Analysis of self-pressurization phenomenon of cryogenic fluid storage tank with thermal diffusion model

Self-pressurization phenomenon is one of the most important problems in the storage of cryogenic liquid. Until now, it has been difficult to predict exact pressurization process due to its complex non-equilibrium thermal behavior. This paper analyzes the self-pressurization with the trend of pressurization curves from experiment using liquid nitrogen with various heat leaks and liquid fractions. The trend of pressurization curves are classified on the basis of shape of pressurization curve. The qualitative relation between transient period, heat leak and liquid fractions is suggested. Thermal diffusion model (TDM) considering thermal stratification and thermal equilibrium model (TEM) can properly predict the respective pressurization curves with suitable condition for each model.     

Numerical simulation of unsteady cavitating flows using a homogenous equilibrium model

 Numerical simulations of two-dimensional cavity flows around a flat plate normal to flow and flows through a 90^∘ bent duct are performed to clarify unsteady behavior under various cavitation conditions. A numerical method applying a TVD-MacCormack scheme with a cavitation model based on a homogenous equilibrium model of compressible gas-liquid two-phase media proposed by the present authors, is applied to solve the cavitating flow. This method permits the simple treatment of the whole gas-liquid two-phase flow field including wave propagation and large interface deformation. Numerical results including detailed observations of unsteady cavity flows and comparisons of predicted results with experimental data are provided. Received: 5 August 2002 / Accepted: 6 January 2003     

Numerical simulation of cavitating flow of liquid helium in venturi channel

The fundamental characteristics of the two-dimensional cavitating flow of liquid helium through a venturi channel near the lambda point are numerically investigated to realize the further development and high performance of new multi-phase superfluid cooling systems. First, the governing equations of the cavitating flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid 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 cavitating flow of liquid helium though venturi channel 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-gas 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.     

Numerical modeling of self-pressurization and pressure control by a thermodynamic vent system in a cryogenic tank

This paper presents a numerical model of a system-level test bed—the multipurpose hydrogen test bed (MHTB) using the Generalized Fluid System Simulation Program (GFSSP). MHTB is representative in size and shape of a space transportation vehicle liquid hydrogen propellant tank, and ground-based testing was performed at NASA Marshall Space Flight Center (MSFC) to generate data for cryogenic storage. GFSSP is a finite volume-based network flow analysis software developed at MSFC and used for thermofluid analysis of propulsion systems. GFSSP has been used to model the self-pressurization and ullage pressure control by the Thermodynamic Vent System (TVS). A TVS typically includes a Joule–Thompson (J–T) expansion device, a two-phase heat exchanger (HEX), and a mixing pump and liquid injector to extract thermal energy from the tank without significant loss of liquid propellant. For the MHTB tank, the HEX and liquid injector are combined into a vertical spray bar assembly. Two GFSSP models (Self-Pressurization and TVS) were separately developed and tested and then integrated to simulate the entire system. The Self-Pressurization model consists of multiple ullage nodes, a propellant node, and solid nodes; it computes the heat transfer through multilayer insulation blankets and calculates heat and mass transfer between the ullage and liquid propellant and the ullage and tank wall. A TVS model calculates the flow through a J–T valve, HEX, and spray and vent systems. Two models are integrated by exchanging data through User Subroutines of both models. Results of the integrated models have been compared with MHTB test data at a 50% fill level. Satisfactory comparison was observed between tests and numerical predictions.     

Frequency characteristics of liquid hydrogen cavitating flow over a NACA0015 hydrofoil

Large eddy simulation on unsteady cavitating flow of liquid hydrogen over a three-dimensional NACA0015 hydrofoil with the attack angle (α) of 6° are carried out to investigate the dynamic features of cavity with the existence of thermal effects. The numerical model considers the compressibility of both liquid and vapor phase, and is validated by comparing the results with the available experimental data. Special emphasis is put on analyzing the frequency characteristics of cavitation cloud. Strouhal number (St) is plotted against σ/2α (σ is cavitation number), and the water cavitation data reported by Andrt et al. are also used as a reference. It is found that the St number for LH₂ cavitation is much smaller than the water, in which the thermal effects are generally not considered, at the same σ/2α value when it is greater than about 2.0, while it returns to the same level as water when σ/2α decreases to below 2.0. The reason is primarily ascribed to the thermal effects, and the detailed explanations are given based on the recognitions that the shedding mechanism of cavitation clouds is predominated by the combined action of the vortex flow and thermal effects. While, when σ/2α decreases to a critical value, the relative effect of the thermal effects on the cavitation dynamics is greatly weakened compared with the mechanism due to the vortex flow, like those in isothermal cavitation flow in traditional fluids. The results provide a deeper understanding of the cryogenic fluid cavitation flow.     

