Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

受水压振荡时饱和砂床的液化与变形特性

为考察饱和砂土地基受到水压振荡作用时的动力响应,根据两相连续介质理论,分析了液化发展、液化区厚度、颗粒速度等.研究结果表明,随着土强度和渗透性的降低与载荷强度的增加,液化发展速率加快;随着土强度的降低和渗透性、载荷强度的增加,变形量增加;如果土的初始分布不均匀,则在渗透性小的位置,应变和孔隙水压力将剧烈变化,这可以解释为什么在一定条件下土中会出现断裂和水层.

Instability from steady and axisymmetric to steady and asymmetric floating half zone convection in a fat liquid bridge of larger Prandtl number

The linear instability analysis of the present paper shows that the thermocapillary convection in a half floating zone of larger Prandtl number has a steady instability mode w(i) = 0 and m = 1 for a fat liquid bridge V = 1.2 with small geometrical aspect ratio A = 0.6. This conclusion is different from the usual idea of hydrothermal instability, and implies that the instability of the system may excite a steady and axial asymmetric state before the onset of oscillation in the ease of large Prandtl number.

Squeeze-film Effects in MEMS Devices with Perforated Plates for Small Amplitude Vibration

Squeeze-film effects of perforated plates for small amplitude vibration are analyzed through modified Reynolds equation (MRE). The analytical analysis reckons in most important influential factors: compressibility of the air, border effects, and the resistance caused by vertical air flow passing through perforated holes. It is found that consideration of air compressibility is necessary for high operating frequency and small ratio of the plate width to the attenuation length. The analytical results presented in this paper agree with ANSYS simulation results better than that under the air incompressibility assumption. The analytical analysis can be used to estimate the squeeze-film effects causing damping and stiffness added to the system. Since the value of Reynolds number involved in this paper is low (< 1), inertial effects are neglected.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Experimental Study of Surface Deformation and Flow Pattern on Buoyant-Thermocapillary Convection

Free surface deformation is one of the most important physical phenomena in fluids with free surface. In the present paper, convection and surface deformation caused by thermocapillary effect in a rectangular cavity were investigated. In ground experiments, the convection was also affected by gravity. The cavity has a horizontal cross section of 52mm×42mm and the thikkness of the liquid layer is 4mm. Temperature difference between two sides of the liquid layer was increased gradually, and the flow in liquid layer will develop from steady to unstable convection. An optical diagnostic system consisting of a revised Michelson interferometer with image processor was developed to study fluid surface deformation in convection, and the displacements of free surface oscillation were determined. PIV technique was adopted to observe the evolution of flow pattern, and the velocity fields were obtained quantitatively. The present experiments demonstrate that surface deformation is quite distinct in buoyant-thermocapillary convection. in order to understand the mechanism of buoyant-thermocapillary convection, not only the hydrothermal wave instability but also the surface wave instability should be discussed.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.

Influence of Liquid Bridge Volume on the Floating Zone Convection

The liquid bridge volume is a critical geometrical parameter in addition to the aspect ratio for onset of oscillation in the floating zone convection. The oscillatory features are generally divided into two characteristic regions: slender liquid bridge region and fat liquid bridge region. The oscillatory modes in two regions are discussed in the present paper.

A Constrained Particle Dynamics for Continuum-Particle Hybrid Method in Micro- and Nano-Fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier-Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.

Thermocapillary Convection in Floating Zones

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.

Pool Boiling In Microgravity: Recent Results And Perspectives For The Project Depa-Sj10

Two research projects on pool boiling in microgravity have been conducted aboard the Chinese recoverable satellites. Ground-based experiments have also been performed both in normal gravity and in short-term microgravity in the Drop Tower Beijing. Steady boiling of R113 on thin platinum wires was studied with a temperature-controlled heating method, while quasi-steady boiling of FC-72 on a plane plate was investigated with an exponentially increasing heating voltage. In the first case, slight enhancement of heat transfer is observed in microgravity, while diminution is evident for high heat flux in the second one. Lateral motions of bubbles on the heaters are observed before their departure in microgravity. The surface oscillation of the merged bubbles due to lateral coalescence between adjacent bubbles drives it to detach from the heaters. The Marangoni effect on the bubble behavior is also discussed. The perspectives for a new project DEPA-SJ10, which has been planned to be flown aboard the Chinese recoverable satellite SJ-10 in the future, are also presented.

Bubble Dynamics In Nucleate Pool Boiling On Thin Wires In Microgravity

A temperature-controlled pool boiling (TCPB) device has been developed to study the bubble behavior and heat transfer in pool boiling phenomenon both in normal gravity and in microgravity. A thin platinum wire of 60 mu m in diameter and 30 mm in length is simultaneously used as heater and thermometer. The fluid is R113 at 0.1 MPa and subcooled by 26 degrees C nominally for all cases. Three modes of heat transfer, namely single-phase natural convection, nucleate boiling, and two-mode transition boiling, are observed in the experiment both in microgravity aboard the 22nd Chinese recoverable satellite and in normal gravity on the ground before and after the space flight. Dynamic behaviors of vapor bubbles observed in these experiments are reported and analyzed in the present paper. In the regime of fully developed nucleate boiling, the interface oscillation due to coalescence of adjacent tiny bubbles is the primary reason of the departure of bubbles in microgravity. On the contrary, in the discrete bubble regime, it's observed that there exist three critical bubble diameters in microgravity, dividing the whole range of the observed bubbles into four regimes. Firstly, tiny bubbles are continually forming and growing on the heating surface before departing slowly from the wire when their sizes exceed some value of the order of 10(-1) mm. The bigger bubbles with about several millimeters in diameter stay on the wire, oscillate along the wire, and coalesce with adjacent bubbles. The biggest bubble with diameter of the order of 10 mm, which was formed immediately after the onset of boiling, stays continuously

An Approximate Method For Calculation Of Fluid Force And Response Of A Circular Cylinder At Lock-In

In this paper, equations calculating lift force of a rigid circular cyclinder at lock-in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cyclinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cyclinders and long flexible circular cyclinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results show the effectiveness of this approximate method.

Thermocapillary Flows In Liquid Bridges Of Molten Tin With Small Aspect Ratios

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved.