Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

Single droplet combustion in a gravitational environment

A theoretical analysis is developed to study the combustion characteristics of a fuel droplet in a gravitational field. The normalized governing system consists of the complete conservation equations inr-z coordinates and includes finite-rate global kinetics. The Clausius-Clapeyron law is applied at the liquid-vapor interface to describe the evaporation process. A modified body-fitted grid generation technique is used to handle irregular boundaries. The effects of changing the droplet diameter and the gravity level are investigated. Under the variation of droplet diameter, flame structures, including isotherms, flame shape, velocity vector field, and mass burning rate are studied in detail. The predicted results exhibit good agreement with experimental data. When the gravity level increases, the computed results show that the flame shape is sensitive to variation in gravity. A simple correlation, , is found. Within the elevated gravity domain of experiment, the computed data agree well with measurements obtained by Okajima and Kumagai [10].In einer theoretischen Studie wird die Verbrennungscharakteristik eines Ethanoltröpfchens in einem Gravitationsfeld untersucht. Die normierten Grundbeziehungen umfassen die vollständigen Erhaltungsgleichungen inr-z-Koordinaten unter Einschluß einer Globalkinetik endlicher Umsatzrate. Das Clausius-Clapeyronsche Gesetz wird an der Flüssigkeits-Dampf-Phasengrenze angesetzt, um den Verdampfungsprozeß zu beschreiben. Eine spezielle Gittergenerierungstechnik ermöglicht die Behandlung irregulärer Berandungen. Die Einflüsse veränderlichen Tropfendurchmessers bzw. variablen Gravitationsniveaus werden untersucht. Bei variablem Tröpfchendurchmesser erfolgt eine Detailuntersuchung der Flammenstrukturen nach Isothermenfeld, Flammenform, Feld der Geschwindigkeitsvektoren und Verbrennungsrate. Die vorausberechneten Ergebnisse stimmen gut mit experimentellen Daten überein. Bei Anstieg des Gravitationsniveaus zeigen die Rechnungen eine empfindliche Veränderlichkeit der Flammenform. Es läßt sich eine einfache Beziehung aufstellen. Im Bereich höheren Gravitationspegels stimmen die berechneten Werte gut mit den Messungen von Okajima und Kumagai [10] überein.Financial support of this research by the National Science Council of the R.O.C., under project NSC 81-0401-E-009-531 is greatly appreciated. The authors also wish to express their gratitude to National Chiao Tung University for providing computer facility.     

The effect of a magnetic field on the rheodynamic behavior of ferromagnetic suspensions

In this work a simplified analytical model and the results of an experimental investigation of the influence of an external magnetic field on the rheological characteristics of a suspension of iron particles in silicon oil is presented. The particles of iron were approximately of a circular shape, from 3 to 5 μm, with a maximum concentration of 10¹⁰ particles/cm³. The viscosity of the carrying fluid varied from 80 to 240 cP.The experimental channel was located in a closed circuit of forced circulation of the ferromagnetic suspension. The entire length of 750 mm was placed in an area of a homogeneous magnetic field, with the velocity vector of the suspension being perpendicular to the direction of the magnetic field. The strength of the magnetic field could be changed continually from 0 to 9000 G.The results obtained are shown in the form of parametrical dependencies of the rheological characteristics of the ferromagnetic suspension. With that, the concentration of the solid phase of the suspension is parametrically changed, along with the strength of the external magnetic field and the viscosity of the carrying fluid.In the range of parameters studied, the external magnetic field leads to a Bingham character of behavior of the ferromagnetic suspension.     

The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK ₀ of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK ₀ is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases. The Project is supported by the National Natural Science Foundation of China.     

Transient combustion of a heating droplet in a gravitational environment

The transient combustion characteristics of a droplet suddenly exposed to the envelope flames in an atmospheric environment are studied numerically. Combustion can be divided into a droplet heating-up and a constant-droplet-temperature burning. The naturally-convective flow is not knowna priori, but provided as part of the solution. During the heating-up stage, the temperature and evaporation rate of droplet increase sharply, and the square of diameter decreases slightly as time proceeds. In the following stage, the droplet temperature remains constant, the evaporation rate and droplet diameter decrease with time. The flowfield of natural convection is also presented to demonstrate its interaction with the flame and the transient process. Finally, the fuel accumulation phenomenon is identified and it results in an reduction of evaporation constant.     

