Advances in Fluid Modeling and Turbulence Measurements

The following sections are included:

• PREFACE

• REVIEWERS LIST

• CONTENTS

There is a perception among the CFD community that turbulence modelling is approaching the end of the road and that large eddy simulation is set to become the dominant technique in the prediction of turbulent engineering flows. The present article examines facets of this perception. It reviews, in broad terms, the current status of both areas, highlighting strengths and weaknesses. It identifies bridges between the two, focusing especially on hybrid formulations and ways in which simulation can aid further developments in turbulence modelling.

The Three Gorges Project (TGP) on the Yangtze River is a largest multipurpose water conservancy project ever built in China as well as in the world. It will benefit mainly in flood control, power generation and navigation improvement. Due to the dam is high and discharge is large, a lot of hydraulic issues have to investigate. Such as hydraulic of the Yangtze River close at the TGP, energy dissipation of spillway flow, navigation hydraulics, river sedimentation, environmental and ecological hydraulic problems and so on. The Chinese government mobilized a great number of scientific and technical people from institutions and universities in whole nation to do research for a long time. The key hydraulic issues have been solved one by one.

This paper presents mainly hydraulic of structures. For example, they are effect of energy dissipater, hydraulic of the deep outlets, and some navigation hydraulic problems.

The shear stress distributions in open-channel flows with favorable pressure gradients are predicted by making use of the equation of motion and the continuity equation under the assumption that the ratio of the friction velocity to the maximum mainflow velocity is almost constant in the streamwise direction. The values of the predicted shear stress are smaller than those of uniform open-channel flows and also decrease with a decrease of the normalized pressure-gradient parameter. The predicted shear stress distributions were in a good agreement with experimental values which were obtained with a two-component laser Doppler anemometer (LDA).

Two-dimensional open-channel flow with a relatively long side concavity was investigated both numerically and experimentally. The purpose of side concavity structure is to supply amenity-oriented environments in medium-sized urban rivers. In the experiments a side concavity was installed on one side of a straight channel and water depth variation and surface flow pattern were measured. The numerical simulation was based on the CIP algorithm for the two-dimensional hyperbolic solver and two-dimensional variation of water surface elevation was calculated using a set of shallow water equations. It was shown that the calculated water depth variations agree fairly well with the experimental results by selecting an appropriate turbulent diffusion coefficient.

In a curved river with permeable obstacles like vegetation, it is conceivable that they make resistance to flow and influence 3-D flow structures including pressure-driven secondary flows. In this study, three-dimensional mean flow structures were measured in a curved open channel with various arrangements of cylindrical roughness elements. The secondary flow cell characteristic of curved channel was generated in the same manner as the smooth rectangular cases, but it was limited in the region outside the roughness area. The developing/decaying process of the secondary flow is almost similar in all cases including the case without roughness. In the case of submerged roughness elements, the secondary flow cell is generated over whole section through the roughness area and the spanwise deference of primary mean velocity becomes very small.

Besides the center-region cell (helical motion), a weaker counterrotating outer-bank cell is often observed in open-channel bends. It could play an important role in the outer bank erosion process because the near bank sediment transport is related to the flow structure. This outer-bank cell cannot be simulated with turbulence closures, such as the standard k-ε model, since they fail to generate the cross-stream turbulence anisotropy. This paper reports simulations of both circulation cells with a non-linear k-ε closure that compare reasonably well with two sets of experimental data.

It is important to consider the effects of secondary currents induced by stream line curvature to predict river channel processes such as the changes of river bed topography during floods. In view of the refinements of model proposed by Kalkwijk & De Vriend, the depth averaged 2-D flow equations including the development and attenuation of secondary currents along a stream line, which were considered by Ikeda et al. and Parker et al. analytically, are developed in a generalized curvilinear coordinate system. A depth averaged equation on the strength of secondary currents, which is derived based on the Engelund model, is transformed into a mathematical form in a generalized curvilinear coordinate. It is shown that the experiments by Hicks et al. can be reproduced well by using the model equations developed in this study.

The structure of open-channel flows is complicated due to the existence of the bottom boundary and free surface. Accurate prediction of the flow structure is important in the assessment of pollutant and sediment loads delivered in the open-channel. This paper presents tests of pressure-strain models and turbulent diffusion models in the Reynolds stress transport equations in the computation of open-channel flows. Numerical experiments include three diffusion models by Daly and Harlow¹, Hanjalic and Launder⁵, and Mellor and Herring¹⁰ and five pressure strain models by Launder, Reece, and Rodi⁹ with and without wall reflection terms, Jones and Musonge⁷, Speziale, Sarkar, and Gatski¹⁵, and Fu, Launder, and Tselepidakis³. Comparisons with experimental data indicate that the diffusion model by Mellor and Herring¹⁰ and the pressure-strain model by Speziale et al.¹⁵ reproduce the measured profile best.

Bulk eddy generation in a hydraulic jump is from the surface roller at the front face of the jump and it is considered as a periodic formation-advection process. A model for estimating the generation frequency of the surface roller is proposed and it is examined experimentally by analyzing the water surface fluctuation downstream of three weak hydraulic jumps based on the fact that the released large eddies may interact with the free surface downstream hence leaving their characteristic signatures. Power spectrum of the surface measurements in each case clearly shows that a band of approximately normal distributed energy centering at a particular frequency exists. The identified center frequencies are found to match the surface-roller formation-release frequencies estimated by the proposed model well.

Characteristics of the flows over a full-span rib in open channels are investigated using two different methods, i.e. an empirical model and a 3D computation. In 3D computations, linear and non-linear k-ε models are employed for the turbulence model. To predict the fundamental flow features with less CPU time than 3D computations, an empirical model is proposed. In the empirical model, the flow is divided into two layers and the basic equations are derived by vertically integrating the continuity and momentum equations in each layer. The results in the empirical model are examined through the comparison with the results in the laboratory test and 3D computations. It is shown that the empirical model is effective to elucidate the fundamental aspects of the phenomena.

The hydrodynamic force acting on a vertical thin-plate has been studied experimentally and numerically under conditions in which the flow is subcritical and the change of water surface is very small. The pressure acting on the upstream and downstream faces of the plate has been characterized and an experimental formula for the drag force has been proposed. Also, the effect of an eddy immediately upstream of the plate on the magnitude and distribution of the pressure has been discussed. The pressure magnitude and distribution on the plate has been calculated numerically by using the two-dimensional incompressible Navier-Stokes equation under simplified conditions, and the hydraulic condition for predicting the pressure has been shown.

Groins are used in curved channels against bank erosion and for maintenance of watercourses used for navigation. Recently groins are used for various purposes so that numerical analysis for the flow is one of useful and important method to estimate the effect of groin quantitatively. In this paper, we discuss the applicability of the 2-D numerical analysis and the 3-D analysis. This 2-D numerical model could represent the distribution of the water level and the depth-averaged velocity U except for the area behind groins. The 3-D computed value of the flow is improved, compared with the 2-D model. This 3-D model could explain the three-dimensional flow around the groin to a certain extent, however, dynamic force was not estimated adequately.

Local scour depth around attracting (120°) submerged spur-dikes was measured in the laboratory using electric resistance bed profiler with under flow condition. Geometry of scour holes and deposit locations are discussed herein. The data collected was sufficient to demonstrate the effects on scour depth of spur-dike length (b); spur-dike height (d) and flow depth (h). It was found that, both maximum scour depth and total scour area around the spur-dike were significantly influence by the length (b) and the height (d) of the spur-dike. However, it has no consistent correlation with the flow depth (h). In all cases the scour occurred in both upstream and downstream area, which means that bank erosion will be a problem under these conditions. Comparison between attracting and repelling (60°) spur-dikes has also been discussed with respect to scour ratios. There was no specific relation between scour ratio (S/d) and opening ratio (α) to predict the maximum scour depth.

