Modelling the Effect of Surface Tension on Immiscible Displacement in a Saturated Porous Medium

Comments are made about the model employed by Chen and Vafai for forced convection in a porous medium channel, with a surface tension effect at the moving interface between two fluids, when one fluid is displaced by the other. A simple situation is analysed, and the circumstances under which surface tension effects are important in this case are clarified.     

The transport of vorticity on rotating Bernoulli surfaces of any geometry in compressible,inviscid flow with applications to turbomachine blade rows

The transport of vorticity is analysed for a compressible, inviscid flow which is steady relative to a reference frame rotating at constant angular velocity. It is shown that Helmholtz's vorticity convection theorem does not apply to this flow but nevertheless the vortex lines are transported on a streamsurface which therefore corresponds to the familiar Bernoulli surface.Explicit, integrated results are obtained for Bernoulli surfaces of any geometry. The transport of the normal component of vorticity is obtained for the general case in closed form, whereas the transport of the streamwise component is closed in form for some cases but involves a time difference integral over the bounding streamlines.Application is made to a turbomachine blade row where the flow between two consecutive blades is examined. Explicit results are obtained for the streamwise vorticity development in the axial flow configuration in terms of the traverse time integral for a particle, taken around the blade profile. The more general mixed flow configuration is also examined where a closed result is obtained only for the incompressible case.     

Surface grid generation with a linkage to geometric generation

This paper describes a new method to generate surface grids over complex configurations defined by a geometric generation system. The scheme is designed for direct utilization of the surface definition provided by a geometric modeller based on a boundary representation (the so-called B-rep modeller). Thus, the conversion of the geometric representation for the surface grid generator is not required. Consequently, this technique eliminates not only laborious tedium in the conversion of data, but also errors in the representation of the surface induced in the process of the conversion. The proposed method is accomplished over several stages. First, the triangulation is performed on the surface of the geometry, on which the area to be grided is laid. Then linear partial differential equations are mapped and solved on these triangular elements. Finally, the surface grid is constructed by searching for the contours inside the solution domain. After the co-ordinate values of the grid points are obtained by a linear interpolation within each triangular element, these values are mapped onto the surface of the geometry through surface parametric functions provided by the B-rep modeller. An example of generating surface grid over a car configuration is given to illustrate the capability of the method.     

Calculation of stationary inviscid flow over three-dimensional bodies

The results of the calculation of inviscid supersonic flow of a perfect gas over a blunt three-dimensional configuration are considered. An explicit finite-difference scheme of second order of accuracy [1] was used for the numerical integration of the hyperbolic system of equations, which was written in divergence form. The region of integration is situated between the body and the outer shock wave. The internal discontinuity surfaces were not separated out and the calculation was made through them. The points on the surface of the body were calculated using relations on characteristics written in a form that makes it possible to calculate flows with strong entropy layers. The results of calculation of flow over a three-dimensional configuration at an angle of attack are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 4, pp. 172–175, July–August, 1980.     

Acoustical-speckle interferometry

When a continuous or pulsed wave of ultrasound is scanned over an object, an echo emanating from the object may be detected. If the echo has a random variation in amplitude vs. position of the beam, the resulting variation is referred to as acoustical speckle. An analysis is presented for utilizing acoustical speckle to determine displacements on the surface or interior of an object. Two experimental configurations, pulse-echo and continuous wave scanning, are treated in the verification of the analysis.     

THE FLUID–STRUCTURE INTERACTION IN SUPPORTING A THIN FLEXIBLE CYLINDRICAL WEB WITH AN AIR CUSHION

The mechanics of the fluid–structure interaction between a thin flexible web, wrapped around a cylindrical drum (reverser), and the air cushion formed by external pressurization through the holes of this drum is analyzed. Derivation of a “new” theory for the moderately large deflections of a thin cylindrical shell to model the web is presented. This theory allows for large web deflections, while using a self-adjusting strain-free reference state for the web in order to keep the circumferential web tension around a constant level. The theory also incorporates the redistribution of the in-plane stress resultants in the axial and shear directions using the Airy stress function. The air-flow is averaged over the height direction of the web-reverser clearance. The surface area of the pressure holes is averaged locally over the total reverser surface. The resulting equations are a modified form of the Navier–Stokes and mass balance equations with nonlinear source terms. The coupled fluid–structure system is solved numerically. The mechanics of the interaction between the web deflections and the air cushion generated by the reverser is explained. The effects of the problem parameters on the overall equilibrium are presented. Parameter distributions which cause the web to contact the reverser are identified, and suggestions are made to avoid this state.     

