Heat transfer during bubble formation

The flow around a gas bubble forming at a submerged orifice without vaporisation is analysed both with and without heat transfer taking place from the bubble surface. The results of experiments are given in which high-speed photography was used to study air bubbling through four different sizes of orifice into water, for the isothermal and diabatic case. A numerical solution of the dimensionless equations using Hamming's modified predictor-corrector method gave excellent agreement with experimental measurements of the bubble volume-time history for both stages of growth as well as predicting accurately the transition point between the two stages. Most of the heat transfer was found to occur almost immediately after the start of bubble growth     

爆炸载荷作用下铀气溶胶形成机理研究

针对铀材料在爆炸载荷作用下形成放射性气溶胶的过程,采用光滑粒子流体动力学方法开展了数值模拟和实验研究。通过将颗粒动力学和SPH方法结合,建立了炸药爆轰作用于铀金属壳的数值模拟模型,以铀材料比内能为气溶胶转化判据,获得了铀材料转化为气溶胶的物理过程,得到了在相同爆炸当量下,不同质量铀材料的气溶胶转化效率,并与实验结果进行了对比分析。结果显示,铀材料在爆炸载荷作用下,当其比内能达到1.9 MJ/kg时,即可认为完全转变为气溶胶,对于本文中的爆炸装置结构形式,当炸药质量为铀材料质量的6倍时,转化率超过90%。实验验证了数值模拟结果,表明该方法能够对铀材料的气溶胶转化过程进行准确描述。     

Effect of orifice shape on bubble formation mechanism

The effect of orifice shape on the mechanism of bubble formation in gas–liquid two-phase flow is investigated experimentally with three different orifice geometries regarding a circle, a square, and a triangle with same cross-sectional areas. The liquid and gas phases are purified water at 20 °C and air at room temperature, respectively. Gas is injected at the rate of 50–1200 mlph into a stagnant pool of liquid in distances of 5, 10, and 15 cm below the liquid surface. The position, velocity, and acceleration of bubbles are measured at bubbles’ centers of mass (CM) and the effects of these parameters on the bubble volume are investigated. Moreover, the forces acting on a bubble are balanced and the effects of geometry and gas flow rate on each force are presented. In addition, the changes of the acting forces versus time are plotted and discussed for a specific condition. Results show the bubbles formed with the square and circular orifice cross-sectional areas have the most and least volumes at detachment, respectively.     

Dynamics as a mechanism preventing the formation of finer and finer microstructure

We study the dynamics of pattern formation in the one-dimensional partial differential equation $$u_u - (W'(u_x ))_x - u_{xxt} + u = 0{\text{ (}}u = u(x,t),{\text{ }}x \in (0,1),{\text{ }}t > 0)$$ proposed recently by Ball, Holmes, James, Pego & Swart [BHJPS] as a mathematical “cartoon” for the dynamic formation of microstructures observed in various crystalline solids. Here W is a double-well potential like 1/4((u _x )² ?1)². What makes this equation interesting and unusual is that it possesses as a Lyapunov function a free energy (consisting of kinetic energy plus a nonconvex “elastic” energy, but no interfacial energy contribution) which does not attain a minimum but favours the formation of finer and finer phase mixtures: $$E[u,u_t ] = \int\limits_0^1 {(\frac{{u_t^2 }}{2} + W(u_x ) + \frac{{u^2 }}{2})dx.}$$ Our analysis of the dynamics confirms the following surprising and striking difference between statics and dynamics, conjectured in [BHJPS] on the basis of numerical simulations of Swart & Holmes [SH]:

?While minimizing the above energy predicts infinitely fine patterns (mathematically: weak but not strong convergence of all minimizing sequences (u _nv_n) of E[u,v] in the Sobolev space W ^{1 p}(0, 1)×L²(0,1)), solutions to the evolution equation of ball et al. typically develop patterns of small but finite length scale (mathematically: strong convergence in W ₁ ^p(0,1)×L²(0,1) of all solutions (u(t),u_t(t)) with low initial energy as time t → ∞).

