A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow

Non-Darcy film condensation over a vertical flat plate within a porous medium is considered. The Forchheimer extended Darcy model is adopted to account for the non-Darcy effects on film condensation in the presence of both gravity and externally forced flow. A general similarity transformation is proposed upon introducing a modified Peclet number based on the total velocity of condensate, resulting from both gravitational force and externally forced flow. This general treatment makes it possible to obtain all possible similarity solutions including the asymptotic results in the four different limiting regimes, namely, Darcy forced convection regime, Forchheimer forced convection regime, Darcy body force predominant regime and Forchheimer body force predominant regime. Appropriate dimensionless groups for distinguishing these asymptotic regimes are found to be the micro-scale Grashof and Reynolds numbers based on the square root of the permeability of the porous medium. Correspondingly, the non-Darcy effect on the heat transfer rate are investigated in terms of these micro-scale dimensionless numbers.     

二阶滑移边界对微型气浮轴承稳态性能的影响

考虑微型气浮轴承的尺寸特征,内部气流不再满足连续流的假设,根据Knudsen数可确定内 部气流为滑移流. 分别利用一阶速度滑移模型和二阶速度滑移模型对连续流的状态方程进行 修改,得到一阶滑移流和二阶滑移流机制下修正的雷诺方程. 利用有限差分法对连续流、一 阶滑移流和二阶滑移流的雷诺方程分别求解,得出相应的承载力和偏位角. 经过对比分析, 发现采用滑移流模型得到的轴承的稳态力学性能与连续流机制的结果存在较大差异,一阶滑 移流与二阶滑移流间的差异随偏心率增加而增加. 说明在MEMS环境下必须考虑滑移流效应 对微型气浮轴承稳态力学性能的影响. 在大偏心率工作状态下,二阶滑移流模型能够得到最 好的结果.     

Chaos in Acoustic Subspace Raised by the Sommerfeld–Kononenko Effect

This paper deals with vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a point excitation by an electric motor of limited power-supply. The whole system is divided into two “exciter - foundation” and “foundation-plate-medium”. In the system “motor-foundation” three classes of steady state regimes are determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions, in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they correspond to chaotic functions. In another mathematical model where the exciter stands directly on an infinite plate (without foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydro-elastic subsystem in the regime of motor shaft rotation. In this case the process of rotation can be approximately described as a solution of the fourth order nonlinear differential equation and may have the same three classes of steady state regimes as the first model. That is the electric motor may generate periodic acoustic waves, modulated waves with an infinite number of frequencies or chaotic acoustic waves in a fluid.     

Necking of biaxially stretched elastic-plastic circular plates

The necking of an elastic-plastic circular plate under uniform radial tensile loading is investigated both within the framework of the three-dimensional theory and within the context of the plane-stress approximation. Attention is restricted to axisymmetric deformations of the plate. The material behavior is described by two different constitutive laws. One is a finite-strain version of the simplest flow-theory of plasticity and the other is a finite-strain generalization of the simplest deformationtheory, which is employed as a simple model of a solid with a vertex on its yield surface. For an initially uniform plate made of an incompressible material, bifurcation from the uniformly stretched state is studied analytically. The regimes of stress and moduli where the governing axisymmetric three-dimensional equations are elliptic, parabolic or hyperbolic are identified. The plane-stress local-necking mode emerges as the appropriate limiting mode from the bifurcation modes available in the elliptic regime. In the elliptic regime, the main qualitative features of the bifurcation behavior are revealed by the plane-stress analysis, although three-dimensional effects delay the onset of necking somewhat. For the deformation theory employed here, the first bifurcation modes are encountered in the parabolic regime if the hardening-rate is sufficiently high. These bifurcations are not revealed by a plane-stress analysis. For a plate with an initial inhomogeneity, the growth of an imperfection is studied by a perturbation method, by a plane-stress analysis of localized necking, and by numerical computations within the framework of the three-dimensional theory. When bifurcation of the corresponding perfect plate takes place in the elliptic regime, the finite element results show that the plane-stress analysis gives reasonably good agreement with the numerical results. When bifurcation of the corresponding perfect plate first occurs in the parabolic regime, then a bifurcation of the imperfect plate is encountered, that is, the finite element stiffness matrix ceases to be positive definite.     

