Thermodynamic characteristic in a cryogenic storage tank under an intermittent sloshing excitation

A numerical calculation model is developed to study the coupled thermal dynamic performance in a cryogenic fuel tank under an intermittent sloshing excitation. Both external heat inputs and the intermittent excitation are realized by User-defined functions. The volume of fluid method is adopted to simulate fluid sloshing, coupled with the mesh motion treatment. Validated against related fluid sloshing experiments, the numerical model was turned out to be acceptable on fluid sloshing prediction. Cooled by subcooled liquid, vapor is always in condensation. The middle vapor pressure test point suffers less from the intermittent excitation and has a linear pressure decrease profile, while the middle liquid pressure test point has fluctuating variations. For vapor and interface temperature monitors, obvious temperature fluctuations appear in the second holding period. While for liquid test points, the temperature profiles experience intensive fluctuations during sloshing periods and stable temperature variation during holding periods. Due to the holding period of external excitation, the tank pressure reduction in intermittent sloshing case is less than that in continuous sloshing case. That is to say the tank pressure decrease rate could be adjusted by proper intermittent excitation. This work is significant to deeply understand fluid sloshing phenomenon under some irregular external excitations in fuel storage tanks.     

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.     

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.     

Study on thermal stratification in liquid hydrogen tank under different gravity levels

In the present study, one CFD model is selected to research the effect of gravity scale on the thermal performance in liquid hydrogen tank. Four gravity levels (1g₀, 10^?1g₀, 10^?2g₀ and 10^?3g₀) are compared to recognize the influence of the reduced gravity on fluid thermal stratification. The results show that with the increasing of the gravity level, the vapor temperature distribution becomes more uniform, and the liquid stratum layer develops faster. Compared the CFD results with the results of two stratification theoretical models, the stratum thickness calculated by CFD model is close to the values of Tellep model. While the stratum temperature of CFD model is much closer to that of Reynolds model. With vortex occurring among two slosh baffles, the streamline in the liquid stratum likes a plume. Influenced by the surface tension in reduced gravity, liquid close to the tank wall moves up with the interface becoming curved. The interface area rises with the decrease of gravity. The gravity of 10^?1g₀ still plays the dominant role with the interface area of 10^?1g₀ being almost the same as that of 1g₀. While for others, the effect of the surface tension shows up gradually.     

Effect of microgravity on flow boiling heat transfer of liquid hydrogen in transportation pipes

The flow boiling phenomenon of liquid hydrogen (LH2) during transportation in microgravity is very different from that under terrestrial condition. In this study, a saturated flow boiling of LH2 in a horizontal tube has been simulated under microgravity condition using coupled level-set and volume of fluid method. The validation of the developed model shows good agreement with the experimental data from the literature. The changes of heat fluxes and pressure drops under different gravitational accelerations were analyzed. And, the variation of heat fluxes with different wall superheat and contact angle were compared between microgravity (10⁻⁴g) and normal gravity (1g) condition. Also, the influence of surface tension were studied under microgravity. The numerical results indicate that the heat flux decrease with the decrement of gravitational acceleration. And the heat transfer ratio decrease with the increment of wall superheat in the nucleate boiling regime. The heat transfer slightly reduce when considering surface tension. In addition, the changes of contact angle have a more significant impact on heat transfer under microgravity condition.     

Aerodynamic simulations of offshore floating wind turbine in platform‐induced pitching motion

Forfloating offshore wind turbines, rotors are under coupled motions of rotating and platform‐induced motions because of hydrodynamics impacts. Notably, the coupled motion of platform pitching and rotor rotating induces unsteadiness and nonlinear aerodynamics in turbine operations; thus having a strong effect on the rotor performances including thrust and power generation. The present work aims at developing a computational fluid dynamics model for simulations of rotor under floating platform induced motions. The rotor motion is realized using arbitrary mesh interface, and wind flows are modelled by incompressible Navier‐Stokes flow solver appended by the k  ? ω shear stress transport turbulence model to resolve turbulence quantities. In order to investigate the fully coupled motion of floating wind turbine, the six degree of freedom solid body motion solver is extended to couple with multiple motions, especially for the motion of rotor coupled with the prescribed surge‐heave‐pitch motion of floating platform. The detailed methodology of multiple motion coupling is also described and discussed in this work. Both steady and unsteady simulations of offshore floating wind turbine are considered in the present work. The steady aerodynamic simulation of offshore floating wind turbine is implemented by the multiple reference frames approach and for the transient simulation, the rotor motion is realized using arbitrary mesh interface. A rigorous benchmark of the present numerical model is performed by comparing to the reported literatures. The detailed elemental thrust and power comparisons of wind turbine are carried out by comparing with the results from FAST developed by National Renewable Energy Laboratory and various existing numerical data with good agreement. The proposed approach is then applied for simulations of National Renewable Energy Laboratory 5MW turbine in coupled platform motion at various wind speeds under a typical load case scenario. Transient effect of flows over turbines rotor is captured with good prediction of turbine performance as compared with existing data from FAST. Copyright © 2016 John Wiley & Sons, Ltd.     

