Simple Velocity Field Research Articles

Contaminant source characterization in a coastal aquifer influenced by tidal forces and density-driven flow

Contaminant source characterization (CSC) plays an important role in environmental forensics and pollution control. Past studies commonly solve the CSC problem in case studies where simple groundwater velocity fields (with e.g. parallel velocity vectors) prevail under steady state conditions. A few studies have addressed CSC in cases where the effect of heterogeneity or wells causes the velocity vectors to deviate from a parallel alignment. More complex transient velocity fields are yet to be addressed in groundwater CSC studies. One key example is coastal aquifers, where density-driven flow and the effect of oceanic forces (e.g. tides and waves) create complex transient velocity fields that lead to deformation of contaminant plumes and enhance mixing processes. The present paper aims to address this challenge by developing and validating a novel solution method for CSC in a coastal aquifer under the effect of tidal forces and density-driven flow. For this purpose, the study combines a numerical model of density-dependent flow and multiple-species solute transport, artificial neural networks, and a customized Kalman filtering technique, termed the ‘constrained restart dual ensemble Kalman filter’ (CRD-EnKF). In this approach, the time series of contaminant concentration downgradient of the source, and salinity concentrations in the transition zone between fresh and saline groundwater is employed for the estimation of contaminant source location and strength. We validated the proposed methodology by using a benchmark problem of a coastal aquifer with sloping beach and tide-induced pressure oscillation at the sea boundary.

Kinematic and Dynamic Conditions in Metal Rolling of Porous Materials

Mathematical modeling of plastic deformations in rolling consists in a consequent combination of the general energetic relationship in plasticity and the variation inequality expressed the principle of minimum of entire deformation energy. A real deformation state in a plastic zone beneath rolls and corresponding kinematic and dynamics conditions on the contact surface are considered as a limited one for the consequent approximate deformation states and are found out by the method of approximated approach. Any realization of this method on personal computers requires a rational construction of a kinematic-possible velocity field in the spatial domain on plastic flow. Using the ordinary propositions and a new assumptions the authors have constructed a simple kinematic-possible velocity field in the plastic zone beneath rolls. On the base of the consequent approach in which the general energetic relationship and the variation inequality are interrelated the authors have been able to find out the geometric, kinematic and dynamics characteristics of plastic deformation’s states in metal rolling.

Dynamo action in sliding plates of anisotropic electrical conductivity.

With materials of anisotropic electrical conductivity, it is possible to generate a dynamo with a simple velocity field, of the type precluded by Cowling's theorems with isotropic materials. Following a previous study by Ruderman and Ruzmaikin [M. S. Ruderman and A. A. Ruzmaikin, Magnetic field generation in an anisotropically conducting fluid, Geophys. Astrophys. Fluid Dyn. 28, 77 (1984)GAFDD30309-192910.1080/03091928408210135], who considered the dynamo effect induced by a uniform shear flow, we determine the conditions for the dynamo threshold when a solid plate is sliding over another one, both with anisotropic electrical conductivity. We obtain numerical solutions for a general class of anisotropy and obtain the conditions for the lowest magnetic Reynolds number, using a collocation Chebyshev method. In a particular geometry of anisotropy and wave number, we also derive an analytical solution, where the eigenvectors are just combinations of four exponential functions. An explicit analytical expression is obtained for the critical magnetic Reynolds number. Above the critical magnetic Reynolds number, we have also derived an analytical expression for the growth rate showing that this is a "very fast" dynamo, extrapolating on the "slow" and "fast" terminology introduced by Vainshtein and Zeldovich [S. I. Vainshtein and Y. B. Zeldovich, Reviews of topical problems: Origin of magnetic fields in astrophysics (turbulent "dynamo" mechanisms), Sov. Phys. Usp. 15, 159 (1972)SOPUAP0038-567010.1070/PU1972v015n02ABEH004960].

An analytical model of plate rolling force with a simple available velocity field and equal perimeter yield criterion

To analyze plate rolling force, a simple available velocity field is first proposed in this article. Based on the velocity field, the internal deformation energy rate and the friction energy rate a...