A strait and a channel straitened by hydraulic structures in estuary are examples of constrictions in an oscillatory open channel flow. The constriction is a reach of sudden reduction in the channel cross section. The flow trough a constriction is usually complex and affected by the boundary geometry. In the case that the channel floor is movable, the bed form becomes complex because local scour and deposition are occurred. In this paper, flow through the constrictions, which constitute two plates with or without a footing set on the both sides of channel, is investigated experimentally. It is the objective of this paper to clarify the relation between the flow and the local scour. In experiments, bed level and velocity were measured and the flow structure was visualized in a cross section of flow. The results show that the dominant flow structure for the local scour in the case of plate with footing is not a horse-shoe vortex but a secondary flow.

The depth-averaged two-dimensional numerical model for simulating channelization processes has been developed and validated, Channelization processes are usually accompanied by changing boundary of flowing water due to bed-deformation and bank erosion. It may be necessary to treat the moving boundary accurately. In order to handle this issue, in the present model, the boundary fitted grid system according to the change in water-edge's line is employed. The model has been successfully applied to simulate several basic channelization processes such as widening in cross-section in a straight channel and a curved channel.

Mountain-river usually shows the steep slopes bed and consists of a sand-gravel mixture with a wide range of grain size, and also is locally crooked. In the present study, the calculations of three dimensional turbulent flow, sediment discharge with sand-gravel mixture and bed variation in the locally crooked river in mountain region, were conducted by means of standard k-ε model, bed load function and continuity equation of sand, respectively. Then, the suitable design of riprap bed protection with natural stones is considered from the result of the turbulence calculation and estimating the shear stress on the bed.

Undisturbed cohesive soil samples, collected from flood channel of the Yoshino River Shikoku Japan, were installed in a straight laboratory channel to investigate process of cohesive bank erosion. The cohesive bank erosion shapes were two types; near water surface and under water surface bank shape and their erosion process were different. At first, physical bank models of near water surface varying in shape were made. These experimental results showed that there was flow separation inside eroded bank of almost all the near water surface bank. A 2-D numerical model was developed to simulate the flow fields of these physical model experiments. The numerical model could reproduce the mean flow of the reverse flow area. Its accuracy is higher for smaller erosion length and angle, but there is some discrepancy for larger erosion length and angle. In the second step, successive physical bank models of the two types, which were similar to the 5.0 hours and equilibrium erosion stage, were made to understand their erosion mechanism. The experimental results showed that the flow properties of near water surface bank shape were different from those of the under water surface bank shape, which signify two different types of erosion mechanism of the two eroded banks.

As energy dissipation of overflow with low Froude Number (Fr) is a Key Problem for the large hydraulic structures. Take normal measures, such as stilling basin, roller bucket, slip bucket or cushion pool and etc., are too difficult to solve this problem. Because of the complementary energy in downstream can made erosion on the riverbanks. A new type dissipator aid at top of the spillway can resolve it. This paper presents on the new type dissipator-combined energy dissipator with Flaring Gate Pier (FGP). The results of model test research and prototype observations for a large hydroproject are described also.

This paper presents a probabilistic approach to flow modeling and measurement, and consists of the following parts: (1) probabilistic formulation of fluid-flow problems, (2) a probability distribution governing the flows and a velocity distribution equation based on it, and (3) an efficient method of discharge measurements in rivers and streams. The probabilistic approach complements the conventional, deterministic approach of hydrodynamics. Results of applying the probability concept in flow modeling are used as a basis to develop an efficient method of flow measurement, by which the flow discharge can be estimated quickly by simple measurements. Results of applying this efficient method in discharge measurements in a natural river are presented and compared with those estimated by the conventional method.

Turbulence measurements in open-channel flows with a side cavity and water dead zone, so called "Wando" in river engineering, were conducted with a two-component LDA system. The aspect ratio (=streamwise-length/spanwise-length of side cavity) is varied as 3, 5 and 10. In the case of the aspect ratio of 3, the strength of the rotation of vortices is the largest. In the case of the aspect ratio of 5, momentum exchange is largest, although the mass exchange is small. In the case of the aspect ratio of 10, a reattachment phenomenon appears in the side cavity. The reattachment length is about 5 times of the spanwise length of the side cavity. A new eddy model in the side cavity "Wando" open-channel flows is proposed here.

This paper concerns with the 2-D distributions of temporally averaged velocity and the characteristics of turbulence during floods in the lower reach of the Yodo River. LSPIV developed by the authors was used for measuring the time series of the instantaneous velocity distributions. The characteristics of the surface velocity distributions are presented in relation to the channel geometry, the non-uniform depth distribution in the channel, hydraulic structure, and channel alignment. The distributions of the Reynolds stress were also discussed in view of the channel geometry.

The effect of geometric shape of the nozzle on the jet behavior was investigated experimentally. Jets from the round entrance nozzle and the square entrance nozzle showed that a potential flow region can be found in the vicinity of nozzles and the vortex trails are observed after the jets are fully developed. For the spiral nozzle, however, the pre-developed turbulence causes the length of potential core to be negligible and the jet trajectory shows a swaying motion. In the zone of established flow, both the Gaussian approximation and the exact solution properly predict the measured data for all cases. Results of the turbulence show that, for the round and square entrance nozzle, the maximum turbulence intensities were found at the boundary between the shear layer and the ambient fluid in the early stage, then the maximum value moves to the centerline as the flow develops. On the contrary, the spiral jet has maximum turbulence intensities at the centerline from the beginning stage, and the maximum values are two to three times as high as those of other cases. Similarity was observed on the distributions of Reynolds stress for every type of nozzles.

In this study, interaction of horizontal jet and free surface was evaluated by the experiment. Since the non-linear phenomena caused by turbulence at the free surface are fully three dimensional, three dimensional free surface shape and velocity distribution just beneath the surface should be simultaneously measured. Here, Stereoscopic Particle Image Velocimetry (stereo-PIV) and Specklegram Method (Tanaka et al. ¹) was combined to visualize free surface and underlying turbulence simultaneously. The test section was a rectangular tank having a free surface. A circular nozzle was set horizontally beneath the free surface to form a jet. The jet interacted with the free surface, causing the wavy free surface condition. The combined optical technique enabled to measured the free surface wave quantitatively in a high accuracy. Using this quantitative surface information and velocity distribution measured by stereo-PIV, correlation between free surface fluctuation and flow field was obtained.

Coherent structures near the wall (streamwise vortices, low-speed streaks, and coherent Reynolds stress producing events) in an open channel flow at Re_τ = 300 are investigated using stereo particle image velocimetry(SPIV) in a cross-stream plane. A time series of 3 velocity components in the plane is converted into an instantaneous full 3 dimensional velocity field by Taylor's hypothesis. It is observed that a pair of counter-rotating quasi-streamwise vortices cause coherent Reynolds stress contributions beside the vortices by their swirling motions. A kinked low-speed streak is also observed below the vortex pair. These structures are consistent with the conceptual model proposed by Jeong et al. (J. Fluid Mech. 332, 185 (1997)), and is the first quantitative experimental verification of the complete combination of configuration among these structures to our knowledge.

Hardware and software for very high temporal and spatial resolution PTV, Particle Tracking Velocimetry, were developed. As hardware, 1 million frames per second video camera was developed. A particle image extraction method from image plane and an automatic tracking algorithm were developed for a high spatial resolution PTV.

Two-dimensional vertical velocity and turbulence profiles using particle image velocimetry (PIV), have been measured in a low Reynolds turbulent free-surface flow over a rough bed within a 7-mm wide steep channel. Despite these uncommon conditions, velocity profiles still follow the classical logarithmic law. No Coles wake law could be adjusted on the data because the free surface has an influence immediately above the log zone. Profiles of fluctuating velocities proved to be in good agreement with classical exponential laws.

