Oscillatory Thermocapillary Flows in Simulated Floating-zones with Time-dependent Temperature Boundary Conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier–Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L=20 [mm] and a diameter D=20 (mm) is considered. A temperature difference ΔT=30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave', but after a transient time the instability is described by the dynamic model of a ‘standing wave', with an azimuthal spatial distribution corresponding to m=1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

Oscillatory thermocapillary flows in simulated floating-zones with time-dependent temperature boundary conditions

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier-Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L = 20 [mm] and a diameter D = 20 (mm) is considered. A temperature difference ΔT = 30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave’, but after a transient time the instability is described by the dynamic model of a ‘standing wave’, with an azimuthal spatial distribution corresponding to m = 1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.     

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface are investigated. The nondimensional analysis predicts that, when convection is important, the characteristic length scale in the flow direction L, and the characteristic temperature difference ΔT₀, can be represented by and , respectively, where L_R and ΔT_T are the reference scales used in the conduction-dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having had L and ΔT₀ defined, the global surface-temperature gradient ( ), the global thermocapillary driving-force, and other interesting features can then be readily determined. Finally, numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations.     

Directional Solidification Using a Baffle in Microgravity

Numerical simulations were performed to optimize the conditions and parameters for directional solidification of Te-doped GaSb in reduced gravity ranging from 10⁻³ to 10⁻⁵g₀. Our key goal was to quantify the velocity and concentration fields with and without a baffle present in the melt. The effect of the distance of the baffle from the solid–liquid interface was investigated. When the baffle is placed 0.5 cm from the solid–liquid interface, acceleration of 10⁻³g₀ does not cause significant interference with segregation. Furthermore, the flow between the baffle and the interface (low Reynolds number “creeping” flow) does not depend on fluid properties (viscosity).     

A micro-gravity simulation of the Marangoni convection

An experimental verification of Marangoni convection in the liquid inter-space between two-coaxial discs is carried out at reduced gravity effect using small Bond's number obtained by choice of small characteristical diameter. Silicon oil is used as working fluid. The upper or lower disc can be heated electrically. The flow is visualized by illuminating fine powder of Titandioxide in the fluid with a vertical “light cut” of about 0.1 mm thickness, which is produced by a laser with a cylindrical glass rod and a microscope objective. Photographs and moving pictures are taken from a TV monitor. From these the vortex configuration and the velocity distribution can be determined, which would be expected for the Marangoni convection in the zero-g condition, for example in the spacelab.     

低温推进剂重定位推力幅值及时序优化

为了减少重定位时间及推进剂消耗量,提升低温末级的机动性及运载能力,采用流体体积函数(VOF)方法开展重定位推力幅值及时序优化研究,分析重定位过程推进剂质心高度、平均动能、卷气率以及平均气泡直径的变化规律,以获得不同推力幅值及推力时序下的重定位时间和推进剂消耗量。结果表明：小推力重定位时间长,推进剂消耗量少;而大推力重定位时间短,推进剂消耗量多。通过合理优化推力时序可以有效减少重定位时间及推进剂消耗量。     

液氧贮箱增压过程研究

采用数值模拟方法对液氧贮箱增压过程进行研究.贮箱内流场采用流体体积函数（VOF）多相流模型考虑,选择标准双方程k-ε湍流模型分析湍流效应,气液两项之间的热量、质量转移通过自定义程序（UDF）求解.获得了贮箱压力、排液流量、气垫温度、液氧温度对贮箱内流场温度分布的影响.计算结果表明,在稳定增压过程中,贮箱液面无扰动,贮箱内温度分层分布;各参数变化时,对贮箱内温度分布的影响主要是温度梯度的变化,并且各工况下液面附近和扩散器附近温度梯度基本相同.     

