Single- and Dual-domain Models of Solute Transport in Alluvial Sediments: the Effects of Heterogeneity Structure and Spatial Scale

Fine-scale heterogeneity of alluvial aquifers controls solute transport in groundwater at the scales relevant for practical applications: the architecture of sedimentary structures might create preferential flow paths (PFPs) or hydraulic barriers, which affect the breakthrough curves (BTCs). Objective of this paper was the assessment of the relevance of single- and dual-domain models for different heterogeneity patterns and scale lengths in alluvial sediments. Three case studies have been analysed with a classical single-domain model (SDM) and with three dual-domain models (DDMs): a dual-porosity model (DPorM) and two dual-permeability models (DPerM), which differ for the presence or the absence of solute exchange between the two domains. The first case study includes numerical tracer tests in metre-scale blocks of alluvial sediments; the second is a laboratory experiment of tracer injection in a decimetre-scale column of homogeneous sand; the third is a field tracer test performed at hectometre scale at the Cape Cod site. The relevance of the solute exchange in the DDMs is analysed with the characteristic advection and exchange times and with the Péclet and Damköhler numbers. The SDM is satisfactory for alluvial sediments with unstructured heterogeneity. The uncoupled DPerM is shown to be a better approach than the DPorM in sediments with PFPs; in this case, the coupled DPerM does not improve significantly the results of the uncoupled DPerM. A minor difference between the results of the three DDMs is observed for sediments in which the non-Fickian behaviour is not clearly determined by the presence of PFPs.     

Comparison of mass transfer models for the numerical prediction of sheet cavitation around a hydrofoil

Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of methods. One strategy consists of using the RANS (Reynolds Averaged Navier Stokes) equations and an additional transport equation for the liquid volume fraction, where mass transfer rate due to cavitation is modelled by a mass transfer model. In this study, we compare three widespread mass transfer models available in literature for the prediction of sheet cavitation around a hydrofoil. These models share the common feature of employing empirical coefficients, to tune the models of condensation and evaporation processes, that can influence the accuracy and stability of the numerical predictions. In order to compare the different mass transfer models fairly and congruently, the empirical coefficients of the different models are first well tuned using an optimization strategy. The resulting well tuned mass transfer models are then compared considering the flow around the NACA66(MOD) and NACA009 hydrofoils. The numerical predictions based on the three different tuned mass transfer models are very close to each other and in agreement with the experimental data. Moreover, the optimization strategy seems to be stable and accurate, and could be extended to additional mass transfer models and further flow problems.     

Parametric data-based turbulence modelling for vortex dominated flows

Computational fluid dynamics simulations employing eddy-viscosity turbulence models remain the baseline numerical tool in the aerospace industry, mainly due to their numerical stability and computational efficiency. However, many industrially relevant cases require a level of accuracy that is not routinely achieved by global turbulence models. The simulation of leading-edge vortices shed at low aspect ratio wings is one such class of flows that remains a challenge for turbulence modelling. A local approach is proposed in which a parametrised eddy-viscosity turbulence model is calibrated using experimental results of configurations and flow conditions similar to the one being analysed. In this paper, the Spalart–Allmaras one-equation model is enhanced with additional source terms, which are exclusively active in the vortex field. An automatic optimisation procedure with experimental data as reference is then applied. The resulting optimised model improves the eddy viscosity distribution for a limited but relevant range of configurations and flow conditions.     

Gravity Effects on Fiber Dynamics in Wall Turbulence

The present study investigated gravity effects on the dynamical behavior of inertial fibers suspended in a vertical channel flow. Direct numerical simulations were performed to obtain the turbulent flow field and the fibers were modelled as prolate spheroidal point particles. For each of the four fiber classes, three different gravity configurations were considered: upward flow with gravity opposing, downward flow with aiding gravity, and channel flow in absence of gravity. Results for the fiber distribution and the translational and rotational fiber motion were reported. In the near-wall region, the presence of gravity resulted in an increased fiber density in the downward flow but a nearly uniform distribution of fibers in upward flow. However, the preferential clustering of fibers in near-wall low-speed streaks was unaffected by gravity. The mean wall-normal or drift velocity of the fibers was higher in the downward flow and lower in the upward flow as compared to the case with no gravity. The suppressed drift velocity in the upward flow resulted in a more uniform fiber distribution throughout the channel in contrast to the near-wall accumulation of fibers in the two other cases. Overall gravity turned out to have negligible effects on some of the statistics of the least inertial fibers whereas the inclusion of gravity had a strong impact for heavier fibers.     