Possible classification of the self-oscillatory spouting regimes of plane vertical submerged jets of a heavy fluid

New results of an experimental investigation of self-oscillatory regimes of plane vertical jet spouting from beneath the free surface of a heavy incompressible fluid are discussed. The experiments were performed on a setup with discharge over a weir. The range of dimensionless jet submergence values on which bifurcation change of spouting regime is observable is studied. It is established that on the Froude number and dimensionless jet submergence ranges considered in the study six characteristic spouting regimes differing in free surface shape and self-oscillation frequency can exist. It is shown that these regimes can be subdivided into three typical groups with respect to the dependence of the self-oscillation period on the jet flow rate. A dimensionless parameter that makes it possible to identify the boundaries of the bifurcation change in spouting regimes is obtained for each of these groups. For certain spouting regimes without the formation of free jets numerical calculations are carried out using the STAR-CD software package; the calculated results are in good agreement with experimental data.     

Self-sustained oscillations of a confined impinging jet

The present paper investigates the dynamics of a laminar plane jet impinging on a flat plate in a channel. An experimental parametric study is carried out to determine the flow regimes at different levels of confinement and Reynolds numbers. For very confined jets, the flow is steady whatever the Reynolds number. The overall structure of the flow is symmetric with respect to the jet axis and is characterized by the presence of recirculation zones at the channel walls. The dynamics is radically different for less confined jets. Above a critical Reynolds number, the flow bifurcates in the form of an oscillating flapping mode of the impinging jet. Analyses of the experimental results provide with a quantitative characterization of this regime in terms of amplitude, wavelength and frequency. This self-oscillating bifurcated flow induces strong sweepings of the target plate by the jet and intense vortex dipole ejections from the impacted wall. Such a regime is expected to be particularly useful in the enhancement of the local heat transfer at relatively low cost in terms of flow rate.     

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers.Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before.Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.     

Linear Eddy Mixing Model Studies of High Karlovitz Number Turbulent Premixed Flames

Turbulent premixed flames exhibit different structural and propagation characteristics with increasing upstream turbulence intensity starting from thin wrinkled flames in the Corrugated Flamelet regimes to a flame with a thicker preheat zone in the Thin Reaction Zone Regime (TRZ) and finally, becoming more disorganized or broken in the Distributed or Broken Reaction Zone (D/BRZ) regimes under intense turbulence. A single comprehensive predictive model that can span all regimes does not currently exist, and in this study we explore the ability of the stand-alone one-dimensional linear-eddy mixing (LEM) model to simulate the flames in all these regimes. Past applications of this 1DLEM model have demonstrated reasonable predictions in the flamelet and TRZ regimes and here, new experiments in the TRZ regime are specifically addressed to evaluate the predictive capability of this model. Additional simulations in the D/BRZ regimes (where no data is currently available) are performed to determine if the model can be extended to the high turbulence regime. Comparison with the data in the TRZ regime shows satisfactory agreement. Analysis suggests varying levels of preheat zone broadening in all the TRZ and D/BRZ cases. While the average heat release distribution for the TRZ cases is nearly identical to the laminar unstrained baseline, changes to the species and heat release distribution are observed only at a high Karlovitz Number K a > 10³. In the D/BRZ regime it is shown that the transition is related to enhanced turbulent diffusion that dominates molecular diffusion effects causing deviations from the laminar baseline.     

