Erosion in conical diffusers in particulate-laden cavitating flow

This paper highlights the serious damage that can occur in diffusing sections of pipework in which a cavitating particulate-laden fluid is flowing. The combined effects of particle erosion and cavitation are shown to remove considerably more material than would be expected from summing the effects of the individual mechanisms. It is demonstrated that, to be sure of avoiding this accelerated surface erosion, the transition from a smaller flow section to a larger one needs to be an abrupt expansion. If pressure recovery is important, a possible design solution is proposed. In the case of swirling flow, the expansion again needs to be abrupt. Evidence was also obtained which showed that, by allowing air to be entrained into the low pressure region in the flow, the cavitation and the erosion can be substantially reduced.     

Mixing in Circular and Non-circular Jets in Crossflow

Coherent structures and mixing in the flow field of a jet in crossflow have been studied using computational (large eddy simulation) and experimental (particle image velocimetry and laser-induced fluorescence) techniques. The mean scalar fields and turbulence statistics as determined by both are compared for circular, elliptic, and square nozzles. For the latter configurations, effects of orientation are considered. The computations reveal that the distribution of a passive scalar in a cross-sectional plane can be single- or double-peaked, depending on the nozzle shape and orientation. A proper orthogonal decomposition of the transverse velocity indicates that coherent structures may be responsible for this phenomenon. Nozzles which have a single-peaked distribution have stronger modes in transverse direction. The global mixing performance is superior for these nozzle types. This is the case for the blunt square nozzle and for the elliptic nozzle with high aspect ratio. It is further demonstrated that the flow field contains large regions in which a passive scalar is transported up the mean gradient (counter-gradient transport) which implies failure of the gradient diffusion hypothesis.     

Transition process in a fluid layer in a rotating paraboloid in response to a sudden change in its angular velocity

The process of establishment of the rigid-body rotation state in a liquid layer in a rotating paraboloid upon a sudden increase in its angular velocity is studied theoretically and experimentally. The theoretical study is performed within the framework of linear shallow-water theory with account for the bottom Ekman friction. Analytical solutions describing the transition process are obtained and the dependence of the establishment time on the liquid depth and the radius of curvature of the paraboloid is investigated. It is shown that the effect of free surface deformation may lead to a significant increase in the establishment time. Good agreement with the results of special laboratory experiments is found.     

Turbulent transport in an inclined jet in crossflow

The present study experimentally investigates a turbulent jet in crossflow relevant to film cooling applications. The jet is inclined at 30°, and its mean velocity is the same as the crossflow. Magnetic resonance imaging is used to obtain the full three-dimensional velocity and concentration fields, whereas Reynolds stresses are obtained along selected planes by Particle Image Velocimetry. The critical role of the counter-rotating vortex pair in the mixing process is apparent from both velocity and concentration fields. The jet entrainment is not significantly higher than in an axisymmetric jet without crossflow, because the proximity of the wall inhibits the turbulent transport. Reynolds shear stresses correlate with velocity and concentration gradients, consistent with the fundamental assumptions of simple turbulence models. However the eddy viscosity is strongly anisotropic and non-homogeneous, being especially low along the leeward side of the jet close to injection. Turbulent diffusion acts to decouple mean velocity and concentration fields, as demonstrated by the drop in concentration flux within the streamtube issued from the hole. Volume-averaged turbulent diffusivity is calculated using a mass–flux balance across the streamtube emanating from the jet hole, and it is found to vary slowly in the streamwise direction. The data are compared with Reynolds-Averaged Navier–Stokes simulations with standard k − ε closure and an optimal turbulent Schmidt number. The computations underestimate the strength of the counter-rotating vortex pair, due to an overestimated eddy viscosity. On the other hand the entrainment is increasingly underpredicted downstream of injection. To capture the correct macroscopic trends, eddy viscosity and eddy diffusivity should vary spatially in different ways. Therefore a constant turbulent Schmidt number formulation is inadequate for this flow.     

Capillary effects in steady-state flow in heterogeneous cores

Effects of capillary heterogeneity at the macroscopic scale have previously been analyzed for static conditions or in the context of outflow end-effects. This paper presents a systematic study for the case of one-dimensional, steady-state flow, that complements recent work on transient displacement. We consider the saturation response to various forms of heterogeneity. Included are analytical results for certain model cases, some general results, and numerical solutions for variously correlated spatial variations. The sensitivity to process parameters, such as rate, heterogeneity length scale and correlation, is studied. Physical interpretations are offered and potential applications in the estimation of heterogeneity are discussed.     

Mean stress in a granular medium in dynamics

In this paper we propose to construct a mean stress tensor for a granular medium, valid in static and in dynamics, which takes into account the contact reactions and the body forces acting at the grain level. A simple analytical example shows that taking account of inertia forces is essential to insure the symmetry of the mean stress tensor in dynamics. Finally, numerical simulations illustrating this definition of the mean stress tensor are presented for a granular medium ensiled.     

Nonlinear waves in electromigration dispersion in a capillary

We construct exact solutions to an unusual nonlinear advection–diffusion equation arising in the study of Taylor–Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave ansatz. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

Advances in modeling of water in the unsaturated zone

This paper reviews recent advances in analytical and numerical solution of problems of water flow through rigid soils in the unsaturated zone. The Richards model remains the most widely accepted and fertile framework for water flow analyses. More general formulations are reserved for the analysis of problems involving macroporosity, thermal effects, and air pressure effects. Many exact and approximate solutions have been derived for particular boundary value problems of homogeneous soils using methods such as quasi-linear analysis, Green-Ampt analysis, perturbation, and the kinematic wave approximation. Numerical simulators have become bigger and more accurate due to improvements in the areas of nonlinear solution procedures, mass conservation, computational efficiency, and computer hardware. Problems of natural heterogeneity have been addressed primarily through application of various stochastic methods to the Richards model. The stochastic formulations generally refute the concept of simple equivalent homogeneous properties, but do themselves offer a certain limited potential for a predictive capability.     

