Abstract of Papers - JHR Volume 35,
1997
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ISSUE NO. 1.BOUNDARY FITTED GRID MODELS FOR TIDAL MOTIONS IN SINGAPORE COASTAL This paper describes the application of a 2D nested model in rectangular coordinates and an orthogonal boundary fitted grid (BFG) model to tidal motions in Singapore coastal waters. The basic mathematical model for shallow water waves in the BFG model is derived from the transformation of corresponding depthaveraged equations in rectangular coordinates. The curvilinear coordinate system is obtained from the solution of a grid generator based on the elliptic generation technique. The BFG model is applied to the Singapore coastal region and its surrounding waters with a complicated domain and internal island groups. The tidal flow behaviour including current circulation, time history of sea levels and currents as well as patterns of residual currents are investigated. The numerical results are successfully compared with the field measurements. NUMERICAL SIMULATION OF WINDINDUCED ENTRAINMENT IN A STABLY STRATIFIED
WATER BASIN This study uses a twodimensional eddy viscosity model to investigate the windinduced entertainment in a twolayer stably stratified water basin. By changing the background stratification and surface shear stress, the calculated entrainment coefficients E show that when Richardson number Ri* is less than a critical Richardson number Ric, entrainment law is in the form of E Y Ri*Ð1. When Ri* > Ric, molecular diffusion can not be neglected. The value of Ric is around the order of Pe1/2, where Pe is the Peclet number. Furthermore, three different mechanisms (upwelling, longitudinal dispersion and vertical mixing) are observed in the numerical simulation. By analysing the time scales of these mechanisms, the interaction among them can be explained. The interaction and the resulted entrainment coefficient are found to be dependent on the aspect ratio of stratified basin. THE PURGING OF SALINE WATER FROM RECTANGULAR AND TRAPEZOIDAL CAVITIES
BY AN OVERFLOW OF TURBULENT SWEET WATER The removal by turbulent convection of a denser, miscible liquid in an abrupt depression that forms a basin at the bottom of a watercourse by this flowing stream has been studied experimentally. Different cavity shapes were examined with various end wall slopes. The effect of these geometric features and the cavity aspect ratio can be summarised effectively by normalizing a nondimensional purging velocity with the square of the densimetric Froude number. OPTIMAL DESIGN OF WATER DISTRIBUTION NETWORKS The paper treats looped networks which have concentrated outflows or uniform outflow along the length of each pipe. An improved model is presented for optimal design of new or partially extended water distribution networks, which operate either by means of gravity or a pump system. The model is based on the method of linear programming and allows the determination of an optimal distribution of commercial diameters for each pipe in the network and the length of the pipes which correspond to these diameters. Also, it is possible to take into account the various functional situations characteristic found during exploitation. THREE-DIMENSIONAL TURBULENT BOUNDARY LAYERS: A REVIEW The nature of threedimensional turbulent boundary layers (3DTBL) are discussed with the intention of applying them to the problems encountered in hydraulic engineering. After introducing the basic concepts of 3DTBL, various crossflow and nearwall similarity models are described. A comparison between the flow situations commonly encountered in hydraulic engineering and in some other branches of fluid mechanics (which initially prompted the development of 3DTBL theories) is made to explore the possibilities of utilising the 3DTBL theories in hydraulic engineering. There appears to be numerous opportunities to fruitfully apply 3DTBL theories in hydraulic engineering. One such application is presented in a companion paper. MODELLING OF STORM WASHOFF OF SUSPENDED SOLIDS FROM IMPERVIOUS SURFACES A mathematical model of suspended solids discharge from impervious surfaces during storm events has been developed. The model continuously simulates two major processes of different time scales; solids buildup at impervious surfaces between two storm events, and solids washoff from the surfaces during storm events. Buildup is modelled using the Sartor and Boyd equation (21) in which the amount of solids available on the surface is an exponential function of antecedent dry weather period duration. The spatial distribution of solid particles over the street surface is also modelled, which is an innovation. The washoff process is divided into three subprocesses that are modelled consecutively. A kinematic wave model is used for overland flow modelling. The particle entrainment into suspension is estimated by two methods. In one, the rainfall and overland flow effects are not separated and the total shear stress is used to predict entrainment. In the other, the rainfall and overland flow effects are treated separately and then summed. An original equation was developed for this method. The model is applied on two small experimental catchments, one at MiljakovacBelgrade, Yugoslavia and the other in Lund, Sweden. The description and verification of the model are presented and discussed in the paper. COUPLED ANALYSIS OF FLUID TRANSIENTS AND STRUCTURAL DYNAMIC RESPONSES