点阵结构空气舵及内部流体热流固耦合研究

开展了钛合金TC4材料激光粉末床熔融(LPBF)工艺研究,在此基础上设计了多孔轻质空气舵模型,并基于有限差分法(FDM),采用三维流固耦合共轭传热数值计算方法,利用流体体积法(VOF)追踪流体自由液面,研究了典型的点阵夹层结构的空气舵内部冷却液动态换热过程的相互影响过程,考虑了冷却液与钛合金材料蒙皮间的耦合传热及湍流换热。结果表明,空气舵的内部流体压强随速度的增加而增加,从而导致流体出口的速度增加。当压强增加到一定程度时,流体的出口以水柱形式喷出。虽然较大的流体速度可以带走较多的热量,但是影响远小于对压强的影响。综合考虑空气舵的服役要求,获得了合适的冷却水入口速度。     

Numerical solution of nonlinear heat problem with moving boundary

Two phase gas–liquid flow in pipes is widely spread in space applications: bubble flows appear in cryogenic components transport through fuel/oxidant supply lines. Another important application is based on the fact that in liquid flows with small bubbles a close contact between the two phases occurs resulting in high rates of transfer between them. The compactness of a system makes it ideally suited to serve as a space-based two-phase bio-reactor which forms an important unit in environmental control and life support system deployed onboard. A numerical method was developed for solving a nonlinear problem of thermal interaction between a spherical gas bubble and surrounding liquid. The system of equations for describing this interaction was formulated. It includes ordinary and nonlinear partial differential equations. The problem was solved using finite-difference technique by dividing the system into spherical layers inside the bubble and employing the new variable which “freezes” the moving boundary of the bubble. A numerical solution is obtained for the problem of radial bubble motion induced by a sudden pressure change in the liquid—a situation which corresponds to the behavior of bubbles beyond a shock wave front when the latter enters a bubble curtain.     

Preliminary results of Texus 8 experiments on effects of surface tension minimum

A stable, observable liquid-gas interface was realized in an experimental cell (3 × 2 × 1 cm) under microgravity conditions. The liquid used was an aqueous 6.24 10^?3 molal solution of n-heptanol. A temperature gradient, established at the interface, resulted in the build-up of a Marangoni convection cell with the liquid flowing in an unusual direction (i.e. at the surface the liquid flowed from the cold to the hot side).The same experiment on Earth gives rise to a Marangoni cell superimposed on buoyancy cells. The Marangoni and the buoyancy cells then turn in opposite directions.     

不同密度比球体入水空泡流体动力特性研究

基于实验与数值计算相结合的方法,针对不同密度比的疏水性球体开展了垂直入水空泡形态及水下流体动力特性研究。建立了基于高速摄像法的小型航行体入水实验系统,并进行了入水空泡高速录像观察。基于VOF方法和动网格技术建立了考虑表面润湿性的回转体入水数值模拟方法。通过与实验结果对比,验证了数值方法的准确性和有效性。基于对实验与数值结果的分析,总结了疏水性球体的入水空泡及水冠发展随密度比与入水冲击速度的变化规律,对比了不同密度比球体在水下空泡夹断前后的流体动力系数。结果表明:随着入水冲击速度的增加,球体动能加大,入水空泡和水冠尺度增大,并从准静态闭合空泡逐渐发展为深闭合及面闭合空泡,临界速度随着密度比的增加而减小。此外,空泡夹断后会形成上下两股高速射流,射流的进一步运动加速了水面及球体附近空泡的溃灭。在流体动力特性方面,球体带空泡航行阶段的时均流体动力系数随密度比的增加而减小,而随入水冲击速度的变化较小,同时空泡夹断会造成流体动力较大波动。     

航天器贮箱大幅液体晃动三维质心面等效模型研究

针对航天器贮箱内的大幅液体晃动建立了三维质心面等效模型,此模型将贮箱内液体等效为位于液体质心处的质点,该质心点可以在质心约束面内任意运动,同时利用质心点动力学方程及接触碰撞模型近似计算液体晃动对贮箱的作用力。质心面等效模型的数值仿真结果与基于VOF方法的流体动力学数值计算结果基本吻合,从而验证了质心面等效模型用于航天器贮箱大幅液体晃动分析的有效性。     