Numerical solution of the problem of the flow of a supersonic gas stream over the upper surface of a delta wing in the expansion region

A numerical method is described for the calculation of supersonic flow over the arbitrary upper surface of a delta wing in the expansion region. The shock wave must be attached everywhere to the leading edge of this wing from the side of the lower surface. The stream flowing over the wing is assumed to be nonviscous. A problem with initial conditions at some plane and with boundary conditions at the wing surface and the characteristic surface is set up for the nonlinear system of equations of gas dynamics. The difference system of equations, which approximates the original system of differential equations on a grid, has a second order of accuracy and is solved by the iteration system proposed in [1]. The initial conditions are determined by the method of establishment of self-similar flow. A number of examples are considered. Comparison is made with the solutions of other authors and with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 76–81, November–December, 1973.The author thanks A. S. II'ina who conducted the calculations and V. S. Tatarenchik for advice.     

Experimental Study of Fracture Permeability for Stimulated Reservoir Volume (SRV) in Shale Formation

“Stimulated reservoir volume”(SRV) makes shale gas production economic through new completion techniques including horizontal wells and multiple hydraulic fractures. However, the mechanism behind these treatments that provide sufficient permeability is not well understood. The effects of different stimulation treatments need to be further explored. To understand the effects of fracture surface roughness, fracture registration, confining pressure, proppant type and distribution mode, fiber and acidizing treatment on fracture permeability, a series of laboratory permeability experiments were performed on fractured cores from shale formation of Shengli Oilfield. The results of this study demonstrate that sedimentary bedding of shale has important influence on matrix permeability. At 35 MPa confining pressure, the permeability of aligned fracture (unpropped and without fracture offset) can increase about 1–3 orders of magnitude over shale matrix. The permeability of displaced fracture can increase about 1–2 orders of magnitude over the aligned fracture. The permeability of fracture propped with proppant can increase about 2–4 orders of magnitude over unpropped fracture. The greater the fracture surface roughness, the higher the permeability. The increasing degree of displaced fracture permeability is not proportional to the amount of fracture offset. In the microfracture of shale, the effect of ceramic proppant is still better than that of quartz sand, and the permeability of a centralized fairway distribution of proppant is about 1.2 times better than an even monolayer distribution of proppant. Under high pressure, proppant is easy to cause the break of fracture faces of brittle shale, and increase local fracture permeability to some extent. However, quartz sand are more easily broken to embed and block microcracks just made, which results in fracture permeability lower than that of ceramic proppant. At the same time, the argillation phenomenon is easy to happen on propped fracture faces of shale, which is one of the main factors that leads to a substantial decline in fracture permeability. The permeability of displaced fracture propped with proppant is greater than that of aligned fracture propped with proppant. Because of added fiber presence, the permeability of microfractures presented in SRV is greatly reduced. The pressure dependence of aligned fractures in shale obeys Walsh’s theory, but the pressure dependence of propped and displaced fractures in shale obeys Walsh’s law over a limited range of pressures. Deviations reflect proppant seating, proppant embedding and breaking. For shale formation with the high carbonate content, acidizing treatment should be carefully implemented. Experimental results may provide more valuable information for effective design of hydraulic fracturing in shale reservoir.     

Generalized Poynting Effects in Predeformed Prismatic Bars

We use the Signorini expansion method to determine second-order Saint-Venant solution for an infinitesimally bent and stretched bar. The bar in the unstressed reference configuration is straight, prismatic, isotropic, homogeneous and made of a second-order elastic material. These solutions and those found earlier for a pretwisted bar give generalized Poynting effects. A bar when bent stretches and the elongation is determined by the first and second-order elasticities, area of cross-section, torsional rigidity, bending vector and the inertia tensor. When an infinitesimally twisted bar is deformed, there is a second-order bending deformation even when there is no resultant bending moment applied on the end faces. This revised version was published online in August 2006 with corrections to the Cover Date.     