Numerical study of liquid nitrogen cavitating flow through nozzles of various shapes

The cavitating flow of cryogenic liquid through a spray nozzle is influenced by many factors, such as unique thermophysical properties of cryogenic liquid, the inflow temperature and the complicated geometrical structure of the spray nozzle. The geometrical parameters of liquid nitrogen spray nozzles have a profound impact on cavitating flow which in turn affects spray atomization characteristics and cooling performance. In present study, CFD simulations are performed to investigate influence of the nozzle geometry on the liquid nitrogen cavitating flow. The mixture model is used to describe the liquid-vapor two phase flow, and both the cavitation and evaporation are considered for the phase change. The predictions of mass flow of liquid nitrogen spray are validated against experimental results. The effects of geometric parameters, including the outlet orifice diameter and the length of nozzle, the inlet edge angle of orifice, the inlet corner radius of orifice, the orifice shape and different positions of swirl vanes, are investigated under a wide range of pressure difference and inflow temperature. The results show that the effects of geometric parameters on cavitating flow show different trends under subcooled conditions compared with saturated temperature conditions. The flow characteristics are more affected by the changes of the inlet edge angle, the inlet corner radius, and the orifice shape. The insert of swirl vanes has an effect on the distribution of the cavitated vapor within the orifice, but it has little influence on flow characteristics. The results could enrich our knowledge of liquid nitrogen cavitating flow in spray nozzles of various shapes.     

低温节流阀流动过程数值模拟和实验研究

对弯折型、旋转型两种节流阀进行数值模拟,研究不同工质下节流阀的温降以及流量特性,结果发现与液氮与液氧相比,甲烷在节流阀内的空化更为严重,汽相出现的较早,汽液分布较为混乱.搭建低温节流阀流动换热实验台,以液氮和甲烷为实验工质研究不同工况下的节流阀的流动特性,将进口过冷度作为影响因素提出新的质量流量关联式,可以准确预测节流...     

Numerical analysis of unsteady behavior of cloud cavitation around a NACA0015 foil

Three-dimensional unsteady cavitating flow around a NACA0015 hydrofoil fixed between the sidewalls was simulated and the mechanism of U-shaped cloud cavity formation was clarified. A local homogeneous model was used for the modeling of the vapor–liquid two-phase medium. The compressible two-phase Navier–Stokes equations as the governing equations were solved. To describe the phase change between water and vapor, the mass transfer model based on the theory of evaporation/condensation on a plane interface was introduced. The cell-centered finite volume method was employed to discretize the governing equations. Assuming turbulent flow, the turbulent eddy viscosity coefficient was computed by using the Baldwin–Lomax model with the Degani–Schiff modification. As a result, even in the case of cavitating flow without sidewalls, the shed cloud cavities has slightly 3D structure, which was not so much large as extending across the whole spanwise direction. On the other hand, in the case of cavitating flow with sidewalls, the end of sheet cavities bows in the spanwise direction because of the development of boundary layer near both sidewalls. After that, due to the occurring of the reentrant jet towards the mid-span region, the sheet cavities breaks off from mid-span region near the leading edge of the hydrofoil, and became the vortical cloud cavities, which have the large-scale U-shaped structure.     

绝热毛细管流量数值计算

根据两相流动的均相流假设 ,建立了绝热毛细管分布参数的稳态数学模型 ,结合制冷工质HFC 134a基于MH状态方程的热力学性质计算模型 ,采用新的基团贡献法计算粘度 ,用熵增判据考虑壅塞流动的影响 ,对绝热毛细管流量进行数值模拟计算。对理论计算结果与相关文献的实验数据进行了比较。针对以HFC 134a为工质的制冷系统 ,编制了一套较为实用的绝热毛细管流量计算软件     

Synthesis of a simulation model for an electromagnetic flowmeter

The principles of constructing a simulation model for an electromagnetic flowmeter are considered by means of which it is possible to carry out research into the metrological characteristics of instruments. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 38–43, May, 2006.     

