Free surface flows

By performing buoyancy-driven fracture experiments in brittle gelatin we observe that the ascent velocity of a fracture containing a finite volume of fluid increases when approaching the free surface. We theoretically describe this free-surface effect and quantify it by introducing an effective depth-dependent fracture toughness and developing an ascent model on the basis of linear fracture mechanics. We develop a successful inversion approach and resolve the actual and critical fracture length and the ascent velocity far away from the free surface from the observation of the fracture tip migration alone. Other parameters, as the fluid volume included in the fracture and the in situ fracture toughness, can be derived. Applying the model and inversion to the 1998 eruption at Piton de la Fournaise, Reunion Island, reveals estimates of the length and critical length of the feeding magma batch, the magma batch volume and the in situ fracture toughness. It further indicates that the ascent velocity of the magma batch was probably much smaller at greater depths and that the batch might have been initiated several months or years before the eruption.

Abstract
Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. In this model, the Reynolds equations and the kinematic free-surface boundary condition are solved simultaneously, so that the water surface elevation can be integrated into the solution and solved for, together with the velocity and pressure fields. An efficient numerical algorithm has been developed, deploying implicit parameters similar to those used in the Crank–Nicholson method, and generating a block tri-diagonal algebraic system of equations. The model has been applied to simulate a range of unsteady flow problems involving relatively strong vertical accelerations. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.

The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The  problem we focus on is the transformation of an incoming solitary wave by the trench(es), and the impact of the resulting wave system on a vertical wall located after the trench(es). The maximum run-up and the maximum force exerted on the wall are calculated for various lengths and heights of the trench(es), and are compared with the corresponding quantities in the absence of them. The calculations have been performed by using the fully nonlinear water-wave equations, in the form of the Hamiltonian coupled-mode theory, recently developed in Papoutsellis et al (Eur. J. Mech. B/Fluids, Vol. 72, 2018, pp. 199–224). Comparisons of the calculated free-surface elevation with existing experimental results indicate that the effect of the vortical flow, inevitably developed within and near the trench(es) but not captured by any potential theory, is not important concerning the frontal wave flow regime. This suggests that the predictions of the run-up and the force on the wall by nonlinear potential theory are expected to be nearly realistic.
The main conclusion of our investigation is that the presence of two tandem trenches in front of the wall may reduce the run-up from (about) 20% to 45% and the force from 15% to 38%., depending on the trench dimensions and the wave amplitude. The percentage reduction is greater for higher waves. The presence of only one trench leads to reductions 1.4 – 1.7 times smaller.

When a layer of static grains on a sufficiently steep slope is disturbed, an upslope-propagating erosion wave, or retrogressive failure, may form that separates the initially static material from a downslope region of flowing grains. This paper shows that a relatively simple depth-averaged avalanche model with frictional hysteresis is sufficient to capture a planar retrogressive failure that is independent of the cross-slope coordinate. The hysteresis is modelled with a non-monotonic effective basal friction law that has static, intermediate (velocity decreasing) and dynamic (velocity increasing) regimes. Both experiments and time-dependent numerical simulations show that steadily travelling retrogressive waves rapidly form in this system and a travelling wave ansatz is therefore used to derive a one-dimensional depth-averaged exact solution. The speed of the wave is determined by a critical point in the ordinary differential equation for the thickness. The critical point lies in the intermediate frictional regime, at the point where the friction exactly balances the downslope component of gravity. The retrogressive wave is therefore a sensitive test of the functional form of the friction law in this regime, where steady uniform flows are unstable and so cannot be used to determine the friction law directly. Upper and lower bounds for the existence of retrogressive waves in terms of the initial layer depth and the slope inclination are found and shown to be in good agreement with the experimentally determined phase diagram. For the friction law proposed by Edwards et al. (J. Fluid. Mech., vol. 823, 2017, pp. 278–315, J. Fluid. Mech., 2019, (submitted)) the magnitude of the wave speed is slightly under-predicted, but, for a given initial layer thickness, the exact solution accurately predicts an increase in the wave speed with higher inclinations. The model also captures the finite wave speed at the onset of retrogressive failure observed in experiments.