Simultaneous measurements of three-dimensional velocity components and free surface elevations were carried out in the Lagoon of Fogliano. Measurements were made in typical spring-summer environmental conditions which are characterised by gentle sea-breeze wind. Two measurement points in the lagoon far from the tide channel were chosen in such a way to evidence the role of wind in generating turbulence. The analysis of velocity data have shown the presence of a significant oscillatory motion due to wind waves which affects the entire water column and which interferes with the lagoon bottom. The decomposition procedure adopted in order to separate the mean, wave and turbulent velocity components has allowed to extract some quantities – turbulent kinetic energy, anisotropy degree, turbulent stresses- characterising the structures of turbulence of the flow under the environmental conditions examined.

Measurements of the turbulent fluctuations in velocity in oscillatory boundary layer flow over a rippled bed are presented for a range of the parameters α/L and β/k. The fluid velocities, both the horizontal and the vertical components, were measured simultaneously using a laser Doppler anemometer. The measurements indicate that the turbulence intensities over ripples are considerably larger than those above comparable flat rough beds. The results also confirm a close link between the vortex structures and turbulence production in the near-bed region. Further, turbulence decay over ripples is compared with that above flat rough beds. Finally, the relative significance of the periodic and the turbulent mixing in the near-bed region above ripples is examined.

Flow developed over the gravity waves are studied experimentally in rectangular duct. The focus is brought into the secondary flow effect on the mean and turbulence intensity distributions. It is found that the secondary flow is significantly excited by the wave motions and its effect reaches to the area far from the interface. The interaction between the flow and the wave motions are analyzed by the correlation coefficient and the conditional sampling procedures.

The paper concisely analyzes the differences between the characteristics of cavitation noise and that of flow noise, discuses the disturbance effect on environment noise due to long cable connecting the transducer. It has demonstrated that the cavitation noise in flowing water, acting as a main source of noise, plays dominant role on Sound Pressure Level (SPL) in high frequency band. Based on the characteristic features of high in frequency, large in SPL and strong in stochastic behavior, it renders the possibility to identify cavitation phenomenon with respect to the increment of SPL and the pulsation of frequency spectrum curve, thus offering a promising approach of cavitation detection. It has monitored the cavitation occurrence in No. 1 tunnel spillway with orifice plate on Xiaolangdi Hydro-project, yielding successive findings.

Direct numerical simulation of a fully-developed open-channel flow has been carried out for a range of subcritical Froude numbers at a fixed friction-velocity Reynolds number of 180. The free surface is approximated by small-amplitude wave theory. The simulation results are presented emphasizing the effects of the Froude number on those turbulence quantities related to the free surface fluctuations. The amplitude of the free-surface fluctuation is found to increase as the square of the Froude number. While statistical quantities involving the vertical velocity component are most influenced by the Froude number but only in the region close to the free surface, quantities related to the pressure fluctuations are influenced over much wider region.

The paper presents an assessment of a new, hybrid turbulence modeling practice applied to the vortex-shedding flow from a square cylinder. This flow case has been considered as an important benchmark before attempting to model complex transient engineering flows. The hybrid model, recently outlined by Basara and Jakirlic [4], has been already validated for a wide range of steady-state flows and has shown a significant improvement in comparison to the k-ε model predictions. The main idea behind this model is to calculate Reynolds stresses in the momentum equations via Boussinesq's formula in conjunction with the redefined structural constant C_μ. A new definition of C_μ employs the Reynolds stresses and turbulent kinetic energy that are available after solving the full Reynolds stress transport equations. In this way, the numerical instabilities arising from full coupling of the momentum equations and the Reynolds stresses from the second-moment turbulence closures are reduced. The present results confirm that the hybrid model delivers a robust solution procedure while preserving most of physical advantages of full Reynolds stress closures over the simple k ~ ε models.

A computational method has been developed for granular mixtures, or non-uniform solid particles, in turbulent liquid flows. The numerical model is based on an Eulerian-Lagrangian approach, in which the carrier fluid is solved on 3D BFC with the Eulerian governing equations while the movements of the individual particles are predicted with a distinct element method (DEM). The fluid-particle interaction is taken into account by a two-way modeling. The computational time can be reduced due to the parallel numerical procedures for both phases on the basis of a domain-decomposition method. The particle segregation is successfully predicted in an oscillating turbulent flow with the present method.

Flux-difference splitting scheme is implemented on the shallow water and mass conservation equations with modified acceleration due to gravity to simulate evolution of gravity currents. The shallow water and mass conservation equations are solved separately. A front condition is enforced using available empirical relationships. The numerical model is applied to simulate the motion of the gravity currents, made of saline water of varying concentration or a water particle mixture, that were observed experimentally. The front velocity and front height are compared with experimental data. The longitudinal profiles of the gravity currents are also presented. Conclusions are drawn regarding the applicability and accuracy of shallow water equations solved by flux-difference splitting scheme for simulating evolution of gravity currents.

In this paper an efficient computation algorithm of the finite element and dynamic linear programming method (the FE&DLP method) in transient three dimensional heat transfer management is developed in order to save computer time and memory. The proposed efficient computational algorithm (the simplified simplex algorithm) makes it possible to obtain an initial basic feasible solution of the simplex method for linear programming without the introduction of artificial variables and to omit the troublesome Phase 1 of the simplex method. Therefore, the proposed algorithm allows us to solve large-scale optimization problems in transient heat transfer management.

This paper introduces pseudo-symplectic Lagrangian schemes for three-dimensional passive scalar advection problems. In the schemes, we adopt the idea of two-dimensional symplectic Lagrangian schemes for passive scalar advection. This research aims at obtaining more fundamental knowledge of the schemes by considering a simple passive scalar advection problem in three-dimensional incompressible steady flows, namely, the ABC flows.

In this paper, we present a finite element scheme based on the Petrov-Galerkin method using exponential weighting functions for computing three-dimensional incompressible viscous fluid flows at high Reynolds numbers. As the time-marching scheme, we adopt effectively the second-order accurate Adams-Bashforth explicit differencing for both convection and diffusion terms. Numerical solutions for flow over a wall-mounted cube and flow around a circular cylinder are presented, and compared with experimental data and other existing numerical data.

Effects of the SUPG (Streamline Upwind/Petrov Galerkin) upwinding are numerically scrutinized by solving an unsteady advection-diffusion equation and unsteady incompressible Navier-Stokes equations, since the SUPG theory is founded solely on a 1-D steady advection-diffusion equation. The numerical results show that, only for problems reaching a steady state, the SUPG formulation works well to suppress the numerical instability caused by non-resolvable boundary layers appearing in linear advection-diffusion problems. However, the SUPG solutions turned out less accurate than the Galerkin solutions for transient advection-diffusion problems and for an incompressible viscous flow problem. It is suggested that the excessive SUPG diffusivity is responsible for the numerical deterioration in unsteady problems.

A first-order accurate FVM numerical model based on FDS techniques for 2D flood flows is presented. The model is implemented on an unstructured triangular grid system. The model is applied to an axisymmetrical 2D dam-break problem to show advantage of the unstructured grid system. The quantitative accuracy and applicability of the model are verified against experimental data on 2D dam-break flood waves propagating in a horizontal dry-bed floodplain. The model is found to predict depth and velocities of flood flows with reasonable accuracy.

The velocity and concentration profiles of two-dimensional steady turbidity currents in submarine canyon are analyzed by the k - ε turbulence model. The performance of this model is tested by saline inclined plumes, close relatives of turbidity currents, in which the buoyancy flux is constant in the flow direction. On the contrary, the negative buoyancy of turbidity currents varies in the flow direction via deposition or erosion of sediments. The present model takes this effect into account through the boundary condition at bottom in use of the sand entrainment coefficient.

Smoothed Particle Hydrodynamics (SPH) is a lagrangian numerical technique which proved its ability to reproduce a large variety of flows. However, the turbulent effects are often neglected when considering SPH simulations, and to date it appears that no specific turbulence model is available for SPH. Two models are presented here, one based on an eddy viscosity assumption, the other one on a Langevin process. Both are tested in the case of a Poiseuille flow in a pipe. Velocity profiles are in good agreement with theory; particularly the log-law is well reproduced near the walls.