Flow and Heat Transfer Characteristics of Two‐Phase Fluid in Inclined Pipes on a Rotation Platform

A rotating platform was used to create dynamic load, and the mixture air–water two‐phase flow and boiling steam–water two‐phase flow were obtained in an inclined test pipe. By changing the parameters, such as inclination of the test pipe, rotational speed, inlet temperature, flow rate, and so on, the experiments for two‐phase flow in the pipe at inclination of 0°, 45°, and 66° were conducted, respectively. The effects of acceleration and inclination on their flow and heat transfer characteristics were investigated. The two‐phase flow patterns in inclined pipes under rotation conditions were caught with a video camera. The images show that the impact mixed flow and churn flow were found in this research. The results show that the acceleration and pipe inclination significantly influence the flow characteristic and heat transfer of the two‐phase pipe flow. As the directions of the dynamic load and the gravity are opposite to the flow direction, the greater the dynamic load and inclination, the higher the pressure drop and the heat emission, and the lower the flow rate, the void fraction, and the fluid temperature. Therefore, the dynamic load and gravity will improve the flow resistance, enhance heat emission and reduce the heat gained by the fluid.     

Numerical investigation on subcooled pool film boiling of liquid hydrogen in different gravities

A clear understanding of bubble dynamics and heat transfer characteristics of hydrogen boiling in microgravity is significant for achieving safe and high-efficiency utilization of liquid hydrogen in space. In the present paper, a numerical simulation model is developed to predict the subcooled pool film boiling for liquid hydrogen in different gravities. The computations are based on the volume of fluid method combined with Lee's phase change model. The results show that the bubble released from the wavy gas-liquid interface might grow to a larger size before departure with the decrease of gravity, and poor heat transfer performance is observed in reduced gravity. However, once the gravity level is low enough or the subcooling of liquid is sufficiently large, instead of bubble formation and release at the vapor-liquid interface, a thin gas film layer is almost observed and maintained in the surface of horizontal flat or wire heater.     

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.     

Solutal thermodiffusion in binary mixture in the presence of g-jitter

The phenomenon of mass flux in a mixture due to a temperature gradient is known as the Soret effect or thermal diffusion. This effect is usually small but can be quite important in the analysis of compositional variation in hydrocarbon reservoirs. Diffusion-dominated experiments on-board the International Space Station will be greatly affected by convective flow due to the residual acceleration field and/or to oscillatory g-jitters caused by several sources. In this paper we are interested in investigating the flow due to thermal diffusion for different oscillatory g-jitters. The model considered is a rectangular rigid cavity filled with a binary mixture of methane and normal butane, subject to a temperature difference on its end walls and radiation heat transfer on the lateral ones. The non-linear differential equations for the mass-thermo-vibrational problem are derived in the case of a unique mode oscillatory acceleration. The full transient Navier–Stokes equations coupled with the mass and heat transfer formulations and the equation of state of the fluid are solved numerically using the finite element technique. Results revealed that the thermal diffusion is important and drives a strong convection. Convection is enhanced and therefore temperature and species profiles distortion from purely diffusive condition increases when a parallel g-jitter is added to the residual gravity, in a destabilizing configuration. The numerical study shows that both residual gravity and g-jitter may be detrimental but also beneficial to achieve purely diffusive conditions, according to the orientation of the vibration direction and the residual gravity vector, relative to the direction of the main density gradient. For the different configurations investigated, the g-jitter is found to reduce compositional variation. When the stable regime is attained, thermal and compositional quantities fluctuate following a mode whose frequency is equal to that of the initially imposed vibration. Even if the temperature fluctuation at a given point remains small, the compositional variation due to residual g-jitter convection is not negligible.     

3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling

The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solid–vapor/liquid–vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid–vapor and solid–vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet’s initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.     

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.     

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).     

Effects of mould filling on evolution of the solid–liquid interface during solidification

This work presents a numerical analysis of simultaneous mould filling and phase change for solidification in a two-dimensional rectangular cavity. The role of residual flow strength and temperature gradients within the solidifying domain, caused by the filling process, on the evolution of solidification interface are investigated. An implicit volume of fluid (VOF)-based algorithm has been employed for simulating the free surface flows during the filling process, while the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modeling is coupled with VOF through User Defined Functions developed in the commercial computational fluid dynamics (CFD) code FLUENT 6.3.26. Comparison between results of the conventional analysis without filling effect and those of the present analysis shows that the residual flow resulting from the filling process significantly influences the progress of the solidification interface. A parametric study is also performed with variables such as cooling rate, filling velocity and filling configuration, in order to investigate the coupled effects of the buoyancy-driven flow and the residual flow on the solidification behavior.     

