An analytical study of frost nucleation and growth during the crystal growth period

An analytical study was made to clarify the fundamental nature of the early stage of crystal growth period of frost formation phenomena. A suitable model was developed by using the principles of crystallization and nucleation theory. The effect of four dominant parameters of frost formation; plate temperature, air temperature, air humidity ratio and Reynolds number, was studied. Ice crystal density variation with temperature reported by cloud physicists is used in the model to predict the density variation of frost during the crystal growth period. The temperature variation in the frost layer is formulated and vapor diffusion through the frost layer is taken in the consideration.     

Taylor instability in a thin fluid layer

Summary The Stokes-Taylor instability of a thin fluid layer is studied by the usual first order perturbation method. The density of the layer is assumed to be constant or to vary exponentially through it. It is bounded on either side by media of constant density. Particular attention is paid to determining the exponential rates of growth of perturbations at the two interfaces, and the effect of the layer in reducing the instability of the interface between the bounding media formed in the absence of the layer. When the layer is of variable density and the acceleration acts in the direction of increasing density, there is an infinity of modes of internal instability which do not affect the interfaces. There are also two modes of interfacial instability which are similar to those occurring when the layer is of constant density.     

The distribution of particles in a shock-induced boundary layer of a dusty gas over a solid surface

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied. The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account. A method for calculating the density profile of dispersed phase near the wall is proposed and some numerical results are given. It is shown that behind the shock wave, there exists a curved thin layer where the density of particles is many times higher than the original one. This dust collection effect may be of essential importance to the problem of dust explosion in industry.     

The effect of anisotropic permeability on free convective boundary layer flow in porous media

The effect of an anisotropic permeability on thermal boundary layer flow in porous media is studied. The convective flow is induced by a vertical, uniformly heated surface embedded in a fluid-saturated medium. A leading-order boundary layer theory is presented. It is shown that the thickness of the resulting boundary layer flow is different from that obtained in an isotropic porous medium. In general, an anisotropic permeability induces a fluid drift in the spanwise direction, the strength of which depends on the precise nature of the anisotropy. Conditions are found which determine whether or not the boundary layer flow is three-dimensional.     

Laboratory observations of interactions of forced plumes with stratified shear layers

Plumes of fluid are often observed in nature to interact with stratified shear layers. Examples of this include chimney plumes hitting inversion-layer ceilings; sewage plumes impinging on unmixed fresh/saltwater interfaces; descending plumes of cold water formed at ice-leads interacting with the oceanic thermocline; and volcano plumes interacting with atmospheric interfaces. Controlled laboratory studies of these phenomena have not previously been described in the literature, and as a result there is a lack of understanding regarding their morphology and dynamics. Thus, a novel set of experiments is described here in which the behaviour of a turbulent plume is observed in the presence of a two-layer ambient. The lower layer, into which the plume initially emerges, is quiescent and at a relatively high density. The upper layer is forced to flow uniformly across the top of the lower layer, and has a lower density. The flow of the resulting plume is characterised by (a) its vertical and lateral spreading in the lower layer; (b) the nature of its extension upstream and downstream at the interface; and (c) the extent to which it penetrates into the upper layer. The behaviour is found to be governed by three non-dimensional parameters: the initial gradient Richardson number of the interface Ri_G, the ratio of the upper layer crossflow speed to the speed of the plume when it first impinges on the interface U_F/U_PI, and the ratio of the plume Monin–Obukhov lengthscale to the lower layer depth L_MO/H_L. Regime diagrams are presented showing the effects of changing these parameters on the plume flow, quantitative relationships are determined, and practical applications of the results are considered.     