Moreover, in order to understand the finer details of why the dynamics fails to mimic the behaviour of minimizing sequences and how solutions select their limiting pattern, we present a detailed analysis of the evolution of a restricted class of initial data — those where the strain field u _x has a transition layer structure; our analysis includes proofs that

?at low energy, the number of phases is in fact exactly preserved, that is, there is no nucleation or coarsening

?transition layers lock in and steepen exponentially fast, converging to discontinuous stationary sharp interfaces as time t → ∞

?the limiting patterns — while not minimizing energy globally — are ‘relative minimizers’ in the weak sense of the calculus of variations, that is, minimizers among all patterns which share the same strain interface positions.

     

2021-09期目录

对连续爆轰发动机中常见的低频爆轰不稳定性现象开展了基于含源项Euler方程的二维数值模拟研究,揭示了低频爆轰不稳定性产生的机理和详细过程。结果表明,燃烧室头部持续存在一些反传激波,这些激波与进气壁面相互作用会产生“进气阻滞点”,导致新鲜气体层不规则分布;不规则新鲜气体层会使爆轰波头上的压强分布随进气阻滞点的分布位置产生周期性变化;随着进气阻滞点产生的位置沿着进气壁面的缓慢移动,爆轰波头每次与采样点相遇时,采样点与上个进气阻滞点之间的距离会逐渐发生变化,因此采样点的压强峰值便产生了低频率的起伏振荡,即形成了所谓的低频爆轰不稳定性。     

Estimating the total effect on a formation during borehole drilling

A stationary mathematical model describing the time-integrated effect on an oil-saturated reservoir during drilling is considered. Calculated results are compared with the solution of the problem in an exact nonstationary formulation. The formation of an invaded zone in straight borehole drilling in water-and oil-saturated reservoirs is studied by numerical modeling. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 113–122, March–April, 2008.     

The elastic behaviour of gels during the structure formation process

Summary A simple modification of the stress-strain relation for a normal viscoelastic material has been derived for a gel with temporary structural bonds which is subjected to small deformations during gelation. This shows that the storage modulus should separate into two parts, one dependent on frequency and the other on the time for which the gel has been allowed to set. The loss modulus should depend only on frequency. These theoretical results, and others concerning creep under constant stress are in general agreement with observations on a number of gels. Exceptions occur, however, in the period immediately after preparation (before continuous structure has formed) and also after long periods of time during which irreversible changes can have occurred. Certain anomalies appear when the basic assumption of the theory are applied to structure formation in gels with permanent bonds, and a possible resolution of these is suggested.

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Zusammenfassung Es wird eine einfache Modifikation der Spannungs-Dehnungs-Beziehungen normaler viskoelastischer Stoffe abgeleitet, durch die das Verhalten eines Gels mit temporärer Bindungsstruktur bei kleinen Deformationen während des Geliervorgangs beschrieben werden kann. Diese sagt voraus, daß der Speichermodul in zwei Teile aufspaltet, wobei der eine von der Frequenz und der andere von der Erstarrungszeit des Gels abhängt. Dagegen sollte der Verlustmodul nur von der Frequenz abhängig sein. Diese theoretischen Voraussagen, sowie die daraus abgeleiteten Folgerungen bezüglich des Kriechens unter konstanter Spannung, stimmen durchweg mit den an einer Anzahl von Gelen gemachten Beobachtungen überein. Abweichungen kommen dagegen in der Zeit unmittelbar nach der Herstellung vor (bevor sich eine durchgehende Struktur gebildet hat) und nach einer so langen Zeitspanne, daß irreversible Strukturänderungen entstanden sein können. Gewisse Anomalien treten in Erscheinung, wenn die Grundvoraussetzungen der Theorie auf die Strukturbildung bei Gelen mit permanenten Bindungen angewendet werden. Hierfür wird eine mögliche Deutung vorgeschlagen.

