Fluid thermal stratification in a non-isothermal liquid hydrogen tank under sloshing excitation

To the safe space operation of cryogenic storage tank, it is significant to study fluid thermal stratification under external heat leaks. In the present paper, a numerical model is established to investigate the thermal performance in a cryogenic liquid hydrogen tank under sloshing excitation. The interface phase change and the external convection heat transfer are considered. To realize fluid sloshing, the dynamic mesh coupled the volume of fluid (VOF) method is used to predict the interface fluctuations. A sinusoidal excitation is implemented via customized user-defined function (UDF) and applied on tank wall. The grid sensitivity study and the experimental validation of the numerical mode are made. It turns out that the present numerical model can be used to simulate the unsteady process in a non-isothermal sloshing tank. Variations of tank pressure, liquid and vapor mass, fluid temperature and thermal stratification are numerically investigated respectively. The results show that the sinusoidal excitation has caused large influence on thermal performance in liquid hydrogen tank. Some valuable conclusions are arrived, which is important to the depth understanding of the non-isothermal performance in a sloshing liquid hydrogen tank and may supply some technique reference for the methods of sloshing suppression.     

Fluid sloshing dynamic performance in a liquid hydrogen tank

In the present study, a numerical model is built to investigate the hydrodynamic performance in a sloshing liquid hydrogen tank under a sinusoidal excitation. The motion mesh coupled the volume of fluid method is adopted to capture the fluctuation of the free surface during sloshing. The sloshing dynamic response of the free surface is specially evaluated. Meanwhile, the sloshing force and moment, and pressure variation are numerically studied. The results show that the free surface has stable interface shapes with “Z” or “S” type profiles in the initial period. As time elapses, the sinusoidal wave propagates, some disturbances occur at the interface with different wave amplitudes. For fluid close to the tank wall, it suffers much more from external excitation with large amplitude fluctuations. For the symmetrically distributed measuring points, opposite fluctuating profiles form with almost the same amplitude. Influenced by fluid motion, the point of the maximum liquid pressure makes fluctuations as well. The measuring points far from the symmetry axis of the tank have severe fluctuating variations. With some valuable conclusions arrived, the present study is significant to the in-depth comprehension on fluid sloshing dynamical behavior in non-isothermal cryogenic tanks.     

Thermodynamic performance on the pressurized discharge process from a cryogenic fuel storage tank

Due to excellent performance, cryogenic propellants, such as liquid hydrogen and liquid oxygen, are widely used in aerospace engineering. However, low storage temperature and low kinetic viscosity bring a lot of technique issues for high efficient thermal management on cryogen. An actual cryogenic fuel storage tank is selected as the research object, and a two-dimensional axial symmetrical computational model is established to study the pressurized discharge process, by adopting the volume of fluid (VOF) model. Both external environment heat leakage and the heat exchange occurring between the liquid and vapor are considered. Compared to the experimental results, the relative error is limited in 20.0%. Based on the developed numerical model, the temperature variation and heat flux through the insulation and tank wall, the pressurized discharge performance and the fluid temperature distribution are analyzed. The results show that during the pressurized discharge process, the lowest temperature appears in the inner side of the foam, and the external heat invasion does not absolutely penetrate into the tank. The vapor mass experiences fluctuating variations, and the vapor is always in condensation. In the first 200s, the temperature of the outflow fluid keeps constant, and then increases gradually. Under the present initial setting, the violent boiling phenomenon does not form during the whole process. The present study is significant to the depth understanding on the pressurized discharge of cryogenic fuels.     

Fluid sloshing thermo-mechanical characteristic in a cryogenic fuel storage tank under different gravity acceleration levels

Fluid sloshing usually causes serious safety issues on the dynamic stability and propellant thermal management during the powered-flight phase of launch vehicle. With the wide using of cryogenic propellants, the coupled thermo-mechanical performance during fluid sloshing becomes more prominent. In the present study, one numerical model is established to simulate fluid sloshing by using the VOF method coupled with the mesh motion treatment. The phase change occurring within the tank is considered. Both the experimental validation and mesh sensitivity analysis are made. It shows that present numerical model is acceptable. Based on the developed numerical model, the effect of different super gravity accelerations on fluid sloshing hydrodynamic characteristic is numerically researched. The fluid pressure variation, the sloshing force and sloshing moment, the interface dynamic response and the interface shape variation are investigated, respectively. It shows that the gravity acceleration has caused obvious influences on fluid sloshing characteristic. When the gravity acceleration is higher than 4g₀, fluid sloshing becomes more obvious and must be paid enough attention. With some valuable conclusions obtained, the present work is of great significance for in-depth understanding of fluid sloshing mechanism.     