OF A PIPELINE SYSTEM Four governing equations are derived to describe the fluid transients and induced structural responses of a fluidfilled pipe system. The equations include the coupling terms related through PoissonÕs coefficient, friction, and fluidconveying in the pipeline. The method of characteristics (for fluid transients) and finite element method (for structural analysis) are used. A feedbackloopiteration approach is adopted to solve the coupled problem. A numerical example problem is presented to investigate the fluidstructural interaction responses. The characteristics of a secondary pressure waves riding on the principal transient waves are presented. ISSUE NO.2.PRESSURE FLUCTUATIONS ON PLUNGE POOL FLOORS The paper describes the pressure fluctuation field on a plunge pool floor subjected to jet impingement. The data for both mean and fluctuating components is presented for a range of velocities, plunge length, plunge pool depths, types of outlet devices, and jet diameters. The data for circular jets are compared in detail with other data available for wide rectangular nappes and rectangular slot jets. The effect of the degree of break-up of the jet before it enters the basin and the effect of air entrainment in the plunge pool is investigated. An example is provided to demonstrate how the findings may be used in practice. MODÈLE TRIDIMENSIONNEL PAR ÉLÉMENTS FINIS POUR SIMULER LES ÉCOULEMENTS
SECONDAIRES: DÉVELOPPEMENT ET VALIDATION This paper presents the formulation of a 3-D finite element hydrodynamic model to simulate secondary currents and their damping in channel bends and flow around obstacles. An emphasis has been focused on the formulation of viscous terms that are responsible for the secondary flow development. Basic equations and associated hypothesis are also presented in this paper. Validation of the model was performed based on different examples. First of all, the model has correctly reproduced velocity profiles of turbulent flow. Secondly, flow recirculation generated by elements such as a groin placed across a flow or by channel bends was well predicted. The comparison between experimental and numerical results confirms the validity of the formulation and the reliability of the approach. SPACE-TIME CORRELATION STRUCTURES OF HORIZONTAL COHERENT VORTICES
IN COMPOUND OPEN-CHANNEL FLOWS BY USING PARTICLE-TRACKING VELOCIMETRY In compound open-channel flows, it is very important to clarify an interaction mechanism between the main-channel and flood-plains induced by coherent vortices, so-called the “intermittent upward secondary currents” and the “large-scale horizontal vortices”, as shown in Figure 1. In the present study, time-averaged structures of secondary currents were revealed experimentally by making use of a two-component fiber-optic Laser Doppler Anemometer (LDA). Next, a new quantitative visualization technique called the “Particle-Tracking Velocimetry (PTV)” was used to investigate evolutionary patterns of horizontal large-scale vortices, which are the ultimate interest in a shallow water flood-plain. By this technique, instantaneous velocity components in arbitrary horizontal plane were obtained at all grid points of laser-light-sheet (LLS) from continuous four images of one particle, and space-time correlation structures of coherent vortices between the main-channel and flood-plain were investigated then using a conditional sampling technique. A RACE-TRACK RECIRCULATING FLUME FOR COHESIVE SEDIMENT RESEARCH We investigate a procedure for carrying out experiments on the erosion of a deposited mud bed by a steady flow in a race-track recirculating flume. This is a large-scale flume 0.5 m wide consisting of two straight sections 16 m long connected by two circular bends. The currents are produced by a vertical disc pump. It is shown that experimental conditions producing uniform erosion over the whole surface of the mud bed are met when the bed is restricted in a limited straight part of the flume. Measurements of the flow kinematics by a Laser Doppler Anemometer performed in clear water confirm that the flow applies a quasi-uniform bottom shear stress over the bed. Stratification effects are suppressed in this facility due to the strong mixing of suspended sediment concentration by the disc pump. A theoretical analysis of stratification effects however indicates that they remain small as long as the depth-averaged concentration is below 13.5 g l-1. A procedure to determine quasi-instantaneous erosion rates from depth-averaged suspended sediment concentration is finally presented. COMPUTATION OF FLOW IN OPEN-CHANNEL TRANSITIONS The supercritical flow in open-channel transitions often produces discontinuities in the flow variables. Depending on the size, shape and kind of channels, the flow can generate normal/oblique shock waves, expansion waves, hydraulic jumps and sometimes complex wave patterns due to multiple reflection of the waves at the boundary and their subsequent interactions with one another. In the numerical simulation of these flows, uniform grid distribution may introduce detrimental effects in the prediction and resolution of the flow details. The use of the presently available numerical schemes to solve these problems on a uniformly spaced grid systems fail to resolve the characteristic flow features and hence do a poor job in simulating the flows. In this paper, MacCormack second-order accurate explicit predictor-corrector scheme is used to solve the two-dimensional depth averaged shallow water equations to numerically simulate the supercritical free-surface flows in open-channel transitions. However, instead of a fixed grid, an adaptive grid system which adjusts itself as the solution evolves is used for a better resolution of the flow properties. In the present approach, Rai and Anderson’s method based on grid speed is used for grid adaptation. In a flow with shock, best solutions are obtained when the coordinate axes are aligned along the shock. Rai and Anderson’s method to cluster the grids are found to fulfill this criteria and thus produces better quality solutions, as compared to those obtained with uniformly distributed grid with a specified number of grid points. RELAXATION OF PORE PRESSURE IN A SLENDER CORE OF A ROCKFILL DAM The relaxation of pore pressure in the core of a rockfill dam, that is caused by a rapid discharge of the