Among others, one of the main activities in the Nuclear Engineering and Fluid Mechanics Department of the Engineering School in Bilbao, is the study of liquid metals behavior. And for this purpose the CFD code FLUENT is being used. Currently, the code is being applied to the use of Lead-Bismuth eutectic (LBE) as the coolant of an accelerator driven system (ADS) and also as the target for a neutron source. In this paper, ANSALDO's Energy Amplifier Demonstration Facility¹ is simulated, paying attention only on the coolant. As it will be later explained, natural convection is a very important issue, because the philosophy for safety systems in nuclear devices tends to consider passive technologies. The purpose is to avoid electrical machines like pumps, so the core should remain coolable, even if there is a blackout. To get this natural circulation, heat transfer plays a main role, and as turbulence enhances the heat transfer, it is important to choose a good turbulence model to correctly simulate this ADS's coolant system.

To promote time and effort savings and to increase efficiency in experiment, practical use of a numerical simulation method has been studied. The velocity distribution at an intake structure of hydraulic experiment model was compared using numerical simulation data and one-dimensional laser doppler anemometry (LDA) measurements. The numerical simulation data of the velocity distribution just downstream of the channel curve with gradual widening was in good agreement with the results obtained by measurement in a laboratory, however, the numerical simulation cannot so well reproduce such a behavior of the experimental contours. Characteristics of the flow, which are needed at the draft designing stage, have been clarified with satisfactory accuracy.

The authors have recently developed a new multiphase LES model for multiphase turbulent flows with a quite large number of dispersed particles. The framework is based on a new formulation of dispersed-particle motion, referred to as GAL (Grid-Averaged Lagrangian) model, which has proper physical background and high computational efficiency. Combining the GAL model with the SGS (Sub-Grid Scale) model for fluid-phase turbulence, we have developed a new multiphase LES model, named GAL-LES model. In this paper, we will outline the GAL-LES model and indicate its performance through the applications to various multiphase turbulent flows such as a plane bubble plume, sheet-flow turbulence under sinusoidal oscillatory flow and a breaking wave.

The purpose of the present paper is to establish the theoretical predictions for the vertical distribution of the undertow inside surf zone. The basic equation of these analytical predictions is based on an eddy-viscosity model and on an assumption that the average shear stress over a wave motion could be described in terms of the different linear function of the vertical distance from the sloping bottom (z') at the two separate regions, which are the upper side and the lower one of the level of the wave trough. In order to solve this basic equation for these analytical predictions of the vertical profile of the undertow, the surface and bottom boundary conditions are given by evaluating the surface vorticity and the bottom mass transport velocity, respectively. According to the analysis, the present theoretical results are in much better agreement with experimental ones rather than those of the other researchers'. The surface vorticity has stronger influences on characteristics of the vertical distribution of the undertow in the surf zone rather than the bottom mass transport velocity, and plays an important role in the present phenomenon.

The objective of this study is to get a sound knowledge on the wave breaking processes initiated by the plunge of jet ejected from overturning wave crest and to make clear relationships of the plunging and spilling breakers to its turbulence structure. Numerical simulations using the VOF method and k-ε model are made to establish an optimum model of the Reynolds stress applicable to turbulent flows in the wave breaking process and to investigate the turbulence structure.

In this study, we have developed a new quasi-3-D turbulence and sediment transport model for shallow water turbulent flows and associated sediment transport in non-equilibrium conditions. These models have been successfully applied to calculating HLS (horizontal large-scale) eddies at a harbor entrance developed by long-period waves and sediment suspension and subsequent transport into the harbor by the HLS eddies. The comparison with the results by a previous horizontal 2-D model clearly demonstrates the importance of the 3-D computation for proper evaluation of the sediment suspension at a harbor entrance and subsequent transport into the harbor by HLS eddies.

In order to understand the characteristics of turbulence generated by waves propagating along the sloping bottom, LDV (Laser Doppler Velocimeter) is used to measure the horizontal particle velocities before wave breaking and inside surf zone respectively. Two typical plunging breaker and spilling breaker are made in wave flume; in addition, two different analytical methods are introduced to analyze the horizontal particle velocities into wave components and turbulent fluctuations. From the experimental results, we find that the turbulent intensity is very small before wave breaking; however, it becomes stronger behind the breaking point and the maximum turbulent intensity is taken place at a distance away from the rear of impinging point.

Oscillatory boundary layer flows have been the subject of numerous experimental and theoretical investigations over the years. Most of these studies mainly considered regular sinusoidal wave motion in the free stream. Present paper describes the experimental facility developed in order to measure bottom boundary layer properties under irregular waves. A set of experimental data for smooth turbulent flow conditions is also presented along with corresponding bottom shear stress variation measured directly by means of a hot-film sensor. The bottom shear stress data from hot-film sensor shows satisfactory agreement with those from fitting of logarithmic velocity profile.

This paper deals with a quasi-3D model of wave-induced currents in the surf zone. A quasi-3D nearshore current model that includes a turbulence model for turbulent kinetic energy is presented. In order to determine eddy viscosity coefficients, one-equation turbulent model is employed. The present model in this study is applied to the prediction of undertow and longshore current velocity on the planner beach and the validity of the model is discussed.

Systematic measurements of subsurface current were made for (i) pure wind waves and (ii) a coexisting system of wind-waves and mechanically generated waves propagating against a wind. For the pure wind wave case, a large-scale secondary flow, i.e., a pair of stationary Langmuir circulations, was observed in a wind-wave tank. This secondary flow was found to be suppressed dramatically by the interaction between wind waves and the mechanically generated waves. The suppression mechanism of the secondary flow is qualitatively consistent with the CL2 model of Langmuir circulations proposed by Craik and Leibovich.

Based on the experimental results, the turbulence structure of the wind and breaker affected water surface bursting layer are investigated in relations to the water particle velocity vector field, velocity spectra, turbulent kinetic energy, Reynolds stress and eddy viscosity coefficient. It is demonstrated that the bursting layer retaining the intensive turbulent kinetic energy and Reynolds stress is generated by strong winds accompanied by breaking waves.

The impulsive pressures on a vertical wall are numerically simulated. Two-dimensional incompressible viscous flow, governed by Navier-Stokes equations, is modeled using a finite difference scheme based on the volume of fluid (VOF) method. As it is difficult to predict impulsive pressures because of numerical noise, called spike noise, an iteration scheme is adopted in the VOF method to overcome and eliminate such spike noise. Comparisons with experimental results indicate that the employed model predicts impulsive pressures qualitatively as well as quantitatively. Although it does not consider compressibility of air, the peak value of the impulsive pressure of a plunging breaker containing a large amount of entrapped air can nevertheless be predicted well.

A VHF Doppler radar is one of remote sensors, which can measure ocean surface current. The measured surface velocity includes the wind-driven current, Stokes drift and complicated flow near sea surface as well. In the present study, a technique of assimilation of the measured ocean surface current into three-dimensional baroclinic flow model is presented. The blending scheme with the vertical eddy diffusion coefficient of the vertical mixing induced by wind stress is examined. It is clarified that the assimilation had a good agreement with the observed vertical flow and density structures. These findings suggest that the assimilation of 3-D baroclinic flow model is necessary for the practical application of the ocean radar in stratified coastal waters.

While there have been many studies conducted to investigate relation between vertical strength of density stratification and tidal mixing, there is no consensus that explains actual vertical mixing in semi-enclosed sea by reason of difficulty in measuring the mixing directly in the field. Hence we developed a free-rising Micro-Scale Profiler (MSP). This MSP rises to the sea surface from the bottom by its self-buoyancy at a speed of 50 cm s^-1. On this ascending way, it measures vertical micro-structures of vertical velocity shear, water temperature, conductivity and depth at a sampling rate of 100 Hz. We collected data of micro-structures with this MSP, water quality and current in Suo-nada sea that is the western part of Seto Inland Sea of Japan. As a result, in the study area a typical two-layer structure was formed: high-temperature low salinity in the upper layer and low-temperature high-salinity in the lower layer. However, the magnitude of the tidal current ranged from 13 to 33 cm s^-1 in the surface layer and was considerable large. Moreover, results indicated that the value of vertical eddy diffusivity (K_z) just above the pycnocline was as large as 5 × 10⁰ cm² s^-1; however the value inside the pycnocline was very small, more than two orders of magnitude smaller than the values just above or just below the pycnocline. This fact suggests that the pycnocline functions as a wall and restricts the water exchange between the upper and lower layers. Moreover, the large value of K_z just above the pycnocline was caused by the increase in the turbulent energy dissipation (ε) that was induced by the turbulent velocity shear generated by the stress on the pycnocline wall.