Effect of gas injection mass flow rates on the thermal behavior in a cryogenic fuel storage tank

Large scale using of liquid hydrogen and liquid oxygen on energy engineering, chemical engineering and petrochemical industries, bring a series of non-equilibrium thermal behaviors within fuel storage tanks. Accurate simulation on the thermal behavior in cryogenic fuel storage tanks is therefore a critical issue to improve the operation safety. In the present study, a 2-dimensional numerical model is developed to predict the active pressurization process and fluid thermal stratification in an aerospace fuel storage tank. Both external heat penetration and heat exchange occurring at the interface are accounted for in detail. The volume of fluid method is adopted to predict the thermal physical process with high-temperature gas injected into the tank. The effect of the gas injection mass flow rate on the tank pressure, the interface phase change, and the fluid temperature distribution are investigated respectively. Finally, some valuable conclusions are obtained. The present study may supply some technique references for the design of the pressurization system.     

A refined analysis of sloshing effects in seismically excited tanks

Sloshing in terms of liquid surface displacement in vertical liquid-filled cylindrical tanks under earthquake excitation is a well studied phenomenon. Various design rules exist for liquid storage tanks to sustain the corresponding liquid pressure due to seismic excitation and to take into account the necessary freeboard. However, usually the sloshing motion is considered under the assumption of a rigid tank with an earthquake excitation at the base circle. The arguments used so far in justifying this assumption are of rather qualitative but not of quantitative nature. Since it is important to have a quantitative measure of that which is neglected, it is the intention of this paper to show that this engineering approach is based on rigorous theoretical quantitative results. Therefore, in this paper coupling of sloshing with the deformations of a flexible tank wall during earthquake excitation is investigated in a refined analysis. In contrast to former papers which have studied the negligible influence of the wall deformations due to sloshing itself, in this paper the more important coupling including the wall deformations caused by the impulsive effect of the contained liquid is taken into account. An analytical procedure is presented which allows one to study explicitly the influence of the wall deformations on both the liquid pressure and the surface elevation for typical wall deformation shapes, i.e. vibration modes. From the rather complex mathematical derivations a simple formula is drawn which enables the engineer to get a quick guess of the magnitude of the influence of the wall deformations on the convective pressure contributions due to sloshing and hence to decide whether or not the assumption of a rigid tank wall is suitable. It is shown that for tanks made of less stiff materials, such as for instant polymers, this rigid wall assumption which is suitable for steel tanks may become questionable.     

基于VOF-DPM模型的离心喷嘴中的燃油流动及雾化特征研究

针对燃油在离心喷嘴中的内部流动及其外部雾化过程,采用VOF-DPM模型对其进行了数值模拟研究。分析了压力对喷嘴出口处空气芯大小和液膜厚度的影响,得到了液膜破碎长度和雾化锥角等雾化特性,应用实验测试结果对数值模拟进行了验证,并与流体体积函数法(VOF)和离散相追踪法(DPM)进行了对比。结果表明：VOF-DPM模型可以真实反映离心喷嘴的内部流动和外部雾化特性,研究发现了与实际雾化过程符合的液膜破碎存在孔洞破碎和边缘破碎两种形式;捕捉到了在液膜表面的波动及气动力共同作用下液膜失稳破碎形成液滴的过程;燃油流动及雾化特性随着压力增加发生变化,喷嘴内空气芯直径增大,出口处液膜厚度减小,液膜的破碎长度下降。     

Investigation on no-vent filling process of liquid hydrogen tank under microgravity condition