water from the reservoir, is controlled by two different time scales. The time scale due to de-consolidation is irrelevant, whereas the time scale due to the displacement rate of the phreatic surface is equal to the ratio between the conductivity and the porosity. If the core is vertical and slender, the motion of the phreatic surface is governed by an ordinary first order differential equation. If the discharge is instantaneous, the equation is separable and has been solved. Experiments with a Hele Shaw cell show that the agreement between theory and experiment is not too good. The explanation is that the discharge of liquid from the reservoir in the Hele Shaw cell is not effectively instantaneous. The practical result implies that the relaxation time is approximately 1 year for a core of a real dam composed of soil whose height and width are 50 and 4 meters, respectively. SEDIMENT IN OSCILLATORY FLOWS OVER A PLANE BED It is well-known that the value of the nearbed sediment concentration peaks near the time of the passage of the wave crest, when the value of the wall stress reaches a maximum. But the presence of a second peak in sediment concentration near the time of flow reversal has also been observed in experiments. Using existing techniques for flow modelling of wave boundary layer and modelling of suspended sediment in combination with a new wall boundary condition for sediment the secondary peak has also been observed in numerical experiments. Evidence suggests that the second peak is caused by a break up in the boundary layer due to flow reversal leading to high diffusivities near the wall. THE EFFECT OF SUB-AQUEOUS DISPOSAL OF MINE TAILINGS IN STANDING WATERS Field observations provided the basis for a numerical model designed to quantify the vertical mass flux of material initially injected at the base of the water column in a small lake; a process called sub-aqueous disposal. Eddy diffusion estimation largely controlled the transport behaviour, highlighting the need for measurements of diffusion in deep strongly stratified environments. The model followed the contaminant development over 40 years and showed that (i) it is unlikely that any material can ever be completely disposed of over realistic scales and (ii) within the bounds limited by uncertainty in eddy diffusivity, turnover penetration and surface layer precipitation-driven flushing are the mechanisms most likely to have bearing on the contaminant distribution. ISSUE NO. 3,THREE-DIMENSIONAL FINITE ELEMENT MODEL TO SIMULATE SECONDARY FLOW:
DEVELOPMENT AND VALIDATION This paper presents the formulation of a 3D finite element hydrodynamic model to simulate secondary currents and their damping in channel bends and flow around obstacles. An emphasis has been focused on the formulation of viscous terms that are responsible for the secondary flow development. Basic equations and associated hypothesis are also presented in this paper. Validation of the model was performed based on different examples. First of all, the model has correctly reproduced velocity profiles of turbulent flow. Secondly, flow re-circulation generated by elements such as a groin placed across a flow or by channel bends was well predicted. The comparison between experimental and numerical results confirms the validity of the formulation and the reliability of the approach. (paper in French) A RACETRACK RE-CIRCULATING FLUME FOR COHESIVE SEDIMENT RESEARCH We investigate a procedure for carrying out experiments on the erosion of a deposited mud bed by a steady flow in a racetrack re-circulating flume. This is a largescale flume 0.5 m wide consisting of two straight sections 16 m long connected by two circular bends. The currents are produced by a vertical disc pump. It is shown that experimental conditions producing uniform erosion over the whole surface of the mud bed are met when the bed is restricted in a limited straight part of the flume. Measurements of the flow kinematics by a Laser Doppler Anemometer performed in clear water confirm that the flow applies a quasiuniform bottom shear stress over the bed. Stratification effects are suppressed in this facility due to the strong mixing of suspended sediment concentration by the disc pump. A theoretical analysis of stratification effects however indicates that they remain small as long as the depthaveraged concentration is below 13.5 g l-1. A procedure to determine quasiinstantaneous erosion rates from depthaveraged suspended sediment concentration is finally presented. A THEORETICAL MODEL OF FLOW OF AN INELASTIC FLUID THROUGH ISOTROPIC
ELASTIC POROUS PIPES A numerical solution of pulsatile flow of an inelastic fluid through porous isotropic elastic pipes is presented. An implicit difference method is used to solve the equations, and to determine the pressure and the flow rate. This study is considered as a step in modelling of flow in blood vessels, but it may also contribute to other important fields such as water desalination or gel filtration. (Paper in French) ON CHOICE OF TURBULENCE MODEL FOR PREDICTION OF FLOWS OVER RIVER BED