磁性液体管道流动的数值模拟

通过将磁性液体的磁化曲线用一个反正切函数来模拟，并且将磁场体积力写成Az的函数形式来模拟磁性液体在圆管申的流动。结果表明，圆管内的磁性液体有最大流量时，磁性液体流在靠近永磁附近呈紊流状态流动，在圆管的最右端，大致呈层流状态流动；圆管内的磁性液体净流量为零时，靠近永磁的磁性液体在原地呈激烈的涡旋流动状态．     

Optimal control of thermal fluid flow using automatic differentiation

The aim of this study is to present a method for numerical optimal control of thermal fluid flow using automatic differentiation (AD). For the optimal control, governing equations are required. The optimal controls that have been previously presented by the present authors’ research group are based on the Boussinesq equations. However, because the numerical results of these equations are not satisfactory, the compressible Navier–Stokes equations are employed in this study. The objective is to determine whether or not the temperature at the objective points can be kept constant by imposing boundary conditions and by controlling the temperature at the control points. To measure the difference between the computed and target temperatures, the square sum of these values is used. The objective points are located at the center of the computational domain while the control points are at the bottom of the computational domain. The weighted gradient method that employs AD for efficiently calculating the gradient is used for the minimization. By using numerical computations, we show the validity of the present method.     

The influence of cavitation on the flow characteristics of liquid nitrogen through spray nozzles: A CFD study

Spray cooling with cryogen could achieve lower temperature level than refrigerant spray. The internal flow conditions within spray nozzles have crucial impacts on the mass flow rate, particle size, spray angle and spray penetration, thereby influencing the cooling performance. In this paper, CFD simulations based on mixture model are performed to study the cavitating flow of liquid nitrogen in spray nozzles. The cavitation model is verified using the experimental results of liquid nitrogen flow over hydrofoil. The numerical models of spray nozzle are validated against the experimental data of the mass flow rate of liquid nitrogen flow through different types of nozzles including the pressure swirl nozzle and the simple convergent nozzle. The numerical studies are performed under a wide range of pressure difference and inflow temperature, and the vapor volume fraction distribution, outlet vapor quality, mass flow rate and discharge coefficient are obtained. The results show that the outlet diameter, the pressure difference, and the inflow temperature significantly influence the mass flow rate of spray nozzles. The increase of the inflow temperature leads to higher saturation pressure, higher cavitation intensity, and more vapor at nozzle outlet, which can significantly reduce mass flow rate. While the discharge coefficient is mainly determined by the inflow temperature and has little dependence on the pressure difference and outlet diameter. Based on the numerical results, correlations of discharge coefficient are proposed for pressure swirl nozzle and simple convergent nozzles, respectively, and the deviation is less than 20% for 93% of data.     

垂直通道内低温液体过冷流动沸腾传热的数值预测模型

ONB和OSV分别是过冷流动沸腾中气泡形成的却始位置及气泡开始挣脱壁面的位置,准确预测ONB及OSV的位置对于分析低温液体的流动沸腾过程具有十分重要的意义.根据传热机理的不同将低温液体过冷流动沸腾通道划分为3个区,建立了各区内沸腾传热的机理模型及各区边界的判断标准,并将新建立的理论模型纳入双流体模型实现了数值求解,根据数值计算的结果可以很方便地判断ONB及OSV的位置.建立的模型有助于从机理上实现低温液体过冷流动沸腾传热的准确预测.     