The present work is dedicated to the modeling of viscous flow past a NACA0012 foil fixed in a current below a free surface. To this end, the δ +-smoothed-particle hydrody-namics (SPH) model has been adopted. This SPH model prevents the inception of the numerical tensile instability in the flow region characterized by negative pressure since a tensile instability control (TIC) has been included. In the TIC, a pressure differencing formulation (PDF) has been adopted for the momentum equation in the flow region characterized by negative pressure. In order to completely remove the numerical noise in the vorticity field, in this work, the PDF is also applied for the region with positive pressure, but except for the free-surface region in order to ensure the free surface stability when wave breaking occurs. The mechanism of PDF being able to eliminate the numerical noise in the vorticity field is also briefly analyzed. In order to reduce the nonconservation of total momentum induced by the PDF, a particle-shifting technique (PST) is implemented in each time step for regularizing the particle position. In the numerical results, δ +-SPH results are validated by the experimental data and other verified numerical results. Improvements of the results of δ +-SPH with PDF with respect to the ones without using PDF are demonstrated. Parametrical studies based on the δ +-SPH model regarding the breaking and non-breaking waves generated by the flow past a submerged foil are also carried out.

In this paper, measurements beneath the interface of the flow past a hydrofoil in water during stalling
conditions are used to characterise the flow field and to extract and to analyse the small eddies using
an original algorithm based on the wavelet transform. The detected eddies are analysed to evaluate their
spatial distribution and their intensity separating the wake of the foil-related from the wake of the
breaker-related eddies. The wake of the foil-related eddies have an almost symmetric distribution of
circulation with slight dominance of counter-clockwise (CCW) eddies, while the breaker-related eddies
have an asymmetric distribution of circulation, and clockwise (CW) eddies are dominant. The joint
probability density function (PDF) of the turbulent kinetic energy (TKE) and the Reynolds shear stress
is computed by referring to the time-averaged values in the area occupied by the eddies. A similar PDF
computed using the instantaneous values during eddies presence shows values of TKE and Reynolds
shear stress roughly twice the average values, i.e., eddies can be associated to larger fluctuations of the
flow field respect to the time average flow field. However, on average, the Reynolds shear stress during
eddy presence is less than the Reynolds shear stress of the time-averaged flow at the same location. The
sign of the Reynolds shear stress is systematically opposite to the time-averaged value in quadrants Q2–
Q4 for CW eddies and in quadrants Q1–Q3 for CCW eddies. Therefore, in the presence of eddies there is a
counter-flux of momentum. The conditional analysis of the terms of the TKE balance indicates that, in the
wake of the foil and during the presence of eddies, the production is 15% stronger than the timeaveraged
production at the same location occupied by the eddies. Beneath the free surface the production
is 30% weaker than the time average. A similar analysis for the advection indicates that, in the wake of
the foil, the advection in the presence of eddies is an order of magnitude greater (in absolute value) than
the advection due to the time-averaged flow at the same location. Additionally, beneath the free surface,
the advection in the presence of eddies is much greater than the average. A similar behaviour can be
observed for the transport term due to turbulence. Therefore, in the presence of eddies, production plus
advection plus transport is enhanced with respect to the average flow and is increased approximately by
40% in the wake of the foil and 20% beneath the free surface.

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by , the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

The dripping dynamics of Newtonian liquids emanating from an inclined nozzle is studied. The fluid viscosity mu flow rate Q, nozzle radius R, and inclination angle theta have been varied independently. The drop breakup times and the different modes of dripping have been identified using high speed imaging. A phase diagram showing the transition between the dripping modes for different theta is constructed in the (We, Ka) space, where We (Weber number) measures the relative importance of inertia to surface tension force and Ka (Kapitza number) measures the relative importance of viscous to surface tension forces. At low values of We and Ka, the system shows a transition from period-1 to limit cycle before chaos. The limit cycle region narrows down with increase in inclination. Further increase in the values of We and Ka gives a direct transition from period-1 to chaos. The new experiments reveal that in the period-1 region, increasing the nozzle inclination angle theta results in lowering of the drop breakup time t(b), suggesting that the surface tension forces cannot hold the drops longer despite the weakened effective gravitational pull. This counter-intuitive finding is further corroborated by pendant drop experiments and computations. More curiously, throughout the period-1 regime, the drop volume is independent of the flow rate. This resulted in a relatively simple correlation for the dimensionless drop volume V = 1.3G(-1)Ka(0.02)(cos theta)(0.37) accurate to within 10% over wide ranges of the independent variables. (C) 2014 Elsevier Masson SAS. All rights reserved.