钟摆状态下湿颗粒坍塌流动行为及其动力相似性

基于建立的湿颗粒离散动力学模型,本文系统研究了钟摆状态下湿颗粒柱在重力驱动下的坍塌流动过程,主要考虑了颗粒粒径、液体表面张力系数和液体含量等参数对系统坍塌流动模式和动力学行为的影响。研究发现,在湿颗粒系统中,颗粒粒径和液体表面张力系数会改变颗粒间的毛细力大小,引起系统发生不同的坍塌流动模式,而液体含量仅定量影响颗粒坍塌后的堆积形态。在此基础上,进一步探讨了不同模式下系统坍塌流动行为与模型参数的相关性,发现无量纲Bond数是决定钟摆状态下湿颗粒物质坍塌流动动力学行为的本质因素。     

Biomimetic flexible plate actuators are faster and more efficient with a passive attachment

Using three-dimensional computer simulations, we probe biomimetic free swimming of an internally actuated flexible plate in the regime near the first natural frequency. The plate is driven by an oscillating internal moment approx-imating the actuation mechanism of a piezoelectric macro fiber composite (MFC) bimorph. We show in our simulations that the addition of a passive attachment increases both swim-ming velocity and efficiency. Specifically, if the active and passive sections are of similar size, the overall performance is the best. We determine that this optimum is a result of two competing factors. If the passive section is too large, then the actuated portion is unable to generate substantial deflection to create sufficient thrust. On the other hand, a large actu-ated section leads to a bending pattern that is inefficient at generating thrust especially at higher frequencies.     

Numerical analysis on the propulsive performance and vortex shedding of fish‐like travelling wavy plate

Numerical analysis is carried out to investigate viscous flow over a travelling wavy plate undergoing lateral motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The two‐dimensional incompressible Navier–Stokes equations are solved using the finite element technique with the deforming‐spatial‐domain/stabilized space–time formulation. The objective of this study is to elucidate hydrodynamic features of flow structure and vortex shedding near the travelling wavy plate and to get into physical insights to the understanding of fish‐like swimming mechanisms in terms of drag reduction and optimal propulsive performance. The effects of some typical parameters, including the phase speed, amplitude, and relative wavelength of travelling wavy plate, on the flow structures, the forces, and the power consumption required for the propulsive motion of the plate are analysed. These results predicted by the present numerical analysis are well consistent with the available data obtained for the wave‐like swimming motion of live fish in nature. Copyright © 2005 John Wiley & Sons, Ltd.     

粘着摩擦系数的分形几何研究

计及作用于接触斑点上的切向力，通过比较作用于接触斑点上的法向弹性载荷与法向塑性载荷，确定了区分弹性接触与塑性接触区域的临界接触斑点面积．总的粘着摩擦系数被表示为弹性接触区与塑性接触区的粘着摩擦系数的组合．假设屈服压力及局部粘着摩擦系数不依赖于接触斑点且等于塑性接触区中的平均值，则总的粘着摩擦系数可用简单的表达式描述．分形几何参数及归一接触面积对于粘着摩擦系数的效应已通过算例表明，研究中，分别考虑了忽略与计及接触斑点的微粒间的相互作用，两种情况的结果完全不同．     

油气爆炸过程火焰燃烧模式的实验估计

首先分析讨论了油气爆炸过程中火焰燃烧模式的估计方法，然后在激波管内进行了低、中、高3次不同初始油气浓度条件下的油气爆炸实验，通过实验数据分别计算出了低、中、高初始油气浓度条件下油气爆炸在初期、中期和后期的丹姆克尔数和湍流雷诺数，最后依靠丹姆克尔数-湍流雷诺数图对低、中、高初始油气浓度条件下油气爆炸初期、中期和后期的火焰燃烧模式进行了定量估计。结果表明:低、中、高初始油气浓度条件下激波管油气爆炸过程初期、中期和后期的火焰燃烧模式均为漩涡内小火焰模式。     

High-speed visualization and PIV measurements of cavitating flows around a semi-circular leading-edge flat plate and NACA0015 hydrofoil