In this study a three-dimensional multi-level numerical model was developed. Based on it the seasonal change of the complicated density current in Hakata Bay was numerically simulated. Some different numerical experiments were carried out in order to make clear the cause of residual currents generated there. The results of this study are as follows : 1) It is confirmed that the spatially asymmetric distribution of river discharge between north and south coastal line affects the residual current pattern of a surface layer at the eastern area of Hakata Bay, but does not affect greatly that of the total area of Hakata Bay. 2) The total quantity of the river discharge is a driving force to generate the residual currents in Hakata Bay.

Kanmon Strait, where more than seven hundreds ships pass in a day, is known as one of the most difficult straits for ship navigation in Japan. We created a new system to forecast more precisely the tidal current in the Kanmon Strait. The system is based upon a numerical simulation model of the whole Kanmon Strait and includes the meteorological effects.

Wave-induced longshore current, river flood flow, and residual tidal current around Mailiao coast are investigated to verify the mechanisms of topographic changes. The computational results show that the separable area governed by different factors is possible. The topographic change in the northern region of reclamation area is dominated by Choshui river sediment deposit. The remarkable longshore current is bounded in the region of water depth less than 5 meters and produced the significant bottom variation in this region. Tide current is important to bottom variation in the region of water depth greater than 10m, and causes significant topographic changes by coupling with wave-induced longshore current in winter monsoon.

Flow and salinity distribution in the Meghna estuary located in the northern Bay of Bengal in Bangladesh has been studied through a two-dimensional depth-integrated modelling system. The coupled salinity model accounts for the density variation in the estuary. Model result shows that the flow dynamics in the estuary is governed by the relative strength of tides and river inflows. Although the estuary, being tide dominated, shows well mixing of saline front, during monsoon huge inflow from the Meghna river causes considerable density stratification. In a two-dimensional depth-integrated approach this has resulted in a significant lowering of flow resistance than that obtained for flow computation alone. The coupled model thus provides a better prediction of flow circulation in the estuary.

This paper describes the predominant property of M₂ component of tidal current and substance dispersion in the Seto Inland Sea, Japan by using numerical modeling. The author calculated the tide and tidal current in the Seto Inland Sea by the vertically averaged two-dimensional mathematical modeling under the conditions of sinusoidal waves of M₂ component (Run-1) and composed waves of 28 tidal components (Run-2). And the author also calculated the salinity distribution in the sea in order to consider water exchange between water in the Seto Inland Sea and water in Pacific Ocean. Good agreements between computed and observed harmonic constants of M₂ component of tide and tidal current are obtained, and the values of harmonic constants of M₂ for both cases of Run-1 and Run-2 show almost the same values. However, tidal residual flow in case of Run-2 is larger than the one of Run-1 because of the non-linear effect of tidal current. By comparison with the salinity distributions of field observation data, relatively large diffusion coefficient of 500 m²/s is estimated as appropriate value for the computed salinity distribution. By using the tuned diffusion coefficient, it is shown that the residence time is about 200 days and 19.3 months are needed for 90% water volume exchange between inland sea water and ocean water.

A laterally averaged two-dimensional hydrodynamic model is developed in this study. The coordinate system is first transformed to minimize the effects of irregularity of bottom and surface. The advection terms of the governing equations are then discretized by an upwind scheme. By employing an explicit scheme for longitudinal direction and an implicit scheme for vertical direction, the model is free from restriction of temporal step size caused by a relatively small grid ratio. To demonstrate the applicability of the model, calculated time histories of free surface displacements and distributions of velocity and salinity are compared with the field measurements of the Keum River Estuary before construction of a barrage. Reasonable agreements are observed.

The flow field of a radial neutrally buoyant turbulent jet discharged horizontally into a wavy environment has been investigated. A set of laser induced fluorescence (LIF) measurement was conducted to measure instantaneous surface elevation and jet centerline movement simultaneously. The measurement shows dynamic changes on jet oscillation due to waves motion. The pattern of jet oscillation due to waves was classified into three categories. A simple physical model was proposed to estimate the jet oscillation in the near field.

Two low Reynolds number k - ϵ models, one k - ω model and two versions of two-layer models are tested against the DNS data of a one dimensional oscillatory boundary layer. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy and Reynolds stress. It is observed that the newer version of k - ϵ model performs very well in predicting the velocity and turbulent kinetic energy, whereas the original version still performs the best in connection with the Reynolds stress. The k - ω model and two layer models underestimate the peak value of turbulent kinetic energy. The bottom shear stress peak is predicted by k - ω model in an excellent manner.

A detailed comparison has been made between rectangular grid and BFC (Boundary Fitted Coordinates) grid computations for effluent current through a curved channel formed by the jetties at the Natori River mouth, Japan. In the computation of the former grid system, it is found that the discretization of the curved jetties causes roughness effect, resulting in rise of water level and reduction of the velocity in the region between the jetties. It is observed the reduction of the velocity becomes more considerable with the increase of grid size. In contrast to this result, much smoother distribution of water surface profile can be obtained using BFC grid system.

This paper describes magnetically driven mini and micro pumps that are developed at the Biomagnetic Engineering Laboratory. In the magnetically driven pumps the actuation is conducted remotely by moving an external magnet, which will interact with a magnetic material coated or impeded on a moving element of the mini or micro pump. The paper presents numerical simulation of a mini pump along with the magnetic interaction between the driving and driven elements. Further a module of micro pump that is being tested is also presented.

Bio-magnetic fluid dynamics is the study of the interaction of biological fluids with an applied steady magnetic field. The composition of the biological fluid dictates the interaction of the fluid with the applied magnetic fields. In general, biological fluids are considered weakly diamagnetic. In order to enhance the magnetic susceptibility of the biological fluid, nano to micron size magnetic particles are tagged to the biological compounds. Nano and micron size magnetic particles are produced in-house for different bio-magnetic applications. Several biomedical applications have recently developed that utilizes the magnetic labeling of cellular components. In this paper the mathematical model that describes the dynamics of the bio-magnetic fluid is discussed. Numerical simulation that utilizes the developed mathematical model to simulate the behavior of the bio-magnetic fluid in a aneurysm is presented. Recent applications of the bio-magnetic fluids will also be presented.

The final target of this research is to establish a method for optimizing the design of a draft tube that is installed to recover the kinetic energy of water flow discharged from a hydraulic turbine runner. For this purpose, detailed measurements of the draft tube internal flows and pressure pulsation were implemented by using a draft tube element model to make it easy to control the inlet swirl flows, and the measured data was compared with the result of the flow analysis. Since the static internal flow in the draft tube was simulated using three-dimensional viscosity analysis using a turbulence model, it is useful as a designing tool for clarifying flow phenomena. And it became clear that the internal flows and the characteristics are largely influenced by the inlet flow velocity distribution, so this fact must be taken into consideration when designing a runner.

In the present paper, a method based on conformal mapping is presented. In this approach, since the potential is given analytically in the circle plan, the Kutta condition can be treated in an analytical manner. This ensures an accurate prediction of the flow development. Furthermore, the procedure is very efficient as the integral equation is solved only once the body is transformed. A brief history of unsteady flow modeling is given in the introduction, followed by the numerical details of the current method. Numerical examples are presented for flapping foil motion and trochoidal propeller model.

