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.     

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.     

低温流体空化特性的数值计算研究

采用数值计算的方法研究了液氮和液氢的空化流动特性。为了考虑温度影响,控制方程采用了连续方程、动量方程及能量方程,并应用二次开发方法在商业软件中引入Merkle 空化模型及物质属性,物性参数随流场温度变化而不断更新。分别对液氮和液氢几个工况进行了计算,并与实验结果进行了对比。结果发现,在液氮和液氢中,当流体温度接近临界点时,热力学效应表现显著。热力学效应显著主要表现在空穴变短、水蒸汽含量减少和汽液界面变的模糊。由于密度比、饱和蒸汽压随温度变化梯度等物质属性的不同,相对液氮,液氢的热力学效应更加明显。     

低温推进剂贮箱增压过程的传热传质数学模拟

针对火箭发动机地面试验中低温液氧贮箱的预增压和增压过程建立了气相空间的传热、传质数学模型.运用实际气体的状态方程、连续性方程、能量守恒方程以及推进剂与气相空间的传热、传质方程等组成了关于气相空间参数的微分方程组,并运用四阶Runge-Kutta算法对其进行求解.获得了气相空间的压力、温度、增压气体流量、液氧挥发速率以及贮箱壁温等参数的变化规律.结果表明,在发动机启动前的预增压过程中,气相空间的温度和压力急剧增加,液氧的挥发速率也增加很快;发动机启动后的保持增压阶段,由于气相空间的体积不断发生变化,气相空间参数的变化趋于平缓,液氧表面向气相空间的传质速率也趋于稳定.     

Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300–311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.     

绕三维水翼非定常空化流动结构的数值与实验研究

为了说明非定常空化的流动机理,该文采用数值与实验相结合的方法对绕三维水翼片状和云状空化流动结构进行了研究.实验在高速水洞中进行,采用高速录像技术观测了片状和云状空化阶段的空穴形态.数值计算基于均相流模型,汽液混合区域密度由质量传输方程调节.利用商业软件二次开发技术引入准确描述空化流场非定常特性的FBM 湍流模型,进行绕三维水翼的数值模拟,获得了随时间变化的空穴形态、压力和速度分布等流场结构.与实验结果对比发现,数值计算结果与实验基本一致.在片状空化阶段,空穴稳定地附着在水翼表面,只有空穴尾部不断的有小空泡团沿着翼弦方向脱落.在云状空化阶段,清楚得描述了空穴的产生-发展-脱落-溃灭的准周期性变化,并准确地捕捉到空泡脱落时,附着在翼型前端的U 型空穴和翼展方向不同强度的反向射流,脱落的空泡由翼型中前部旋涡状脱落.     

Preliminary results on acoustic modelling of cavitating propellers

The numerical prediction of the acoustic pressure field induced by cavitating marine propellers is addressed. A hydrodynamic model for transient sheet cavitation on propellers in non–uniform inviscid flow is coupled with a hydroacoustic model based on the Ffowcs Williams–Hawkings equation. The proposed hydroacoustic approach, novel to marine applications, allows to split the noise signature into thickness and loading term contributions. Both hydrodynamic and hydroacoustic model equations are solved via boundary integral formulations. Numerical predictions of the propeller noise by using the Ffowcs Williams–Hawkings equation are compared to those obtained by a classical Bernoulli equation approach. The influence of cavitation on the noise waveforms is discussed by comparing non–cavitating and cavitating propeller flow results. The authors wish to thank Prof. S.A. Kinnas for providing a detailed documentation of the experiment used as the test case in the present analysis. The present work was supported by the Ministero dei Trasporti e della Navigazione in the frame of INSEAN Research Program 2000–02.     

泵内压降和水力损失耦合诱导泵内液氮空化研究

为了研究泵内压降和水力损失耦合诱导泵内液氮空化,采用Zwart空化模型和RNG k-ε湍流模型,并使用CEL语言将饱和蒸气压随温度变化函数关系式导入CFX软件中进行求解,对不同流量下低温泵的空化特性曲线进行分析。研究结果表明,低温泵内压力、温度和空泡体积分数分布与空化的发展程度有关,由于水力损失的作用,小流量工况下,泵内会出现涡状流,从而对叶轮内空化产生影响。     

Computational fluid dynamic study on cavitation in liquid nitrogen

Cavitation is the formation of vapor bubbles within a liquid where flow dynamics cause the local static pressure to drop below the vapor pressure. This paper presents the steady computational fluid dynamic (CFD) results of cavitation in liquid nitrogen flow through hydrofoils and ogives with so-called “full cavitation model”. The model is reexamined to assess the performance prediction from the standpoint of cryogenic fluids with the assumption of thermal equilibrium between vapor phase and liquid phase. The fluid thermodynamic properties are specified along the saturation line using the “Gaspak 3.2” databank. The thermal effects and accompanying property variations due to phase change are modeled rigorously. The thermodynamic cavitation framework is validated against experimental data of NASA hydrofoil and ogive. The global sensibility of the cavitation solution with respect to the cavitation model coefficients and the free-stream velocity is investigated in detail and the choking phenomenon is reported with high Mach number. The full cavitation model with the default coefficients is applicable for cavitation prediction in liquid nitrogen, taking into account of the thermodynamic effects.     