Theoretical study about the Marangoni convection in a liquid column in zero-gravity

The thermal Marangoni effect on the surface of a liquid bridge induces a convection inside the liquid. For an imposed arbitrary periodic axial circumferential temperature distribution on the liquid surface the velocity distributions in radial-, angular- and axial direction are determined theoretically by solving the linearized Navier-Stokes equations. Of particular interest is the effect of the viscosity parameter $\text{v}\text{a}{}^2$ and axial wave length to diameter ratio $\text{l}\text{a}$. It was found that the increase of viscosity decreases the magnitude of the velocity distributions and that for small axial wave length to diameter ratios the radial- and axial velocities exhibit peak values close to the free surface of the liquid. This is in a less pronounced way also true for the angular velocity, which shows for increasing moderate values $\text{l}\text{a}\text{(0 ≤}\text{l}\text{a}\text{≤ 2}$) a strong increase in magnitude and for larger axial wavelength a decrease again. For increasing axial wavelength the peak value of the radial- and axial velocity shifts towards the center of the liquid bridge, of which for a further increase a decrease of the magnitude appears.     

A study of detonation in methane/air clouds

In the present paper, we study the problem of detonation in unconfined, gaseous mixtures of methane/oxygen/nitrogen. A numerical simulation approach is employed in which we use a one-dimensional (spherical symmetry), time-dependent computer model to simulate the coupled compressible fluid dynamics-chemical kinetics processes which occur upon direct initiation of detonation. We establish the magnitude of explosive yield of tetryl required to initiate detonation in mixtures of CH₄ + 2O₂ with varying degrees of nitrogen dilution, up to and including stoichiometric . The numerical simulations illustrate the features of direct initiation observed in many experimental investigations, e.g. shock-wave breakaway followed by detonation reestablishment via a quasi-steady, oscillatory flow regime which occurs before the establishment of a steadily propagating spherical detonation. Our results compare well with recent experimental data obtained by Bull et al. (1976) over the range of tetryl masses studied by them. We find that tetryl explosive masses in excess of 10⁷ grams would be required to initiate detonation in an unconfined, stoichiometric mixture.     

The effect of small vibrations on Marangoni convection and the free surface of a liquid bridge

The effects of small vibrations on Marangoni convection were investigated experimentally using a liquid bridge of 5 cSt silicone oil with a disk diameter of 7.0 mm, and an aspect ratio close to 0.5. Experiments were performed to determine the critical temperature difference data for no vibration case and with small vibrations applied. The experimental results have shown that the effect of small vibrations on the onset of oscillatory flow is small since the critical temperature difference data for different aspect ratios were not affected by the vibrations. To clarify the surface oscillation phenomena induced by external vibrations, a 3-D numerical simulation model was also developed using a level set algorithm to predict the surface oscillations of isothermal silicone oil bridges. By subjecting the liquid bridge to small vibrations, the surface oscillation characteristics were predicted numerically, and the numerical results compared well with the predictions of an analytical model proposed previously. Furthermore, the effect of small vibrations on the surface vibration amplitude of the liquid bridge is also discussed.     

Investigation of thermosolutally caused convection during Bridgman-growth of BiSbTe3-mixed crystals at normal and reduced gravity

