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     

Laser heating: jet emanating from laser induced cavity

Laser heating of steel surface and cavity formation during laser irradiation pulse are investigated. The recession of the solid surface due to melting and evaporation is modeled using an energy method. Jet emerging from the laser induced cavity and expanding into stagnant water, resembling laser shock processing, is also simulated. Governing flow equations are solved numerically using a control volume approach employing a moving mesh in the solution domain. This is because of the recessing surfaces of the vapor, liquid and solid phases during the heating pulse. It is found that mushy zone size at liquid–vapor interface is larger than that of at solid–liquid interface. Expansion of the vapor jet, emanating from the cavity and expanding into stagnant water ambient, is high in the axial direction in the early heating period, and as the time progresses the radial expansion of the jet becomes visible due to pressure build up in the jet frontal area. Considerably high recoil pressure is developed in the cavity due to high recession velocity of cavity surface and expansion velocity of vapor jet.     

Model for boiling explosion during rapid liquid heating

The process of rapid liquid heating with a linearly increasing boundary temperature condition has been simulated by applying the analytical solution of 1D semi-infinite heat conduction in association with the molecular theory of homogeneous nucleation boiling. A control volume having the size of a characteristic critical cluster at the liquid boundary is considered, and the corresponding energy balance equation is obtained by considering two parallel competing processes that take place inside the control volume, namely, transient external energy deposition and internal energy consumption due to bubble nucleation and subsequent growth. Depending on the instantaneous rate of external energy deposition and boiling heat consumption within the control volume, a particular state is defined as the boiling explosion condition in which bubble generation and growth cause the liquid sensible energy to decrease. The obtained results are presented in terms of the average liquid temperature rise within the control volume, maximum attainable liquid temperature before boiling explosion and the time required to achieve the condition of boiling explosion. The model is applied for the case of water heating at atmospheric pressure with initial and boundary conditions identical to those reported in the literature. Model predictions concerning boiling explosion are found to be in good agreement with the experimental observations. The boiling explosion condition as predicted by the present model is verified by comparing the heat flux across the liquid–vapor interface with the corresponding limit of maximum possible heat flux, q_max,max, at the time of boiling explosion. A comparative study between the actual heat flux and the limit of maximum heat flux, q_max,max, at the time of boiling explosion for different rates of boundary heating indicates that, with much higher boundary heating rates, it is possible to heat the liquid to a much higher temperature before theoretical instantaneous boiling explosion occurs.     

超音速分离管中水蒸气凝结相变的数值研究

基于超音速分离管中混合气体流动属于伴随凝结相变的可压缩、跨音速的特点,建立了考虑传质效应与非平衡凝结过程的数学模型,并采用数值方法对伴随水蒸气凝结的超音速分离管中的流动进行分析研究。以空气、水蒸气及液态水为流动介质,采用两相流动中的VOF模型结合凝结相变模型以及组分传输模型,研究不同进出口参数及不同水蒸气含量对凝结流场的影响。研究结果表明,所建立的分离管内部非平衡凝结相变模型可以较好的再现超音速流中的凝结成核及液滴生长过程;数值计算结果表明,入口压力、温度及水蒸气含量对分离管内流动凝结过程有直接且重要的影响。因此在进行超音速分离管设计时,考虑温度压力参数的同时,考虑水蒸气含量对分离管性能的影响也是非常重要的。     

Liquid phase evaporation on the normal shock wave in moist air transonic flows in nozzles

This paper presents a numerical analysis of the atmospheric air transonic flow through de Laval nozzles.By nature,atmospheric air always contains a certain amount of water vapor.The calculations were made using a Laval nozzle with a high expansion rate and a convergent-divergent (CD) "half-nozzle",referred to as a transonic diffuser,with a much slower expansion rate.The calculations were performed using an in-house CFD code.The computational model made it possible to simulate the formation of the liquid phase due to spontaneous condensation of water vapor contained in moist air.The transonic flow calculations also take account of the presence of a normal shock wave in the nozzle supersonic part to analyze the effect of the liquid phase evaporation.     

Shock waves in multiphase flow of fuel–coolant interaction

The interaction of fuel and coolant (FCI) is a complex multiphase process due to the fact that the fragmentation and heat transfer process are not easy to cast in simple mathematical formulas. This paper, a theoretical model has been developed by considering multiphase flow shock wave propagating of fuel–coolant interaction. Analysis of a steady-state vapour explosion in one dimension has been carried out by applying the conservation laws of mass, momentum, energy and the appropriate equation of state for an interaction of molten dioxide uranium and water. Using the model, we predicted the pressure magnitudes behind shock wave of vapour explosion varied with the initial volume fraction of vapour, melt mass concentrations, liquid entrained fraction and when they were considered as dangerous.     