Development of highly effective cryogenic printed circuit heat exchanger (PCHE) with low axial conduction

This paper presents the results of an experimental investigation of the thermal and hydraulic performance of a printed circuit heat exchanger (PCHE) for use in the cryogenic temperature region. Compact PCHEs with multiple corrugated, longitudinal flow microchannels were fabricated using chemical etching and diffusion bonding to evaluate their thermal and hydraulic performance. The testing of the PCHEs was conducted with helium gas at cryogenic temperatures. The pressure drop and thermal effectiveness values obtained from the measured pressures and temperatures are discussed. The thermal performance was predominantly affected by the axial conduction heat transfer in the low Reynolds number ranges of theses experiments. A simple performance calculation model is presented, and the effectiveness calculated from the model is compared with the experimental data. The design of the cryogenic PCHE was then modified to reduce axial conduction losses.     

低温液体容器无损存储传热模型

分析了低温液体容器无损存储时的传热规律,并建立了传热模型,得出了反映储罐绝热层温度变化的微分方程式。采用数值差分法可以求解出绝热层内部温度变化规律,从而推出储罐内液体的温度和压力的变化规律。     

空化射流形成的判据和冲蚀机理

阐述了空化射流研究简况和空化形成机理。讨论了用于描述空化是否发生和空化程度的空化数的合理性,认为用空化数不能判断射流的空化状态;流场中具有绝对压强小于或等于汽化压强的区域是射流空化的必要条件;在高环境压强下,必须采取特殊的减压措施才有可能实现空化。针对空化射流比普通射流冲蚀能力强的事实,分析了Rayleigh空穴湮灭冲击压强计算公式存在的问题,给出了空化射流的射流质量脉动引发作用在靶体表面上的压强脉动是导致靶体容易破坏的主要原因。     

An automatic low temperature heat switch

A heat switch for use at cryogenic temperatures is described. It utilizes the pressure-dependence of thermal conductivity of gases and the decrease of vapour pressure with temperature. The switching temperature can be varied widely by changing the working gas. Due to the absence of mechanically moving parts, lifetime and reliability are high. A thermal conductivity on/off ratio of 500 can easily be achieved.     

Experimental study on the double-evaporator thermosiphon for cooling HTS (high temperature superconductor) system

A cryogenic thermosiphons is an efficient heat transfer device between a cryocooler and a thermal load that is to be cooled. This paper presents an idea of thermosiphon which contains two vertically-separated evaporators. This unique configuration of the thermosiphon is suitable for the purpose of cooling simultaneously two superconducting bearings of the HTS (high temperature superconducting) flywheel system at the same temperature. A so-called double-evaporator thermosiphon was designed, fabricated and tested using nitrogen as the working fluid under sub-atmospheric pressure condition. The interior thermal condition of the double-evaporator thermosiphon was examined in detail during its cool-down process according to the internal thermal states. The double-evaporator thermosiphon has operated successfully at steady-state operation under sub-atmospheric pressure. At the heat flow of 10.6 W, the total temperature difference of the thermosiphon was only 1.59 K and the temperature difference between the evaporators was 0.64 K. The temperature difference of two evaporators is attributed to the conductive thermal resistance of the adiabatic section between the evaporators. The method to reduce this temperature difference has been investigated and presented in this paper. The proper area selection of condenser, evaporator 1, and evaporator 2 was studied by using thermal resistance model to optimize the performance of a thermosiphon. The superior heat transfer characteristic of the double-evaporator thermosiphon without involving any cryogenic pump can be a great potential advantage for cooling HTS bulk modules that are separated vertically.     

Estimation of vapour pressure and partial pressure of subliming compounds by low-pressure thermogravimetry

A method for the estimation of vapour pressure and partial pressure of subliming compounds under reduced pressure, using rising temperature thermogravimetry, is described in this paper. The method is based on our recently developed procedure to estimate the vapour pressure from ambient pressure thermogravimetric data using Langmuir equation. Using benzoic acid as the calibration standard, vapour pressure-temperature curves are calculated at 80, 160 and 1000 mbar for salicylic acid and vanadyl bis-2,4-pentanedionate, a precursor used for chemical vapour deposition of vanadium oxides. Using a modification of the Langmuir equation, the partial pressure of these materials at different total pressures is also determined as a function of temperature. Such data can be useful for the deposition of multi-metal oxide thin films or doped thin films by chemical vapour deposition (CVD).     