Artificial viscosity in comoving curvilinear coordinates: towards a differential geometrically consistent implicit advection scheme

AbstractWe propose a modification for the tensor of artificial viscosity employable for generally comoving, curvilinear grids. We present a strong conservation form for the equations of radiation hydrodynamics for studying nonlinear pulsations of stars. However, the modification we propose is of general mathematical nature. We study a differential geometrically consistent artificial viscosity analytically and visualize a comparison of our approach to previous implementations by applying it to a simple self-similar velocity field which has a direct application in stars as the fundamental mode of pulsation is radial. We first give a general introduction to artificial viscosity and motivate its application in numerical computations. We then show how a tensor of artificial viscosity has to be designed when going beyond common static Eulerian or Lagrangian comoving rectangular grids. We derive and state the modified equations which include metrical terms that adjust the isotropic (pressure) part of the tensor of artificial viscosity.

Unconstrained vector nonlinear dynamic shell formulation applied to Fluid Structure Interaction

Fluid Structure Interaction (FSI) is a well-developed subject and several authors constantly provide improvements in related solution processes. The aim of this paper is to present an improvement in the shell formulation regarding large displacement analysis applied to FSI problems, i.e., a new curved shell finite element based on positions and unconstrained vector mappings is coupled with a compressible 3D fluid flow Finite Element approach. This improvement is important when an initial simple fluid velocity field cannot replace embedded shell movements, or when the shell closure changes position in a way that large rotations are present. The proposed formulation does not use the concept of rotations, resulting in an algorithm that conserves linear and angular momentum for large rigid body displacements when using the well established Newmark time integrator. Other advantages of this formulation are the use of complete stress–strain relations and the possibility of solving thin or thick shells developing large displacements and small strains. Numerical examples are presented in order to validate the proposed shell formulation regarding FSI applications.

Limit analysis of hollow spheres or spheroids with Hill orthotropic matrix

Recent theoretical studies of the literature are concerned by the hollow sphere or spheroid (confocal) problems with orthotropic Hill type matrix. They have been developed in the framework of the limit analysis kinematical approach by using very simple trial velocity fields. The present Note provides, through numerical upper and lower bounds, a rigorous assessment of the approximate criteria derived in these theoretical works. To this end, existing static 3D codes for a von Mises matrix have been easily extended to the orthotropic case. Conversely, instead of the non-obvious extension of the existing kinematic codes, a new original mixed approach has been elaborated on the basis of the plane strain structure formulation earlier developed by F. Pastor (2007). Indeed, such a formulation does not need the expressions of the unit dissipated powers. Interestingly, it delivers a numerical code better conditioned and notably more rapid than the previous one, while preserving the rigorous upper bound character of the corresponding numerical results. The efficiency of the whole approach is first demonstrated through comparisons of the results to the analytical upper bounds of Benzerga and Besson (2001) or Monchiet et al. (2008) in the case of spherical voids in the Hill matrix. Moreover, we provide upper and lower bounds results for the hollow spheroid with the Hill matrix which are compared to those of Monchiet et al. (2008).

Hydrodynamic conditions induce changes in secretion level and glycosylation patterns of Von Willebrand factor (vWF) in endothelial cells

The effect of low-speed agitation on the level of secretion and glycosylation patterns of the Von Willebrand factor in endothelial cells cultured in 6-cm Petri dishes located in a rotating platform was studied. In this simple system, complex and non-intuitive velocity fields arise. As revealed by simple calculations of tangential velocities and CFD analysis, flow behavior strongly varies as a function of radial distance and rotational velocity. We found significant differences in both secretion level and glycosylation extent and completeness, as a result of relatively small changes in rotational speed. Results obtained support the hypothesis that differences in hydrodynamic conditions may induce important changes in the secretion and assembly of glycoproteins in mammalian cell cultures.

A numerical study of passive scalar evolution in peripheral regions

We study the effect of slip and no-slip wall boundaries on the decay rate of a passive scalar in a spatially smooth and random in time velocity field. Numerical simulations are carried out to verify the effect of the peripheral (near-wall) regions on the decay of the scalar variance. Using two kinematic flow models with simple velocity fields, we show that, in the case of slip boundaries, the passive scalar is characterized by an initial rapid stirring followed by an exponential decay of the scalar variance. In stark contrast, results for the case with no-slip boundaries show that, following an initial rapid stirring of the scalar within the bulk, there is an intermediate-time regime where the variance follows a power-law decay. This intermediate regime is established as a result of the trapping of the scalar in the peripheral regions near the no-slip walls. Finally, the behavior of the scalar variance switches to a final regime that is characterized by an exponential decay rate. The results presented here indicate that the recent ensemble-based theories regarding the evolution of a passive scalar in the peripheral regions correctly predict the main stages of the scalar evolution that arise in a single flow realization.