A numerical study has been performed to test two recent two-layer turbulence models for the capability of simulating effects of periodic wakes on boundary layer transition. The two models combining the standard k - ε model in the bulk of the flow with a one-equation model near the wall are implemented in a two-dimensional Navier-Stokes code. A flow on a flat plate disturbed by periodic wakes is chosen as test case. The wakes generated by rotating circular cylinders cause an unsteady laminar-turbulent transition of the boundary layer along the plate. The numerical simulations with one of the models are found to be in good agreement with the experimental data. The main aspects of the boundary layer development are predicted well. The other model appears to be not suited for simulating unsteady transition.

Multi-Scale Viscosity (MSV) model is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. We assume that flow inside an "ideal" channel is always stable, i.e. laminar, but the turbulence is a process of developing of external perturbations due to wall roughness, inlet conditions and other factors. We also assume that real flows are always affected by perturbations of any possible scale lower than the size of the channel. The turbulence can be modeled in form of internal or "turbulent" viscosity.

The main idea of MSV can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of local turbulent Reynolds number below some critical one. Thus, in MSV, the only empirical parameter is the critical Reynolds number.

MSV model has been applied to the fully-developed turbulent flows in straight channels such as a circular tube and annular channel. Friction factor and velocity profiles predicted with MSV are in a good agreement with numerous experimental data.

The MSV model can be classified as "zero-order" integral model of turbulence. Because of its simplicity, MSV can be easily implemented for calculation of fully-developed turbulent flows in straight channels of arbitrary shapes.

Considerable sensitivities are investigated in using natural convection for cooling large pools. Such a flow occurred in a sump cooling concept for a water cooled reactor. The related SUCOS model experiments were analyzed by means of the FLUTAN code. The numerical interpretations show, the natural convection in large pools is strongly influenced by local thermal disturbances, either due to structures in the fluid domain, or by bounding structures interacting thermally with the fluid. These experiment specific disturbances must be recorded in the numerical model in order to achieve adequate simulations of the heat transport. Some geometric imperfections of horizontal coolers or heaters could also have tremendous influences. As a consequence, not only the numerical model has to record all relevant phenomena as realistic as possible, but also the model experiment.

EDF is preparing a new generation of two-phase CFD codes, able to handle the whole range of void fraction and flow configurations. In order to achieve this goal, new numerical methods are being developed and tested: an elliptic based one and an hyperbolic based one. In this paper, first results are presented.

Multi-dimensional analyses have been expected with expanding computation resources for gas-liquid two-phase flow. We recently developed models for bubble turbulent diffusion and bubble diameter to predict the phase distribution by a multi-dimensional two-fluid model. This study was performed to verify our model. The verification was performed using databases under diameter; 9 mm to 155 mm, pressure; atmospheric to 4.9 MPa, flow rate; superficial gas velocity = 0.01 to 5.5 m/s and superficial liquid one = 0.0 to 4.3 m/s, fluid combination; air-water or steam-water. Through the assessments, our model was found to be applicable to the wide range of flow conditions including the effect of pipe diameter. The shape of phase distribution and the average void fraction are predicted well qualitatively and quantitatively. Since the model is established using the ratio of bubble diameter to eddy size as a key-parameter, the ratio is one of important parameters to develop the constitutive equations in the multi-dimensional two-fluid model.

Siphon outlets of pump discharge lines are used in pumping plants. It is necessary to evacuate air downstream from siphon outlets as bubble entrainment by water flow after plant start-up. A numerical method has been developed for prediction of gas-liquid two-phase flow dynamics during self-priming of the siphon outlets by using a two-dimensional extended two-fluid model. This method is appropriate for the present purpose because it can treat free surface of water layer on inclined wall and entrained bubbly mixture in a water pool, both of which occur in siphon outlets. Experiments were carried out by using a 1/15 scale test-section. The calculated results of transient water level and pressures in the simulated siphon outlets were in good agreement with the experimental data. The results reveal that the present method can predict key hydrodynamic phenomena in siphon self-priming process and the present method is a useful tool for design of actual large-scale siphon outlets.

Experimental and numerical studies are made on the effect of interfacial wave on turbulence modification on air-water annular flow in a vertically arranged round tube. Gas-phase turbulence structure and characteristics such as time-averaged velocity profile, fluctuation velocity profile, energy spectrum, and auto-correlation coefficient are quantitatively measured by using the hot-wire anemometer. Followings are noted from the experimental results. (1) Time-averaged velocity profiles are modified to sharpened shape compared with single-phase flow. (2) Fluctuation velocity in axial direction becomes larger than that of single-phase flow through the all-radial position. (3) Turbulence in annular flow is modified to coherent structure, which should be affected by gas-liquid periodically moving wavy interface. Numerical simulation for solving turbulence structures of gas-phase considering the effect of liquid film behavior flowing on the pipe wall was also carried out. Liquid film is assumed to be surface roughness moving with the velocity of liquid film. Averaged velocity and turbulent velocity were calculated with k - ε model. The numerical results are qualitatively consistent with the experimental results obtained in the present study.

Fundamental experiments on the mixing of horizontally-injected high-density solution in vertically-upward water flow have been performed by using a small apparatus. Mixing patterns observed in the experiments have been classified to complete mixing (entrainment) and incomplete mixing (entrainment). In the complete mixing, the injected high-density solution is mixed (entrained) completely into the vertically-upward water flow. Numerical calculations have been performed by solving a continuity equation and momentum equations for the total fluid together with mass transfer equation for the solute, taking density change into account. The calculations have underestimated somewhat the boundary upward water flow rates of complete/incomplete mixing observed in the experiments.

Characteristics of mixing and fluid temperature fluctuation in tee pipes were investigated through experiments. Flow in a mixing tee pipe could be classified into three patterns, stratified flow, turn flow and wall impingement flow. A flow pattern map could be made by using the velocity ratio and the diameter ratio of the main and branch pipes. Mixing characteristics and temperature fluctuation in the tee pipe depended greatly on the flow pattern. Turn flow, especially when branch flow was in the center of the main pipe or tended to be opposite the branch pipe, could promote mixing and suppress the fluid temperature fluctuation. Moreover, a tee junction arrangement was proposed using a downstream bent pipe as a mixing promoter. The experiments clarified that the bent pipe could best enhance mixing when the branch pipe in the tee came from the opposite direction to the bend.

Fluid-structure thermal interaction phenomena characterized by stationary random temperature fluctuations, namely thermal striping, are observed in the downstream region of a T-junction piping system in a liquid metal fast reactor. Therefore the piping walls located in the downstream region must be protected against the stationary random thermal process which might induce high-cycle fatigue. This paper describes the evaluation system based on numerical simulation methods for the thermal striping, and numerical results of the thermal striping in a T-junction piping system under the various parameters: velocity ratio and diameter ratio between both the pipes and Reynolds number. Then detailed turbulence mixing process at the T-junction piping region due to arched vortexes generating lower frequency fluctuations are evaluated through a separate numerical analysis of a fundamental water experiment.

We performed a water experiment on parallel triple-jet and a calculation using a direct numerical simulation (DNS) for a quantification of thermal striping. The local temperatures and velocities were measured by using thermocouples and the particle image velocimetry (PIV), respectively. The calculation was carried out using the quasi-DNS code, DINUS-3, which was based on the finite difference method. The oscillation of the jets obtained from the flow visualization was related to the movements of the twin vortices between the jets by using the PIV. The experimental temperatures/velocities results were close to the numerical results. The heat transportation among the jets was evaluated by using the turbulent heat fluxes obtained from the quasi-DNS.

An analytical formula of the Strouhal number for the flow pulsation promoting the turbulent mixing in rod gaps was derived. This formula validates the application of a flow pulsation model to rod gaps with a spacer grid where the flow pulsation would be affected. The non-dimensional eddy thermal diffusivity in a rod gap with a spacer grid was calculated by using the k-ε turbulent model and Kim and Park's flow pulsation model with this formula. Using this result as an input for a subchannel analysis code, the data of an experiment with a mock-up of PWR fuel assembly was analyzed. The result satisfactorily verified the application of the model.