A LOCALLY IMPLICIT SCHEME FOR TURBULENT FLOWS ON DYNAMIC MESHES

A locally implicit scheme with an anisotropic dissipation model is developed on dynamic quadrilateral-triangular meshes. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low-Reynolds-number k  ? ε turbulence model are solved to study turbulent flows over vibrating blades with negative interblade phase angle. A treatment of viscous flux on quadrilateral-triangular mesh is also presented. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, the turbulent flow around an NACA 0012 airfoil is investigated. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which includes the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady flow behaviors for turbulent flows over vibrating blades with negative interblade phase angle are demonstrated.     

Numerical simulation of steam–water two‐phase flow under dynamic load

A separated‐phase physical model for steam–water two‐phase flow on a rotating platform was developed. The mesh generation for a horizontal pipe was conducted, and the finite volume method was used to discretize the equations. Equations were solved with the SIMPLE algorithm after setting the initial and boundary conditions. Predicted results were compared with experimental data, and they agreed well with each other. The results showed that the fluid outlet pressure and pressure drop in the test section increased with increasing dynamic load. However, the effective heat transferred to the fluid decreased with the increase of dynamic load. The developed model can be used to simulate the gas–liquid two‐phase flow under different gravity or rotary conditions.     

Numerical simulation and experimental validation of a helical double-pipe vertical condenser

A predictive model is developed to describe heat transfer and fluid dynamic behavior of a helical double-pipe vertical condenser used in an absorption heat transformer integrated to a water purification process. The condenser uses water as working fluid connected in countercurrent. Heat transfer by conduction in the internal tube wall is considered; in addition the change of phase is carried out into the internal tube. The dynamic model considers equations of continuity, momentum and energy in each flow. The discretized governing equations are coupled using an implicit step by step method. Comparison of the numerical simulation over range of experimental data presented in the heat device is applied to validate the model developed. The model is also evaluated of form dynamic to determine the principal operation variables that affect the condenser with the main objective to optimize and control the system. A variation of mass flow rate in the internal pipe induces important changes on the heat flux that the pressure and temperature.     

排架支撑式渡槽排架损伤下地震响应分析

以洗耳河渡槽为例,以弹塑性梁单元模拟排架,采用有限体积法、ALE及二阶迎风格式模拟槽内水体,建立了二维槽—水耦合体,分析了横向地震作用下的排架损伤下渡槽动力非线性响应,并与线弹性梁单元模拟排架的分析结果进行对比。结果表明,在所选地震波横向作用下,排架发生损伤造成了刚度下降、结构振动周期延长,从而逼近水体的一阶晃动周期,引起了槽—水耦合体内水体的大幅晃动;排架损伤后槽底水平位移增大而水平加速度减小,槽内水体作用于槽体底部的动水压力、倾覆力矩、倾覆力减小。     

Validation of fully implicit method for simulation of flows with interfaces using primitive variables

This paper describes applications of the fully implicit procedure for computing flow of two immiscible fluids. Six problems in two and three dimensions are solved to highlight effects of grid size, pressure smoothing, TVD convection scheme and geometric and fluid dynamic evaluations of surface tension force. Free surface and cavity flows are considered in which effect of sloshing, interface merger and splitting as well as splashing are included. Wherever possible, present solutions are compared with results of previous experiments and/or numerical computations. Computational details such as grid size, time step, under-relaxation factors, mass/volume conservation are reported.     

The evaluation of the diffuse interface method for phase change simulations using OpenFOAM

In the present study, a new solver named phaseChangeHeatFoam is implemented on the OpenFOAM cfd package to simulate boiling and condensation. The solver is capturing the interface between two immiscible phases with a color function volume of fluid (CF‐VOF) method. The two fluids (vapor and liquid) are assumed Newtonian and incompressible. The surface tension is modeled with continuous surface force (CSF) which is improved with a Lafaurie filter to suppress the spurious current. The mass flux across the interface in the phase change process is determined by either Lee or Tanasawa mass transfer models. Additionally, the slight variation of saturation temperature with local pressure is considered with the simplified Clausius–Clapeyron relation. The coupled velocity pressure equation is solved using the PIMPLE algorithm. The new solver is validated and examined with (i) Stefan problem, (ii) two‐dimensional film boiling, (iii) the film condensation on a horizontal plate, (iv) the laminar film condensation over a vertical plate, and (v) bubble condensation in subcooled boiling. The present study shows the capability of a diffuse interface method in accurate simulation of the phase change process and it is expected to be instructive for further numerical studies in this area.