Two-phase flow in heterogeneous porous media: The method of large-scale averaging

The analysis of two-phase flow in porous media begins with the Stokes equations and an appropriate set of boundary conditions. Local volume averaging can then be used to produce the well known extension of Darcy's law for two-phase flow. In addition, a method of closure exists that can be used to predict the individual permeability tensors for each phase. For a heterogeneous porous medium, the local volume average closure problem becomes exceedingly complex and an alternate theoretical resolution of the problem is necessary. This is provided by the method of large-scale averaging which is used to average the Darcy-scale equations over a region that is large compared to the length scale of the heterogeneities. In this paper we present the derivation of the large-scale averaged continuity and momentum equations, and we develop a method of closure that can be used to predict the large-scale permeability tensors and the large-scale capillary pressure. The closure problem is limited by the principle of local mechanical equilibrium. This means that the local fluid distribution is determined by capillary pressure-saturation relations and is not constrained by the solution of an evolutionary transport equation. Special attention is given to the fact that both fluids can be trapped in regions where the saturation is equal to the irreducible saturation, in addition to being trapped in regions where the saturation is greater than the irreducible saturation. Theoretical results are given for stratified porous media and a two-dimensional model for a heterogeneous porous medium.     

Experimental study of ventilated cavity flow over a 3-D wall-mounted fence

Ventilated cavity flow over a fixed height 3-D wall-mounted fence is experimentally investigated in a cavitation tunnel for a range of free-stream conditions. The impact of 3-D effects on cavity topology is examined, along with the dependence of the cavitation number and drag on the volumetric flow rate coefficient, fence height based Froude number and vapour pressure based cavitation number. Three different flow regimes are identified throughout the range of cavitation numbers for a particular free-stream condition. Generally, the cavity has a typical re-entrant jet closure the intensity of which is found to increase linearly with increasing Froude number. This increase in re-entrant jet intensity causes an increase in drag with Froude number for constant volumetric flow rate coefficient. At low Froude numbers the closure mechanism transitions from a single to a split re-entrant jet. The parameters used to characterize the cavity topology show a linear dependence on Froude number irrespective of the closure mode. The cavity topology and drag are found to be independent of vapour pressure based cavitation number.     

Multiphase CFD-simulation of bubbly pipe flow: A code comparison

CFD simulations of dispersed bubbly flow on the scale of technical equipment become feasible within the Eulerian two-fluid framework of interpenetrating continua. For practical applications suitable closure relations are required which describe the interfacial exchange processes. Implementations of such closures have been provided in major commercial codes for years, but more recently there is a growing interest also in open source packages among which in particular OpenFOAM has become widely known.In the present work a set of closure relations suitable for adiabatic bubbly flow has been implemented in OpenFOAM. Selection of closure models has been based on previous experience with ANSYS-CFX. Great effort has been made to match all details of the models so that only residual differences due to different numerical procedures would be expected in the results. Unfortunately this was not the case and the value of one empirical model parameter had to be changed in order to obtain similar results. Under this provision the new open source implementation is validated and shown to be comparable to commercial codes.     

Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model

The possibility of predicting the exact long wave linear stability boundary via the two-fluid (TF) model for horizontal and inclined stratified two-phase flow is examined. The application of the TF model requires the introduction of empirical closure relations for the velocity profile shape factors and for the wave induced wall and interfacial shear stresses. The latter are recognized as the problematic closure laws. In order to explore the closure relations effects and to suggest the necessary modifications that can improve the stability predictions of the TF model, the results are compared with the exact long wave solution of the Orr–Sommerfeld equations for the two-plate geometry. It is demonstrated that with the shape factors corrections and the inclusion of wave induced stresses effects, the TF model is able to fully reproduce the exact long wave neutral stability curves. The wave induced shear stresses in phase with the wave slope, which give rise to the so called “sheltering force”, were found to have a remarkable destabilizing effect in many cases of horizontal and inclined flows. In such cases, the sheltering effects must be included in the TF model, otherwise the region of smooth stratified flow would be significantly over predicted. Based on the results of the exact analysis, a simple closure relation for the sheltering term in the TF model is provided.     

Modeling fluid-particle interaction in dilute-phase turbulent liquid-particle flow simulation

The present work examines the predictive capability of a two-fluid CFD model that is based on the kinetic theory of granular flow in simulating dilute-phase turbulent liquid-particle pipe flows in which the inter-stitial fluid effect on the particle fluctuating motion is significant.The impacts of employing different drag correlations and turbulence closure models to describe the fluid-particle interactions(i.e.drag force and long-range interaction)are examined at both the mean and fluctuating velocity levels.The model pre-dictions are validated using experimental data of turbulent liquid-particle flows in a vertical pipe at different particle Reynolds numbers(ReP > 400 and ReP < 400),which characterize the importance of the vortex shedding phenomenon in the fluid-phase turbulence modulation.The results indicate that(1)the fluctuating velocity level predictions at different ReP are highly sensitive to the drag correlation selec-tion and(2)different turbulence closure models must be employed to accurately describe the long-range fluid-particle interaction in each phase.In general,good agreement is found between the model predic-tions and the experimental data at both the mean and fluctuating velocity levels provided that appropriate combinations of the drag correlation and the turbulence closure model are selected depending on Rep.     

