Characteristics of solitary waves on a running film down an inclined plane under an electrostatic field

For the study on the nonlinear dynamics of thin-film flow running down an inclined plane under the effect of an electrostatic field, the mechanism of solitary waves has been examined by using a global bifurcation theory. First, the existence of solitary waves has been chased by using an orbit homoclinic to a fixed point of saddle-focus type in a linearized third-order ordinary differential equation which resulted from the evolution equation in a steady moving frame. Then, the trajectories with several kinds of solitary waves have also been searched numerically for the nonlinear system. In addition, the behavior of these waves has been directly confirmed by integrating the initial-value problem. The slightly perturbed waves at the inception eventually evolve downstream into almost permanent pulse-like solitary waves through the processes of coalescence and repulsion of the triggered subharmonics. In the global aspects the flow system at a given Reynolds number becomes more unstable and chaotic than when there is no electrostatic force applied.     

Long-wave instabilities of film flow under an electrostatic field

The free-surface behavior of a viscous liquid layer flowing down an inclined plane by gravity and interacting with an overlying uniform electrostatic field is examined in the limit of long-wave approximation. Both linear and nonlinear stability analyses are performed to address two-dimensional surface-wave evolution initiating from a flat interface. The growth of a periodic disturbance is first investigated for a linear analysis, and then to examine the nonlinear surface-wave instabilities the evolution equation for film height is solved numerically by a Fourier-spectral method. For small evolution time the calculated nonlinear modes of instability are consistent with the results obtained from the linear theory. The effect of an electrostatic field increases the wavenumbers showing a maximum linear growth rate as well as a cutoff. A significant phenomenon as Reynolds number is increasing is the appearance of the catastrophic surface waves in the long run whenever any initial wavenumber making a traveling wave linearly unstable is employed into the initial simple-harmonic disturbance.     

Instabilities induced by an electrostatic field over the film flow down an inclined plane

A study of the instabilities in the interaction of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the long-wave stability conditions are studied by perturbing the evolution equation of film height about its steady-state solution. Three limits of flow systems are considered, i.e., static state, Reynolds number Re = 0(1) and Re = 0(1/ξ). Here ξ(≪1) is the ratio of the characteristic length scale parallel to the flow to the primary film thickness. Next, the long-wave behavior of the thin film flow is examined with the electrostatic potential of a Gaussian function in the two limits of Reynolds number, i.e., Re = 0(1) and Re =0(l/≪). These results are also compared with those from a full-scale explicit calculation. Finally, wave-growth rates are calculated from the Orr-Sommerfeld equation to show the stability to wave number with and without the electric field. The effect of the electric field is to lessen the range of the wave number in which the thin film flow remains stable.     

The effects of an electrostatic field and air stream on water jet break-up length

An experimental study of the break-up length of a circular section liquid jet subject to the combined action of a coaxial airstream and an electrostatic field is reported. A high speed photographic technique has been employed and the results have been correlated empirically by the following dimensionless equation: where “b” and “k” are functions of Reynolds number.     

The effect of an electrostatic field on inviscid liquid flow down an inclined plane

For a study of nonlinear wave motion under an electrostatic field, the Korteweg-de Vries (KdV) equation for inviscid liquid film flowing under gravity down an inclined plane has been derived, and the effect of the electric field on the stability of a solitary wave as a solution of the KdV equation is examined. Under a constant electrostatic potential the stability of the wave is not affected. However, with a slowly varying potential it becomes unstable.     

A numerical solution of the wavy motion on a falling liquid film

Wavy motion in falling liquid films enhances heat and mass transfer significantly; therefore, it is important to successfully model this motion for the purpose of heat and mass transfer calculations. In this study, a simple and promising numerical spectral method is developed to solve the periodic wavy film flow equations. With the wave number and the wave celerity specified to be those of the most unstable waves from existing linear stability analysis, the results are found to be good when compared with the existing experimental data for small (Re < 50) and moderate (50 < Re < 150) Reynolds numbers. It is worth noting that many important absorption problems fall in the low and moderate Reynolds number regimes. For higher Reynolds number flows (Re > 150), the solutions are still obtainable but may not be realistic owing to the invalidity of the linear stability analysis and the asymptotic wavy-state assumption in the high Reynolds number flow.     

