鼓泡吸收和液膜吸收进行了模拟,获得了不同压力下气液相产物的浓度,并与实验结果进行了对比。结果表明:气液相产物的实验结果与模拟结果吻合,且模型的氮元素守恒率高于90%;最佳吸收压力为1.5 MPa;吸附在反应器壁面的液膜对于NOx有较强的吸收作用,液膜的成分主要是HNO3。     

COSMO-RS based CFD model for flat surface evaporation of non-ideal liquid mixtures

A new layer evaporation model for multi-component real liquid mixtures, based on activity coefficient calculation on quantum chemical basis is presented. The proposed method applies the COSMO-RS theory for the estimation of vapour–liquid equilibrium of non-ideal solutions and the Maxwell–Stefan diffusion and convection theory for the calculation of gas phase transport characteristics of the components. Computational fluid dynamics (CFD) simulation by COMSOL Multiphysics and solvation mixture thermodynamics by COSMOtherm program packages have been used to perform the calculations for the quasi-equilibrium evaporation of compounds from liquid surface. The activity coefficients, the liquid and vapour phase compositions, the cumulative and components evaporation fluxes have been computed. The good predictive ability of the resulting simulation model was tested on experimental evaporation data of 2–5 components mixtures.     

Numerical modeling of liquid water motion in a polymer electrolyte fuel cell

A three dimensional transient model fully coupling the two phase flow, species transport, heat transport, and electrochemical processes is developed to investigate the liquid water formation and transport in a polymer electrolyte fuel cell (PEFC). This model is based on the multiphase mixture (M2) formulation with a complete treatment of two phase transport throughout the PEFC, including gas channels, enabling modeling the liquid water motion in the entire PEFC. This work particularly focuses on the liquid water accumulation and transport in gas channels. It is revealed that the liquid water accumulation in gas channels mainly relies on three mechanisms and in the anode and cathode may rely on different mechanisms. The transport of liquid water in the anode channel basically follows a condensation–evaporation mechanism, in sharp contrast to the hydrodynamic transport of liquid water in the cathode channel. Liquid water in the cathode channel can finally flow outside from the exit along with the exhaust gas. As the presence of liquid water in gas channels alters the flow regime involved, from the single phase homogeneous flow to two phase flow, the flow resistance is found to significantly increase.     

Prediction of ash flow temperature based on liquid phase mass fraction by FactSage

To investigate the relationship between flow temperature (FT) and the temperature that corresponds to different liquid phase mass fractions, the FTs of 10 coal ashes and 45 synthetic ashes were tested by an ash-fusion-temperature analyzer. The linear correlation between the FT and the temperature that corresponded to a 90% liquid phase (T₉₀) calculated by FactSage was: FT = 245.837 + 0.765T₉₀, and its correlation coefficients was 0.91. This model may be more accurate for low Si/Al coal. The differences between measured and predicted FT based on the model were in the measuring error range.     

Theoretical and experimental study of volumetric change rate during phase change process

The solid‐to‐liquid phase change material can be used to convert the thermal energy of low quality into mechanical energy. Its volumetric change rate has a great effect on the converting efficiency. The mathematical model of the volumetric change rate for the phase change processes of hexadecane within a cylindrical container was presented. A special experimental device was designed and constructed to verify the numerical model. The results at different Stefan numbers of the experiments matched well with those from the numerical simulations. The influences of Stefan number, Biot number and radius of cylinder on the volumetric change rate were studied and analyzed. The results showed that the volumetric change rate depends on the mass fraction of liquid phase and the difference between liquid and solid density of the materials. All the factors affecting the phase change rate will influence the volumetric change rate. The volumetric expansion rate is less than theoretical value under an external pressure. While a high‐pressure situation is taken into consideration, the numerical model should also be modified by adding a function calculating density varying with pressure to ensure that the model operates properly. The power output can be enhanced by reducing the total time of melting. It can also be improved when the phase change material is partly melted at a volumetric expansion rate less than 100% of the total value. Copyright © 2008 John Wiley & Sons, Ltd.     