Modelling turbulent separated flow in the context of aerodynamic applications

In contrast to rapid advances in computing, numerical methods and visualisation, the predictive capabilities of statistical models of turbulence are limited and improve only slowly, despite much intensive research in the recent past. The intuitive nature of turbulence modelling, its strong reliance on calibration and validation, the extreme sensitivity of model performance to seemingly minor variations in modelling details and flow conditions, and the fact that the non-local dynamics of turbulence are not well captured by single-point closure, all conspire to make turbulence modelling an especially demanding component of CFD, but one that is crucially important for the correct prediction of complex flows. This applies in particular to separation from streamlined bodies, which is, from a computational point of view, the most challenging flow feature in aeronautical CFD.This paper reviews some aspects of the foundation and application of turbulence models to flows that relate to aeronautical practice, with particular emphasis being placed on turbulence-transport models at a closure level higher than that based on the Boussinesq-viscosity hypothesis. Following a review of basic modelling issues, including aspects of linear-eddy-viscosity two-equation modelling, some recent experience and current work on predicting separation from continuous surfaces with non-linear eddy-viscosity models and second-moment closure are reported. The predictive performance of several anisotropy-resolving models is illustrated by reference to computational solutions for a number of flows, both two- and three-dimensional, some compressible and others incompressible.     

Contribution to single-point closure Reynolds-stress modelling of inhomogeneous flow

This paper is concerned with recent advances in the development of near wall-normal-free Reynolds-stress models, whose single point closure formulation, based on the inhomogeneity direction concept, is completely independent of the distance from the wall, and of the normal to the wall direction. In the present approach the direction of the inhomogeneity unit vector is decoupled from the coefficient functions of the inhomogeneous terms. A study of the relative influence of the particular closures used for the rapid redistribution terms and for the turbulent diffusion is undertaken, through comparison with measurements, and with a baseline Reynolds-stress model (RSM) using geometric wall normals. It is shown that wall-normal-free rsms can be reformulated as a projection on a tensorial basis that includes the inhomogeneity direction unit vector, suggesting that the theory of the redistribution tensor closure should be revised by taking into account inhomogeneity effects in the tensorial integrity basis used for its representation. PACS 47.32.Fg; 47.85.Gj; 47.27.Eq     

Investigation of closure approximations for fiber orientation distribution in contracting turbulent flow

We have investigated the orientation state of a dilute fiber suspension flow in a planar contraction at high Reynolds numbers in turbulent flow. High speed imaging is used to directly measure the orientation distribution function at different downstream positions along the contraction centerline. The results from the direct measurement of the orientation distribution are used to evaluate the existing closure models. The results show that the fitted orthotropic and natural closure approximations give almost identical results with the best agreement to the orientation distribution in the contraction flow considered here.     

Plane problem of cavitation flow around an oblique cascade of profiles

The solution of the direct and inverse problems of the flow around a plane cascade of profiles with partial and supercavitation for closure of the caverns on one vortex singularity is presented. A method of designing an optimal cascade from the viewpoint of hydrodynamic quality is given on the basis of this solution.     

Hydraulic jumps in two-layer flow with a free surface

This paper presents a closure relation which describes hydraulic jumps in two-layer flows with a free surface over a flat bottom. This relation is derived from the momentum equations for each layer, which, subject to the condition of conservation of the total momentum and mass of each layer, become conservative in a sense. It is shown that use of this relation provides a reduction in the total energy at the jump.     

A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.     

First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow

This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper. To cite this article: N. Bellomo, V. Coscia, C. R. Mecanique 333 (2005).     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

The influence of interfacial pressure forces on the character of two-phase flow model equations

Equations for two-phase flow are developed where the interfacial pressure p_i is the closure variable. The assumption that p_i is constant leads to variations of the single pressure model with several aphysical properties. Use of more realistic pressure distributions, for flow about solid particles, produces a model displaying added mass and drag effects and having real characteristic roots.     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Predicting turbulent flow in a staggered tube bundle

This paper presents the results of calculations performed for the turbulent, incompressible flow around a staggered array of tubes for which carefully obtained experimental results are available as part of an established ERCOFTAC-IAHR test case. The Reynolds-averaged Navier–Stokes equations are solved using a pressure-based finite volume algorithm, using collocated cell vertex store on an unstructured and adaptive mesh of tetrahedra. Turbulence closure is obtained with a truncated form of a low-Reynolds number k– model developed by Yang and Shih. The computational domain covers all seven rows of tubes used in the experimental study and periodic flow is allowed to develop naturally. The results of the computations are surprisingly good and compare favourably with results obtained by others using a wide range of alternative k– models for a single cylinder with periodic inflow and outflow boundaries on structured meshes.     

Large-eddy simulation of stratified channel flow

An investigation of large-eddy simulation (LES) for turbulent channel flow with buoyancy effects was performed by solving the resolved incompressible Navier-Stokes equations under the Boussinesq approximation. The Smagorinsky eddy-viscosity model and Yoshizawa eddy-viscosity model were used to describe the unresolved subgrid scale (SGS) fluctuations respectively. After some numerical testing, the latter was further simplified so that it can be used in the dynamic model closure. A LES code was developed for parallel computations by using the parallel technique, and was run on the Dawn-1000 parallel computer. To demonstrate the viability and accuracy of the code, our results are compared with and found in good agreement with available LES results. The project supported by the National Natural Science Foundation of China and by the Youngster Funding of Academia Sinica