FORMS. A fully developed turbulent open channel flow with a bed consisting of a spaceperiodic array of triangular elements has been numerically simulated. The solution procedure is based on the pressurecorrection finite volume method with a collocated variable arrangement. Decoupling of the equations, inherent to the collated variable arrangement, is avoided by using wellknown Rhie and Chow interpolation technique. Reynolds stresses are approximated using ke and a full transport Reynoldsstress models of turbulence. Wall boundary condition takes into account wall roughness while the free surface is treated as a symmetry plane for all variables apart from the turbulence kinetic energy. Comparisons between prediction and the measurements indicate that the ke model of turbulence is capable of predicting the main features of the flow to the acceptable level of accuracy. LINEAR AND ANGULAR MOMENTUM CONSERVATION IN HYDRAULIC JUMP The present paper deals with the integral conservation of linear momentum and angular momentum in the stationary hydraulic jump in a wide rectangular channel. The flow is considered to be divided into a mainstream, that conveys the total liquid discharge, and a roller, in which no average mass transport occurs. Referring to the infinitely large case, a purely two dimensional motion is considered. The interface between the two flow regions is a streamline, corresponding to a stream function value equal to the total discharge per unit width. The present approach consists in satisfying the mechanical balances of mass, momentum and angular momentum, while no (large scale) constitutive relation is assumed for the turbulent motion of the liquid. Regarding the stress tensor, hydrostatic normal pressure distribution is assumed, while nothing is assumed regarding shear stresses, except that viscous stresses are negligible with respect to turbulent stresses. A paradox is put in evidence, that in the classical hydraulic jump (specific force conserving solution) angular momentum conservation is apparently not satisfied. Taking into account of integral balances not only in terms of linear horizontal momentum but also in linear vertical momentum and angular momentum the paradox is overcome. Under some simplified assumptions regarding uniform horizontal velocity distribution in the mainstream, and negligibility of horizontal momentum and angular momentum in the roller with respect to other terms, an analytical solution is obtained in terms of free surface profile, mainstream thickness and roller thickness. Average shear stresses acting on the mainstream by the roller and power losses for unit weight may be theoretically derived. Assuming as known the growth rate of the mainstream at the beginning of the jump, also the length of jump, here assumed identical to the length of the roller, may be determined, together with the volume of the roller, the volume of the mainstream and the volume of the whole stream between the sequent depths. THE EVOLUTION OF EQUATIONS FROM HYDRAULIC DATA, PART I: THEORY Even as hydroinformatics continues to elaborate more advanced operational tools, languages and environments for engineering and management practice, it necessarily also promotes a number of concepts and methodologies that are eminently applicable within the more traditional areas of hydraulic research. Among the many new possibilities thereby introduced, that of evolving equations from hydraulic data using evolutionary algorithms has a particularly wide range of applications. The present paper is in two parts, the first of which introduces the subject and outlines its theory, while the second is given over to four representative applications and to some of the most immediate lessons that may be drawn from these. The first of the applications is derived from a hydrologic model but provides equations with purely hydraulic interpretations. The second, taken from sediment transport studies, raises the question of ambiguity in the identification of “thresholds” in physical processes. It also provides a means for analysing the significance of variables and indicates the need, or otherwise, for introducing further variables. A third example, based upon physical observations of salt water intrusion in estuaries, introduces the application of the present methods to accelerating prediction processes, while the fourth example extends this kind of application to cover numerically generated data, in this case appertaining to the case of flow resistance in the presence of vegetation. CONVECTION OF PARTICLE THERMALS The motion induced by particle thermals (a cloud of heavy particles released into an otherwise stagnant fluid) has been investigated by a threedimensional numerical model. The model formulation is based on the governing equations for the conservation of mass, momentum and density excess, assuming the discrete particles can be represented by a continuous field of density difference with a specified settling velocity, and the Boussinesq approximation is valid. A mixing length model is used to represent the induced turbulence because of the existence of a welldefined length scale (the cloud size). A sensitivity analysis on the model parameters has been performed and suitable values of the parameters are identified and used in the subsequent model simulation. The model simulation results reveal an inverse relationship between the rate of spreading of the cloud and the settling velocity, and show that the frontal velocity approaches the settling velocity in the ultimate stage. These findings are supported by physical experiments. ISSUE NO. 4,LEE WAVES AND HYDRODYNAMICAL LOADS DUE TO THE MOTION OF A SUBMERGED
HORIZONTAL CIRCULAR CYLINDER IN A THREELAYER FLUID Laboratory experiments and analytical studies investigating the interaction of twodimensional, uniform stratified flow with a submerged horizontal circular cylinder are presented. Measurements were made of the interfacial waves formed behind the cylinder towed horizontally at constant speeds, and of the drag and lift forces exerted on the cylinder. An analytical linear model that describes the wave field and the associated wave induced drag force is formulated. In this model, the water is modeled as a uniform flow of three layers of inviscid and immiscible fluids. A solution is found for the case of the cylinder located in the upper layer. The experiments showed that large amplitude first mode internal waves are generated when the cylinder is towed at about one half of the long wave celerity of first mode waves, and that drag and lift forces change significantly with stratification. The analytical model demonstrates the role of a finite stratified layer. For the shorter waves it predicts wave lengths well, but it underestimates wave heights and drag. Better performance was obtained by introducing an effective cylinder radius factor. For the longer waves an inviscid model seems improper and the model is not applicable. The results are applied to the proposed submerged tube bridge across Høgsfjorden in Norway. THE EFFECT OF AN INTERMITTANT FLAPPING MOTION ON THE PROPERTIES OF
