Important Flow Phenomena Research Articles

URANS simulation of the turbulent flow in tight lattice bundle

The flow structure in tight lattice is still of great interest to nuclear industry. An accurate prediction of flow parameter in subchannels of tight lattice is likable. Unsteady Reynolds averaged Navier Stokes (URANS) is a promising approach to achieve this goal. The implementation of URANS approach will be validated by comparing computational results with the experimental data of Krauss. In this paper, the turbulent flow with different Reynolds number (5000–215000) and different pitch-to-diameter(P/D) (1.005–1.2) are simulated with computational fluid dynamics (CFD) code CFX12. The effects of the Reynolds number and the bundle geometry (P/D) on wall shear stress, turbulent kinetic energy, turbulent mixing and large scale coherent structure in tight lattice are analyzed in details. It is hoped that the present work will contribute to the understanding of these important flow phenomena and facilitate the prediction and design of rod bundles.

Investigation of Fluid Flow Out of a Microcavity Using μ PIV

This article presents the results of an experimental and corresponding analytical investigation of fluid flow out of a shallow microcavity (dimple) due to surface shear. An experimental test rig was designed, developed, and used to demonstrate shear-driven fluid flow out of a microcavity. The experimental test rig consists of a flat steel belt driven against a microcavity filled with a fluid. Microparticle image velocimetry (μ PIV) was employed to visualize the shear-driven cavity flow and generate the streamline contours of the flow field. Two different sets of experiments were conducted. The first set examines the important factors that affect the flow field, and these include the cavity depth-to-width ratio (aspect ratio) and the speed of the flat belt. The second set of experiments was designed to observe the important fluid flow phenomena including the extraction and stagnation of the fluid above and below a critical cavity depth. A model was also developed using the computational fluid dynamic software COMSOL Multiphysics (1) to corroborate the experimental and analytical results. The results are in good agreement.

Evaluation of computational fluid dynamic methods for reactor safety analysis (ECORA)

The objective of the ECORA project is the evaluation of computational fluid dynamics (CFD) software for reactor safety applications, resulting in best practice guidelines (BPG) for an efficient use of CFD for reactor safety problems. The project schedule is as follows: (i) establishment of BPGs for use of CFD codes, for judgement of CFD calculations and for assessment of experimental data; (ii) assessment of CFD simulations for three-dimensional flows in LWR primary systems and containments; (iii) quality-controlled CFD simulations for selected UPTF and SETH PANDA test cases; and (iv) demonstration of CFD code customisation for PTS analysis by implementation and validation of improved turbulence and two-phase flow models. The project started in October 2001 and is for a period of 36 months. The project consortium consists of 12 partners combining thermal-hydraulic experts, code developers, safety experts and engineers from nuclear industry and research organizations. At mid-term, the following results were achieved: (i) BPGs are available for simulations of reactor safety relevant flows. These BPGs have found interest in the European projects FLOMIX-R, ASTAR and ITEM; (ii) important flow phenomena for PTS and containment flows have been identified; (iii) experimental data featuring these phenomena have been selected and described in a standardised manner suitable for simulation with CFD methods; (iii) surveys of existing CFD calculations and experimental data for containment and primary loop flows have been performed and documented; (iv) first results for simulations of PTS-relevant single-phase and two-phase flow cases are available. Documentation is available via the internet at http://domino.grs.de/ecora/ecora.nsf. The models developed within the project are implemented in industrial and commercial CFD software packages and are therefore accessible by industry and research institutions.

Simulating interfacial deformation by arbitrary Lagrangian–Eulerian approach

One of chief advantages of using the simplified arbitrary Lagrangian–Eulerian (Simplified ALE) method is that the time dependent interfacial problem of fluid layers, which is often treated as moving boundary problem, can be simulated with a technique of the rezoning and remeshing involved in the method. In this text, a numerical technique based on the simplified arbitrary Lagrangian–Eulerian method for simulating the behavior of time-dependent interfacial stratified fluids of viscoelastic nature is described to understand the numerical method. Particularly in dealing with viscoelastic fluid flow of an integral-type constitutive equation, the strain history is obtained by the memory integration method in a moving Lagrangian grid. Excess distortion of mesh elements due to fluid straining is overcome by the use of an arbitrary Lagrangian–Eulerian treatment of the continuous mesh rezoning. Specially in this text the scheme is applied to simulate an interfacial deformation of stratified fluids at model Y-junctions of two laminar layers. From the results of a benchmark calculation, the present scheme is found to show good agreement with a previous numerical work of the finite element method and predict some important flow phenomena that can appear in the flow geometry of viscoelastic fluids in experiments.