Reappearance of azimuthal waves in turbulent Taylor-Couette flow at large aspect ratio

Velocity field data were acquired for Taylor-Couette flow in the annular gap between an inner rotating cylinder and a stationary concentric outer cylinder using particle image velocimetry (PIV) in a meridional plane of the annulus. Data were acquired for several rotational Reynolds numbers with the ratio of the rotational and critical Reynolds numbers ranging from 6 to 200, corresponding to flow states ranging from laminar wavy Taylor vortex flow to turbulent Taylor vortex flow. Spatial correlations of velocity fluctuations were found to exhibit a sharp decrease as R, the ratio of Reynolds number to the critical Reynolds number, increases from 16, indicating the disappearance of azimuthal waves and the onset of turbulence, reaching a minimum at R=18. However, correlation lengths subsequently increase with increasing R, displaying a secondary peak from 20?R?38, suggesting the reappearance of azimuthal waves. The reemergence of azimuthal waves was confirmed through other methods including analysis of the axial velocity. At still higher Reynolds numbers, correlation lengths decay once again. The magnitude and Reynolds number associated with the secondary peak in the fluctuation velocity correlations were found to be dependent on the location of the basis point used in the calculations. Specifically, correlation lengths were longest near the outer cylinder in the inflow boundary and near the inner cylinder in the outflow boundary. This was shown to be due to the spatial dependence of Reynolds stresses in turbulent Taylor-Couette flow.     

Transport phenomena under unsteady conditions in an agitated vessel

An experimental study of transport phenomena at the wall of an agitated vessel with a propeller impeller under unsteady conditions is reported. The transient in heat transfer at the wall is caused by a step change in the speed of agitation from an initial static condition. The results are expressed in terms of a rise in modified “j-factor” above the initial free convection value and the number of revolutions taken by the impeller from the start of agitation. Also, an attempt has been made to find an analogy beween heat and momentum transfer. Results are given for the power in terms of Euler number plotted against the impeller Reynolds number. An empirical expression is also given for the transient heat transfer considering the system as a pure first order one with time delay. A “time-factor” constant which gives the number of impeller revolutions for 63.2% of the change from the initial to a final steady state is expressed as a function of impeller Reynolds number (10² to 10⁶) and fluid Prandtl number (6 to 10⁶).     

Hydrodynamic behavior of an electrified thin film flowing down an inclined plane at high Reynolds numbers

To answer the questions on the dynamics of thin liquid flow down an inclined plane at high Reynolds numbers subjected to a uniform normal electrostatic field, we have derived evolution equations describing the free-surface behavior by using the von Kármán-Pohlhausen approximation. The integration of the evolution equations is numerically performed to address two-dimensional finite-amplitude surface-wave propagation modes. The growth of a periodic disturbance is first examined to compare with the results linear-stability theory, and then to investigate the nonlinear surface-wave behavior the evolution equations are solved numerically by a Fourier-spectral method. For small evolution time the computed nonlinear modes of instability are well consistent with the results from the linear theory. The effect of an electrostatic field makes the flow system significantly unstable.     

Computational simulation of cold spray process assisted by electrostatic force

The integrated model of compressible thermofluid, splat formation and coating formation for the cold spray process has been established. In-flight behavior of nano-micro particles and the interaction between the shock wave and the particles in a supersonic jet flow impinging onto the substrate and further effect of electrostatic force on the particle acceleration are clarified in detail by carrying out a real-time computational simulation. The optimal particle diameters for an impinging particle velocity exceeding critical velocity exist. Particles with the diameter of submicron interact with shock wave and particles are decelerated prior to the impact. However, the particles can be accelerated considerably by utilizing electrostatic forces even in the presence of unavoidable shock waves. Finally, based on the integrated model, the coating thickness in an electrostatic assisted cold spray process is evaluated.     

Finite-amplitude surface waves on a thin film flow subject to a unipolar-charge injection

The interaction of an electric field with a dielectric liquid film is investigated as it drains under gravity down an inclined plane electrode emitting uniform positive ions into the liquid region. By applying long-wave approximation to the governing equations, the evolution equation for the free surface is derived up to the first order of a thin film parameter ξ To investigate the space charge effect on the development of a finite-amplitude surface wave, a neutral stability condition is obtained as a critical Reynolds number through a linear stability analysis, and the amplitude and velocity of a periodic disturbance are also calculated within a supercritically stable flow region. The presence of a unipolar space charge in the fluid makes a steady surface wave take on even higher amplitude and faster wave speed compared with the case of no space charge.     

Failure Waves in Glass

Failure waves have been recently observed in glass plates and rods struck by high-speed projectiles. These waves propagate into material that has been prestressed by a compressive shock. The wave propagation speed exceeds the maximum crack speed and is not constant. Behind the failure wave there is a total loss of tensile strength and a substantial drop in shear strength. The failure is explosive, leading to radial expansion in unconfined targets and presurization in confined targets.     

超声空化对换热器场协同影响研究

针对超声波在防除垢对换热器场协同的影响,采用FLUENT软件中的两相流模型、空化模型和标准k-ε的湍流模型,获得流场压强随时间步长的变化规律——流场波动呈类似正弦波波动.引入空化数的概念;利用π定理推导雷诺数和空化数的函数关系——雷诺数与空化数呈幂函数关系,雷诺数随着空化数的增加而减小;根据场协同原理,表示出空化数和场...     