MERGING PLUMES Experiments with merging buoyant jets revealed the existence of an intermittent flapping motion in the flow trajectory. The flapping commences beyond the point where the initially axisymmetric buoyant jets merge to form a plane plume. The size and relative positions of largescale vortices on either boundary of the plane plume determine whether the flapping flow state occurs. The effect of the flapping on the short term timeaveraged flow properties was measured and the flapping was found to increase the spreading rate and also change the shape of the concentration fluctuation distribution in the plane plumes. The intermittent presence of flapping in plane plumes is shown to be the cause of widely accepted differences between plane and axisymmetric plumes. The new findings on the flapping behaviour were used to improve an integral model which describes merging buoyant jets. COUPLING OF A LAGRANGIAN MODEL WITH A CFD CODE: APPLICATION TO THE
NUMERICAL MODELLING OF THE TURBULENT DISPERSION OF DROPLETS IN A TURBULENT
PIPE FLOW A Lagrangian approach is used to quantify the dispersion of particles in turbulent flows. Particles are tracked in a turbulent field taking into account crossing trajectory effects by solving their equation of motion. Further the CFD Phoenics* [1] code allows to model the turbulence of the carrier phase in which the particles disperse: a (K-e) model supplemented with algebraic stress relations deduced from a second order closure scheme is used here. The coupled EulerianLagrangian model is then optimized by taking into account a spacetime random distribution for the turbulent scales. Droplets dispersion predictions are presented for the turbulent pipe flow experienced by Calabrese & Middleman [2], and the computational results agree well with their experimental results. * More information can be found on web site: http/www.cranfield.ac.uk/public/sme/cfd/phoenics/ PROPERTIES OF THE DEADZONE MODEL OF LONGITUDINAL DISPERSION IN RIVERS
The dead zone equations were solved with the use of the Laplace transform technics. The solution was a base to derive the three moments of the pollution concentration distribution in a river. They differ from the moments published so far, because they were calculated from the solution of the pure boundary problem. This approach is easier to apply in calculations of the pollution concentration distributions and it covers a wider range of cases when we deal with natural field data. Main features of the model equations were analysed from the point of view of the theory of dynamic systems. The transfer function was derived and analysed as well as the frequencyresponse function. The dispersion relation for the dead zone equations was also obtained and analysed for different parameters of the model. ENTROPY BASED DESIGN APPROACH OF THRESHOLD ALLUVIAL CHANNELS A new approach has been developed for designing the shape and dimensions of the cross section of a straight threshold channel based on the concepts of entropy and probability. A formula for the lateral distribution of transverse slopes, and hence the crosssectional bank profile, was derived by the entropymaximisation principle and the calculus of variations. The bank profile is a new type of simple parabolic curve. The results of numerical experiments based on the approach of boundary shear stress distribution support the conclusion that the entropybased channel bank profile is at threshold. Bank profile equations are coupled with an appropriate frictional relationship to obtain a new design method. Channel dimensions and bank profiles predicted by this method are compared with those given by other design methods. The predicted channel dimensions are in reasonable agreement with laboratory experimental data. TURBULENT FLOWS OVER SMOOTH ERODIBLE SAND BEDS IN FLUMES The characteristic flow parameters of an open channel flow with an erodible hydraulically smooth sand bed were investigated for sand grains at rest, and for the flow regime in which an intermittent transport occurs. The experimental results show the following: (1) The grains are only transported by sweeps. (2) The sediment transport is responsible for up to 30% of the wall shear velocity. (3) No noticeable drag reducing effect occurs. (4) At high intermittent sediment transport the sweep frequency was found to be constant over the water depth. (5) With increasing wall shear stress the intensity distribution of the sweeps becomes more homogeneous and the maxima smaller. All these results are discussed based on a quadrant analysis of the main features of the socalled coherent structures of turbulent flows. A TWO-COMPONENT ACOUSTIC VELOCITY PROFILER FOR USE IN TURBULENT OPENCHANNEL
FLOW The characteristics of an ultrasonic instrument, the bistatic acoustic Doppler velocity profiler (ADVP) are described. The bistatic system can measure profiles of two components of the instantaneous velocity vector with no restrictions on the flow conditions. Results of the bistatic ADVP measurements of water velocity and turbulence in uniform flow in laboratory open channels, were found to coincide well with the laws for mean velocity, variance and Reynold’s stress. This indicates that the turbulence scales are sufficiently resolved in the ADVP measurements. Twodimensional flow patterns derived from the ADVP measurements demonstrate the presence of coherent structures. The instrument was found to be a useful research tool for nonintrusive and accurate instantaneous profile measurements under turbulent flow conditions unaffected by water quality. ISSUE NO. 5EXPERIMENTAL STUDY OF STEADY AND UNSTEADY FREE SURFACE FLOWS WITH