In order to investigate the no-vent filling performance under microgravity, the computational fluid dynamic (CFD) method is introduced to the study, where a model aiming at filling a liquid hydrogen (LH₂) receiver tank is especially established. In this model, the solid and fluid regions are considered together to predict the coupled heat transfer process. The phase change effect during the filling process is also taken into account by embedding a pair of mass and heat transfer models into the CFD software FLUENT, one of which involves liquid flash driven by pressure difference between the fluid saturated pressure and the tank pressure, and the other one indicates and calculates the evaporation–condensation process driven by temperature difference between fluid and its saturated state. This CFD model, verified by experimental data, could accurately simulate the no-vent filling process with good flexibility. Moreover, no-vent filling processes under different gravities are comparatively analyzed and the effects of four factors including inlet configuration, inlet liquid temperature, initial wall temperature and inlet flow rate, are discussed, respectively. Main conclusions could be made as follows: 1) Compared to the situations in normal gravity, the no-vent filling in microgravity experiences a more adequate liquid–vapor mix, which results in a more steady pressure response and better filling performance. 2) Inlet configuration seems to have negligible effect on the no-vent filling performance under microgravity since liquid could easily reach the tank wall and then cause a sufficient fluid-wall contact under any inlet condition. 3) Higher initial tank wall temperature may directly cause a higher pressure rise in the beginning, while this effect on the final pressure is not significant. Sufficient precooling and reasonable inlet liquid subcooled degree are suggested to guarantee the reliability and efficiency of the no-vent fill under microgravity.     

Numerical investigation of the coupled heat transfer of liquefied gas storage tanks

It is a common situation that the liquefied gas tanks are always heated by the outer hot environments, which affecting the safety of the tanks. In this paper, numerical studies were conducted to reveal the heat transfer characteristics of this circumstance. The coupled heat transfer process among the thermal environment, the tank wall and the fluid in the tank was thoroughly investigated by simultaneously solving the temperature fields of both the solid region and the fluid region as well as the flow fields of both the liquid phase and the vapor phase inner the tank. The results showed that affected by the near wall flow and the wall boiling, the heat transfer presented different patterns in the stable thermal stratification stage and the de-stratification stage. In the stable stratification stage, the heat flux from the liquid phase wall to the medium distributed uniformly along the axial direction of the tank, while in the de-stratification stage, it differed a lot at the different positions.     

Experimental study on thermodynamic vent system with different influence factors

A ground experiment is established to investigate the pressure control performance of thermodynamic vent system (TVS) with HCFC123. Different influence factors, including tank pressure control bands, circulation volume flow rates, and heat loads, are investigated separately. The variations of tank pressure and fluid temperature are analyzed in different operation process. To compare the performance of TVS with that of direct venting, the tank heat leakage is solved with a quasi‐steady heat transfer model. With the actual penetration heat into tank determined, the performance comparison is made between direct venting and TVS. The results show that the increase rate of tank pressure rises with the heat load during the pressurization process. While the bulk fluid is still subcooled, great tank pressure control and fluid cooling could be obtained by increasing the circulation flow rate in the mixing injection process. With the cold capacity generated by the throttling process, both the vapor and liquid should be well cooled. For the case of No.3 to 4, as the refrigeration capacity of TVS could not eliminate the accumulated heat load timely, the fluid has a temperature increase in the early stage of throttling process. While for the case of No.6, with the fluid being cooled sufficiently, both the vapor and liquid have received great temperature control. Compared with the direct venting, the recovery ratio of venting gas loss generated by TVS ranges from 30% to 145%, which shows the TVS has a large advantage on exhaust saving.     

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.     

Generalized quantitative criteria for predicting the rate-controlling mechanism for vapor bubble growth in superheated liquids

Criteria are presented for predicting the relative importance of the inertia of the liquid and heat transfer in the liquid as controlling effects for spherically symmetric vapor bubble growth in liquids. The coupled governing equations including both of the above effects are first cast in appropriate dimensionless forms. Then numerical solutions of the coupled equations are compared to the limiting solutions for solely liquid inertia and solely heat transfer controlled growth processes, in order to determine the respective regions of importance of these two mechanisms. The cases of growth initiated by a step decrease and a linear decrease in system pressure are both considered. The criteria are developed for the case of an idealized fluid having a constant vapor density and a linear vapor pressure curve, and then shown to be approximately independent of the vapor density and pressure relations of the particular fluid. The applicability and usefulness of the criteria are supported and illustrated by comparison of predictions based on them with previous theoretical and experimental results taken from the literature.     