CFD simulation of heat transfer and phase change characteristics of the cryogenic liquid hydrogen tank under microgravity conditions

The heat transfer and phase change processes of cryogenic liquid hydrogen (LH₂) in the tank have an important influence on the working performance of the liquid hydrogen-liquid oxygen storage and supply system of rockets and spacecrafts. In this study, we use the RANS method coupled with Lee model and VOF (volume of fraction) method to solve Navier-stokes equations. The Lee model is adopted to describe the phase change process of liquid hydrogen, and the VOF method is utilized to calculate free surface by solving the advection equation of volume fraction. The model is used to simulate the heat transfer and phase change processes of the cryogenic liquid hydrogen in the storage tank with the different gravitational accelerations, initial temperature, and liquid fill ratios of liquid hydrogen. Numerical results indicate greater gravitational acceleration enhances buoyancy and convection, enhancing convective heat transfer and evaporation processes in the tank. When the acceleration of gravity increases from 10^?2 g0 to 10^?5 g0, gaseous hydrogen mass increases from 0.0157 kg to 0.0244 kg at 200s. With the increase of initial liquid hydrogen temperature, the heat required to raise the liquid hydrogen to saturation temperature decreases and causes more liquid hydrogen to evaporate and cools the gas hydrogen temperature. More cryogenic liquid hydrogen (i.e., larger the fill ratio) makes the average fluid temperature in the tank lower. A 12.5% reduction in the fill ratio resulted in a decrease in fluid temperature from 20.35 K to 20.15 K (a reduction of about 0.1%, at 200s).     

Temperature effects on the effective thermal conductivity of phase change materials with two distinctive phases

This study reports on an analytical estimation of the effective thermal conductivity of phase change materials (PCMs) and its dependence upon temperature. During the phase change process, two distinctive phases (solid to liquid) co-exist and the effective thermal conductivity of the PCM varies significantly with temperature. To analytically estimate the variation, the classical Series model assuming one-dimensional (1D) heat conduction normal to the solid–liquid interface was employed. For model validation, experimental measurements with paraffin were conducted covering a wide range of temperature (including the phase change temperature). It was demonstrated that the effective thermal conductivity varies mainly with the fraction of liquid (or solid) phase, bounded by the solid phase conductivity as well as the liquid phase conductivity, whilst the fraction of the liquid phase increased non-linearly with increasing temperature.     

A molecular dynamics simulation investigation of fuel droplet in evolving ambient conditions

Molecular dynamics simulations are applied to model fuel droplet surrounded by air in a spatially and temporally evolving environment. A numerical procedure is developed to include chemical reactions into molecular dynamics. The model reaction is chosen to allow investigation of the position of chemical reactions (gas phase, surface, liquid phase) and the behavior of typical products (alcohols and aldehydes). A liquid droplet at molecular scale is seen as a network of fuel molecules interacting with oxygen, nitrogen, and products of chemical fuel breakdown. A molecule is evaporating when it loosens from the network and diffuses into the air. Naturally, fuel molecules from the gas phase, oxygen and nitrogen molecules can also be adsorbed in the reverse process into the liquid phase. Thus, in the presented simulations the time and length scales of transport processes – oxygen adsorption, diffusion, and fuel evaporation are directly determined by molecular level processes and not by model constants. In addition, using ab initio calculations it is proven that the reaction barriers in liquid and gas phases are similar.     

Analysis of a counter-current vapor flow absorber

Analytical investigation of a combined heat and mass transfer process in a counter-current ammonia-water based absorber is presented. The model accounts for both liquid and vapor phase mass transfer resistances, and uses empirical correlations to predict the heat and mass transfer coefficients. The model was used to analyze a lamella plate based absorber with falling film absorption. A finite difference technique was employed to solve the numerical model. It was found that the major portion of the mass transfer resistance lies primarily in the liquid phase. A parametric analysis was also conducted to assess the effect of various parameters on the performance of the absorber.     

含二氧化硅气凝胶和相变材料三层玻璃窗热性能分析

为了研究含二氧化硅气凝胶和相变材料三层玻璃窗对严寒地区建筑能耗的影响,建立了相变材料层与其他透明壁层结合发生的传热数值模型。分析了含二氧化硅气凝胶和相变材料三层玻璃窗在不同二氧化硅气凝胶厚度、导热系数和不同保温材料下的动态热调节性能,得到了含二氧化硅气凝胶和相变材料三层玻璃窗内表面热流密度和液相率随时间的变化规律。结果表明:随着二氧化硅气凝胶厚度增加,总传热量降低和液相率增加,当二氧化硅气凝胶厚度为20～30 mm时,可以实现有效的利用太阳能;随着二氧化硅气凝胶导热系数增加,总传热量升高和液相率降低;当二氧化硅气凝胶的导热系数从0.022降低到0.014 W/(m·K)时,最大液相率从0.83增加到1.00。二氧化硅作为保温层比相变材料作为保温层具有更好的保温隔热作用。     

Direct simulation of spray cooling: Effect of vapor bubble growth and liquid droplet impact on heat transfer