Design and simulation of the micromixer with chaotic advection in twisted microchannels.

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.

Petalling of plates under explosive and impact loading

Failure by petalling occurs when thin plates are struck by cylindro-conical projectiles. Similar deformation mode is produced by a localized explosion on a plate. In either case, high circumferential strains induced in the target material cause radial cracking and the subsequent rotation of the affected plate material resulting in a number of symmetric petals. A new analytical method of treating this problem is proposed by developing a simple and realistic velocity and displacement fields. The progressive tearing is quantified using the CTOD criterion while bending deformation of cylindrical petals is described by the propagating hinge line with decreasing local curvature. The above two modes are coupled through the local bent radius of the petal. Closed form solution is derived for the total energy absorbed by the system, the number of petals, and the final deformed shape of the plate as a function of plate flow stress, thickness, and parameters of the external loading. The present solution compares well with experimental results of Nurick and Radford (In: Reddy BD (editor) Recent developments in computational and applied mechanics. A volume in honour of John B. Martin. 1997: p. 276–301) and Landkof and Goldsmith (Int J Solids Struct 1993;21:245–66) as well as empirical equations published in the literature.

A simple approach to plane strain extrusion with dead metal zone using upper-bound theorem

This paper treats the upper-bound approach to the problem of rigid-plastic deformation in case where the configuration of the deformation zone is previously unknown. The plane strain forward extrusion process with the so-called dead metal zone is analysed by assuming a simple velocity field. The calculations are carried out for the material with or without strain hardening or strain rate sensitivity and for various reduction ratios. The numerical results show that the region of the dead metal zone becomes smaller with the increase in the reduction ratio. The calculated punch forces agree with the experimental ones fairly well. Furthermore, it is found that the dead metal zone becomes larger with increasing the strain hardening as well as the strain rate sensitivity of the material.

An upper bound analysis of the square-die extrusion of non-axisymmetric sections

A simple kinematically-admissible velocity field is proposed to determine the final-stage extrusion load and average length of the extruded products in the square die extrusion of non-axisymmetric bars from round billets. The proposed velocity field is applied to the square-die extrusion of regular polygonal-shaped bars, trochoidal gear-shaped bars and rectangular-shaped bars. The profile function of a rectangular is approximated by using a Fourier series. Experiments have been carried out with hard-solder billets at room temperature using various shaped dies. The theoretical predictions of the extrusion load are in good agreement with the experimental results and there is generally reasonable correlations of average length of the extruded products, between theory and experiment.

Upper-bound analysis of the rotary forging of a cylindrical billet

Rotary forging, an incremental forming processes, is a cost-effective forming method for the cold forging of intricate parts to net shape. The workpiece is gradually deformed between an upper conical die having orbital motion with an inclined rotating axis, and the lower die moving upwards. For the analysis of this forging process, a simple velocity field which can satisfy all of the velocity boundary conditions is proposed. From the derived velocity field the upper-bound force is determined by minimizing the total power consumption with respect to some chosen parameters, and velocity distribution is investigated also. Experiments are carried out with carbon steel (AISI1020, AISI1045) and aluminium (6061) and the results then compared with theoretical results. The theoretical predictions of forming force are shown to be in good correspondence with the experimental measurements. Therefore, this analysis seems to be available for the prediction of the forming force and to investigate the influence of the forming parameters on the design of the forging process.

Upper-bound analysis of square-die forward extrusion

The present study is the preliminary research for the derivation of the generalized velocity field in three-dimensional square-die forward extrusion. As a fundamental model, the square-die forward extrusion of circular-shaped bars from regular polygonal billets is chosen and a simple kinematically-admissible velocity field is proposed. From the proposed velocity field, the upper-bound extrusion load, the velocity distribution and the average length of the extruded billets are determined by minimizing the total power consumption with respect to chosen parameters. Experiments have been carried out with hard-solder billets at room temperature. The theoretical predictions of the extrusion load are in good agreement with the experimental results and there is also a reasonable agreement in the average extruded length between theory and experiment.