Mass transfer enhancement by gravity waves at a liquid–vapour interface

Experimental results on mass transfer enhancement by large amplitude gravity waves at a liquid–gas/vapour interface are presented. The waves are sub-harmonically excited in a circular cylinder that is partially filled with liquid, by oscillating the cylinder in the direction normal to the liquid surface. The lowest asymmetric sloshing mode (1, 1) as well as the axisymmetric mode (0, 1) are considered in the limit of large fluid depth approximation and for wave amplitudes that include breaking. The fluids used are low viscosity and low surface tension liquids of low boiling point temperatures. In the mass transfer experiments the lower part of the test cell is filled with cold liquid and the upper part with gas, generally vapour, at a temperature above the saturation temperature. When the interface is at rest and the gas is vapour, the pressure decrease due to condensation is small. In the presence of large amplitude sloshing the condensation rate is large and the pressure decreases rapidly and substantially. A model is developed that expresses the pressure variation in terms of a Jacob number, interfacial temperature gradient and an effective diffusion coefficient. The effective dimensionless diffusion coefficient is the relevant similarity parameter and is determined in the experiments. In Appendix A results are presented for conditions of evaporation in the presence of a non-condensable gas.     

Investigation of heat and mass transfer between the two phases of an evaporating droplet stream using laser-induced fluorescence techniques: Comparison with modeling

Heat and mass exchanges between the two phases of a spray is a key point for the understanding of physical phenomena occurring during spray evaporation in a combustion chamber. Development and validation of physical models and computational tools dealing with spray evaporation requires experimental databases on both liquid and gas phases. This paper reports an experimental study of evaporating acetone droplets streaming linearly at moderate ambient temperatures up to 75 °C. Two-color laser-induced fluorescence is used to characterize the temporal evolution of droplet mean temperature. Simultaneously, fuel vapor distribution in the gas phase surrounding the droplet stream is investigated using acetone planar laser-induced fluorescence.Temperature measurements are compared to simplified heat and mass transfer model taking into account variable physical properties, droplet-to-droplet interactions and internal fluid circulation within the droplets. The droplet surface temperature, calculated with the model, is used to initiate the numerical simulation of fuel vapor diffusion and transport in the gas phase, assuming thermodynamic equilibrium at the droplet surface. Influence of droplet diameter and droplet spacing on the fuel vapor concentration field is investigated and numerical results are compared with experiments.     

基于ALE有限元法的储液罐耦合竖动响应研究

推导了一种基于ALE描述弱可压缩液体与结构非线性耦合求解的分步有限元数值计算法,速度与压力使用同阶线性插值,并对耦合系统的竖动响应进行了分析.通过二维黏性流体大晃动问题实例计算,验证了该法简便、可行有效.     

Numerical approach to analyze fluid flow in a type C tank for liquefied hydrogen carrier (part 1: Sloshing flow)

The demand for clean energy use has been increasing worldwide, and hydrogen has attracted attention as an alternative energy source. The efficient transport of hydrogen must be established such that hydrogen may be used as an energy source. In this study, we considered the influences of various parameters in the transportation of liquefied hydrogen using type C tanks in shipping vessels. The sloshing and thermal flows were considered in the transportation of liquefied hydrogen, which exists as a cryogenic liquid at ?253 °C. In this study, the sloshing flow was analyzed using a numerical approach. A multiphase sloshing simulation was performed using the volume of fluid method for the observation and analysis of the internal flow. First, a sloshing experiment according to the gas-liquid density ratio performed by other researchers was utilized to verify the simulation technique and investigate the characteristics of liquefied hydrogen. Based on the results of this experiment, a sloshing simulation was then performed for a type C cargo tank for liquefied hydrogen carriers under three different filling level conditions. The sloshing impact pressure inside of the tank was measured via simulation and subjected to statistical analysis. In addition, the influence of sloshing flow on the appendages installed inside of the type C tank (stiffened ring and swash bulkhead) was quantitatively evaluated. In particular, the influence of the sloshing flow inside of the type C tank on the appendages can be utilized as an important indicator at the design stage. Furthermore, if such sloshing impact forces are repeatedly experienced over an extended period of time under cryogenic conditions, the behavior of the tank and appendages must be analyzed in terms of fatigue and brittle failure to ensure the safety of the transportation operation.     