Effect of waves on reaeration

Mechanically generated surface waves and their influence on oxygen transfer were investigated. The experiments were conducted in a reaeration column (Reynolds number from 125–937). The water surface was set in oscillatory motion to simulate periodic surface level fluctuation. The wave frequency used ranged from 0.125 Hz to 0.425 Hz for various wave heights ranging from 0.15 cm to 1.5 cm. After bleeding the water column with nitrogen, dissolved oxygen concentration was measured over time below the water surface. A modified surface renewal model was proposed and found to describe the oxygen transfer phenomenon well. In addition, it was found that the mean film thickness δ_D, may be used as the characteristic length to describe the reaeration process under the influence of small perturbation and surface water waves. The proposed model was also extended to include the reaeration process under larger waves reported by other researchers. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4839–4845, 2013     

Quantitative Schlieren Measurement of Explosively‐Driven Shock Wave Density,Temperature, and Pressure Profiles

Shock waves produced from the detonation of laboratory‐scale explosive charges are characterized using high‐speed, quantitative schlieren imaging. This imaging allows the refractive index gradient field to be measured and converted to a density field using an Abel deconvolution. The density field is used in conjunction with simultaneous piezoelectric pressure measurements to determine the shock wave temperature decay profile. Alternatively, the shock wave pressure decay profile can be estimated by assuming the shape of the temperature decay. Results are presented for two explosive sources. The results demonstrate the ability to measure both temperature and pressure decay profiles optically for spherical shock waves that have detached from the driving explosion product gases.     

Enhanced mixing of Newtonian fluids in a stirred vessel using impeller speed modulation

This paper reports on an experimental study of mixing intensification using speed modulation of a six‐blade Rushton turbine in a stirred vessel. Mixing times were measured using a non‐intrusive technique based on direct visualisation of an acid‐base reaction in a Newtonian fluid. The impeller speed modulation was achieved by using two waveforms: a square wave and a sine wave. The amplitude was fixed between a maximum Reynolds number of Re_max = 60 and minimum Reynolds numbers of Re_min = 40 or 30. The wave periods were varied (10, 20, or 40 s) in order to compare the effects of unsteady stirring on mixing performance. It was observed that a square wave protocol with the shortest wave period and the larger amplitude resulted in the shortest time to destroy the observed isolated mixing regions (IMRs), which are known to exist in stirred vessels operating at low Reynolds number. However, the sine wave protocol led to a slow diffusive mechanism in which IMR structures reached an asymptotic volume and remained visible even after several hours. The results are presented and discussed using digital photographs taken at different time intervals during experimentation.     

Liquid film properties in two-phase annular flow

Experimental measurements have been made of the properties of falling liquid films of water with and without the addition of polymeric drag reducing agents. It was found that the presence of the drag reducing agent stabilised the film, delaying the disturbance wave transition to higher Reynolds numbers and decreasing the frequency of these waves. A small increase in wave velocity and base film thickness was also found.     

Combustion modes and flame propagation criteria for an encumbered space

The topic is analyzed. Experiments have been performed with fuel—air mixtures in a porous medium. Measurements have been made on the velocity and pressure in the detonation and combustion waves, together with the critical initial parameters and the limits to the Peclet number. The mean detonation rate has been found to fall and the ignition has been found to be retarded in a porous medium when the wave passes through a free gap.Combustion and Flame Institute, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 30, No. 4, pp. 52–60, July–August, 1994.     

Explosion of a cylindrical charge above a rigid surface

We investigated the explosion of a cylindrical charge, which lies on a rigid surface or is positioned at some height above it. The explosion is modeled by the jump between the background and the region occupied by gas at a high pressure, density, and temperature. In an analogous formulation, the explosion from the Tunguska meteorite impact [1–4] was modeled by spherical and cylindrical explosive waves which consider the gravitational back pressure. Explosions from charges with nontraditional shapes have been studied [5–8]. Reflections of an explosive wave from a point charge from a rigid surface have been examined [9–10]. A more complete review of investigations on the spatial effects of forming propagating explosive waves can be found in [11].Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 27, No. 6, pp. 131–134, November–December, 1991     

转盘离心粒化中丝状成粒特性

针对转盘离心粒化工艺,以水为工质开展可视化实验。采用高速摄影仪对液膜波动、液丝断裂等粒化过程进行了捕捉,并利用MATLAB自编程序对获得的图像进行了处理。分析了离心粒化过程中液丝形成过程以及液丝断裂形成液滴的过程。研究了运行工况对液丝、液滴形成机制的影响。讨论了液丝形成对液滴形成的影响并获得了Weber数、Reynolds数对粒化效果的影响程度。结果表明,表面不稳定波是形成液丝的主要因素,且液丝在Rayleigh不稳定性的作用下断裂形成液滴。升高转速或者减小流量有利于获得均匀的小液滴。Weber数对液丝、液滴形成具有显著影响;Reynolds数仅对液丝数目有显著影响。