Numerical study of gas-cyclone airflow: an investigation of turbulence modelling approaches

A numerical study of unsteady single-phase vortical flow inside a cyclone is presented. Two different geometric configurations have been considered, with the goal of assessing several different turbulence modelling approaches for this class of problem. The models investigated include three Reynolds-averaged Navier–Stokes models: a commonly used two-equation eddy-viscosity model, a differential Reynolds stress model (DRSM) and an eddy-viscosity model sensitised to rotational and curvature (RC) effects which was recently developed and implemented into a commercial CFD (computational fluid dynamics) code by the authors. Results were also obtained using large eddy simulation (LES). The computational results are analysed and compared with available experimental data. The RC-sensitised eddy-viscosity model shows significant improvement over the standard eddy-viscosity model. The RC-sensitised model, DRSM and LES model predictions of the mean flowfield are in good agreement with the experimental data. The results suggest that curvature- and rotation-sensitive eddy-viscosity models may provide a practical alternative to more computationally intensive approaches.     

Computation and experimental validation of N_{2}-CH_{4}-Ar mixture flows behind normal shock wave

Different vibration-dissociation-vibration coupling models have been used to compute the nonequilibrium N-CH-Ar mixture flow behind a normal shock wave. A three-temperature model was used and the diffuse nature of vibrational relaxation at high temperatures was accounted for. The numerical results obtained with the Treanor and Marrone model (preferential or non preferential) and the Park model of vibration-dissociation-vibration coupling are compared. These results show that the temperatures and the concentrations are mainly affected by the value of the characteristic temperature U in the preferential model of Marrone and Treanor. An assessment of the more realistic model was realized by comparing numerical results with shock tube experiments. The influence of argon addition on the nonequilibrium emission of CN behind the shock wave was also numerically studied and compared to experimental measurements. Received 1 September 1995 / Accepted 10 December 1996     

The effect of boundary curvature on the stress response of linear and branched polyethylenes in a contraction�Cexpansion flow

The effect of flow-boundary curvature on the principal stress difference (PSD) profiles observed through a contraction?Cexpansion (CE) slit flow is evaluated for three different polyethylenes exhibiting increasing levels of branching. Studies were performed using both experimental optical techniques and computational simulations, in the latter case to evaluate the ability of constitutive models to predict these complex flows. The materials were characterised using linear and extensional rheology, which were fitted to the multi-mode ROLIE-POLY and POM-POM models depending upon material branching. Three CE-slit geometries were used; with sharp corners, and with rounding equal to one quarter and one half of the slit length. These created a mixed, but primarily simple shear flow, with different levels of extension and shear depending upon the level of curvature. The PSD developed from an initial Newtonian profile to increasing levels of asymmetry between the inlet and the outlet flow as the level of material branching increased. The rounding was found to lead to the delocalisation of PSD within the flow and removal of the stress singularity from the corner of the CE-slit. It also led to a decrease in the pressure drop across the geometry and an ??opening out?? of features such as downstream stress fangs to create downstream ??crab-claws??. Matching between experiments and simulations for the time evolution of flow from start up for each material in the various geometries illustrated good agreement for both models.     