Dynamics of a vapor bubble on a heated substrate

The dynamics of a vapor bubble between its liquid phase and a heated plate is studied in relation to the breakdown and recovery of the film boiling. By examining the expansion and the contraction of the vapor bubble the film boiling and transition boiling states are predicted. Conservation laws in the vapor, solid, and liquid phases are invoked along with fully nonlinear, coupled, free boundary conditions. These coupled system of equations are reduced to a single evolution equation for the local thickness of the vapor bubble by using a long-wave asymptotics, which is then solved numerically to yield the transient motion of the vapor bubble. Of the numerous parameters involved in this complex phenomenon we focus on the effects of the degree of superheat from the solid plate, that of the supercooling through the liquid, and the wetting/dewetting characteristics of the liquid on the solid plate. A material property of the substrate thus is incorporated into the criteria for the film boiling based on hydrodynamic models.     

快速降压环境下盐水液滴蒸发过程的传热传质研究

采用VOF（Volume of Fluid）自由表面捕捉方法对盐水液滴蒸发过程中气液界面进行追踪,建立了降压环境下单个盐水液滴的蒸发模型,并通过盐水液滴蒸发的实验数据验证了此模型。通过对盐水液滴在相变过程中的形态变化以及传热传质特性的分析,研究了液滴内部温度、速度、蒸汽分布以及液滴形态等随时间的变化情况,分析了影响盐水液滴降压蒸发过程的主要因素。结果表明：在降压蒸发过程中液滴形态变化和环境中蒸汽的分布会随速度场的变化而变化;蒸发过程中初始盐组分质量浓度越大的液滴蒸发速率越缓慢,最终能达到的液滴最低中心温度越高,且液滴中心温度回升速度越慢、回升时间也越晚;液滴初始温度对蒸发速率影响较大,初始温度越高,表面蒸发速率越快,液滴中心温度回升速度越快。     

Physical mechanisms of heat transfer during single bubble nucleate boiling of FC-72 under saturation conditions. II: Theoretical analysis

This paper is the second part of a two-part study concerning the dynamics of heat transfer during the nucleation process of FC-72 liquid. The experimental findings on the nature of different heat transfer mechanisms involved in the nucleation process were discussed in part I. In this paper, the experimental results are compared with the existing boiling models. The boiling models based on dominance of a single mechanism of heat transfer did not match the experimental results. However, the Rohsenow model was found to closely predict the heat transfer through the microconvection mechanism that is primarily active outside the bubble/surface contact area. An existing transient conduction model was modified to predict the surface heat transfer during the rewetting process (i.e. transient conduction mechanism). This model takes into account the gradual rewetting of the surface during the transient conduction process rather than a simple sudden surface coverage assumption commonly used in the boiling literature. The initial superheat energy of the microlayer (i.e. microlayer sensible energy) was accurately calculated and found to significantly contribute in microlayer evaporation. This even exceeded the direct wall heat transfer to microlayer at high surface superheat temperatures. A composite model was introduced that closely matches our experimental results. It incorporates models for three mechanisms of heat transfer including microlayer evaporation, transient conduction, microconvection, as well as their influence area and activation time. The significance of this development is that, for the first time, all submodels of the composite correlation were independently verified using experimental results.     

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.     

垂直窄缝通道内环状流沸腾传热特性

本研究基于液膜和蒸汽的质量、动量和能量方程,建立了均匀热流垂直窄缝通道内环状流沸腾传热模型,通过相关文献估算环状流起始点处液膜厚度,利用有限差分法对环状流模型方程组进行数值求解,得到沿流道环状流区域的液膜厚度,并进一步预测了局部沸腾传热系数,结果表明:环状流区域的局部沸腾传热系数随质量流量和干度的增加而增加,与Kenning关联式对比,模型预测沸腾传热系数较关联式计算值偏低。将不同工况下的226组两相环状流实验数据与模型预测结果进行对比,平均绝对误差为18.2%。     

An Equation of State for Fluids by Applying the Tower—Well Potential Model

A simple theoretical equation of state is derived by applying the Tower-Well potential model about the molecular distribution based on the generalized van der Waals partition function. It needs only three molecular parameters which have distinct physical meanings. The resulting equation of state predicts rather well the vapor pressures, saturated liquid volumes, saturated vapor volumes and PVT thermodynamic properties of polar and structurally complex molecules over a wide temperature and pressure range.     

Theoretical analysis of the stability of vapor film in subcooled film boiling on a horizontal wire

Linear stability analysis of a thin vapor film in subcooled film boiling on a horizontal cylinder is reported. The effects of liquid inertia, vapor viscosity and compressibility, and heat transfer were taken into account. Theoretical predictions of the heat transfer coefficient at the neutral stability point were compared with experimental data at the minimum-heat-flux point that was obtained during rapid quenching of thin horizontal wires in water and ethanol. At high liquid subcooling, the experimental value was 60% of the theoretical prediction irrespective of the wire diameter and quenching liquid. This difference was considered to be due to the nonuniformity of the vapor film which was neglected in the theoretical analysis. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 219–235, 1997     

Rethinking “BLEVE explosion” after liquid hydrogen storage tank rupture in a fire