带尾翼水下自然超空泡射弹数值模拟研究

基于Navier-Stokes方程,考虑气液间相变,采用大涡模拟湍流模型,PISO算法及VOF方法,利用自行开发的程序对绕三维带尾翼水下自然超空泡射弹的非定常空泡流动进行了数值模拟研究.通过计算结果得到超空泡从射弹头部初生至完全包裹弹身的形成过程.在此基础上,计算不同攻角条件下的超空泡形态,并给出射弹表面空泡厚度分布曲线,分析不同攻角对超空泡形态特性的影响规律,以及在零攻角条件下,分析尾翼对空泡形态的影响.另外计算不同空化数条件下的超空泡无量纲长度和厚度,将计算结果与实验数据进行对比,两者吻合较好.研究结果为进一步研究水下高速射弹的水动力特性和弹道特性问题提供理论基础.     

On the role of a balancing load in the problem of aerodynamic drag minimization in the supersonic flight regime

The problem of reducing the aerodynamic losses through balancing in the supersonic flight regime is considered. An analysis and a comparison of the drag components due to the aerodynamic surface deformation and the balancing weigh distribution is made with reference to the examples of a zero-thickness airfoil and a three-dimensional configuration of an aircraft with a wing of complicated planform. It is shown that minimum values of the aerodynamic drag are achieved as a result of complex optimization including the dead load mass as a varied parameter.     

Reformation Instability in Elastic Solids

The reformation of a body fundamentally involves the mapping of one natural reference configuration of it into another natural reference configuration. The mass and the constitutive properties of the material remain unaltered, but the overall shape of the reference configuration generally changes. If, when a natural reference configuration is distorted, there is a portion of the boundary of the body that is displacement controlled, then a reformation of the body must be such that the original displacement controlled part of the boundary and its reformation are identical. In common applications that involve reformation, the remainder of the boundary is traction-free and a reformation essentially involves a change of the morphology of this traction-free surface. For example, undulations are often a characteristic feature of the reformation of a free, plane boundary surface. Reformations are a result of a material instability and they may associate with a chemically induced diffusive processes in which particles of the body move into preferred places. Fundamentally, a reformation is generated in response to the drive to lower the total stored energy of the body. In this work we are not concerned with the physical processes that take place during reformation, but rather we are concerned with characterizing the onset of the instability. We develop a variational characterization of the reformation instability for a nonlinear elastic body and we include the effect of surface energy. As an example, we consider the axial deformation of a circular cylinder and argue that small scale nano-wires, for which the diameter-to-length ratio is sufficiently small, are expected to be stable with respect to spatial variations when extended. Moreover, we observe that if the surfacial energy function is sufficiently convex at the undistorted state such wires may also be stable with respect to spatial variations when compressed. We then show that such small scale nano-wires are unstable with respect to reformation when either extended or compressed.     

Residual mass and flow regimes for the immiscible liquid–liquid displacement in a plane channel

The motion of two immiscible liquids in a plane channel is analyzed for the case in which the flow conditions and the interactions between the liquids and the solid surface maintain the displaced fluid attached to the wall. The Galerkin Finite Element Method is used to compute the velocity field and the configuration of the interface between the two fluids. We compare the residual mass fraction left on the wall with its two counterparts in capillary tubes, namely residual mass fraction and dimensionless layer thickness of the displaced fluid. The main result of this comparison was that although there is a qualitative similarity concerning the layer thickness between the two cases, the residual fraction of mass presented an important difference, showing that when the aspect ratio of the capillary passage is large there is an increase in the displacement efficiency. The thickness of the displaced liquid film attached to the channel walls is a function of the capillary number (Ca) and the viscosity ratio (N_μ). A map of streamlines in the Cartesian space (Ca, N_μ) with the different flow regimes of the problem is presented. We also showed that we can adapt the available analytical results obtained for gas-displacement in capillary tubes to the plane channel case, for low values of Ca.     

A shape control model for piezo-elastic structures based on divergence free electric displacement

A model simulating the effects of the control potential on the static configuration of a piezo-elastic structure is presented. This model is centred on the electric displacement field, which is shown to be divergence free. Thus, the surface charge effect no control over the configuration of a piezo-elastic structure, save for the control potential derived through passive or active control. Results show that at zero gain the proposed model resembles a structure free from piezoelectric control. Thus, no fictituous stiffness is introduced as is the case with models presented in the literature.     