激波诱导含灰气体边界层中的粒子分布

本文研究当激波沿着一个固体表面等速地穿越含灰气体运动时所诱导的层流边界层特性。考虑了作用在气体边界层中球形粒子的 Saffman 升力,建议了一种计算近壁区中弥散相密度剖面的方法,并给出了数值计算结果。本文结果表明:在激波后方存在着一个弯曲的薄层区域,其中的粒子密度可以比其波前原始值增加许多倍。这种粒子聚集效应对于工业中粉尘爆炸等实际问题具有重要意义。     

大气边界层流场的模拟与大气边界层风洞

动态风荷载测试数据的可靠性依赖于大气边界层流场的正确模拟。本文根据作者在ＦＤ－４大气边界层风洞中,进行大气边界层流场调试时,就如何准确模拟自然风的四个参数方面所积累经验的总结。     

The onset of penetrative double-diffusive convection

The onset of double-diffusive convection in a horizontal fluid layer is studied. The density is assumed to depend quadratically on the temperature and linearly on the solute concentration. Under the Boussinesq approximation, the linear stability of the conduction state is investigated with respect to the oscillatory and steady convection modes. For steady onset, the critical thermal Rayleigh number is found to be a double-valued function of the solutal Rayleigh number as long as the relative maximum of the density profile exists within the fluid layer. Driving mechanisms of the steady convections are discussed.     

Analysis of current induced by long internal solitary waves in stratified ocean

An approximate theoretical expression for the current induced by long internal solitary waves is presented when the ocean is continuously or two-layer stratified. Particular attention is paid to characterizing velocity fields in terms of magnitude, flow components, and their temporal evolution/spatial distribution. For the two-layer case, the effects of the upper/lower layer depths and the relative layer density difference upon the induced current are further studied. The results show that the horizontal components are basically uniform in each layer with a shear at the interface. In contrast, the vertical counterparts vary monotonically in the direction of the water depth in each layer while they change sign across the interface or when the wave peak passes through. In addition, though the vertical components are generally one order of magnitude smaller than the horizontal ones, they can never be neglected in predicting the heave response of floating platforms in gravitationally neutral balance. Comparisons are made between the partial theoretical results and the observational field data. Future research directions regarding the internal wave induced flow field are also indicated.     

Quantitative schlieren measurements of coherent structures in a cavity shear layer

Quantitative flow-field data were obtained in a planar shear layer spanning an open cavity with an extension of the schlieren method. The technique is based on the measurement of light-intensity fluctuations in a real-time schlieren image. Data were collected using a fiber-optic sensor embedded in the imaging screen coupled to a photodetector. Time-resolved measurements of the instantaneous density gradient at a point in the two dimensional flow cross section were thus obtained. Detailed surveys were carried out with both the optical instrument as well as a hot wire at a Mach number of 0.25 and with the optical instrument alone at a Mach number of 0.6. A comparison of the results shows that the non-intrusive technique can accurately measure the growth rates of instability waves in the initial “linear” region of the shear layer. The density-gradient fluctuations measured at different locations (and times) were synchronized by using a microphone inside the cavity as a reference and integrated to yield profiles of the density fluctuations associated with the dominant large-scale structures in the shear layer. Such quantitative visualization is expected to clarify the mechanism of sound generation by shear-layer impingement at the cavity trailing edge and elucidate the nature of this sound source. Received: 28 December 1999/Accepted: 15 March 2000     

The Onset and Nonlinear Regimes of Convection in a Two-Layer System of Fluid and Porous Medium Saturated by the Fluid

The onset of convection and its nonlinear regimes in a heated from below two-layer system consisting of a horizontal pure fluid layer and porous medium saturated by the same fluid is studied under the conditions of static gravitational field. The problem is solved numerically by the finite-difference method. The competition between the long-wave and short-wave convective modes at various ratios of the porous layer to the fluid layer thicknesses is analyzed. The data on the nature of convective motion excitation and flow structure transformation are obtained for the range of the Rayleigh numbers up to quintuple supercriticality. It has been found that in the case of a thick porous layer the steady-state convective regime occurring after the establishment of the mechanical equilibrium becomes unstable and gives way to the oscillatory regime at some value of the Rayleigh number. As the Rayleigh number grows further the oscillatory regime of convection is again replaced by the steady-state convective regime.     

Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

Interfacial energy effects within the framework of strain gradient plasticity

In the framework of strain gradient plasticity, a solid body with boundary surface playing the role of a dissipative boundary layer endowed with surface tension and surface energy, is addressed. Using the so-called residual-based gradient plasticity theory, the state equations and the higher order boundary conditions are derived quite naturally for both the bulk material and the boundary layer. A phenomenological constitutive model is envisioned, in which the bulk material and the boundary layer obey (rate independent associative) coupled plasticity evolution laws, with kinematic hardening laws of differential nature for the bulk material, but of nondifferential nature for the layer. A combined global maximum dissipation principle is shown to hold. The higher order boundary conditions are discussed in details and categorized in relation to some peculiar features of the boundary surface, and their basic role in the coupling of the bulk/layer plasticity evolution laws is pointed out. The case of an internal interface is also studied. An illustrative example relating to a shear model exhibiting energetic size effects is presented. The theory provides a unified view on gradient plasticity with interfacial energy effects.     

One-dimensional compression of bounded volumes of a self-gravitating gas

Unsteady plane and spherically-symmetric self-gravitating gas flows are analytically and numerically studied. It is assumed that the gas is enclosed in a plane layer of finite thickness or in a bounded spherical volume. Two characteristic compression patterns are established, namely, a quasiperiodic regime in which gravitational equilibrium is attained and a fast compression regime with a many orders increase in the density. The quasiperiodic regime is realized when the layer thickness is fairly small as compared with the Jeans length. The fast compression occurs when the layer thickness is greater than the Jeans length.     

Investigation of convection in a horizontal cylindrical layer of a saturated porous medium

The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness.     

Change in the wind flow regime in stratified lakes

Wind flows in meromictic saline lakes in which the water column is not mixed to the bottom for at least one year are studied. This leads to the formation of upper and depth layers with small density gradients, between which there is a water layer with a large density gradient. It has been shown that, depending on the density stratification and the wind speed, wind flows (in the vertical plane) of two types are possible: with one or two circulation zones. For a two-layer lake model, a criterion for the change in the wind flow regime is proposed.     

平板湍流边界层的声辐射

基于平板湍流边界层的壁压起伏波数—频率谱 ,给出了一种湍流边界层声辐射的估算方法 ,并对光滑平板湍流边界层和平板表面粗糙度引起的湍流边界层声辐射进行了分析。结果表明 :湍流边界层声辐射是一种四极子声辐射 ,且其辐射声能集中于平板表面粗糙度引起的湍流边界层声辐射 ;光滑平板湍流边界层的声辐射也不可忽略。     

Stability of stratified shear flows in channels with variable cross sections

For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found. Furthermore, the instability of the bounded shear layer is studied in two cases: (i) the density which takes two different constant values in two layers and (ii) the density which takes three different constant values in three layers. In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity. It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.     

Experimental investigation of turbulent entrainment in an annulus with moving sidewalls

The establishment of a turbulent mixed layer in a two-layer stratified shear flow, and the rate of entrainment into that layer were studied experimentally in a modified annulus. The modification of the conventional annulus was made by replacing the upper rotating screen with inner rotating sidewalls, extending over the upper half of the channel, so that the flow in the upper layer was nearly uniform and almost laminar, while the bottom layer was quiescent. Vertical density profile measurements were conducted using single electrode conductivity probes. The flow was visualized during the various stages of the experiment using the hydrogen bubble technique.After the start of the sidewalls rotation, the upper layer accelerates from rest, and consequently a transition process is taking place during which the initial density interface between the two layers is developed into a turbulent mixed layer. This turbulent layer is bounded by two sharp interfaces, each separating it from an outer non-turbulent zone. The generation of this five-layer structure seemed to be dominated by instabilities activated by the velocity difference between the upper and lower layer.Once a turbulent mixed layer is formed, entrainment of nonturbulent fluid into that layer is taking place causing its thickness to increase continuously. Depending on the overall Richardson number, based on the channel width, the slope of the entrainment law curve was found to have two different values, each indicating the dominance of a different source of turbulent energy production. For relatively low Richardson numbers, the slope is close to -1.8, implying that the velocity shear across each interface contributes significantly to the entrainment. On the other hand, for larger Richardson numbers the slope is about -1.25, in agreement with previous results of shear-free entrainment experiments.The measured velocity profiles indicate that as long as the mixed layer is not too thick, the radial inhomogeneities are small and the flow may be considered as nearly one-dimensional. It seems, therefore, that for the understanding of entrainment processes occurring in realistic stratified flows, the modified annulus is a more reliable tool than the conventional one.