Fingering patterns on an expanding miscible drop in a rotating Hele‐Shaw cell

We perform a detailed numerical study for the evolution of an expanding miscible drop in a rotating Hele‐Shaw cell. Two mathematical formulations applied to model the coating layer expansion during practical spin‐coating process, such as thinning of the layer by cell pressing and drop spreading outward due to injection, are investigated. Including miscible interfacial stresses, we focus on the investigation of dynamical and morphological influences of two different stabilizing parameters: the gap width parameter for the pressing cell and the injecting strength. In the case of a pressing cell, the fingering features of the expanding miscible drop, such as the critical radius, are distinct from those ones in the experiments of spin coating due to the different distributions of the inherent radial velocity. On the other hand, the global interfacial evolutions of an expanding drop with an additional injection bear remarkable resemblances to their immiscible counterparts. The better agreement for an injecting model suggests its appropriateness when we simulate the emerging fingering instabilities in the spin‐coating process. Moreover, we investigate the effects of Coriolis force at higher miscible Bond numbers. Coriolis force affects significantly the onset of fingering instability and the tilting angles of fingers. These stable effects are in line with the results from the previous studies for miscible and immiscible flow fields. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical simulations of interfacial instabilities on a rotating miscible droplet in a time‐dependent gap Hele–Shaw cell with significant Coriolis effects

Interfacial instability of a rotating miscible droplet with significant Coriolis force in a Hele–Shaw cell is simulated numerically. The influences of the relevant control parameters are first discussed qualitatively by fingering patterns. More vigorous fingerings are found at higher rotational effects, a lower viscosity contrast and a weaker effective surface tension (Korteweg constant). For a time‐dependent gap Hele–Shaw cell, a higher cell lifting rate makes the rotating droplet bear an inward straining flow, which leads to fingering enhancement. On the contrary, a higher pressing rate provides more stable effects by additional squeezing outward flow. A quantitative analysis between the Coriolis effects and tilting angles of fingers is addressed. For arbitrary combinations of all relevant control parameters, the values of tilting angles follow a nearly linear relationship with the Coriolis effects. We estimate the correlation between the relevant control parameters (dimensionless Coriolis factor Re, viscosity parameter R, cell lifting rate a) and tilting angles (θ) of fingers that can be approximated as for significant Korteweg stresses. Copyright © 2005 John Wiley & Sons, Ltd.     

Phase Behaviour,Fluid Properties and Recovery Efficiency of Immiscible and Miscible Condensate Displacements by SCCO<Subscript>2</Subscript> Injection: Experimental Investigation

This paper presents a quantitative investigation of the interfacial tension dependent relative permeability (IFT-DRP) and displacement efficiency of supercritical CO₂ injection into gas-condensate reservoirs. A high-pressure high-temperature experimental laboratory was established to simulate reservoir conditions and to perform relative permeability measurements on sandstone cores at a constant reservoir temperature of 95°C and displacement velocity of 10 cm/h. This investigation covers immiscible displacements (1100 and 2100 psi), near-miscible displacement (3000 psi) and miscible displacements (4500 and 5900 psi). The coreflooding results demonstrated that displacement pressure is a key factor governing the attainment of optimum sweep efficiency. The ultimate condensate recovery increased by almost threefold when CO₂ was injected at near-miscible conditions (i.e., 23.40% ultimate recovery at 1100 psi compared to 69.70% at 3000 psi). Miscible flooding was found to give the optimum condensate recovery (9% extra ultimate recovery compared to near-miscible injection). Besides improving the ultimate recovery, miscible floods provided better mobility ratios and delayed gas breakthrough (0.62 PV BT at 5900 psi compared to 0.21 PV BT at 1100 psi). In addition to the elimination of IFT forces in miscible displacements, favourable ratios of fluid properties and phase behaviour relationships between the SCCO₂ and condensate were believed to be the driving force for the improved recovery as they provided a stabilising effect on the displacement front and stimulated swelling of the condensate volume. This paper incorporates the theoretical aspects of phase behaviour and fluid properties that largely affect the microscopic displacement efficiency and serves as a practical guideline for operators to aid their project designs and enhance their recovery capabilities.     

Intensity of singular stress fields causing interfacial debonding at the end of a fiber under pullout force and transverse tension

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pullout force. Those singular stresses have not been discussed yet in the previous studies for pullout problems although they are important for causing interfacial initial debonding. The body force method is used to formulate those problems as a system of singular integral equations where unknowns are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions. In order to compare the results with the previous solutions, tension problems of a fiber in a semi-infinite body are also considered. Then, generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated for various geometrical conditions with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed for pullout problems.     

Numerical study on the dynamics of a two-raft wave energy conversion device

This paper presents a dynamic analysis of a two-raft wave energy conversion device based on the three-dimensional wave radiation-diffraction method. The device consists of two hinged cylindrical rafts of elliptical cross section and a power take-off system at the joint. The effect of raft length, linear damping and spring coefficient in the power take off (PTO) system, axis ratio (ratio of minor axis to major axis of raft elliptical cross section) and raft radius of gyration on wave energy capture factor has been investigated in frequency domain, while the effects of a nonlinear Coulomb power take-off, raft radius of gyration and latching control have been studied in time domain. The difference in the performance of a raft-typed device obtained using a linear damping and a Coulomb damping is also illustrated.     

Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

致密砂岩垂直裂缝井CO2混相驱试井模型研究

向地层注入CO2可以有效地提高致密砂岩原油采收率,常规的试井解释数学模型不能满足致密砂岩无限导流垂直裂缝井CO2混相驱试井解释的需求．因此,基于渗流力学基本原理建立考虑应力敏感影响的无限导流垂直裂缝井CO2混相驱试井解释数学模型,利用Laplace变换、摄动变换和Stehfest数值反演的方法进行求解,编程绘制典型特征曲线并进行敏感性分析．研究表明：该模型典型特征曲线共划分为八个流动阶段．由于应力敏感效应的影响,径向流阶段内、外区压力导数曲线不再是0.5和0.5M13水平线,而是呈“上翘”的曲线,并且应力敏感系数越大,曲线“上翘”越明显;混相区压力导数曲线符合幂律型变化指数规律且高于(1-n)/(3-n)斜率直线;内区、混相区半径和M12的变化都会使得外区压力曲线升高;通过该模型可以有效地对致密砂岩压裂井CO2混相驱试井资料进行解释．     

Heat transfer experiments in rotating boundary layer flow

The influence of Coriolis force on heat transfer in a rotating transitional boundary layer has been experimentally investigated. The experiments have been conducted for local Görtler numbers up to 150. Heat transfer measurements have been performed for a flat plate with nearly uniform heat flux applied to the surface, where the temperature was measured by the thermochromic liquid crystal method. The results indicate that heat transfer is enhanced when Coriolis force acts towards the wall, i.e., on the pressure surface. The velocity measurements under equivalent conditions show that Coriolis instability induces counter-rotating longitudinal vortices which augment the lateral transport of the fluid on the pressure surface. On the other hand, the heat transfer on the suction surface remains at the same level as compared to the case without system rotation. As a consequence, the heat transfer coefficient on the pressure surface is 1.8 times higher than that measured on the suction surface when averaged over the measured surface.     

Description of local dilatancy and local rotation of granular assemblies by microstretch modeling

This study investigates the microstretch continuum modeling of granular assemblies while accounting for both the dilatant and rotational degrees of freedom of a macroelement. By introducing the solid volume fraction and the gyration radius of a granular system, the balance equations of the microstretch continuum are transformed into a new formulation of evolution equations comprising six variables: the solid volume fraction, the gyration radius, the velocity field, the averaged angular velocity, the rate of gyration radius, and the internal energy. The bulk microinertia density, the averaged angular velocity, and the microgyration tensor at a macroscopic point are obtained in terms of discrete physical quantities. The bulk part and the rotational part of the microgyration tensor are proposed as the two indices to measure the local dilatancy and local rotation of granular assemblies. It is demonstrated in the numerical simulation that the two indices can be used to identify the shear band evolution in a granular system under a biaxial compression.     

Laminar jet contraction and velocity distribution in immiscible liquid-liquid systems

The flow behavior of a Newtonian liquid jet injected vertically into an immiscible Newtonian liquid phase is analyzed. Boundary-layer type approximations are used to simplify the general equations, and an approximate momentum-integral type numerical solution is obtained. This solution predicts the velocity distribution in each phase and the jet radius. The effects on jet behavior of the five dimensionless groups needed to characterize the gravitational, interfacial tension and viscous forces are shown. In particular the importance of the continuous phase viscosity is demonstrated. Experimental measurements of jet radius confirm the essential features of the analysis and illustrate the shortcomings of the approximate solution.     

A note on the centrifugal scaling of horizontal,isothermal, liquid-gas flows without mass transfer

The use of rotation to simulate increased gravity in scale models of horizontal liquid-gas flows is examined. The influences of Coriolis forces and natural gravity in the model are seen to be small provided that high rotation rates are used, and large length scale-down factors can then be achieved. The modelling of compressibility and gas-viscosity effects, however, is not normally possible and these must therefore be small in the original flow.     

Flow field investigation in rotating rib-roughened channel by means of particle image velocimetry

The turbulent velocity field over the rib-roughened wall of an orthogonally rotating channel is investigated by means of two-dimensional particle image velocimetry (PIV). The flow direction is outward, with a bulk Reynolds number of 1.5 × 10⁴ and a rotation number ranging from 0.3 to 0.38. The measurements are obtained along the wall-normal/streamwise plane at mid-span. The PIV system rotates with the channel, allowing to measure directly the relative flow velocity with high spatial resolution. Coriolis forces affect the stability of the boundary layer and free shear layer. Due to the different levels of shear layer entrainment, the reattachment point is moved downstream (upstream) under stabilizing (destabilizing) rotation, with respect to the stationary case. Further increase in rotation number pushes further the reattachment point in stabilizing rotation, but does not change the recirculation length in destabilizing rotation. Turbulent activity is inhibited along the leading wall, both in the boundary layer and in the separated shear layer; the opposite is true along the trailing wall. Coriolis forces affect indirectly the production of turbulent kinetic energy via the Reynolds shear stresses and the mean shear. Two-point correlation is used to characterize the coherent motion of the separated shear layer. Destabilizing rotation is found to promote large-scale coherent motions and accordingly leads to larger integral length scales; on the other hand, the spanwise vortices created in the separating shear layer downstream of the rib are less organized and tend to be disrupted by the three-dimensional turbulence promoted by the rotation. The latter observation is consistent with the distributions of span-wise vortices detected in instantaneous flow realizations.     