WATER-CLAY MIXTURES The steady and unsteady free-surface flow of hyperconcentrated water-kaolinite clay mixtures is analysed experimentally. These mixtures exhibit non-Newtonian behaviour if volumetric concentrations of solid particles exceed about 10%. The viscosity-concentration correlations, determined by rotary viscometer, indicate that the Bingham model can be used to describe such fluids. Using the rheological parameters of this model, the water-clay laminar flow friction factors can be determined either by calculating the Reynolds and Hedstr”m numbers, or by applying the concept of the extended Reynolds number. A quantitative analysis of the unsteady dam-break type of the free-surface flow is presented, giving a comparison of flow depth profiles and propagation rates between the investigated mixtures and water. AIR-WATER FLOWS IN PARTIALLY-FILLED CONDUITS Supercritical open channel flows are characterised by a large amount of “white waters”. Although free-surface aeration was investigated for steep chutes, flow aeration down partially-filled pipes received little attention. A re-analysis of partially-filled pipe data (VOLKART 1982,1985) is presented. The results indicate that the air concentration and velocity distributions can be estimated by simple expressions. The study provides new information for the design of storm waterways, sewers and tunnel spillways where flow aeration may occur. HYDRAULICS OF TWO-LAYER ARRESTED WEDGE FLOWS An experimental and analytical study of the hydraulics of two layer exchange flows in and beyond the limit of arresting barotropic net flow is presented. These arrested wedge flows are a limiting case of the inviscid, one dimensional, two-layer theory. The two-layer equations are modified to include the effects of friction and flow nonuniformity. A boundary layer model, along with the resultant Coriolis coefficients, was used with the modified hydraulic theory to compare with laboratory experiments. NUMERICAL PREDICTION OF THREE-DIMENSIONAL MIXING IN A COMPOUND OPEN
CHANNEL A numerical model has been developed to simulate time-dependent turbulent flows in open channels, including the transport of dissolved materials. The turbulence closure is provided by two algebraic eddy viscosity models. This paper’s main focus is on the assessment of those two models’ predicting capabilities for an open channel with compound cross section. A three-dimensional turbulent flow field and the transport of a neutrally buoyant solute are modelled. The results of the simulation are compared with experimental data and with similar calculations obtained using more advanced turbulence models. Considerations are made regarding the choice of the appropriate Schmidt number for the modelling of turbulent mass transport, and the use of anisotropic eddy diffusivity to account for different mixing rates along the vertical and transverse directions. Conclusions are drawn regarding the accuracy of the two models and their advantages and drawbacks when compared with more advanced turbulence models. MODELLING DO CONDITIONS IN STREAMS USING LAGRANGIAN ADVECTION METHOD
Advection, dispersion, and kinetics govern the transport of biochemical oxygen demand and dissolved oxygen in streams. Analytical solutions of the governing equations are scarce; numerical methods are the tool commonly used to solve problems having arbitrary geometries and flows. However, the numerical solution of advection may produce numerical damping or oscillation. Some existing methods are therefore applicable only for advection-dominated flows, others have narrow discretization limits, or are computationally expensive. The simple method developed in this study is intended to relax these limitations. The method solves advection with a Lagrangian method and solves the diffusive and kinetics terms using an Eulerian method. The Lagrangian method uses a simple cubic spline interpolation that does not require the solution of additional transport equations. Analytical solutions and a convolution approach verified the accuracy of the method; the method permitted to obtain some new solutions for unsteady input and unsteady flow. The method was verified by successfully reproducing a set of field data. NUMERICAL AND EXPERIMENTAL WATER TRANSIENTS IN SEWER PIPES The paper deals with transient transcritical flow in closed sewer pipe. Among the various shock-capturing schemes used for solving hyperbolic systems of conservation laws, an upwind scheme is adopted in such a way that automatic description of hydraulic jumps and bores becomes possible by a steep variation of hydraulic variables over a few grid points. The Pavia Flux Predictor scheme (P.F.P.) was selected, because of its simplicity, robustness and physical consistency. To validate the numerical model, experiments were carried out for a steep slope circular pipe. An application to flush flows at sewer heads is also presented in a context of parsimonious water consumption. SIMULATION OF OIL SPILLS FROM UNDERWATER ACCIDENTS PART I: MODEL DEVELOPMENT