不同界面计算方法对液滴在电场作用下变形数值模拟精度的影响

液滴在电场作用下的变形是电流体动力学的基础课题之一,表面张力的计算精度对液滴变形量的模拟结果有重要影响。本文以开源计算流体动力学平台OpenFOAM的VOF模型为框架,研究了MULES和isoAdvector两类界面更新算法与相分数梯度和RDF函数两类曲率算法对电场作用下液滴变形模拟精度的影响。研究表明,isoAdvector算法相比MULES算法对网格密度的要求更低,但其耦合相分数梯度算法计算表面张力的误差较高。isoAdvector算法耦合RDF函数算法计算误差较低,并且在使用轴对称网格时,只有该算法能够同时处理液滴平行于电场和垂直于电场方向的变形,得到的数值结果与解析解吻合较好。     

On the effect of a high-frequency magnetic field on the instability of a plasma

The action of a high-frequency magnetic field on low-frequency instabilities of a plasma is considered. The harmonics of the high-frequency field that appear under these conditions are taken into account. It is shown that their effect on the reduction of the growth rate of the instability is weak. However, in analyzing the oscillation spectrum consideration of these harmonics is necessary, since they have the same growth rate as does the suppressed instability. It is well known that in a plasma situated in a strong magnetic field H_0Z unstable oscillations develop, the most dangerous being electrostatic oscillations that propagate almost perpendicular to the magnetic field (k k_¦). These oscillations have the form of troughs extended almost along H_0Z. If it were possible by some method to create conditions under which particles of one species (either electrons or ions) would have time to traverse the distance between the humps of the troughs in a time considerably shorter than the period 2/ of the unstable oscillations, then the potential of the instability would be smoothed out (i.e., the instability would be suppressed). This may be achieved by exciting a high-frequency magnetic field H₁(t) = H₁ cos t( ) in the plasma, which is oriented perpendicular to the constant field H_0z. Then the crossing of the humps by the particles is achieved as a result of motion with thermal velocities along the resultant curved magnetic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 10–14, March–April, 1971.The author thank A. V. Gordeev for fruitful discussions.     

An analysis of the d-law departure during droplet evaporation in microgravity

The d²-law validity during n-decane droplet vaporization in microgravity environment is examined experimentally. Two sets of experiments are performed, under normal and microgravity, in stagnant hot atmospheric environment. The environment temperature is varied in the range up to 967 K. The droplet is suspended onto the cross point of two micro-fibers of 14 μm in diameter. This technique enables to greatly minimize the effect of fiber on droplet heat and mass transfer. The results show that, for ambient temperatures below approximately 950 K, departure from the d²-law is observed during droplet vaporization in microgravity environment. In addition, the droplet lifetime is longer in microgravity than in normal gravity under the same ambient test conditions. However, for temperatures exceeding approximately 950 K, the experimental results demonstrate that the d²-law holds throughout the entire droplet lifetime, and the mass transfer rate is identical in both microgravity and normal gravity environments.     

The effect of nozzle layout on droplet ejection of a piezo-electrically actuated micro-atomizer

We study here effects of nozzle layout on the droplet ejection of a micro atomizer, which was fabricated with the arrayed nozzles by the MEMS technology and actuated by a piezoelectric disc. A theoretical model was first built for this piezoelectric-liquid-structure coupling system to characterize the acoustic wave propagation in the liquid chamber, which determined the droplet formation out of nozzles. The modal analysis was carried out numerically to predict resonant frequencies and simulate the corresponding pressure wave field. By comparing the amplitude contours of pressure wave on the liquid-solid interface at nozzle inlets with the designed nozzle layout, behaviors of the device under different vibration modes can be predicted. Experimentally, an impedance analyzer was used to measure the resonant frequencies of the system. Three types of atomizers with different nozzle layouts were fabricated for measuring the effect of nozzle distribution on the ejection performance. The visualization experiment of droplet generation was carried out and volume flow rates of these devices were measured. The good agreement between the experiment and the prediction proved that only the increase of nozzles may not enhance the droplet generation and a design of nozzle distribution from a viewpoint of frequency is necessary for a resonant related atomizer. The project supported by the National Natural Science Foundation of China (50405001).     

Influence of heat and mass transfer on the ignition and NOx formation in single droplet combustion

The effect of heat and mass transfer on the ignition, and in a second step on the nitrogen oxide (NO _x ) generation, of single burning droplets is examined in a numerical study. Spherical symmetry with no gravity and no forced convection is presumed; ambient temperature is set at 500 K, below the auto-ignition point. The essentials of a forced droplet ignition by an external energy source are introduced. Two methods are applied: heat introduction at a fixed radial position r and heat introduction at a fixed local equivalence ratio ϕ _r . This study’s distinctiveness compared to previous research is its focus on and its combination of partially pre-vaporized droplets and detailed chemistry, both being technically relevant in kerosene and diesel fuel combustion. The fuel of choice is n-decane (C₁₀H₂₂), and NO _x production is studied exemplarily as a representative group of pollutant emissions. The conducted simulations show a decrease of NO _x formation with an increase of the pre-vaporization rate \Uppsi. \Uppsi. This decrease is generally valid for both methods of heat introduction. However, results on flame stabilization and NO _x production reveal a high sensitivity to parameters of the ignition model. The burning behavior during the initial stages is dominated by the ignition position. Extracting heat from the exhaust gas region of burning droplets shows no impact on the flame position nor on the relative NO _x production. As a consequence, a well-founded modeling of the investigated droplet regime needs to resort to an iterative adaptation of the heat introduction parameters based on the findings of droplet burning and exhaust gas production.     

