Resonance Driven by Horizontal Oscillations of a Vessel Occupied by a Fluid Heated from Above

Unsteady convection driven by periodic horizontal displacements of a rectangular cavity heated from below is investigated numerically. The resonance effects clearly manifest themselves in the frequency dependence of the induced convection flow. These effects appear at a sufficient temperature difference (Grashof number G>10⁴) and a considerable amplitude of the horizontal displacements of the cavity. The dependence of the parameters (resonance frequency and amplitude under resonance conditions) on the problem parameters (Grashof and Prandtl numbers and the cavity length/height ratio) and the method are found. Estimates show that the effects in question can be detected under laboratory conditions.     

Wave Motions in a Two-Layer Fluid Driven by Small Oscillations of a Cylinder Intersecting the Interface

The plane problem of steady-state small oscillations of a horizontal cylinder located at the interface between two fluids of different densities and indefinite depth is considered in the linear formulation. Boundary integral equations for the surface source distribution are derived. The behavior of the distributed singularities at points of intersection of the body contour and the interface is investigated. The problem of oscillations of a circular cylinder is solved by the multipole expansion method. The apparent mass and damping coefficients of the radiation problem and the reflection coefficient of the problem of scattering of an impinging wave by a floating body are calculated.     

Jet Outflow from a Small Hole in a Plane

On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].     

流体驱动高速运动机构的张开过程模拟

通过计算流体力学、动网格技术和刚体动力学,对水中高速运动柱体上厚板受水流冲击绕销轴加速打开过程进行了仿真分析.计算了厚板从初始位置到与缓冲管接触的张开过程中,厚板周围流场、压强分布、流体对厚板的驱动力矩及厚板的运动规律,并通过与试验结果的对比,验证了计算结果的有效性.计算结果表明:柱体运动速度越快,厚板张开速度越快,受到的驱动力矩越大.研究结果为分析运动机构结构强度提供冲击载荷的时间历程.     

Propagation of Normal Waves Through a Fluid Contained in a Thin-Walled Cylinder

The properties of normal axisymmetric waves propagating through a perfect compressible fluid contained in an elastic thin-walled cylinder are investigated. The problem is solved using the complete system of equations of the dynamic theory of elasticity. The effects of interaction between elastic and fluid waves are studied within a wide frequency range. The numerical results are classified on the basis of data on the properties of partial subsystems. Partial subsystems are those for which the interaction effects are insignificant. For special cases of compound waveguides, the dispersion spectra are constructed and the kinematic and energy characteristics of normal waves are analyzed. Particular attention is given to the lowest normal wave, which has specific properties and participates in the elastic–liquid interaction over a wide frequency range.     

Radial Flow of Non-Newtonian Power-Law Fluid in a Rough-Walled Fracture: Effect of Fluid Rheology

Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots.     

Computational Modeling of Fluid Flow through a Fracture in Permeable Rock

Laminar, single-phase, finite-volume solutions to the Navier–Stokes equations of fluid flow through a fracture within permeable media have been obtained. The fracture geometry was acquired from computed tomography scans of a fracture in Berea sandstone, capturing the small-scale roughness of these natural fluid conduits. First, the roughness of the two-dimensional fracture profiles was analyzed and shown to be similar to Brownian fractal structures. The permeability and tortuosity of each fracture profile was determined from simulations of fluid flow through these geometries with impermeable fracture walls. A surrounding permeable medium, assumed to obey Darcy’s Law with permeabilities from 0.2 to 2,000 millidarcies, was then included in the analysis. A series of simulations for flows in fractured permeable rocks was performed, and the results were used to develop a relationship between the flow rate and pressure loss for fractures in porous rocks. The resulting friction-factor, which accounts for the fracture geometric properties, is similar to the cubic law; it has the potential to be of use in discrete fracture reservoir-scale simulations of fluid flow through highly fractured geologic formations with appreciable matrix permeability. The observed fluid flow from the surrounding permeable medium to the fracture was significant when the resistance within the fracture and the medium were of the same order. An increase in the volumetric flow rate within the fracture profile increased by more than 5% was observed for flows within high permeability-fractured porous media.     

Ideal Gas Outflow from a Cylindrical or Spherical Source into a Vacuum

The solutions of initial and boundary value problems of the outflow of an ideal (inviscid and non-heat-conducting) gas from cylindrical and spherical sources into a vacuum are obtained. Time is measured from the moment, when the source is turned on; at this moment the source is surrounded by a vacuum. The entropy, flow rate, and the Mach number of the gas outflowing from the source are given, together with the source radius; the Mach number can be greater of or equal to unity. If the source radius is greater than zero, then the flow domain in the “radial coordinate–time” plane consists of the stationary source flow and adjoining non-self-similar centered expansion wave consisting of C^?-characteristics. The stationary flow is described by the known formulas, while the expansion wave is calculated by the method of characteristics. The calculations by this method confirm the earlier obtained laws for large values of the radial coordinate. The interface between the vacuum and the expansion wave is the straight trajectory of particles and, at the same time, a unique rectilinear C^?-characteristic. For the source of zero radius (“pointwise” source) the velocity, density, and speed of sound of the outflowing gas are infinite. The gas velocity remains infinite everywhere, while the density and speed of sound become zero for any non-zero values of the radial coordinate. For the pointwise source the problem of outflow into a vacuum is self-similar. In the plane of the “self-similar” velocity and speed of sound its solution is given by three singular points of a differential equation in these variables. At one of these points the self-similar velocity is infinite, the self-similar speed of sound is zero, and the self-similar independent variable varies from zero to infinity, with the exception of the extreme values.     