Unstructured finite volume discretization of two‐dimensional depth‐averaged shallow water equations with porosity

This paper deals with the numerical discretization of two‐dimensional depth‐averaged models with porosity. The equations solved by these models are similar to the classic shallow water equations, but include additional terms to account for the effect of small‐scale impervious obstructions which are not resolved by the numerical mesh because their size is smaller or similar to the average mesh size. These small‐scale obstructions diminish the available storage volume on a given region, reduce the effective cross section for the water to flow, and increase the head losses due to additional drag forces and turbulence. In shallow water models with porosity these effects are modelled introducing an effective porosity parameter in the mass and momentum conservation equations, and including an additional drag source term in the momentum equations. This paper presents and compares two different numerical discretizations for the two‐dimensional shallow water equations with porosity, both of them are high‐order schemes. The numerical schemes proposed are well‐balanced, in the sense that they preserve naturally the exact hydrostatic solution without the need of high‐order corrections in the source terms. At the same time they are able to deal accurately with regions of zero porosity, where the water cannot flow. Several numerical test cases are used in order to verify the properties of the discretization schemes proposed. Copyright © 2009 John Wiley & Sons, Ltd.     

Control of flow geometry using electromagnetic body forcing

This paper presents conceptual experiments and simulations aiming at controlling flow geometries. Such flow design is performed by driving electromagnetically a shallow layer of brine, the forcing being generated by a transverse electrical current and different combinations of permanent magnets placed underneath the brine supporting wall. It is shown how different basic flow characteristics can be obtained with a single pair of magnets, by varying the angle with the electrical current. These basic flows are proposed as potential building blocks for advanced and complex flows studies. Three typical flow structures are presented to illustrate these building blocks. The discussion is then extended to multi-scale geometry by using blocks of various sizes. The flow is analysed using complementary experiments and numerical simulations. A good agreement is found between the 3D simulations and the experiments for both velocity and acceleration fields, which allows a higher degree of confidence in designing and modelling such flows. As the control of the flow geometry is important for mixing, in particular at low Reynolds number, we also illustrate the different stirring properties of the electromagnetically forced flows by comparing visualisations of passive scalars. They reveal complementary mixing properties for each of the building blocks.     

Asymptotic Analysis of Solute Transport with Linear Nonequilibrium Sorption in Porous Media

We analysed the asymptotic behaviour of breakthrough curves (BTCs) obtained after a single pulse injection in a 1D flow domain. Five different types of solute transport with nonequilibrium sorption were considered. The properties of the porous medium were assumed to be spatially constant. For long times, the concentration at a fixed position in time was found to decay like exp(–t) where depends on both the transport parameters and the parameters describing the nonequilibrium process. The results from the asymptotic analysis were compared with 1D numerical transport calculations. For all cases examined a good agreement between numerical calculations and the asymptotic analysis was found. The results from the asymptotic analysis provide an alternative way to determine transport and sorption related parameters from BTCs. The derived relationships between and the model parameters are however only valid for large times. This requires that the very low concentrations need to be measured and not only the bulk mass, too. By either increasing or decreasing the velocity during BTC experiments additional asymptotic equations are obtained which can be used to determine the value of the model parameters. The results from the asymptotic analysis can also be used in standard inverse modelling techniques to either obtain good initial guesses or to reduce the parameter space. The fact that linear nonequilibrium processes decay like exp(–t) can be used to qualitatively evaluate observed BTCs. The asymptotic analysis can also be easily extended to a larger class of transport problems (e.g. transport of solutes with microbial decay) provided that the overall transport problem remains linear in the concentration.     

Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid

The VOF method is adopted for the finite element analysis of transient fluid flow with a free surface. In particular, an adaptation technique for generating an adaptive grid is incorporated to capture a higher resolution of the free surface configuration. An adaptive grid is created through the refinement and mergence of elements. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. Also, three techniques based on the VOF method are newly developed to increase the accuracy of the analysis, namely the filling pattern, advection treatment and free surface smoothing techniques. Using the proposed numerical techniques, radial flow with a point source and the collapse of a dam are analysed. The numerical results agree well with the theoretical solutions as well as with the experimental results. Through comparisons with the numerical results of several cases using different grids, the efficiency of the proposed technique is verified. © 1998 by John Wiley & Sons, Ltd.     