An experimental study and model validation of a membrane humidifier for PEM fuel cell humidification control

This paper presents an experimental study and model validation of an external membrane humidifier for PEM fuel cell humidification control. Membrane humidification behavior was investigated with steady-state and dynamic tests. Steady-state test results show that the membrane vapor transfer rate increases significantly with water channel temperature, air channel temperature, and air flow rate. Water channel pressure has little effect on the vapor transfer rate and thus can be neglected in the system modeling. Dynamic test results reveal that the membrane humidifier has a non-minimum phase (NMP) behavior, which presents extra challenges for control system design. Based on the test data, a new water vapor transfer coefficient for Nafion membrane was obtained. This coefficient increases exponentially with the membrane temperature. The test results were also used to validate a thermodynamic model for membrane humidification. It is shown that the model prediction agrees well with the experimental results. The validated model provides an important tool for external humidifier design and fuel cell humidification control.     

High-pressure vaporization modeling of multi-component petroleum–biofuel mixtures under engine conditions

Numerical simulation of the vaporization of multi-component liquid fuels under high-pressure conditions is conducted in this study. A high-pressure drop vaporization model is developed by considering the high-pressure phase equilibrium which equates the fugacity of each component in both liquid and vapor phases. Peng–Robinson equation of state is used for the calculation of fugacity. To model the vaporization of diesel fuel under high-pressure conditions, continuous thermodynamics based on a gamma distribution is coupled with phase equilibrium by correlating the parameters of the equation of state with the molecular weights of the continuous components. The high-pressure vaporization model is validated using the experimental data of n-heptane drops under different ambient pressures and temperatures. Good levels of agreement are obtained in drop size history. Predicted results of the vaporization of diesel fuel drops show that increasing ambient pressure leads to a shorter drop lifetime under high temperature conditions (e.g., 900 K). On the other hand, at a slightly lower temperature of 700 K, the drop lifetime increases as the ambient pressure increases. It is found that the net affects of high ambient pressure on drop vaporization are determined by two competing factors, namely, reduced mass transfer number and reduced enthalpy of vaporization. The model was further applied to biodiesel and its blends with diesel fuel. The fuel blend is modeled based on a method that continuous thermodynamics is used to model diesel fuel and biodiesel is modeled as a mixture of its five representative components. Results of single drop vaporization history show that drop lifetime increases as the volume fraction of biodiesel in the fuel blend increases. This phenomenon reveals the low vaporization rate of biodiesel that has a higher critical temperature than diesel fuel. It is also observed that the volume fraction of biodiesel in the fuel blend increases during vaporization and its vapor concentrates near the tip of the liquid spray while diesel fuel vapor is around the entire liquid spray.     

涡流室式柴油机燃油蒸发过程的三维数值模拟

建立了高温高压条件下的油滴蒸发模型,并在不同的工质压力和温度下对模型进行了验证,模型计算结果和实验结果吻合良好。将此油滴蒸发模型和油膜蒸发模型相结合,应用到涡流室式柴油机的燃油蒸发过程中,通过三维数值模拟计算,研究了燃油蒸发过程中燃料蒸气浓度和工质温度场的变化历程以及燃油蒸发对涡流室平均温度和平均压力的影响。     

Effective Modeling of Conjugate Heat Transfer and Hydraulics for the Regenerative Cooling Design of Kerosene Rocket Engines

The present work is motivated to develop a unified framework to simulate multi-physical processes which are crucial for trade-off design of liquid rocket thrust chambers among propulsive performance, regenerative cooling, and pressure budget. In this paper, an effective modeling of conjugate heat transfer and hydraulics through the regenerative cooling passage has been performed to quantitatively evaluate detailed cooling designs, including spirally twisted channels and bidirectionally branched circuit, as well as to provide the wall heat flux to a compressible reacting flow solver in an interactively coupled manner. The kerosene fuel used as coolant is modeled by a three-component physical surrogate, and the fluid properties required for calculation of a Nusselt number correlation and empirical resistance coefficients are computed over the entire thermodynamic states from compressed liquid to supercritical fluid using the NIST SUPERTRAPP. The present method has been applied to an actual regeneratively cooled thrust chamber and validated against measurement of hot-firing tests in terms of temperature increase and pressure drop of the coolant through the cooling passages. Based on the numerical results, supplementary effects of peripheral fuel cooling injection and thermal barrier coating are addressed.