Development and validation of a three-dimensional morphological model

Computer modeling of sediment transport patterns is generally recognized as a valuable tool for understanding and predicting morphological developments. In practice, state-of-the-art computer models are one- or two-dimensional (depth-averaged) and have a limited ability to model many of the important three-dimensional flow phenomena found in nature. This paper presents the implementation and validation of sediment transport formulations within the proven DELFT3D three-dimensional (hydrostatic, free surface) flow solver. The paper briefly discusses the operation of the DELFT3D-FLOW module, presents the key features of the formulations used to model both suspended and bedload transport of noncohesive sediment, and describes the implemented morphological updating scheme. The modeling of the three-dimensional effects of waves is also discussed. Following the details of the implementation, the results of a number of validation studies are presented. The model is shown to perform well in several theoretical, laboratory, and real-life situations.

Isothermal slip flow over curved surfaces

It has long been recognised that the no-slip-boundary condition employed in the Navier–Stokes equations can only be applied when the Knudsen number, Kn⩽10 −3. If the Knudsen number is increased beyond this value, rarefaction effects start to influence the flow and the molecular collision frequency per unit area becomes too small to maintain the no-slip-boundary condition. Unfortunately, Maxwell's famous slip equation describing the velocity discontinuity at the wall is often misapplied when analysing flows over curved or rotating boundaries. In the present study, a generalised version of Maxwell's slip equation is used to investigate low Knudsen number isothermal flow over walls with substantial curvature. The generalised slip equation is written in terms of the tangential shear stress to overcome the limitations of the conventional slip-boundary treatment. The study considers a number of fundamental, but challenging, rarefied flow problems and demonstrates that Maxwell's conventional slip equation is unable to capture important flow phenomena over curved or rotating surfaces.

Studies on natural convection-induced flow and thermal behaviour inside electronic equipment cabinet model

In the present work, an important basic flow phenomenon, natural convection-induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the energy equation are solved based on the finite difference method. A generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behaviour inside an electronic equipment cabinet model, which is very difficult, if not impossible, to gather by experiment.

Optimal control of unsteady compressible viscous flows

AbstractThe control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.

Detection of fluctuating density gradient flow field in shock wave boundary layer interactions using laser Schlieren system

This paper demonstrates the feasibility of laser Schlieren system in studying unsteady shock motion in important flow phenomena such as shock wave/boundary layer interactions. Time-dependent voltage signals from multichannel measurements reveal important aspects of flow behavior such as amplitude and velocity of shock motion, frequency content, and cross-correlation functions in a very straightforward way. Tests were performed on a Halis axisymmetric configuration in a hypersonic flow with air and CO2.

Characterization of Single Phase Flows in Stirred Tanks via Computer Automated Radioactive Particle Tracking (CARPT)

Single phase flows in stirred tanks have been extensively characterized using different experimental techniques like Hot Wire Anemometry1, Laser Doppler Anemometry2, and Digital Particle Imaging Velocimetry3. None of these techniques however, show much promise for the interrogation of opaque multiphase flows. Hence, little or no information of the local fluid dynamics of multiphase flows in stirred tanks is available. Non-optical techniques like Computer Automated Radioactive Particle Tracking (CARPT) and Computed Tomography (CT) have been successfully applied to probe a variety of multiphase reactors4–5 such as bubble columns6–7, risers8 etc., over a range of dispersed phase holdups. CARPT provides the local fluid dynamic information such as velocities and the turbulence parameters throughout the system that is investigated. CT provides time averaged local dispersed phase holdup profiles in various planes of the entire reactor. In this study, it is proposed to extend these techniques to characterize gas-liquid flows in stirred tank reactors. As a first step, CARPT is implemented in characterization of single phase flows in stirred tanks. CARPT experiments have been performed with water at 150 rpm in a 0.20m cylindrical tank quipped with a six bladed Rushton turbine (0.067m dia) conforming to the standard Holland and Chapman9 configuration. The CARPT technique is shown to capture some of the important flow phenomena observed in such flows, like the two recirculating loops above and below the impeller and the dead zones at the bottom of the tank. Radial pumping numbers determined by CARPT (0.67 near the impeller tip) compare reasonably well with data reported in the literature. Comparison of the complete three dimensional mean velocity profiles from CARPT with similar PIV, LDA and other data reported in the literature reveals that CARPT captures the right order of magnitude of the radial and the tangential velocities. Comparisons of the fluctuating velocity components, like the root mean squared (rms) velocity and the turbulent kinetic energy, suggest that the CARPT experiments were limited by large tracer particle size (dp = 2.3 mm) from sampling the high frequency fluctuations of the fluid. In addition, the three dimensional profiles of the components of the Reynolds stress tensor are measured. The detailed comparisons, even with the large tracer particle, indicate that CARPT measurements capture all the important qualitative features of the flow and quantitatively capture the right order of magnitude of the mean flow parameters. The quantitative comparisons suggest that the current size of the tracer particle restricts it from responding completely to the fluid phase fluctuations. Some Lagrangian measures of the fluid dynamics like the ‘Sojourn’ time distributions (STDs) in different zones of the reactor, Circulation Time Distributions (CTDs), Particle Return Maps to specific planes, Poincarre sections and Hurst exponents are evaluated from the collected CARPT data.

A Lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT)

In this study, computer-automated radioactive particle tracking (CARPT) is implemented for the first time in the characterization of flows in stirred tanks. Both the experimental technique and the experimental set-up are discussed. The CARPT technique is seen to capture qualitatively most of the important flow phenomena observed in stirred tank flows, like the two recirculating loops above and below the impeller and the dead zones at the bottom of the tank. The CARPT data is also used to extract “Sojourn” time distributions in different zones of the reactor. These distributions are used to partially quantify the observed dead and active zones in the tank.

An arbitrary Lagrangian–Eulerian approach for simulating stratified viscoelastic fluids

A numerical technique based on the simplified arbitrary Lagrangian–Eulerian (simplified ALE) method for simulating the behavior of time-dependent interfacial stratified fluids is described. From the calculation of an integral-type constitutive equation, the strain history is obtained by the memory integration method in a moving Lagrangian grid. Excess distortion of mesh elements due to fluid straining is overcome by the use of an arbitrary Lagrangian–Eulerian treatment of the continuous mesh re-zoning. The scheme is applied to simulate an interfacial deformation of stratified fluids at the Y-junction of two laminar layers. From results of a benchmark calculation, the present scheme is found to show good agreement with previous numerical works of pure viscous and shear-thinning fluids. Moreover, the present results predict some important flow phenomena that can appear in the flow geometry of viscoelastic fluids.

Ecoulement instationnaire dans un diffuseur aubé d'une pompe centrifuge

This paper describes experimental and computational work to examine the unsteady flow field in the vaned diffuser of a medium specific speed pump. The aim of this project is to verify a commercialy available Navier-Stokes program with a k-E turbulence model and to improve our understanding of the complex unsteady three-dimensional flow field associated with the interaction between a pump impeller and its vaned diffuser. The paper provides the results of experiments carried out using Laser Doppler Anemometry (LDA), in which time-resolved details of the unsteady flow field in a vaned diffuser of a medium specific speed pump have been obtained as a function of the local position of the pump impeller blades. The static pressures were also measured at the hub and shroud side of the diffuser. The measurement results have been analysed to elucidate some interesting flow features observed in this typical pump diffuser. These include unsteady recirculation of the flow from the diffuser into the impeller at partload and flow separation in the diffuser channel. The unsteady flow simulation of a two dimensional diffuser showed the capabilities and the limits of a Navier Stokes program with k-E turbulence model. The comparisons of the simulation results with experimental data identify that this simple computational model with a time periodic inlet profile is able to show important flow phenomena. In terms of the flow field and pressure rise there is no substantial difference between the predictions of a steady simulation and the time-average of an unsteady simulation.

Effective parameters for multiphase flow in layered soils

This paper examines whether practical and useful effective parameters can be developed and used in the complex case of multiphase flow in heterogeneous porous formations. Strong nonlinearities in the governing flow equations make exact evaluation of effective parameters difficult, and several shortcomings in the published work to date are identified. In particular, an important multiphase flow phenomenon, fingering, has yet to be properly treated. This may be a severe limitation because, as demonstrated in two-dimensional laboratory experiments, the presence of heterogeneities will provide conditions suitable for the generation of fingers. The development of fingers introduces a new length scale into the hierarchy of heterogeneity scales exhibited by natural porous formations, the finger diameter. Experimentally, it is observed that finger development allows fluid to by-pass a significant fraction of the porous media, increasing the front velocity and reducing the degree of large-scale entrapment. As explicit consideration of fingering has yet to be included in the evaluation of effective parameters for multiphase flow, including unsaturated flow, such phenomena may not be accurately represented in the approaches developed thus far. The experimental observations suggest that when the scale of an oil plume is much larger than the heterogeneity length scale then a large-scale flow model based on the local flow equations should describe the overall flow, even in the presence of local fingering. Nevertheless, the challenging problem of deriving the appropriate effective properties remains.