This paper describes the benchmark analysis results of Rapid Boron Dilution (RBD) transient tests. The RBD transient tests were carried out at University of Maryland. The data were obtained as a part of the International Standard Problem No. 43, ISP-43, for code assessment. Nuclear Power Engineering Corporation (NUPEC) participated the benchmark analysis of ISP-43 with the PLASHY code. The PLASHY code is a general purpose single-phase fluid analysis code, developed by NUPEC. The code has two types of module, Cartesian/Cylindrical coordinate system module and BFC module. In order to reduce the computing time, the Cartesian/Cylindrical coordinate system module was employed. All calculations were done on a parallel computer, IBM SP2, by using the 12 of 76 CPU units. The calculated results were judged to agree with the test data taking scattering width of test data into consideration. The turbulent mixing and resulting 3D-flow pattern and temperature distribution, however, were considered to be an important issue in computer simulation of the ISP-43, and thus we are performing a comparison between the detail temperature distribution obtained from T/C data and the calculated results.

The paper presents thermal experiments performed in the SSC RF IPPE on the ADS window target model. Brief description of the model, specific features of structure, measurement system and some methodological approaches are presented. Eutectic lead-bismuth alloy is modeled here by eutectic sodium-potassium alloy. The following characteristics of the target model were measured directly and estimated by processing: coolant flow rate, model power, absolute temperature of the coolant with a distance from the membrane of the target, absolute temperature of the membrane surface, mean square value and pulsating component of coolant temperature, as well as membrane temperature. Measurements have shown a great pulsations of temperature existing at the membrane surface that must be taken into account in analysis of strength of real target system. Experimental temperature fields (present work) and velocity fields measured earlier [1] make up a complete database for verification of 2D and 3D thermohydraulic codes.

There is a long cavity flow in a branch pipe with a closed end for a nuclear plant. It carries hot coolant and makes thermal stratification at its front, where a big temperature gradient can exist. If the stratification varies, thermal stress may occur in the pipe wall. We have made an engineering model to predict the location of the stratification in a vertical pipe based on an experiment at temperature of 20 to 60°C. Applying the model to a cavity flow at high temperature, the calculated values showed good agreement with the measured values.

The authors investigated hydrodynamic factors to cause the gas entrainment from the surface of coolant flowing in a reactor vessel. The flow characteristics were established for the water flow, which is fed into a three-dimensional rectangular cell that represents the flow field in a reactor.

Existence of predominant types of flow, such as the colliding flow, circulating flow and vertical eddy, were established by results of measurement on the distribution of flow velocity. The steady state three-dimensional flow in the flow field was also demonstrated. Difference in the flow velocity between area at the center of water tank and near the side wall of it and momentary variation of three-dimensional flow velocity near the water surface were also found. It was concluded from these results that the air entrainment is caused by the interference between the steady state circulating flow and momentary and local variation of flow velocity.

A wind tunnel experiment was conducted to investigate the thermal buoyancy effects on tracer gas concentration fluctuation in a simulated unstable stratified boundary layer. Tracer gas was released from an elevated point source and instantaneous concentrations were measured using a high-frequency-response flame ionization detector. Turbulence statistics of concentration fluctuations, including the variance, spectra, probability density functions and peak values, were compared with those measured under neutral stability conditions. Under unstable conditions, spectral and probability distributions showed similar profiles at different heights in the plume as the plume was thoroughly mixed by the turbulence mixing activated by the heated surface. In spite of the differences observed in plume dispersion, the peak concentrations agree well with those predicted from the lognormal distribution in regions where the concentration fluctuation intensities are between 0.3 and 1.5, and the exponential distribution in regions where the intensities are more than 1.0 under both cases.

In the paper, based on the full set of primitive non-hydrostatic and prognostic equations the three-dimensional k-ε model of turbulent atmospheric boundary layer is described and analyzed. The closed system of equations is solved by finite volume method for mean flow characteristics, turbulent kinetic energy and energy dissipation rate. The numerical results are verified by comparison with the measurement data of the wind tunnel experiments. Based on the simulation results the paper discusses two modifications of the model proposed by Detering, Etling 1985 and Duynkerke 1988. The simulation results are compared with the wind field measurement carried out by the von Karman Institute (Costa et al. 1994), which provides mean and turbulent field data for a neutrally stratified flow over isolated, three-dimensional hill of a conic shape.The numerical studies of the influence of wind speed and roughness of ground surface on the length of recirculation zone behind a cube obstacle are also presented for the case of neutral atmospheric boundary layer.

Turbulent flow past a complex topography, represented by an idealized two-dimensional hill with gentle slope is simulated by LES technique. Flow Reynolds number is moderately high to exhibit difficulties in the mostly sought boundary conditions in LES of practical flows. Simulations are performed first with commonly used boundary conditions to illustrate their inadequacies. A new wall model described by the usual wall function superimposed by fluctuation related to local and instantaneous pressure gradient is proposed and tested. It is found that results of simulations by the proposed method are closer to the experimental data in terms of mean velocity and wake size and it is a better alternative to the existing conventional log-law and non-slip conditions.

Modeling the budgets of heat, water vapor, and carbon dioxide within three-dimensional vegetation was tried in this work. This model consists of three submodels: a model for a turbulent flow within vegetation, a model for radiation transfer within vegetation, and a stomatal conductance model. We adopted our own turbulence model for the flow within vegetation. Ross's model for radiation transfer within vegetation and a stomatal conductance model by Collatz, et al. were adopted in this work. These three submodels were integrated into the present model.

This model was applied to a single tree. The following results were made apparent from this work:

1) Ranges of low air temperature, high humidity, and low carbon dioxide concentration were found widely spread across the rear of the tree. However, the rates of transpiration and photosynthesis were strong in the front and top parts of the tree where leaves received the direct solar radiation.

2) A great deal of short wave radiation absorbed by leaves was released through transpiration.

3) The influence of long wave radiation on the energy balance within the tree was not negligible.

4) The sensible heat transfer due to water vapor flux from leaves hardly affected the energy balance within the tree. These facts indicate that the results from the turbulence model for dry air is almost equal to those of the turbulence model for moist air.

5) The heat exchange due to the release of O₂ and the fixation of CO₂ which photosynthesis brings about can be omitted in computing the heat balance within a tree.

Concentration fluctuation of stack gas around a meshed truss cubical building is calculated. Stack gas is emitted continuously from the roof of the building. The meshed truss cubical building simulates a building composed of many pipes and structures. The flow field is calculated using large eddy simulation. Concentration is calculated using large eddy simulation and the puff method, in which small volumes of the tracer gas are divided and combined according to the calculation mesh size. In order to avoid numerical viscous effects, the puff method is applied in the regions near to the stack. Obtained flow and concentration calculation results are compared with those of the wind tunnel. Though disagreement for mean, concentration fluctuation intensity and peak concentration is observed, the regions in which the disagreement is observed are restricted; otherwise, good agreement with those obtained by the wind tunnel experiment is obtained.

As one of measures for controlling the emission of carbon dioxide (CO₂) into the atmosphere, attention is focused on making effective use of the ability of the ocean to absorb CO₂, and an evaluation is performed on the ability to isolate CO₂ from the atmosphere by emitting CO₂ into areas deeper than the middle layer of the ocean. In the first stage of this research, the Pacific three-dimensional circulation model was revised to enhance the accuracy of the circulation model further. The results of calculation almost correspond to the results of known literature and the estimated results from observations that were obtained by Michida(1997). If the projection of tracking is deeper than 2000m depth, particles never reach 1000m depth at any point and aim of this study will be succeeded.