Modelling hot flat-rolling of components having curved profiles-part I. Deformation analysis

A complete mathematical model of the Variable Gap flat-Rolling (VGR) process for producing components with variable thickness under hot working conditions is presented. The model is composed of separate submodels for deformation, flow stress, roll force and temperature. Sub-modelling approach allows changes and new developments to be easily incorporated. A three-dimensional deformation analysis of the workpiece based on the upper bound theorem is carried out. A simple velocity field is proposed. To preserve the theoretical consistency, an equivalent coefficient of friction is adopted for roll force calculation. Furthermore, the basic assumption of rigid perfectly-plastic material is modified by introducing the concept of isotropic rate-dependency. Satisfactory results were obtained in spread, torque and force prediction.

Penetration of a rigid projectile into an elastic-plastic target of finite thickness

This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

Suppression of Dipping Noise and Multiples Using 3D Pre-Stack Time Migration

Conventional imaging of seismic data includes an approximate NMO and DMO prior to velocity analysis. The NMO and DMO imaging steps are approximate only in the sense that an approximate (simple) velocity field is used; the algorithms themselves are accurate. After velocity analysis, NMO is re-applied with the more detailed velocity field derived from the analyses. In the constant velocity case, DMO is almost independent of velocity and the iterative procedure described above plus post-stack migration yields an accurate image. The derived velocities may also be used for multiple suppression. Also, DMO itself may change the stacking velocities of dipping noise in such a way as to suppress the noise. An improved approach to velocity estimation and imaging is to apply the conventional approximate NMO and DMO and then also to apply an approximate zero-offset time migration to each common offset dataset prior to velocity analysis (3D MOVES). After velocity analysis, the NMO is re-applied and the data stacked. Post stack, either a residual migration or full diffraction plus full time or depth migration is applied. The pre-stack migration is either a constant velocity or single function v(z) algorithm. This is consistent with the NMO, DMO approach of accurate algorithms in an approximate velocity field. The algorithms are fast and can be inverted post stack to allow depth migration. The technique has been extensively used in 2D and 3D for imaging primaries and yielding accurate velocities. However, as with DMO, the derived velocity field may also be used for multiple suppression and the migration process may itself attenuate noise and multiples. For example, multiple diffractions may be focused and then attenuated in the stack process or with standard de-multiple methods. Alternatively, dipping noise and multiples may be migrated up dip and be located above the NMO mute pattern at middle and far offsets; the subsequent NMO, mute and stack remove the multiples from the data. In these applications, the migration process should be viewed as a transformation rather than an imaging tool, and the velocity used for migration need not be geologically correct, i.e. the velocity is a transformation parameter which is tuned to obtain the optimum noise suppression. Optimal imaging is obtained with residual, post-stack migration.

Numerical aspects of wave forces on an artificial island

Abstract The wave forces on an artificial island standing on the sea‐bed are investigated by the proposed hybrid method. A boundary integral equation is developed for the inner fluid domain encompassing the arbitrarily shaped island, while an eigenfunction expansion is used to represent a simple velocity field in the outer fluid domain. Applying the natural boundary condition on the matching surface, the wave force and moment on the wetted surface of the island are found according to the calculated velocity potentials. A gravity step circular dock is used as a test case to confirm the present computation. As a practical application of the present method, numerical results for an elliptical artificial island are presented.

Richardson's Barotropic Forecast: A Reappraisal

Abstract To elucidate his numerical technique and to examine the effectiveness of geostrophic initial winds, Lewis Fry Richardson carried out an idealized forecast using the linear shallow-water equations and simple analytical pressure and velocity fields. This barotropic forecast has been repeated and extended using a global numerical model, and the results are presented in this paper. Richardson's conclusions regarding the use of geostrophic winds as initial data are reconsidered. An analysis of Richardson's data into normal modes shows that almost 85% of the energy is accounted for by a single eigenmode, the gravest symmetric rotational Hough mode, which travels westward with a period of about five days. This five-day wave has been detected in analyses of stratospheric data. It is striking that the fields chosen by Richardson on considerations of smoothness should so closely resemble a natural oscillation of the atmosphere. The numerical model employed in this study uses an implicit differencing techni...