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With 3 figures     

格栅-空腔自激振荡流场扰动形成机理研究

格栅-空腔流动会引发流场自激振荡现象,产生结构振动及噪声问题.研究此类现象的形成机理对相关设备的减振降噪设计具有重要意义.目前已知这种现象是在流场正逆向两种扰动的耦合作用下形成的,但上述两种扰动的形成机理尚未明确.针对该问题,建立了格栅-空腔流动数值模型,并进行非稳态数值模拟.通过分析压力振荡数据及流场结构演化过程,对...     

Jet formation and penetration mechanism of W typed shaped charge

Existing classical shaped charges are well known for their longer jets capable of achieving large hole depth to hole diameter ratios in metallic targets. However, in some situations, there arises demand to obtain 1：1 ratio for hole depth to hole diameter which is beyond normal shaped charges capability. A new variant of shape charge, named W typed shape charge （WSC）, is proposed in this paper, which can meet the demand of 1：1 ratio, and is based on the geometry that can produce annular jets upon proper initiation scheme. In this paper, we present formation and penetration results of WSC based on three different schemes. We also show that not all WSC designs can form annular jets, only annularly initiated WSC, which also fulfils the ＂Internal-External Liners Equal-Impulse＂ criterion, has the capability to form annular jet. The experimental and numerical results show that when the ratio between annular initiation ring diameter and the charge diameter is 0.75, an annular jet is formed, which was also supported by high speed photographs performed in vacuum. 2D numerical simulations are performed with indigenously developed simulation software, where Eulerian approach with multi-material interface tracking algorithm is utilized, to find various mechanisms involved during jet formation process. The calculation results are found in good agreement with the experimental results, indicating that the interface treatment algorithm proposed in this paper can not only deal with large deformation problem, but also depict clearly the variation of materials interface. It is especially suitable for simulation of the process from liner collapse to formation of shaped charge jet.     

The mechanism of drop formation from gas or vapour bubbles

This paper presents an interpretation of the mechanism of drop formation due to bubbles of gas or vapour travelling upwards through a liquid and collapsing at the liquid-gas interface. Size-distribution of entrained drops are obtained as a function of height and bubble sizes. Parabolic trajectories have been taken in consideration and an equation is given for the maximum height of drops.

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Zusammenfassung Eine Erklärung für die Bildung von Tropfen an der freien Flüssigkeitsoberfläche beim Zerplatzen von aufsteigenden Gas- oder Dampfblasen wird hier gegeben. Die Größenverteilung der abgeschleuderten Tropfen wird als Funktion der Schleuderhöhe und der Blasengröße erhalten. Parabolische Schleuderbahnen wurden berücksichtigt und eine Gleichung für die maximale Schleuderhöhe der Tropfen angegeben.

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Symbols surface tension - amplitude of the surface disturbance - _w density of liquid - a density of gas - kinematic viscosity - D _d diameter of droplet - D _j diameter of jet - E _d drop energy - E _j total energy absorbed by the jet - E _o energy release by collapsing bubble - E _p potential energy - E _R drag energy - E _s surface tension energy - F vertical force - G _j gravitational force acting on jet - H maximum trajectory height - L length of jet - L _opt length of separated upper portion of jet - l length unseparated lower portion of jet - M mass of water which must be set in motion to fill the crater - m mass of droplet - P _g gas pressure - P _l liquid pressure - P _i inside pressure - P _o outside pressure - R ₁,R ₂ curvatures of bubble - R _j radius of jet - R radius of spherical bubble - R* frictional drag force of jet - R _D frictional drag force of droplet - S ₁ surface tension force - t _F impulse time - t time of break-up of jet - U mean velocity acquired by the massM - v droplet velocity - V ₀ initial velocity of droplet - W ₁ gravitational force     

Mechanics of water pore formation in lipid membrane under electric field

Transmembrane water pores are crucial for sub-stance transport through cell membranes via membrane fusion, such as in neural communication. However, the molecular mechanism of water pore formation is not clear. In this study, we apply all-atom molecular dynamics and bias-exchange metadynamics simulations to study the pro-cess of water pore formation under an electric field. We show that water molecules can enter a membrane under an electric field and form a water pore of a few nanometers in diame-ter. These water molecules disturb the interactions between lipid head groups and the ordered arrangement of lipids. Fol-lowing the movement of water molecules, the lipid head groups are rotated and driven into the hydrophobic region of the membrane. The reorientated lipid head groups inside the membrane form a hydrophilic surface of the water pore. This study reveals the atomic details of how an electric field influences the movement of water molecules and lipid head groups, resulting in water pore formation.     