A three-dimensional comprehensive numerical model is developed to simulate the behaviour of buoyant oil jets that result from underwater accidents. The numerical model is developed based on a Lagrangian integral technique. The model can simulate the behaviour of oil in stratified or unstratified ocean environments. Both the shear induced entrainment and the forced entrainment are considered in the model. The presence of a multi-directional ambient current is considered. The fluid in the buoyant jet can be a liquid, gas or liquid/gas mixture, which is typical of many underwater oil-related accidents. The model formulation includes the diffusion and dissolution of oil from the jet to the ambient environment. This paper presents the model development including the governing equations and the numerical discretization. A companion paper presents the verification of the model and applications to several cases. MOVEMENTS OF A SPHERE ROLLING DOWN AN INCLINED PLANE Released from rest on an inclined smooth plane in a stationary fluid, a sphere accelerates along the plane under the influence of gravity and eventually reaches a terminal velocity. The variations of velocity with time and distance, the terminal velocity, the terminal distance (the practical distance required for a sphere from rest to its terminal velocity), are investigated through laboratory experiments and a theoretical analysis. The relationship of the drag coefficient and the Reynolds number for the moving sphere with its terminal velocity is obtained and compared with that in the free fall. The effect of proximity of sidewalls of the flume on the fluid drag acting on the steady movement of the sphere is evaluated. The terminal velocity and the terminal distance against the sediment number are presented in dimensionless graphs. Given bed inclination as well as the properties of the fluid and the sphere, the terminal velocity and the terminal distance can be determined directly from the graphs. The experiments of the steady movement for a sphere rolling down a rough inclined boundary are also presented. ICE-COVER INFLUENCE ON FLOW STRUCTURE OVER DUNES Laser-Doppler-velocimetry mappings of open-water and covered dune-bed flows show how cover presence and roughness influence overall channel resistance and flow structure, including turbulence quantities. The mappings show that skin friction along the upstream slope of dunes does not decrease, and may even increase initially, in response to cover presence and increasing cover roughness. Such an increase may be the immediate mechanism whereby an ice cover causes dunes to flatten. The mappings also show that dunes modify distributions of velocity and Reynolds stress from their flat-bed shapes to the extent that the two-layer hypothesis (which suggests ice-covered flows can be treated as a sandwich of two free-surface flows) for analysis of ice-covered flow is not accurate for dune-bed channels.
ISSUE NO. 6SPECIAL ISSUE BY SECTION III.3 FLUID PHENOMENA IN ENERGY EXCHANGES
NON-LINEAR EDDY-VISCOSITY MODELLING OF SEPARATED FLOWS The paper reviews some recent developments in the area of non-linear eddy-viscosity modelling and investigates the performance of several model variants when these are applied to flows with complex strain. The formulation of this type of model has been motivated by the desire to combine the advantageous numerical properties and economy of linear Boussinesq-viscosity models with the superior predictive performance of second-moment closure, which is mathematically complex and numerically challenging. The rationale, fundamental principles and inherent properties of non-linear stress-strain relationships are considered first in general terms, with particular emphasis being placed on the mechanisms by which normal-stress anisotropy and sensitivity to curvature strain are represented. This is followed by a review of several particular model forms and the principal elements of their derivation. The models are then applied to four two-dimensional flows featuring, inter alia, strong curvature, irrotational straining, separation from curved surfaces and transition. The computational results presented demonstrate that the models possess predictive characteristics which are qualitatively similar to those of second-moment closure. However, quantitative agreement between predictions and reality varies considerably among the models, and this reflects the strong reliance of the models on the quality of the closure approximations adopted and their sensitivity to the details of the calibration process. REFINED TURBULENCE MODELLING FOR POWER GENERATION INDUSTRY CFD applications in the context of power plants illustrate the detailed three-dimensional studies in complex geometries that are possible today, with a special emphasis on the necessity of solving the time-dependent equations. These routine simulations give a much more detailed representation of many flow configurations than was possible with scale models in the design stage of the plants, thus increasing their safety and life span. Aside from these global simulations conducted with standard models, use of Second Moment Closures is shown to better represent the effects of body forces, such as buoyancy and rotation, encountered in sub components of the plant. Finally Large Eddy Simulation is introduced on unstructured meshes and the related needs concerning fluid/structure coupling and unsteady thermal loading in plant components are described. DIRECT NUMERICAL SIMULATION OF TURBULENCE IN AN INTERNALLY HEATED
CONVECTIVE FLUID LAYER AND IMPLICATIONS FOR STATISTICAL MODELLING Direct numerical simulations (DNS) are reported for the convection in an internally heated convective fluid layer which is bounded by rigid isothermal horizontal walls at equal temperature. The simulations for a fluid Prandtl number of seven cover seven distinct internal Rayleigh numbers in the range $10^5 \leq Ra_I \leq 10^9$. From the numerical database the changes of convective patterns and dynamics for increasing $Ra_I$, i.e. increasing turbulence intensity, are analysed. To support the development and improvement of statistical turbulence models for this special type of convection, turbulence data for mean and fluctuating temperature and velocities are provided. For the simulation with $Ra_I=10^8$ budgets of turbulence kinetic energy $k$ and vertical turbulent heat flux $\overline{u_3'T'}$ are presented. In addition, closure assumptions commonly used in statistical turbulence models are tested against the DNS data. It is found that the turbulent diffusive transport of $k$ and $\overline{u_3'T'}$ is strongly underestimated by standard models. The modelling of the turbulent heat fluxes by a turbulent Prandtl number approach is totally inadequate for internally heated convection. Instead, a second moment closure for $\overline{u_i'T'}$ is required. ISOTHERMAL STUDY OF THE FLOW AT THE JUNCTION BETWEEN AN AUXILIARY