The basic purpose of this study was to determine a way to change the frequency of vortex shedding from rectangular bodies, both alone and together, by evading the resonance between their natural frequency and the frequency at which they shed vortex in the wind. In order to do this, we equipped a fillet in the corner of each body. We conducted a numerical prediction of the frequency of shedding vortex for bodies with and without fillets. In each case, the wind velocity was at most 9 m/s, which is the mean wind condition of daily life, and wind was simulated from every direction at each body. By equipping a fillet to a box, its Strouhal number increased. However, the Strouhal number did not change when the magnitude between the fillet and projected length of the rectangular body was more than about 40%. Within the present range of wind velocity, Strouhal numbers increased linearly to Reynolds numbers and decreased linearly with larger pitches between adjacent bodies. These numerical results can be useful as practical predictions of the frequency of vortex shedding within the wind conditions of daily life from single and multiple rectangular bodies, with and without fillets.

This paper describes the determination of cross-sectional shape of a trapezoidal embankment so as to be an effective countermeasure to avoid the damages due to the wind-blown sand on sandy beaches. The series of numerical simulations corresponding to the experiments have been carried out and compared to discuss how the change of slope of the trapezoidal artificial embankment works to the flow situation around it. In conclusion, the authors wish to show the conditional functions of the effective shape of the artificial embankment to the wind-blown sand confirmed by examinations through out this research work.

In this study, a three-dimensional hydrodynamic and heat transport is constructed for Lake Yanaka. Results from the model are compared well with field data. The main objective of the present paper is to shed some light on the influence of wind forcing treatment on flow circulation pattern and water temperature distribution.

The environmental water temperatures in Ise Bay are characterized by a few degrees higher in the nearshore area than in the area off the shore. From the results of the field observation and the numerical experiment, it is estimated that the phenomenon peculiar to Ise Bay can be explained as follows. In the innermost area of Ise Bay, the vertical structure of water temperature is of an inverse stratification, which is caused by the salinity stabilizing the density stratification against much fresh water supplied even in winter. In consequence, the estuary circulation is maintained even in winter. The warm and salty water upwells from the lower layer in the innermost area of the bay and a higher temperature zone is formed. These phenomena are reinforced by the northern or north-westerly wind, prominent in winter, and the higher temperature zone spreads in the innermost area of the bay.

A quasi 3-dimensional flow model and a water quality model (the Chesapeake Bay Model) were applied to a hypothetical power station to determine whether it is possible that the intake and discharge of cooling water for a station located on a closed inland bay might bring beneficial change to the oceanic environment. The results of the flow and water quality calculations show that the intake and discharge of cooling water promote water exchange in the inland bay; in particular, there is accelerated exchange of the nutrient - enriched water inside the bay with cleaner water from outside the bay, so that there is at least a possibility that water quality will gradually be improved. In addition, bottom water is continuously being pumped up in front of the power plant, causing water quality elements to change in a concentric circular pattern; significant water quality changes are limited to the region within which the sea water temperature rises 1 °C or more.

The following sections are included:

• Introduction

• The DORA algorithm
  • Solution of the kinematic problem

• Solving the dual problem using the DORA methodology

• Application to the field case of Reggio Calabria (Italy)

• Conclusions

• References

Continuous field observations of water temperature, conductivity, turbidity and flow velocity were performed at a central point of Lake Shinji, a shallow lagoon in Japan, in summer for a month. Observational results revealed that turbidity in the overlying water showed a distinct diel variation, independent on the existence of the stratification. As wind-induced wave diurnally developed when the atmosphere became unstable in the afternoon, and as wind-induced wave propagated to the bottom layer even under the stratified condition in the water column, diurnal fluctuation of resuspension was possible under stratified conditions. Furthermore, experimental results showed that sediment resuspension enhanced phosphate release rate from the sediment under anoxic condition. As anoxic water often develops under stratified conditions, these results strongly indicate that the anoxic resuspension caused by the wind-induced wave enhances phosphate release from the sediment.

For the purpose of predicting performance of airlift pumps in deep seawater, a one-dimensional numerical simulation code based on the two-fluid model has been developed. In order to verify the numerical simulation code, an in-situ experiment on lifting up seawater from 30m depth was carried out at sea and the results were compared with predicted performance. Furthermore the performance of airlift pump at the larger water depth (up to 1500m depth) was discussed with the developed numerical simulation code.

Knowledge of seawater intrusion to aquifer is very important for the efficient use of groundwater in coastal area. The objective of this paper is to investigate on seawater intrusion behavior to multi-layered coastal aquifers by numerical simulations. The governing equations are the equation of groundwater flow and the advection-dispersion equation of saline water transport to fresh water aquifers. The Streamline-Upwind/Petrov-Galerkin (SUPG) method is employed to surmount the instability of numerical solution of the advection-dispersion equation for the steady state that occurs when the element Peclet number is large. Meanwhile, for the unsteady-state simulation, the explicit characteristic-Galerkin method is utilized to save both time and capacity for computation. The simulation is carried out using dimensionless governing equations to generalize the application. The results indicate that the simulation method used in this study is quite effective to understand seawater intrusion behavior in multi-layered coastal aquifer. It is also observed that the investigation of the structure of multi-layered aquifer is important for optimal intake of ground water in a coastal area.

Simultaneous heat, moisture and DNAPL transport due to diurnal soil-atmosphere interaction in four different unsaturated land elements is investigated by one-dimensional numerical simulation. SALSA coupled with DNAPL transport equations predicts its migration in subsoil from the initially top contaminated layer. The results indicated the significance of vegetation cover and other soil properties on soil heat and moisture budgets and hence DNAPL volatilization and migration to higher soil depth. Forest and porous pavement elements respectively showed the minimum and maximum fluctuations in soil temperatures and water contents. DNAPL in aqueous phase penetrated to relatively deeper soils in forest element. This penetration depth decreased for short grass, bare soil and porous pavement elements respectively. The gas phase transport into the lower soil is comparatively smaller. However, the tendency of downward transport is similar to that in liquid phase.

Soil and groundwater contamination due to spilling and leakage of DNAPL is one of the major environmental problems in developed nations. Knowledge of DNAPL penetration behavior in pore scale is essentially important to get understanding of their migration in saturated porous media. DNAPL penetration through water saturated single pore and element of vertical parallel pores are investigated experimentally in this paper. Various models used in the study are made of uniform diameter glass-spheres arranged on horizontal planes to form triangular and rectangular shaped pores. The experimental results for single pore model indicate that the ratio (V/S) (V: Total DNAPL volume in the pore just before snap-off or residual volume after snap-off, S: Pore neck space) decreases exponentially as pore size increases. The residual DNAPL volume in a pore after snap-off is found to be proportional to pore area. In DNAPL ponding experiment, penetration depth is observed to be proportional to ponding height and pore neck area. The penetration behavior is dependent on DNAPL and porous medium characteristics.

A novel model for 3-phase fluid flow through a deformable fissured porous media is presented. The set of governing equations, in addition to the traditionally used continuity equation, consists of equilibrium equation and therefore a coupled model is utilized. The well-known Galerkin finite element method for spatial discretization along with Kantrovich-type temporal discretization is applied where solid phase deformation as well as fluids' pressure are considered as the primary unknowns. Other unknowns are calculated based on the primary unknowns, hence a highly non-linear system is introduced. The obtained results show a significantly different behavior for the porous media where the fluid flow is coupled with deformability of the media.

In order to theoretically investigate the characteristics of in-situ electrokinetic removal of heavy metals from groundwater by numerical simulation, a mathematical flow model has been developed based on the physico-chemical transport processes in contaminated aquifers. The results of the numerical simulations indicate that the electromigration removal of heavy metals is effective specially for local separation and accumulation, and injection and drainage of purge water is essential to carry away the ions with effluent.

A mathematical model is developed to analyze heat, moisture and volatile organic compound (VOC) transport with water evaporation and VOC volatilization in an unsaturated porous medium. The model consists of equations of mass and heat conservation in five components: liquid water, water vapor, VOC dissolved in water, VOC gas, and heat energy. Laboratory tests have been carried out to determine parameters and constants in the model, and numerical analyses are discussed. The results of vaporization tests with 1% methanol solution show that the model can explain moisture and VOC transport in unsaturated soil. It is thus concluded that the developed model is suitable for analyzing coupled heat, moisture and VOC transport in unsaturated soils.

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