HFC32 vaporisation inside a Brazed Plate Heat Exchanger (BPHE): Experimental measurements and IR thermography analysis

This paper presents HFC32 average boiling heat transfer coefficients and pressure drops measured inside a small Brazed Plate Heat Exchanger (BPHE): the effects of heat flux, saturation temperature (pressure), and outlet conditions are investigated. The experimental tests were carried out at four different saturation temperatures (5, 10, 15, and 20 °C) and four different evaporator outlet conditions (vapour quality around 0.80 and 1.00, vapour super-heating around 5 and 10 °C). The average heat transfer coefficients show great sensitivity to heat flux and outlet conditions and weak sensitivity to saturation temperature (pressure). The saturated boiling heat transfer coefficients were compared with a new model for refrigerant vaporisation inside BPHE (Longo et al., 2015): the mean absolute percentage deviation between calculated and experimental data is 4.7%. The heat transfer and pressure drop measurements are complemented with a IR thermography analysis for a better understanding of the vaporisation process inside a BPHE.     

Theoretical study for safe and efficient energy transfer to deeply implanted devices using ultrasound

The goal of this paper is to prove that a safe and efficient energy transfer is possible between an external transducer located on the patient's skin and a device deeply implanted in the abdomen. An ultrasound propagation model based on the Rayleigh-Sommerfeld diffraction integral is coupled with the data from the Visible Human Project to account for the geometry of the organs in the body. The model is able to predict the amount of acoustic power received by the device for different acoustic paths. The acoustic model is validated by comparison with measurements in water and in heterogeneous liquid phantoms. Care is taken to minimize adverse bioeffects-mainly temperature rise and cavitation in tissues. Simulations based on the bio-heat transfer equation are performed to check that thermal effects are indeed small.     

Wave-shaping of pulse tube cryocooler components for improved performance

The method of wave-shaping acoustic resonators is applied to an inertance type cryogenic pulse tube refrigerator (IPTR) to improve its performance. A detailed time-dependent axisymmetric experimentally validated computational fluid dynamic (CFD) model of the PTR is used to predict its performance. The continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the PTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The wave-shaped regenerator and pulse tube studied have cone geometries and the effects of different cone angles and the orientation (nozzle v/s diffuser mode) on the system performance are investigated. The resultant spatio-temporal pressure, temperature and velocity fields in the regenerator and pulse tube components are evaluated. The performance of these wave-shaped PTRs is compared to the performance of a non wave-shaped system with cylindrical components. Better cooling is predicted for the cryocooler using wave-shaped components oriented in the diffuser mode.     

Entwicklung eines Ionisationsmanometers mit Feldemitterkathode

Development of an ion gauge with field emissionin cryogenic vacuum environments cathode for pressure measurements The measurement of UHV or even XHV pressures in low‐temperature vacuum systems has always been considered as a metrological problem. In principle, conventional hot‐cathode ion gauges can be used for pressure measurement in cryogenic vacuum environments. However, as a consequence of their high heat generation several disadvantages must be taken into account. With the development of an ion gauge of extractor‐type whose heat‐generating thermionic cathode is replaced by a non‐thermal field emission cathode, a promising approach to realize a reliable pressure gauge for cryogenic vacuum applications can be presented in this paper. The gauge equipped with a CNT cathode was investigated both experimentally and by numerical simulations in terms of their operating characteristics. It has been successfully demonstrated that the modified extractor gauge works reliably under low temperature conditions and provides meaningful pressure readings.     

Experimental study on the thermal hydraulic performance of plate-fin heat exchangers for cryogenic applications

Efficient and compact plate-fin heat exchangers are critical for large-scale helium liquefaction/refrigeration systems as they constitute major part in the cold box. This study experimentally explores the heat transfer and pressure drop behaviors of helium gas at low temperature in four types of plate-fin channels, namely offset-strip and perforated fins, with different geometrical parameters. A series of cryogenic experiments at approximately liquid nitrogen temperature are carried out to measure the Colburn j factors and Fanning friction f factors with a wide range of Reynolds number. Besides, to reveal the performance variations under different operating temperatures, comparative experiments respectively conducted at room temperature and liquid nitrogen temperature are implemented. The results show that in comparison with the performance data at room temperature, most of j factors are relatively smaller perhaps because the lower aluminum thermal conductivity and higher Prandtl Number at low temperature. Meanwhile, the f factors corresponding to cryogenic conditions exhibit slightly larger even though the core pressure drops show considerable reductions. In contrast to the calculated results from the frequently-used performance curves (Chen and Shen, 1993), the Root Mean Squared Errors of j and f values are correlated within 8.38% and 6.97% for one perforated fin core, 41.29% and 34.97% for three OSF cores, respectively. For OSFs, further comparisons with the previous empirical correlations from literatures are conducted to verify the accuracy of each correlation. Generally, most of the calculated results predict acceptably within the deviations of ±25% for the j factors, while the predicted results express relatively large deviations for the f factors. Therefore, it may be revealed that most of the existing correlations were not able to accurately predict the experimental data in consideration of the performance differences under realistic cryogenic operating conditions, which could have significant influences during the design process of cryogenic heat exchangers.