Vortex intensification in convective cells

The intensification of single vortices in convective flows swirled by the Coriolis force is studied numerically. The initial disturbances, specified against the background of a steady cell, are coaxial with the cell flow and have various swirl directions, intensities, and dimensions. It is shown that the vortices are intensified no matter whether the direction of disturbing vortex rotation is co- or counter-directional with the Coriolis force. If the disturbance intensity is small as compared with that of the convective-cell flow, the growth of the azimuthal velocity circulation in the perturbing vortices depends linearly on their initial circulation. For such vortices, the energy increase is proportional to the characteristic vortex radius to the power –5/3.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 62–68. Original Russian Text Copyright © 2004 by Ivanov and Povarnitsyn.     

Steady-state axisymmetric flows of an incompressible fluid through rotating porous media with regard to the Coriolis force

Exact solutions to the problem of steady-state axisymmetric flow of an incompressible fluid through rotating rigid body with regard to the centrifugal and Coriolis forces are constructed. The case of the locally transversally isotropic porous skeleton and the quadratic resistance force in the law of flow is considered. Estimates of the practical applicability of the solutions obtained are given. An analysis of increase in the length of the trajectory of a liquid particle due to its deviation from the radial direction in the frame of reference connected with the skeleton is carried out. This is of interest for applications related to deep-bed filtration of suspensions.     

Multiphase flow of miscible liquids: jets and drops

Drops and jets of liquids that are miscible with the surrounding bulk liquid are present in many processes from cleaning surfaces with the aid of liquid soaps to the creation of biocompatible implants for drug delivery. Although the interactions of immiscible drops and jets show similarities to miscible systems, the small, transient interfacial tension associated with miscible systems create distinct outcomes such as intricate droplet shapes and breakup resistant jets. Experiments have been conducted to understand several basic multiphase flow problems involving miscible liquids. Using high-speed imaging of the morphological evolution of the flows, we have been able to show that these processes are controlled by interfacial tensions. Further multiphase flows include investigating miscible jets, which allow the creation of fibers from inelastic materials that are otherwise difficult to process due to capillary breakup. This work shows that stabilization from the diminishing interfacial tensions of the miscible jets allows various elongated morphologies to be formed.     

The effect of oblateness in the perturbed restricted three-body problem

In this paper the restricted three-body problem is generalized in the sense that the effects of oblateness of the three participating bodies as well as the small perturbations in the Coriolis and centrifugal forces are considered. The existence of equilibrium points, their linear stability and the periodic orbits around these points are studied under these effects. It is found that the positions of the collinear points and y-coordinate of the triangular points are not affected by the small perturbations in the Coriolis force. While x-coordinate of the triangular points is neither affected by the small perturbations in the Coriolis force nor the oblateness of the third body. Furthermore, the critical mass value and the elements of periodic orbits around the equilibrium points such as the semi-major and the semi-minor axes, the angular frequencies and corresponding periods may change by all the parameters of oblateness as well as the small perturbations in the Coriolis and centrifugal forces. This model could be applicable to send satellite or place telescope in stable regions in space.     

Radial Viscous Fingering in Case of Poorly Miscible Fluids

The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous one is investigated. A special case of poorly miscible fluids is considered when corresponding dimensionless criteria—capillary and Peclet numbers—both tend to infinity. Brinkman model which additionally takes into account small viscous forces in a plane of the cell is used to describe the displacement process. Linear analysis shows a stabilizing effect of viscous forces and reveals a geometrical similarity criterion, namely the ratio of the interface’s radius to the gap between the cell’s plates. The displacement patterns, obtained numerically under Brinkman model, are very sensitive to the discovered criterion. The comparison with available experimental data is acceptable.     

The effect of mechanical and thermal anisotropy on the stability of gravity driven convection in rotating porous media in the presence of thermal non-equilibrium

We investigate Rayleigh–Benard convection in a porous layer subjected to gravitational and Coriolis body forces, when the fluid and solid phases are not in local thermodynamic equilibrium. The Darcy model (extended to include Coriolis effects and anisotropic permeability) is used to describe the flow, whilst the two-equation model is used for the energy equation (for the solid and fluid phases separately). The linear stability theory is used to evaluate the critical Rayleigh number for the onset of convection and the effect of both thermal and mechanical anisotropy on the critical Rayleigh number is discussed.