Immiscible Displacement of a Wetting Fluid by a Non-wetting One at High Capillary Number in a Micro-model Containing a Single Fracture

Most reservoirs in Iran are heterogeneous fractured carbonate reservoirs. Heterogeneity causes an earlier breakthrough and an unstable front which leads to a lower recovery. A series of experiments were conducted whereby the distilled water displaced n-Decane in strongly oil-wet glass micro-models containing a single fracture. Experimental data from image analysis of immiscible displacement processes are used to modify the Buckley?CLeverett and fractional flow equations by a heterogeneity factor. It is shown that the heterogeneity factor in the modified equations can be expressed as a function of fracture length and orientation.     

Geometric Characteristics of Fracture‐Associated Space and Crack Propagation in a Material

It is shown that fracture can be treated as a process occurring in the Finsler space. The use of the Finsler space allows one to construct a delaminated manifold whose characteristics are related to the defect structure of the medium. A method of determining the fractal dimension of fracture is developed using the concept of crack propagation along geodesics.     

Pulsatory Turbulent Compressible Fluid Flow and Propagation of Pressure Waves in a Channel

The properties of the damping coefficient and phase velocity of propagation of small-amplitude pressure waves as functions of the oscillation frequency are investigated for the turbulent flow of a weakly compressible fluid in a circular pipe. The wall friction is found by solving numerically the equation of motion and the relaxation equations for the turbulent shear stress and viscosity which provide the basis for a turbulent transfer model developed for unsteady conditions. The properties are explained in terms of an analysis of the calculated data on turbulent transfer. The results obtained are compared with experiments.     

Propagation of Normal Axisymmetric Waves in Compliant Elastic Cylinders Filled with and Immersed in a Fluid

The paper studies the relationship between the physical characteristics of a cylinder and the properties of normal axisymmetric waves in elastic–liquid waveguides. The cylinder is made of a compliant material in which the velocity of shear waves is less than the sonic velocity in a perfect compressible liquid. The complete system of dynamic elasticity equations and the wave equation are used to describe the wave fields in the elastic cylinder and fluid, respectively. This approach allows obtaining the dispersion characteristics of coupled normal waves in compound waveguides over wide ranges of frequencies and wavelengths. The curves of real, imaginary, and complex wave numbers versus frequency are plotted for specific pairs of waveguide materials. Computations are carried out for a thick-walled cylinder filled with a fluid and immersed in either vacuum or a fluid. It is found out that compliant and rigid materials of the cylinder affect differently the wave interaction process in elastic–liquid waveguides     

激波喷出过程和在林带中的传播

运用激波管技术研究了激波从管口喷出和在林带中传播这两个基本问题。给出了三方面的结果 :揭示了激波从管口喷出时的复杂流场 ,显示了主激波弯曲和衰减 ,二次激波的形成和合拢 ,涡环的长大和发展 ,以及涡环前缘出现正激波等基本物理现象 ;显示了激波在林带中的传播过程 ,取得了激波遇林地的反射 ,马赫杆形成 ,激波与林冠的相遇 ,林冠对涡环的阻滞效应等纹影照片 ;沿激波在林地的传播方向测量了地面压力 ,证实林带有明显的消波效应。     

Propagation of harmonic elastic waves from a curvilinear cylindrical cavity

International Applied Mechanics -     

Structure of Averaged Flow Driven by a Vibrating Body with a Large-Curvature Edge

The averaged viscous incompressible fluid flow driven by a vibrating body with a large-curvature edge is investigated experimentally and numerically. The case of an axisymmetric body immersed in fluid and performing translational vibrations along its axis is considered. Experiments carried out on fluids of various viscosity over a wide vibration frequency and amplitude range and direct numerical calculations based on the complete time-dependent equations of viscous fluid dynamics show that the global structure of the averaged flow significantly depends on the relation between the curvature radius of the body edge and the viscous skin-layer thickness. Different averaged flow regimes are detected and the flow restructuring process is investigated as a function of the vibration amplitude and frequency.     

The Diffusion of a Population¶Partly Driven by its Preferences

The goal of this paper is to investigate a stationary model for the diffusion of a population when the diffusion coefficient at one location depends on the population at another. This could simulate, for instance, attraction or repulsion between the species considered. Accepted May 29, 2000?Published online November 24, 2000