Cavitating flows around a flat plate with semi-circular leading edge and a NACA0015 hydrofoil at attack angles ranging from 0° to 9° and with varying cavitation number are investigated using high-speed-imaging visualization (HIV) and particle-imaging velocimetry (PIV). Several known types of cavitation common to both foils, but also some different patterns, were observed. At small angles of incidence (less than 3°), cavitation on the plate begins in the form of a streak array (bubble-band) whereas on the hydrofoil as traveling bubbles. For the regimes with developed cavitation on the NACA0015 hydrofoil, the scattered and discontinuous bubble streaks branch and grow but subsequently merge into bubble clouds forming a remarkably regular lattice pattern. Once the incidence angle increased to 9°, the cavitation on the hydrofoil changed to a streaky pattern like that on the plate at small attack angles, whereas the regime on the plate showed no significant changes. The PIV method proved to be usable for measuring the instantaneous velocity also in the gas–vapor phase, albeit with reduced accuracy that was evaluated and accounted for on the basis of the effective (validation-surviving) number of imaging samples. The time-averaged velocity and turbulence moments show that the incipience of cavitation is governed by the development of the carrier-fluid flow around the foil leading edges, but the subsequent flow pattern depends strongly on the cavitation regime displaying markedly different distributions compared to the non-cavitating case. The main cavitation parameters: the maximum cavity length, the cloud cavity streamwise dimensions and the cloud shedding Strouhal number are analyzed and presented in function of the cavitation number and the attack angle in different scaling. The measurements confirm qualitatively the trends reported in the literature, but show also some quantitative differences, notably between the two foils considered.     

Navier-Stokes方程二阶速度滑移边界条件的检验

对微尺度气体流动,Navier-Stokes方程和一阶速度滑移边界条件的结果与实验数据相比,在滑移区相互符合,在过渡领域则显著偏离.为改善Navier-Stokes方程在过渡领域的表现,有些研究者尝试引入二阶速度滑移边界条件,如Cercignani模型,Deissler模型和Beskok-Karniadakis模型.以微槽道气体流动为例,将Navier-Stokes方程在不同的二阶速度滑移模型下的结果与动理论的直接模拟Monte Carlo(DSMC)方法和信息保存(IP)方法以及实验数据进行比较.在所考察的3种具有代表性的二阶速度滑移模型中,Cercignani模型表现最好,其所给出的质量流率在Knudsen数为0.4时仍与DSMC和IP结果相符;然而,细致比较表明,Cercignani模型给出的物面滑移速度及其附近的速度分布在滑流区和过渡领域的分界处(Kn=0.1)已明显偏离DSMC和IP的结果.     

圆柱绕流流场结构的大涡模拟研究

为进一步揭示绕流现象的形成机理,本文分别对处于层流稳态区、尾流过渡区、剪切层转换区Re分别为26、200、1.4×105的三种典型流态下的单圆柱绕流进行了二维数值模拟研究。Re为26时应用层流模型直接求解N-S方程,而Re分别为200、1.4×105时使用大涡模拟的方法进行计算。数值模拟很好地再现了稳定的涡旋结构、周期性交替脱落的卡门涡街结构、不规则的涡旋结构,在此基础上分析了尾流结构的基本特征及其压强分布规律、平均的流场特性、积分参数(如升力系数、阻力系数、斯特劳哈尔等),并与有关研究成果进行了对比。研究发现,采用不同流动介质时流场特性有所差异,空气为介质时的计算结果更符合实验的成果,而水为介质时计算结果偏差较大,这主要是由尾流涡旋产生的不合理负压造成的。     