Numerical modeling of multiphase flow using level set method is discussed. The 2-D model considers the effect of surface tension between liquid and vapor, gravity, phase change and viscosity. The level set method is used to capture the movement of the free surface. The detail of incorporating the mechanism of phase change in the incompressible Navier–Stokes equations using the level set method is described. The governing equations are solved using the finite difference method. The computer model is used to study the spray cooling phenomenon in the micro environment of about 40 μm thick liquid layer with vapor bubble growing due to nucleation. The importance of studying the heat transfer mechanism in thin liquid film for spray cooling is identified. The flow and heat transfer details are presented for two cases: (1) when the vapor bubble grows due to nucleation and (2) merges with the vapor layer above the liquid layer and when a liquid droplet impacts the thin liquid layer with vapor bubble growing.     

Numerical study of two‐phase flow of liquid helium in a vertical converging‐diverging nozzle

The fundamental characteristics of the two‐dimensional gas‐liquid two‐phase flow of liquid helium through a vertical converging‐diverging duct near the lambda point are numerically investigated to realize the further development and high performance of new multiphase superfluid cooling systems. First, the governing equations of the two‐phase flow of liquid helium based on the unsteady thermal nonequilibrium multifluid model with generalized curvilinear coordinates system are presented, and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two‐dimensional structure of the gas‐liquid two‐phase flow of liquid helium though vertical converging‐diverging nozzle is shown in detail, and it is also found that the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid‐ to vapor‐phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 432–448, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20071     

Numerical investigation of the thermal mechanism of the solid-liquid phase changing process

由于相变换热储能技术可以协调能量在时间和空间尺度的分配,成为了目前研究的热点问题。本工作用焓值法分别对充填低温无机盐相变材料的二维和三维管壳式相变储能换热器模型的储/放热特性进行了模拟研究,采用Boussinesq近似研究了液相区密度变化引起的自然对流的影响。研究表明换热器的入口温度对相变换热效率影响显著;在储热过程中自然对流发挥了重要作用,换热效率与液相区的运动状态直接相关,而放热过程中的热交换主要依靠热传导完成;三维模拟的结果表明换热管出口温度与管壁的平均努赛尔数高度相关,且换热管水平放置的换热效率略低于竖直放置。     

Capillary rise in a circular tube with interfacial condensation process

In this work, we develop a theoretical model for the spontaneous imbibition process of a non-isothermal liquid body in a capillary tube. The imbibition front is in contact with a saturated vapor originating a direct condensation at the interface. In the mathematical model, the liquid phase has been coupled with the saturated vapor through the interfacial heat flux condition. The model predicts the evolution for the imbibition front being present the phase change occurring in the imbibition front at a constant rate, which is driven by a temperature difference at the interface between the liquid and the saturated vapor. The results shown a deviation from the Lucas–Washburn solution for the imbibition front, as a function of the dimensionless parameter involved in the analysis: the Jakob number, Ja; β representing the ratio of a characteristic equilibrium height to the characteristic thermal penetration, and ε, which depends on the physical properties of the liquid that penetrates the capillary tube.     

A Numerical Method for Multiphase Incompressible Thermal Flows with Solid–Liquid and Liquid–Vapor Phase Transformations

ABSTRACT

A numerical method for multiphase incompressible thermal flows with solid–liquid and liquid–vapor phase transformations is presented. The flow is mainly driven by thermocapillary force and vaporization. Based on the level set method and mixture continuum model, a set of governing equations valid for solid, liquid, and vapor phases is derived, considering phase boundary conditions as source terms in the transport equations. The vaporization process is treated as a source term in the continuity equation. The model developed is applied to the laser welding process, where the flow is coupled with optical phenomena. Formation and collapse of a laser-created hole is simulated.     

A new model of phase change process for thermal energy storage

Thermal energy can be converted into mechanical energy through the melting process of a phase change material (PCM). A PCM mixed with an insoluble liquid has higher energy converting efficiency during the whole melting process, where the massive microvacuum formed during the freezing process is filled by the insoluble liquid, which increases utilization of the volume change. The traditional theoretical model of the phase change process is unable to sufficiently describe the mixed PCM; therefore, a new model aimed at analyzing the characteristics of the volumetric change rate, as well as the freezing and melting times of the mixed PCM, is theoretically constructed. In this paper, the effective heat capacity method is used, and the effects of porosity are considered when the PCM is in the solid state. Comparisons of this model with the traditional model are carried out using both simulations and experiments for different pressures and geometric structures. Our results indicate that the introduced model has better accuracy when describing the phase change process of the pure PCM mixed with an insoluble liquid.