The gvosdover effect in a low pressure arc constrained by its own magnetic field

This paper continues the calculations of a preceding one (Theoretical investigation of the first order magnetic self-striction in a low pressure arc with remote walls) and indicates a method for adding the Gvosdover effect (reduction in electron mobility by ion-electron scattering) to the corrections introduced in that paper. The case of mercury vapor is, again, treated as an example. The model predicts the slightly rising volt-ampere characteristics pertaining to related cylindrical arcs, and also shows some discontinuities and instabilities not found in the cylindrical case. This investigation was supported by the Westinghouse Research Laboratories.     

Studies on theory and modeling of droplet and spray combustion in China: a review

Acta Mechanica Sinica - Combustion phenomena were discovered still in far ancient time of China. From the 50’s of the last century, owing to the fast development of energy and power,...     

磁场效应对甲烷爆炸影响的机理

为了揭示磁场对甲烷爆炸特征的影响机理,开展了磁场对甲烷爆炸影响实验,得出了磁场对甲烷爆炸压力、火焰传播速度、爆炸产物组分及体积分数的影响规律。利用Chemkin-Pro软件模拟甲烷爆炸链式反应过程,得到了甲烷爆炸过程中的关键自由基和基元反应。通过理论计算,对不同自由基在磁场作用下的受力进行分析,揭示了磁场对甲烷爆炸的影响机理。研究结果表明,磁场能够降低甲烷爆炸压力和火焰传播速度,降低CO和CO₂的生成量,增加甲烷的残余量;·H、·O、·OH、·CH₃、·CH₂O是甲烷爆炸的关键自由基,由于·O的磁化率较高,被吸引到磁感线密集的区域,·O与其他自由基的碰撞几率减少,从而降低·HCO→CO→CO₂的链式反应速率,导致CO和CO₂生成量降低,且甲烷爆炸强度降低。     

Influence of the hall effect on plasma compressibility in a strong toroidal magnetic field

The development of the tearing instability is studied in the presence of a high toroidal magnetic field and a high plasma conductivity. The variation of the plasma density is shown to be significant in this case. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 3–9, March–April, 1998.     

Spin-up and spin-down dynamics of a liquid metal driven by a single rotating magnetic field pulse

This paper presents a study concerning the transient dynamics of the flow field inside a liquid metal filling a finite cylindrical container: The flow is created by applying a rotating magnetic field (RMF) in the form of a single pulse. The flow structure is governed by an impulsive spin-up from the rest state which is followed by a spin-down phase, with the fluid in a state of inertia. The pulse length has been found to have a distinct influence on the transient fluid flow. Two cases are considered: an enclosed cavity and a cavity with a free surface, in order to show that in both cases the recirculating flow in the radial-meridional plane displays periodical reversals. This phenomena is especially pronounced if the pulse length of the electromagnetic forcing corresponds to the so-called initial adjustment phase as defined by Nikrityuk, Ungarish, Eckert, Grundmann [P.A. Nikrityuk, M. Ungarish, K. Eckert, R. Grundmann, Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder. A numerical and analytical study, Phys. Fluids 17 (2005) 067101–0671016].     

The influence of the hall effect on the current structure in a plasma flow with a spatially periodic magnetic field

The structure of the electric fields and current is studied for stationary plasma flow in an axially symmetric, spatially periodic magnetic field. The problem is solved in the magnetohydrodynamic approximation with allowance for the Hall term in the generalized Ohm's law equation. It is assumed that the magnetic Reynolds number and the interaction parameter are small.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 11–16, September–October, 1972.The author thanks N. A. Khizhnyak and A. A. Kalmykov for useful discussions.     

The viscosity of a plasma in a strong magnetic field

The viscosity of a plasma is studied under conditions in which a magnetic field influences particle collisions. The expressions obtained for the viscosity coefficients differ significantly from those obtained in the normal theory. It is shown that in sufficiently strong magnetic fields a temperature difference arises between the electron and ion plasma components which is proportional to the drift velocity and depends logarithmically on the magnetic field strength.