Permanently electrostatic dissipative (ESD) property via polymer blending: Rheology and ESD property of blends of PETG/ESD polymer

AbstractRheological and electrical properties were studied on blends of a PETG polyester (cyclohexanedimethanol‐modified polyethylene terephthalate) and an inherently static dissipative high molecular weight polyether based copolymer, hereafter referred to as ESD polymer. Several important electrical properties and flow phenomena have been observed. First of all, the PETG blends could result in ESD protected material with excellent performance and a minimal effect on physical properties and melt processability. The rheological characterization reveals that the ESD polymer has a high melt viscosity even at a temperature more than 150 degrees above its melting temperature and that it exhibits pseudoplastic behavior. The PETG melt shows a near constant dynamic viscosity at a low frequency region. The viscosity of the ESD polymer and PETG melt exhibits a cross over at the temperature range from 200–220°C; the PETG melt is the lower viscosity component at low shear rate and the ESD polymer is the lower viscosity component at high shear rate. This appears to result in the existence of a small composition difference in the thickness direction of an injection‐molded ESD polymer/PETG part, with a greater fraction of the ESD polymer component in the skin section. This, in turn, could enhance the surface conductivity of the skin region of an injection‐molded part. © 1993 John Wiley & Sons, Inc.

Groundwater Flow in Low‐Permeability Environments

Certain geologic media are known to have small permeability; subsurface environments composed of these media and lacking well developed secondary permeability have groundwater flow sytems with many distinctive characteristics. Moreover, groundwater flow in these environments appears to influence the evolution of certain hydrologic, geologic, and geochemical systems, may affect the accumulation of pertroleum and ores, and probably has a role in the structural evolution of parts of the crust. Such environments are also important in the context of waste disposal. This review attempts to synthesize the diverse contributions of various disciplines to the problem of flow in low‐permeability environments. Problems hindering analysis are enumerated together with suggested approaches to overcoming them. A common thread running through the discussion is the significance of size‐ and time‐scale limitations of the ability to directly observe flow behavior and make measurements of parameters. These limitations have resulted in rather distinct small‐ and large‐scale approaches to the problem. The first part of the review considers experimental investigations of low‐permeability flow, including in situ testing; these are generally conducted on temporal and spatial scales which are relatively small compared with those of interest. Results from this work have provided increasingly detailed information about many aspects of the flow but leave certain questions unanswered. Recent advances in laboratory and in situ testing techniques have permitted measurements of permeability and storage properties in progressively “tighter” media and investigation of transient flow under these conditions. However, very large hydraulic gradients are still required for the tests; an observational gap exists for typical in situ gradients. The applicability of Darcy's law in this range is therefore untested, although claims of observed non‐Darcian behavior appear flawed. Two important nonhydraulic flow phenomena, osmosis and ultrafiltration, are experimentally well established in prepared clays but have been incompletely investigated, particularly in undisturbed geologic media. Small‐scale experimental results form much of the basis for analyses of flow in low‐permeability environments which occurs on scales of time and size too large to permit direct observation. Such large‐scale flow behavior is the focus of the second part of the review. Extrapolation of small‐scale experimental experience becomes an important and sometimes controversial problem in this context. In large flow systems under steady state conditions the regional permeability can sometimes be determined, but systems with transient flow are more difficult to analyze. The complexity of the problem is enhanced by the sensitivity of large‐scale flow to the effects of slow geologic processes. One‐dimensional studies have begun to elucidate how simple burial or exhumation can generate transient flow conditions by changing the state of stress and temperature and by burial metamorphism. Investigation of the more complex problem of the interaction of geologic processes and flow in two and three dimensions is just beginning. Because these transient flow analyses have largely been based on flow in experimental scale systems or in relatively permeable systems, deformation in response to effective stress changes is generally treated as linearly elastic; however, this treatment creates difficulties for the long periods of interest because viscoelastic deformation is probably significant. Also, large‐scale flow simulations in argillaceous environments generally have neglected osmosis and ultrafiltration, in part because extrapolation of laboratory experience with coupled flow to large scales under in situ conditions is controversial. Nevertheless, the effects are potentially quite important because the coupled flow might cause ultra long lived transient conditions. The difficulties associated with analysis are matched by those of characterizing hydrologic conditions in tight environments; measurements of hydraulic head and sampling of pore fluids have been done only rarely because of the practical difficulties involved. These problems are also discussed in the second part of this paper.