A modified drag model for power-law fluid-particle flow used in computational fluid dynamics simulation

A modified drag model for the power-law fluid-particle flow considering effects of rheological properties was proposed. At high particle concentrations (ε_s ≥ 0.2), based on the Ergun equation, the cross-sectional shape and the tortuosity of the pore channel are considered, and the apparent flow behavior index and consistency coefficient of the power-law fluid at the surface of the particles are corrected. At low particle concentrations (ε_s < 0.2), based on the Wen-Yu drag model, the modified Reynolds number for power-law fluid and the relational expression between drag coefficient for single particle and Reynolds number that considers the effect of the flow behavior index are adopted. Numerical simulations for the power-law fluid-particle flow in the fluidized bed were carried out using the non-Newtonian drag model. The effects of rheological parameters on the drag coefficient were analyzed. The comparisons of simulation and experiment show that the modified drag model predicts reasonable void fraction under different rheological parameters, particle diameters, and liquid velocities in both low particle concentrations and high particle concentrations. The increase in flow behavior index and consistency coefficient increases the drag coefficient between the two phases and decreases the average particle concentration within the bed.     

Numerical simulation of two‐phase flow in pipes using Godunov method

The partial differential equations that describe two‐phase flows in pipes are highly non‐linear due to the strong dependence between pressure and wave celerity. The possible appearance of shock waves makes Godunov schemes very attractive, for they can handle such discontinuities automatically. Fluxes at the cell interfaces are computed by solving a Riemann problem. To do so, an approximate state, non‐iterative solver designed in a previous study is used. The treatment of boundary conditions uses an iterative procedure. Existing approximations for the sound celerity under the isothermal assumption are generalized to other situations. A comparison between the isothermal and the adiabatic assumptions shows that such assumptions play an important role in the behaviour of the solution. Finally, numerical results obtained using the first‐order Godunov method on representative test cases are presented and the need for higher‐order reconstruction techniques is acknowledged. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical simulation of multilayer deposition in an obstructed channel flow

Simulation of multilayer deposition of dry aerosol particles in turbulent flows has gained a growing interest in various industrial and research applications. The multilayer deposition of carbonaceous aerosol particles in a turbulent channel flow obstructed by a succession of square ribs is here numerically investigated. The multilayer particle bed growth on the various wall surfaces affects the air flow, which in turn affects the overall deposition rate. An iterative numerical procedure is therefore suggested to simulate the evolution of the graphite layer. The iterative process used to reproduce the layer build-up is decomposed as follows: Reynolds-Avergared Navier Stokes is employed to generate the flow field. The turbulent dispersion of the particles is reproduced through the use of a continuous random walk model. After statistically sufficient deposition of particulate matter, the layer build-up is computed using mechanics of dry granular material. The layer build-up model shows good agreement with data obtained from experimental tests carried out on-site.     

A model of thermal conductivity of nanofluids with interfacial shells

We derive an expression for the effective thermal conductivity of nanofluids with interfacial shells. Comparing with conventional models, the expression is not only depended on the thermal conductivity of the solid and liquid and their relative volume fraction, but also depended on the particle size and interfacial properties. The theoretical results on the effective thermal conductivity of CuO/water and CuO/ethylene glycol nanofluids are in good agreement with the experimental data.     

Numerical simulation of fluid flow and temperature field in keyhole double‐sided arc welding process on stainless steel

Double‐sided arc welding process powered by a single supply is a type of novel high‐production process. In comparison with the conventional single‐sided arc welding, this process has remarkable advantages in enhancing penetration, minimizing distortion and improving welding production. In this paper, a three‐dimensional steady numerical model is developed for the heat transfer and fluid flow in plasma arc (PA)–gas tungsten arc (GTA) double‐sided keyhole welding process. The model considers the surface tension gradient, electromagnetic force and buoyancy force. A CCD camera is used to observe the size and shape of the keyhole and weld pool. The acquired images are analysed through image processing to obtain the surface diameters of the keyhole on the two sides. A double‐V‐shaped keyhole geometry is then proposed and its characteristic parameters are derived from the images and cross‐section of weld bead. In the numerical model, the keyhole cavum within the weld pool is treated as a whole quality, whose temperature is fixed at the boiling point of the workpiece material. The heat exchange between the keyhole and weld pool is treated as an interior boundary of the workpiece. Based on the numerical model, the distributions of the fluid flow and temperature field are calculated. A comparison of cross‐section of the weld bead with the experimental result shows that the numerical model's accuracy is reasonable. Copyright © 2005 John Wiley & Sons, Ltd.