Closure of microcracks during unloading and the formation of reverse dislocations

Conclusion During unloading, local closure of the crack is followed by the emission of the first pair of reverse dislocations. The formation of an area of local contact during unloading occurs with a bang; the critical SIF of the external loads at this moment coincides with the value of the overall SIF of the field of the primary sessile dislocations. There is always a free gap between the crack tip and the area of local contact. External loads acting in the crack plane and not resulting in a stress concentration at the crack front play an important role in the emission of reverse dislocations (in particular, they may block their departure from the S-structure).Pacific Oceanological Institute, Academy of Sciences of the USSR, Vladivostok. Translated from Prikladnaya Mekhanika, Vol. 24, No. 7, pp. 3–18, July, 1988.     

On the problem of funnel formation during liquid outflow from vessels

The process of funnel formation during unsteady outflow of initially still water under gravity through one or two circular holes in the bottom of a prismatic vessel rectangular in plan is analyzed experimentally and numerically. The process is studied for various locations of the sinkholes, for vessel bottoms and walls with areas that differ in roughness, and for several values of the initial water depth h ₀. A sufficient, but not necessary, condition for the absence of vortex funnels is formulated. On the basis of a method proposed for determining the fluid rotation direction in vortex funnels, regions are found such that above sinkholes located in them vortex funnels with a given rotation direction are formed, as well as lines such that for sinkhole centers positioned on them stable vortex funnels are not formed. These results are confirmed by numerical calculations and experiments. At different times t the structure of the circumferential velocity field in the sinkhole cross-section is investigated. In the sinkhole crosssection, at several levels above it, and in the outflowing jet the dependence of the integral moment of the circumferential velocities on time and the initial depth is found. The time dependences of the flow-rate characteristics (flow-rate coefficient and volume flow-rate) are obtained for various initial depths and compared with results known in hydraulics. On the range of determining parameters investigated it is established that the fluid depth in the vessel at which a vortex funnel begins to be formed is independent of the initial water depth. The numerical calculations were carried out using STAR-CD software (license of the Institute of Mechanics of Moscow State University) tested in experiments on water outflow from prismatic vessels circular and rectangular in plan.     

Simulation of the formation of hydrates during gas flow in tubes

Problems of the freezing and decomposition of gaseous hydrates on gas pipeline walls are considered. This process is governed by heat transfer between the gas and surrounding rocks. Simultaneous study of the transport equations in the tube and the heat conduction equations in the hydrate and surrounding rocks makes it possible to follow the variation of the thickness of the hydrate layer in time and with respect to the coordinate. It is shown that there exist gas flow regimes in which there is self-purification of the tube wall of hydrate due to heating of the surrounding rocks. On the other hand, it is possible to have regimes in which there is complete blocking of the flow section by the hydrates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–112, September–October, 1982.     

The formation of a liquid bridge during the coalescence of drops

This paper examines a mathematical model for the coalescence of two viscous liquid volumes in an inviscid gas or in a vacuum which removes the pressure singularity at the instant of impact inherent in the classical formulation of the continuum model. The very early stages of coalescence are examined in order to study the formation of the liquid bridge in two cases: (i) for two infinitely long, coalescing liquid cylinders; and (ii) for two coalescing spheres. Numerical solutions are computed for the velocity and pressure fields in the flow in both cases, and they confirm the removal of the pressure singularity. Also, the free-surface position at small times is determined.