The underlying physical mechanisms leading to the generation of blast waves after liquid hydrogen (LH2) storage tank rupture in a fire are not yet fully understood. This makes it difficult to develop predictive models and validate them against a very limited number of experiments. This study aims at the development of a CFD model able to predict maximum pressure in the blast wave after the LH2 storage tank rupture in a fire. The performed critical review of previous works and the thorough numerical analysis of BMW experiments (LH2 storage pressure in the range 2.0–11.3 bar abs) allowed us to conclude that the maximum pressure in the blast wave is generated by gaseous phase starting shock enhanced by combustion reaction of hydrogen at the contact surface with heated by the shock air. The boiling liquid expanding vapour explosion (BLEVE) pressure peak follows the gaseous phase blast and is smaller in amplitude. The CFD model validated recently against high-pressure hydrogen storage tank rupture in fire experiments is essentially updated in this study to account for cryogenic conditions of LH2 storage. The simulation results provided insight into the blast wave and combustion dynamics, demonstrating that combustion at the contact surface contributes significantly to the generated blast wave, increasing the overpressure at 3 m from the tank up to 5 times. The developed CFD model can be used as a contemporary tool for hydrogen safety engineering, e.g. for assessment of hazard distances from LH2 storage.     

Homogeneous non-equilibrium two-phase choked flow modeling

The estimation of the release conditions is critical input to subsequent risk assessment accident analysis. To this respect a new homogeneous non-equilibrium two-phase model is proposed to simulate the depressurization from stagnation conditions leading to the bubbly flow regime. The proposed model, being intermediate between HEM (homogeneous equilibrium) and HFM (homogeneous frozen) models, presents no discontinuity in the liquid phase depressurization path gradient and therefore no discontinuity in sound speed. The proposed model is successfully validated against the NASA hydrogen critical flow experiments and compared against predictions from both HEM and HFM, using hydrogen physical properties from NIST. An increase of the pressure difference between stagnation and the intersection of isentropic with saturation line leads to increase of the choked mass flux, decrease of the throat to stagnation pressure ratio, decrease of the liquid superheat and decrease of the vapor quality. The proposed model was found to overestimate the experimental throat mass fluxes by no more than 10% and underestimate the experimental throat to stagnation pressure ratios by no more than 50%, while predicted liquid superheat values range from 3.8 to 11% of the saturation temperature. Deviations between models were found to increase for low values of the pressure difference parameter, where non-equilibrium effects become more important. Under these conditions the throat mass flux is underestimated by maximum 20% by HEM and overestimated up to 32% by HFM, while the throat to stagnation pressure ratio is overestimated by up to 72% and underestimated by 80% respectively.     

Pool Boiling Heat Transfer in Diluted Water/Glycerol Binary Solutions

Pool boiling heat transfer in water/glycerol binary solutions has been experimentally investigated on a horizontal rod heater. The experiments have been performed at various concentrations (zero to 35% mass glycerol) and heat fluxes up to 92 kW m^?2 at atmospheric pressure. The experimental values of boiling heat transfer coefficient have been compared to main existing correlations. It has been shown that the various predictions are significantly inconsistent. Based on the high difference between relative volatilities of water and glycerol, a simple model has been proposed to predict the boiling heat transfer coefficient. The applicability of this model is limited to low concentrations of glycerol and medium/low heat fluxes; however, the predictions are accurate. The proposed model is anticipated to be extendable to other binary systems in which the vapor pressure of one constituent is considerably higher when compared to the other component.     

Generalized stability theory of vapor film in subcooled film boiling on a sphere

The previously proposed stability theory of vapor film in subcooled film boiling on a sphere was generalized to take account of interaction between base flow and perturbed components. A disturbance of standing wave type was assumed to be superimposed on the base flows of surrounding liquid and vapor film. For the surrounding liquid, the wave equation was applied to the whole region including the boundary layer and the energy equation was solved analytically by introducing a simplifying assumption. For the vapor film, the basic equations were solved by an integral method. By use of compatibility conditions at the liquid–vapor interface, the solutions for the surrounding liquid and the vapor film were combined to yield an algebraic relation among the vapor film thickness, the order of disturbance and the complex amplification factor of disturbance. The numerical solutions of critical vapor film thickness at which the real part of complex amplification factor was equal to zero were obtained for the disturbances of the zeroth, first and second orders. The numerical results indicated that the vapor film was most unstable for the disturbance of the zeroth order (i.e., uniform disturbance). The calculated value of the critical vapor film thickness for the uniform disturbance compared well with the average vapor film thickness at the minimum-heat-flux point obtained from the immersion cooling experiments of spheres in water at high liquid subcoolings.     

Boiling of small droplets

Analysis is reported of the boiling of small diameter suspended droplets, such as found in emulsions. A one-dimensional model considers both the energy and momentum equations, and effects of differences in fluid and thermodynamic properties between the droplet and the surrounding liquid are examined. Results are presented in the form of time varying bubble radius and temperature. The initial boiling of the droplet is insensitive to the surrounding liquid and droplet diameter, while the final evaporation rate is strongly affected by the properties of the surrounding liquid. After a droplet has completely evaporated, the vapor bubble expands and contracts via radial oscillations near the Minnaert frequency for isothermal bubbles. Thermal damping is observed but the model does not capture acoustic damping.     

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.