进化算法与确定性算法在优化控制问题中的收敛性对比

对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率．两种方法都与分散武优化策略-Nash对策进行了结合，并成功地应用于优化控制问题。计算模型采用绕NACA0012翼型的位流流场．区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场，使用4种不同的方法进行当地流场解的耦合，这些算法可以通过当地的流场解求得全局流场解。数值计算结果的对比表明．进化算法可以得到与共轭梯度法相同的计算结果．并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景。     

A numerical study of the turbulent flow around the stern of ship models

The present work is concerned with the numerical calculation of the turbulent flow field around the stern of ship models. The finite volume approximation is employed to solve the Reynolds equations in the physical domain using a body-fitted, locally orthogonal curvilinear co-ordinate system. The Reynolds stresses are modelled according to the standard k-ε turbulence model. Various numerical schemes (i.e. hybrid, skew upwind and central differencing) are examined and grid dependence tests have been performed to compare calculated with experimental results. Moreover, a direct solution of the momentum equations within the near-wall region is tried to avoid the disadvantages of the wall function approach. Comparisons between calculations and measurements are made for two ship models, i.e. the SSPA and HSVA model.     

Turbulent breaking of overturning gravity waves below a critical level

The interaction of an internal gravity wave with its evolving critical layer and the subsequent generation of turbulence by overturning waves are studied by three-dimensional numerical simulations. The simulation describes the flow of a stably stratified Boussinesq fluid between a bottom wavy surface and a top flat surface, both without friction and adiabatic. The amplitude of the surface wave amounts to about 0.03 of the layer depth. The horizontal flow velocity is negative near the lower surface, positive near the top surface with uniform shear and zero mean value. The bulk Richardson number is one. The flow over the wavy surface induces a standing gravity wave causing a critical layer at mid altitude. After a successful comparison of a two-dimensional version of the model with experimental observations (Thorpe [21]), results obtained with two different models of viscosity are discussed: a direct numerical simulation (DNS) with constant viscosity and a large-eddy simulation (LES) where the subgrid scales are modelled by a stability-dependent first-order closure. Both simulations are similar in the build-up of a primary overturning roll and show the expected early stage of the interaction between wave and critical level. Afterwards, the flows become nonlinear and evolve differently in both cases: the flow structure in the DNS consists of coherent smaller-scale secondary rolls with increasing vertical depth. On the other hand, in the LES the convectively unstable primary roll collapses into three-dimensional turbulence. The results show that convectively overturning regions are always formed but the details of breaking and the resulting structure of the mixed layer depend on the effective Reynolds number of the flow. With sufficient viscous damping, three-dimensional turbulent convective instabilities are more easily suppressed than two-dimensional laminar overturning.     

热喷干扰气体模型对飞行器气动特性影响分析

针对不同气体模型对高超声速飞行器喷流反作用控制系统(RCS)热喷干扰流场模拟的计算效率和准确性问题, 基于喷流燃气物理化学模型, 通过数值求解含化学反应源项的三维N-S方程, 建立了飞行器RCS热喷干扰流场数值模拟方法, 分别采用化学反应流、反应冻结流、二元异质流以及空气喷流四种气体模型开展了典型外形热喷干扰流场的数值模拟, 研究了不同气体模型对热喷干扰流场结构、飞行器气动力热特性的影响, 分析了不同马赫数、飞行高度下的变化规律. 研究表明: 化学反应流模型计算精度较高, 计算与风洞试验数据的吻合程度优于其他三种简化模型; 在本文的低空条件下, 采用简化模型进行热喷干扰流场数值模拟, 会低估分离区大小, 使飞行器气动力特性预测出现偏差, 同时也会低估表面热环境, 对防热系统设计不利, 随着马赫数增加, 简化模型对气动力热特性预估的误差进一步增大, 同时不同简化模型之间的差异也进一步增大; 飞行高度较高时, 模型之间的差异减小, 此时可采用简化模型进行计算以提高计算效率. 本文的研究结果可为飞行器热喷干扰流场数值模拟及喷流反作用控制系统设计提供参考.      