Study of Three-Dimensional Viscous Flows in an Axial Compressor Cascade Including Tip Leakage Effects Using a SIMPLE-Based Algorithm

A multisweep space-marching solver based on a modified version of the SIMPLE algorithm was employed to study the three-dimensional flow field through a linear cascade. Three cases were tested: one with moderate loading, one with high loading, and one with high loading and tip clearance. The results of the numerical simulation were compared with available experimental measurements, and the agreement between the two was found satisfactory. The numerical simulation provided insight into several important endwall flow phenomena such as the interaction between the leakage and passage vortices, the interaction between the leakage vortex and the wake, the effect of leakage flow and loading on losses and secondary kinetic energy, the suction side corner separation, and the blowing of this separation by the leakage flow.

Shelf circulation cells

Considerable insight has recently been gained into the dynamics of continental-shelf circulation through a simplification of the governing equations, resulting in a parabolic equation for the pressure field. Solutions of this equation appear to model realistically important flow phenomena, notably the effects of winds and coastal geography in setting up half-open coastal circulation cells, and an associated trapped pressure field. Circulation cells should be established mainly on the inner shelf, according to theory, i.e. within about 30 km of the coast, and should be important agents of mass exchange. In the present paper the theory of shelf circulation is reviewed with an emphasis on its most general predictions. Then the question is examined of how a considerable body of evidence on coastal sea-level variations in response to wind, longshore sea-level gradients, longshore and cross-shore currents can be interpreted in the theoretical framework.

Modelling Pore Structure By 2-D And 3-D Networks With ApplicationTo Sandstones

Abstract The Present investigation is a study of the properties of 2-dimensional (2-D) and 3-D network models of capillary tubes generalized for any pore size distribution. These properties include:the breakthrough condition subject to the step-by-step invasion of a non-wetting phase into an empty (evacuated) 2-D or 3-D "network;the accessibility of pores; andthe "pseudo' dead-end pore fractions, characteristic of the fractional amount of the non-conducting penetrated pore volume. It was found that for infinitely deep networks the breakthrough condition is defined by the coordination number Z and the dimensionality of the network through the relations PrZ =2 and PrZ = 1.5 for 2-D and 3-D networks, respectively. 2-D networks do not allow the existence of bicontinua and, as such, they cannot simulate realistically 2-phase flow phenomena. Generalized saturation plots for the accessibility of pores and the pseudo dead-end pore fractions have been established. It was found that the accessibility of pores and the pseudo dead-end pore fractions are determined by (i) the dimensionality of the network, (ii) the coordination numberof the network and (iii) the topology of pore interconnectedness at the microscopic level. The accessibility of pores found in the network analysis of the penetration process into 2-D and 3-D networks has been criticallytested by using:the experimentally known mercury porosimetry capillary pressure curves of two sandstone samples of known "complete" pore size distribution and the experimentally determined accessibility junctions; andthe saturation at breakthrough observed in mercury penetration experiments. It was established that:the accessibility of pores predicted by the network Analysis of 2-D and 3-D network models of randomly distributed capillary tubes does not agree quantitatively with the quantities obtained experimentally;when the length of a capillary is of the same order of magnitude as its diameter, the saturation predicted at breakthrough is about 30% to 80%;with bulges present in the middle of capillary segments a lower-order relationship between the volume and the entry diameter of the segments could be assumed. Fairly good simulations of the experimental capillary pressure curve and the accessibility of pores have been obtained in the case of 3-D networks by assuming that the volume of a capillary segment is proportional to its entry diameter. Introduction EQUILIBRIUM AND TRANSPORT PHENOMENA in a porous medium are strongly dependent on the pore structure of the medium. As the macroscopic properties of a porous medium depend on the pore structure, a thorough understanding of this is important for the purpose of correlating various processes that involve porous media, The customary pore structure parameters, such as the porosity, the hydraulic diameter and the pore-of-entry size distribution, are insufficient for the interpretation of some important static phenomena (i.e. capillary pressure curves) and flow phenomena (i.e. relative permeabilities) in porous media, Permeable porous media contain 3-D networksconsisting of capillary segments or pores of various sizes.

Determination of parameters in convected Maxwell model from linear viscoelastic parameters

AbstractOwing to its simplicity and general ability to correctly portray a number of important flow phenomena, the two‐parameter Maxwell model has been employed in a number of important engineering studies. The relation of this equation to linear viscoelasticity and to some molecular theories is considered. A new rule is developed which shows how the shear‐dependent relaxation time and viscosity of the Maxwell model can be determined from linear viscoelastic parameters. It is thus shown that the two‐parameter Maxwell model may be more general than earlier anticipated.