Transport of radionuclides in isolated fractures in crystalline rocks

This paper presents a generalization of a computational method for the prediction of solute dispersion in fractured porous media. This method is specially useful for the prediction of subsurface flows in crystalline rocks. The model now includes a linear kinetics mechanism to represent the effects of sorption of radionuclides in the rock matrix. The method is improved in its accuracy and provides results useful for the assessment of radionuclide migration in high-level, radioactive waste repositories. Results including verification (analytical) and physical test simulations are given. These results provide a partial validation of the numerical model.     

On hysteresis in elasto-plasticity and in ferromagnetism

We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl–Ishlinski models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems.

We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model.     

Oscillations in two wells drilled in a confined aquifer

If two wells are connected to a confined aquifer and the water level in one of the wells is perturbed, damped oscillations in the wells might occur. A criterion in terms of nondimensional parameters is derived which tells when the damping is critical.     

Permanent Fronts in Two-Phase Flows in a Porous Medium

A family of exact solutions for a model of a one-dimensional horizontal flow of two immiscible, incompressible fluids in a porous medium, including the effects of capillary pressure, is obtained analytically by solving the governing singular parabolic nonlinear diffusion equation. Each solution has the form of a permanent front propagating with a constant velocity. It is shown that, for every propagation velocity, there exists a set of permanent fronts all of which are moving with this velocity in an inflowing wetting–outflowing non-wetting flow configuration. Global bifurcations of this set, with the front velocity as a bifurcation parameter, are investigated analytically and numerically in detail in the case when the permeabilities and the capillary pressure are linear functions of the wetting phase saturation. Main results for the nonlinear Brooks–Corey model are also presented. In both models three global bifurcations occur. By using a geometric dynamical system approach, the nonlinear stability of the permanent fronts is established analytically. Based on the permanent front solutions, an interpretation of the dynamics of an arbitrary front of finite extent in the model is given as follows. The instantaneous upstream (downstream) velocity of an arbitrary non-quasistationary front is equal to the velocity of a permanent front whose shape coincides up to two leading orders with the instantaneous shape of the non-quasistationary front at the upstream (respectively, downstream) location. The upstream and downstream locations of the front undergo instantaneous translations governed by modified nonsingular hyperbolic equations. The portion of the front in between these locations undergoes a diffusive redistribution governed by a nonsingular nonlinear parabolic diffusion equation. We have proposed a numerical approach based on a parabolic–hyperbolic domain decomposition for computing non-quasistationary fronts.     

Spatially localized states in Marangoni convection in binary mixtures

Two-dimensional Marangoni convection in binary mixtures is studied in periodic domains with large spatial period in the horizontal. For negative Soret coefficients convection may set in via growing oscillations which evolve into standing waves. With increasing amplitude these waves undergo a transition to traveling waves, and then to more complex waveforms. Out of this state emerge stable stationary spatially localized structures embedded in a background of small amplitude standing waves. The relation of these states to the time-independent spatially localized states that characterize the so-called pinning region is investigated by exploring the stability properties of the latter, and the associated instabilities are studied using direct numerical simulation in time.     

Genetic disorders in haematological practice in India

Haemoglobinopathies represent a significant national health burden in India. The distribution of specific disorders varies geographically and by community. Heterozygote frequencies of beta-thalassaemia range from 1 to 15%, resulting in an estimated 20 million carriers. HbS is mainly present in tribal and non-caste communities, with carrier prevalences of up to 40%. By comparison, alpha-thalassaemia carriers are found in both the caste and tribal communities, and can reach a frequency of >90% in the latter case. Community control of haemoglobinopathies relies mainly on out-reach education programmes and genetic counselling, with antenatal diagnosis offered in specific major centres. Only partial data are available on the prevalence of haemophilia, but it has been estimated that there are some 50,000 affected individuals nationwide, with an additional 1,500 new cases born each year. RFLP-based techniques have been established to detect mutations in the factor VIII and IX genes, enabling the limited introduction of carrier detection and antenatal diagnosis.     

Heating zone dynamics in in situ combustion

The integrodifferential equation of the quasisteady regime of a moving in situ combustion front is obtained and its exact solution is constructed in a particular case; the possibility of the heat generated at the combustion front being projected into the region ahead of the front is analyzed and the heating zone dynamics in the reservoir and the surrounding rock are investigated. In a number of studies of in situ combustion it is assumed that an increase in the water-air factor or, what amounts to the same thing, an increase in convection velocity in the reservoir leads to the total transfer of the heat into the region ahead of the combustion front [1–3]. In [3] the area of the heating zone ahead of the combustion front was calculated in accordance with the Marx-Longenheim model [4]. Below, on the basis of exact solutions of model problems it is shown that in the case of quasisteady Newtonian heat transfer between the surrounding medium, when the latter is assumed to be a thermal reservoir, i.e., maintain a constant temperature, this projection of heat is possible if the convection velocity exceeds the velocity of the combustion front. In the case of unsteady heat transfer in accordance with the Leverrier model there is no total projection of heat into the region in question; in the steady-state regime a limited heating zone, proportional in depth to the square of the difference of the convection and combustion front velocities, is formed ahead of the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–172, July–August, 1987.The author wishes to thank V. M. Entov for his valuable advice and useful discussions.     

Advance in Experimental Mechanics in Asia-2006

In order to offer an opening platform for researchers in Experimental Mechanics community from Asia and other regions to communicate their achievement, the Editorial Committee of Journal of Experimental Mechanics decided to publish an international series…