Numerical and experimental investigation of a serpentine inlet duct

This article presents a numerical and experimental investigation of the flow inside an ultra-compact, serpentine inlet duct. The numerical analysis used two flow solvers: FLUENT®, a commercial code, and UNS3D, an in-house code. The flow was modelled using the Reynolds-averaged Navier-Stokes equations. The turbulence effects were modelled by using the shear-stress transport k–ω model. The numerical investigation was compared against experimental data obtained in an open-circuit, low-speed wind tunnel in the Fluid Dynamics Laboratory at Texas A&M University. The numerical simulations and experimental testing were performed to reveal the separation points and the strong secondary flow phenomena within the inlet. UNS3D overpredicted the location of the first separation point by 9 mm and the location of the second separation point by 1 mm, while the area-averaged pressure loss coefficient was 5% higher than in the experiment. The numerical results of UNS3D agreed better with the experiment than those of FLUENT.     

Two-dimensional flow in a fractured medium

Transport processes within a liquid-filled fractured reservoir can be modelled using a double-diffusive mechanism in fracture and block. Then it is commonly assumed that the flow in the block is purely one-dimensional (e.g. vertical). Lateral flow within the block will, however, become significant at long times. Avdonin has given an analytic solution for the pressure response in an infinite fissure bounded by two homogeneous half-spaces, allowing vertical flow only in the blocks. We extend this solution to include horizontal flow in the blocks. There are significant qualitative differences between the two cases. In particular, we find that if fluid is injected at a constant rate into the fissure and horizontal flow in the blocks is allowed, then the long-time pressure response of the fissure/block assembly has the same character as that due to a line source in a homogeneous anisotropic porous medium.     

A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite

A 3-D constitutive model for polycrystalline shape memory alloys (SMAs), based on a modified phase transformation diagram, is presented. The model takes into account both direct conversion of austenite into detwinned martensite as well as the detwinning of self-accommodated martensite. This model is suitable for performing numerical simulations on SMA materials undergoing complex thermomechanical loading paths in stress–temperature space. The model is based on thermodynamic potentials and utilizes three internal variables to predict the phase transformation and detwinning of martensite in polycrystalline SMAs. Complementing the theoretical developments, experimental data are presented showing that the phase transformation temperatures for the self-accommodated martensite to austenite and detwinned martensite to austenite transformations are different. Determination of some of the SMA material parameters from such experimental data is also discussed. The paper concludes with several numerical examples of boundary value problems with complex thermomechanical loading paths which demonstrate the capabilities of the model.     

Numerical Approach of the Permeability of a Macroporous Bioceramic with Interconnected Spherical Pores

Manufacturing a hybrid bone substitute requires a dynamic culture of the cells preliminarily seeded in a scaffold through a flow of physiological fluid. The velocity, pressure, and the distribution of fluid flow in this kind of macroporous medium are the important keys. Because of the difficulties in determining these parameters by experiment, a numerical approach has been chosen. One of the primary step of this study consists in the determination of permeability K. In this article, two types of structure of macroporous bioceramics are concerned. One is the interconnected pore spheres arranged either simple cubic, body-centered cubic or face-centered cubic systems. The other is the interconnected pore spheres randomly arranged. Based on Darcy??s law, the permeability K was calculated for many cases (type, porosity) by simulating the fluid flow through a small representative volume. These results are compared with some previous models such as Ergun, Carman?CKozeny, Rumpf?CGupte, and Du Plessis. The limits of Darcy??s law and the above-mentioned models have been determined using numerical simulation. The result showed that the porous media with spherical interconnected pores of BCC systems can be used to replace a complex random system in a range of porosity from 0.71 to 0.76 (i.e., porosity of our scaffolds). This assumption is validated for a pressure gradient lower the 1,000?Pa m^?C1 and a simple polynomial relation linking permeability and porosity (0.71?C0.76) has been established.