Modelling of Two-Component Turbulent Mass and Heat Transfer in Air-Fed Pressurised Suits

In this paper the modelling of an important industrial problem is addressed, which involves the two-component turbulent flow with heat transfer that takes place inside protective clothing. The geometry of the flow boundaries is reconstructed in a CAD system from photogrammetry scan data. The overall model is sufficiently realistic to allow, after validation, design improvements to be tested. Those presented here allow the reduction of hotspots over the worker’s body surface and increase thermal comfort.     

Non-contact boundary layer profiler using low-coherence self-referencing velocimetry

A spatially self-referencing velocimetry system based on low-coherence interferometry has been developed. The measurement technique is contactless and relies on the interference between back-reflected light from an arbitrary reference surface and seeding particles in the flow. The measurement location and the flow velocity are measured relative to the reference surface’s location and velocity, respectively. Scanning of the measurement location along the beam direction does not require mechanical movement of the sensor head. The reference surface (which can move or vibrate relative to the sensor head) can be either an external object or the surface of a body over which measurements are to be performed. The absolute spatial accuracy and the spatial resolution only depend on the coherence length of the light source (tens of microns for a superluminescent diode). The prototype is an all-fiber assembly. An optical fiber of arbitrary length connects the self-contained optical and electronics setup to the sensor head. Proof-of-principle measurements in water (Taylor–Couette flow) and in air (Blasius boundary layer) are reported in this paper.     

Rotation of the thrust vector of a two-dimensional nozzle by means of displacing the critical surface

The method of thrust vector deflection by means of displacing the critical surface of a nozzle is numerically and experimentally investigated. The displacement is realized at the expense of extending rotatable walls, or deflectors, into the flow; in this case, one of the edges of the critical surface is displaced from the throat onto the deflector surface. Two nozzle configurations, with short and long deflectors, are studied. The thrust vector deflection angles and the nozzle thrust coefficients are determined in the thrust vector deflection regime. For the configuration with long deflectors the angle of rotation of the thrust vector amounts to 30° and is determined by the effect of jet ejection toward the opposite wall, similar with the Coanda effect.     

Mechanical experiments to identify homogeneous bodies

All bodies are inhomogeneous at some scale but experience has shown that some of these bodies can be idealized as a homogeneous body. Here we examine which bodies can be idealized as a homogeneous body when they are subjected to a non-dissipative mechanical process. This is done by studying circumstances in which an inhomogeneous body admits pure stretch homogeneous deformations. Then, we devise experiments wherein these circumstances are prevented. If homogeneous deformation is observed in these devised experiments, the body could be modeled as a homogeneous body. We limit our analysis to a class of isotropic elastic bodies deforming from a stress free reference configuration whose Cauchy stress is explicitly related to left Cauchy–Green deformation tensor. It is further assumed that the constitutive relation is differentiable function of the position vector of material particles in the stress free reference configuration. Then, we find that a cuboid made of compressible and isotropic material could be modeled as a homogeneous body if it deforms homogeneously due to the application of the normal stresses on all of its six faces and the magnitude of the normal stresses on three orthogonal faces are different. A cuboid made of incompressible and isotropic material could be modeled as a homogeneous body, if it deforms homogeneously in two different biaxial experiments, such that the plane in which the forces are applied in the two biaxial experiments is mutually orthogonal.     

Investigation on convective heat transfer over a rotating disk with discrete pins

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk surface with discrete pins was conducted by the use of RNG k–ε turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characteristics on the rotating surface were analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk becomes stronger and the transition from laminar to turbulent occurs at the outer radius of rotating disk, which resulting in heat transfer enhancement. The pins on the disk make the pumping action of a rotating disk weaker. Simultaneously, they also act as perturbing elements to the cyclone flow near the rotating disk surface, making the overall heat transfer to be enhanced. The needle pins have higher convective heat transfer capacity than the discrete ring pins with the same extend pin areas.     

Contact interaction of a rigid die with an elastic layer during frictional heating

A formulation and solution are presented for the static thermoelastic problem of the sliding of a rigid die on the surface of an elastic layer with a fixed base. Frictional heating which occurs in accordance with Amonton's law is taken in account. With the assumption that the die is insulated, the problem is reduced to a system of two integral equations for contact pressure and a function which is a linear combination of the temperature and heat flux on the contact surface. A numerical algorithm is proposed for solving the system. A study is made of the effect of the reduction brought about in the size of the contact area by the steady generation of heat during the interaction of the layer and die with parabolic and semicylindrical bases. I. Franko University, Lvov, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 130–138, January, 2000.