BiSbTe₃-mixed crystals have been grown at normal and reduced gravity (during the MIR'97-mission) using a Bridgman-configuration of the TITUS facility. The distribution of the components in the melt, and so the homogeneity of the growing crystal, is strongly influenced by the flow in the melt even in the case of weak convection. The flow configuration in the melt especially in front of the solid-liquid phase boundary can be investigated by means of a segregation analysis of the system components and an additional Pb-dopant. The BiSbTe₃-system is because of its hydro-dynamic properties a typical representative of semiconductor melts (low Prandtl number, high Schmidt number) but there are also some special properties relating to the segregationally caused enrichment of the lighter tellurium at the phase boundary and the resulting solutal destabilities. Experimental experiences from segregation analysis have shown that the mass transport in the melt at normal gravity is mainly influenced by convective mixing determined by thermally and solutally caused buoyancy forces. Numerical simulations have been performed for the real experimentally used configurations. These simulations have shown that a strong coupling of thermal and solutal effects exists and have given axial as well as radial segregation profiles being in excellent agreement with the experimental results for the vertical normal gravity grown crystals. For micro gravity conditions a reduction of the flow velocity of more than two orders of magnitude (depending on the micro gravity level and the direction of the residual acceleration) resulting in diffusion controlled component segregation has been predicted.The results of the two micro gravity grown crystals, especially the axial and radial segregation profiles as a sensitive indicator for the flow configuration in front of the phase boundary will be given and discussed in the paper. They will be compared with the results of numerical simulations of the melt flow for the real processing parameters measured during the TITUS growth processes and with experimental as well as numerical results for vertical normal gravity grown reference Samples.     

Effects of variable transport properties on thermal Marangoni flows

The effects of temperature dependence of the diffusion coefficients on the solution fields of Thermal Marangoni Flows in micro-gravity is analyzed by using an unsteady—variable mesh—two dimensional—finite difference numerical code to solve the full Navier-Stokes equations.A typical cylindrical floating zone geometry is analyzed and the estimation of the deviations caused by considering a temperature-dependent variable viscosity is verified with respect to the most important field parameters (streamlines, isotherms, isobars, Nusselt heating curves, velocity and temperature profiles).Comparison with TEXUS experiment is finally performed.     

无塌陷型面出流及输送管内推进剂利用技术研究

针对火箭通用芯级氧箱的共底贮箱结构，通过理论分析及数值仿真，提出了“无塌陷型面+消漩叶片”的出流方案，并通过优化型面起始点半径，确保出流过程中不产生明显的液面塌陷。仿真及缩比试验结果表明，相比传统的“圆盘+倒锥”出流方案，贮箱推进剂在无塌陷型面出流方案下的出流过程中，没有明显的气液掺混或漩涡夹气现象，贮箱内推进剂可得到充分利用。在此基础上，利用Wallis两相漂移模型对输送管内两相介质传播速度进行了理论研究，并结合出流过程中气泡运动速度的试验结果，提出了输送管内推进剂的可用量准则。     

离心式喷嘴全流场数值模拟

将离心式喷嘴流场数值模拟由内流场扩展至外流场,将喷嘴出口的一段区域纳入计算域,探索用数值模拟方法研究全流场的流动特性并在此基础上对雾化特性进行分析。计算结果给出全流场的液膜形状以及气涡与液膜共存的流场结构,直接给出雾化锥角。采用VOF方法捕捉气液界面,湍流模型选择RNG双方程模型,对容积分数方程选择积分平均型TVD格式...     

Heating and acceleration of charged particles during magnetic dipolarizations

In this paper, we analyzed the thermal and energy characteristics of the plasma components observed during the magnetic dipolarizations in the near tail by the Cluster satellites. It was previously found that the first dipolarization the ratio of proton and electron temperatures (T _p/T _e) was ~6–7. At the time of the observation of the first dipolarization front T _p/T _e decreases by up to ~3–4. The minimum value T _p/T _e (~2.0) is observed behind the front during the turbulent dipolarization phase. Decreases in T _p/T _e observed at this time are associated with an increase in T _e, whereas the proton temperature either decreases or remains unchanged. Decreases of the value T _p/T _e during the magnetic dipolarizations coincide with increase in wave activity in the wide frequency band up to electron gyrofrequency f _ce. High-frequency modes can resonantly interact with electrons causing their heating. The acceleration of ions with different masses up to energies of several hundred kiloelectron-volts is also observed during dipolarizations. In this case, the index of the energy spectrum decreases (a fraction of energetic ions increases) during the enhancement of low-frequency electromagnetic fluctuations at frequencies that correspond to the gyrofrequency of this ion component. Thus, we can conclude that the processes of the interaction between waves and particles play an important role in increasing the energy of plasma particles during magnetic dipolarizations.