Wave-flow theory for a thin viscous liquid layer

On the basis of a simplified system of equations we study the process of development and stability of wave flows in a thin layer of a viscous liquid. Any unstable disturbance of the laminar flow grows and leads to the establishment of the wave regime. The time to establish the flow changes little for large flow rates, but increases sharply with reduction of the flow rate. Given the same amplitudes of the initial disturbances, the optimum regimes which provide the greatest flow rate in a layer of given average thickness develop more rapidly than the other regimes. All the wave regimes are unstable to disturbances in the form of traveling waves. With moderate flow rates, the optimum regimes will be most stable to near-by disturbances.Strictly periodic wave flows in a thin layer of a viscous liquid under the influence of the gravity force were calculated in [1], Various flow wave regimes which differ in wavelength can theoretically be established for a given liquid flow rate. In particular, there is a wavelength for which the flowing layer exhibits minimum average thickness (and maximum flow rate for a given average thickness). These optimum regimes correspond closely to the experimental data [2]; however, with regard to calculation technique these regimes are no different from the others. In the following we make a comparison of the wave regimes on the basis of the nature of their development and stability.     

Single droplet impingement of urea water solution on a heated substrate

In the present work, impingement behaviour of an aqueous urea solution is investigated experimentally. The effects of droplet diameter, impact velocity and substrate temperature are evaluated by monitoring single droplet impingement with a high-speed camera. Results allow the formulation of four different interaction regimes and a regime map depending on hydrodynamic and thermal parameters is proposed. The regimes deposition, splash, boiling-induced breakup, rebound with breakup and the transition boundaries are discussed in detail. Results show that the solute significantly affects the outcome of droplet impingement promoting droplet disintegration by enhanced nucleation and bubble formation. Comparison with literature data reveal the strong dependency of droplet impact behavior on the Weber number as a combination of initial droplet diameter and impact velocity.     

Improved droplet breakup models for spray applications

The current study examines the performance of two zero-dimensional (0D) aerodynamically-induced breakup models, utilized for the prediction of droplet deformation during the breakup process in the bag, multi-mode and sheet-thinning regimes. The first model investigated is an improved version of the widely used Taylor analogy breakup (TAB) model, which compared to other models has the advantage of having an analytic solution. Following, a model based on the modified Navier–Stokes (M-NS) is examined. The parameters of both models are estimated based upon published experimental data for the bag breakup regime and CFD simulations with Diesel droplets performed as part of this work for the multi-mode and sheet-thinning regimes, for which there is a scarcity of experimental data. Both models show good accuracy in the prediction of the temporal evolution of droplet deformation in the three breakup regimes, compared to the experimental data and the CFD simulations. It is found that the best performance of the two is achieved with the M-NS model. Finally, a unified secondary breakup model is presented, which incorporates various models found in the literature, i.e. TAB, non-linear TAB (NLTAB), droplet deformation and breakup (DDB) and M-NS, into one equation using adjustable coefficients, allowing to switch among the different models.     

Improvement of the acoustic black hole effect by using energy transfer due to geometric nonlinearity

Acoustic Black Hole effect (ABH) is a passive vibration damping technique without added mass based on flexural waves properties in thin structures with variable thickness. A common implementation is a plate edge where the thickness is locally reduced with a power law profile and covered with a viscoelastic layer. The plate displacement in the small thickness region is large and easily exceeds the plate thickness. This is the origin of geometric nonlinearity which can generate couplings between linear eigenmodes of the structure and induce energy transfer between low and high frequency regimes. This phenomenon may be used to increase the efficiency of the ABH treatment in the low frequency regime where it is usually inefficient. An experimental investigation evidenced that usual ABH implementation gives rise to measurable geometric nonlinearity and typical nonlinear phenomena. In particular, strongly nonlinear regime and wave turbulence are reported. The nonlinear ABH beam is then modeled as a von Kármán plate with variable thickness. The model is solved numerically by using a modal method combined with an energy-conserving time integration scheme. The effects of both the thickness profile and the damping layer are then investigated in order to improve the damping properties of an ABH beam. It is found that a compromise between the two effects can lead to an important gain of efficiency in the low frequency range.