LINE AND PRIMARY CIRCUIT OF PRESSURISED WATER REACTORS This paper deals with an experimental and numerical study of an isothermal flow at the junction of a high Reynolds number piping system and both very small and zero flow-rate pipe. The motivation is to understand and model the hydraulic behaviour of various auxiliary lines connected to the primary circuit of Pressurised Water Reactors. Experimental data have been obtained on a hydraulic mock-up using flow visualisation method and particle image velocimetry (PIV). They shown an helicoidal flow extending along the auxiliary pipe. Numerical calculations performed with the 3D ESTET code are presented and contrast the performance between a k-epsilon eddy viscosity model and a second moment closure turbulence model. Coarse (100 000), medium (400 000) and fine (1 500 000) meshes were used to test the influence from mesh. The numerical results obtained with the second moment closure turbulence model and the finest mesh confirm the swirl flow structure into the dead leg observed on the mock-up. On the other hand the k-epsilon eddy viscosity model is not able to predict the vortex penetration along the auxiliary pipe. These results illustrate the necessity to use second moment closure turbulence model to simulate flows in piping system dead legs. MODELLING OF LMFBR FUEL PIN TEMPERATURE BEHAVIOR USING WATER This paper describes the possibilities for modeling of non-uniform temperature behavior around the fuel pins in reactors cooled by liquid metal using water. The temperature non-uniformities arise due to non-symmetric heat removal from the pin.The data on heat transfer to mercury, sodium-potassium alloy and water in compact pin bundles found in the State Scientific Center of Russian Federation “Institute of Physics & Power Engineering” are analyzed here. The principles of thermal similarity of fuel pins form the basis of the analysis mentioned. PASSIVE DECAY HEAT REMOVAL IN ADVANCED NUCLEAR REACTORS Passive safety systems are being considered in advanced reactor designs to provide inherent stability for the nuclear reactor and passive shutdown and to provide guaranteed removal of decay heat. The overall objective of this paper is to review the safety implications of this design trend and to provide a state-of-the-art commentary on related research. This paper compares different types of advanced decay heat removal systems and identifies typical key scenarios in which passive systems play an important preventative or mitigative role. The adequacy of the relevant experimental data-base, to aid the understanding of the essential physics and for code validation, is assessed. It is concluded that appropriate experimental programmes have been carried out by vendors for the purposes of design certification, but many of these data are not freely available. Further EU programmes which should add to the available data are now in progress. The current generation models/codes are also reviewed. The thermal-hydraulics codes for existing plant can be applied for predicting overall system behaviour in advanced plant, although these suffer from certain fundamental weaknesses e.g. in the modelling of thermal mixing. CFD codes are being increasingly used to overcome this short coming in modelling capability. These require further validation however, particularly for reactor safety applications where multi-phase flows are important. LARGE EDDY SIMULATIONS IN NUCLEAR REACTORS THERMAL-HYDRAULICS Nuclear industry requires detailed computations of thermal-hydraulic phenomena in different regions of nuclear reactors. It is interesting to know how Large Eddy Simulation method can be applied to the computation of turbulent flows inside a reactor vessel. The examples presented show that physical complex flows become accessible to the simulation: confined mixing layers, stratified shear flows, externally excited turbulent jets. In all cases, correct predictions were obtained for velocity and thermal fields statistics (mean values, mean standard deviations, Strouhal numbers,) and also for the dynamics of the flow (onset of instabilities, dynamics of vortices). Furthermore a better understanding of the vortex structures should make possible the active control of the flow (jet spreading rate, mixing enhancement) and develops better engineering applications. THERMAL PROPAGATION EFFECTS IN A VERTICAL TURBULENT FLOW BEHIND A
JET BLOCK - A BENCHMARK EXERCISE The IAHR Working Group on Advanced Nuclear Reactors Thermal Hydraulics has carried out a Benchmark exercise on thermal propagation effects in a vertical turbulent flow behind a jet block, with water and sodium as the working fluid. The jet block initiates a multi-jet flow, where all jets have the same velocity, and the central jet is heated. The main interest aims at the developing temperature field downstream. A total of 8 computational methods were applied to the Benchmark problem. They cover the adaptation of mesh grid and boundary conditions, the use of various differencing schemes for reducing numerical diffusion, adjustment of the turbulent Prandtl number, and the investigation of buoyancy effects within the turbulence model equations. Most of the predictions achieved by the applied computational methods come close to the experimental data when the turbulent Prandtl number is adjusted to give agreement with control results which were part of the issued Benchmark problem description. As one of the important findings, however, it turned out that this tuning of the turbulent Prandtl number can be dispensed with by upgrading the computational methods with the transport equations of turbulent heat flux. |