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The free surface dynamics excited by grid stirred turbulence is analysed with a Lagrangian approach, with the analytical model calibrated by using experimental results. The Lagrangian
model for free surface oscillations has been developed by assuming that coherent structures in the water layer close to the free interface have the shape of blobs and are mobilized
by a periodic force. The blobs are assumed to behave like nonlinear oscillators with different spring stiffness in upwelling and downwelling and neglecting viscosity as first  approximation. In order to calibrate the model, a set of experiments in a grid stirred tank was used where free surface elevation time series were measured and all the necessary variables were computed.
Through calibration and with some working assumptions, the radius of the blobs is
shown to be of the order of the integral vertical length scale of turbulence. The forced oscillations are analysed by the method of Rauscher (1938) [1] to predict the amplitude of the
oscillations, possible resonances and discontinuities in the amplitude–frequency space. If the forcing term has multiple harmonics, in some cases a blow up of the oscillator is forecast.
Some tests including a small damping, in order to evaluate the effects of viscosity, show that a jump is expected in the amplitude–frequency diagram and a range of unstable frequency. The presence of a small damping should also prevent the blow up for multiple harmonics in the forcing term.

Based on the constant boundary element method in a 3D numerical wave tank, a hybrid radiation condition which is the composition of the multi-transmitting formula (MTF) method and the damping zone is studied. Numerical solutions show excellent agreements with the analytical ones, which verify the effectiveness of the hybrid method. This method can be considered as a trimming of the MTF condition, or an extension of the damping zone method, and has good ability of simulating irregular waves with relatively large frequency span.

Numerical study on a hybrid water wave radiation condition by a 3D boundary element method. Available from: https://www.researchgate.net/publication/256995756_Numerical_study_on_a_hybrid_water_wave_radiation_condition_by_a_3D_boundary_element_method.

This paper analyses the interaction between the
turbulence and free surface. The phenomenon takes place
in many natural flows and industrial processes. In the
present experiments, turbulence is generated by a vertically
oscillating grid moving beneath the free surface. Fluid
velocity has been measured through a hot-film anemometer,
and the free surface elevation has been measured by an
ultrasonic sensor. Integral length scales and several turbulence
estimators have been computed. In order to detect
the generation of turbulence near the free surface, the
correlation between free surface elevation and the underneath
flow velocity has been studied, as well as the time lag
between turbulence and free surface. The free surface
dynamics has been characterized by a velocity scale and a
length scale. The kinetic energy associated with the free
surface fluctuations increases with the Reynolds number at
a rate depending on the frequency of the grid movement.
For Reynolds number larger than &1000, however, the
relationships collapse to a single curve characterized by a
lower rate. The present experiments do not achieve the
inertial sub-range in the vertical velocity fluctuations, and
the estimated spectrum decays with an exponent smaller
than -3, which is the typical value for the two-dimensional
turbulence in the inertial sub-range. The macro length
scale, estimated by using the Taylor’s frozen turbulence
hypothesis, experiences a decay away from the grid, which
follows reasonably well the profile of Thompson and
Turner (J Fluid Mechanics 67: 349–368, 1975). The micro
length scale reduces immediately beneath the free surface,
which can be interpreted by the increase of dissipation rate
in the subsurface layer. The classification diagram by
Brocchini and Peregrine (J Fluid Mech 449: 225–254,
2001) indicates that most tests fall in the weak turbulence
domain, but some tests fall in the wavy domain. The vertical
velocity fluctuations and the free surface level show a
significant correlation with a negative phase lag, that is, the
free surface fluctuations are ahead of the vertical velocity
fluctuations.

A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in the present paper. The tangent of hyperbola for interface capturing (THINC) scheme is applied for capturing complex free surfaces. The new model is capable of simulating a flow with violently varied free surface. A series of computations are conducted to assess the developed algorithm and its versatility. These tests include the collapse of water column with and without an obstacle, sloshing in a fixed tank, the generation of regular waves in a tank, the generation of extreme waves in a tank. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results.

In this article we present a 2D and 3D practical interface tracking algorithm to reconstruct and advect the interfaces of interfacial flows. The improved volume-of-fluid (VOF) method in this work is composed of three major components: namely (1) the modified piecewise linear interface calculation (PLIC) based interfacial reconstruction; (2) the Lagrangian split fluid advection and (3) redistribution of volume fraction. Most advanced VOF methods employed by the PLIC technique have faced some problems to extend from 2D to 3D study, because the increase in complexity of the geometry primitives involved has made implementations excessively difficult and ultimately infeasible. The improved algorithm in this study is used to capture the interface of the immiscible fluids which are applicable both in 2D and 3D spaces. A computationally efficient and second-order accurate interface reconstruction method is applied. The normal estimation of the interface is approximated by combining the centered column scheme and the Youngs' method. Besides, a linear mapping technique is implemented to improve the efficiency of numerical simulations with regard to the approximation of capturing the interface. The sequence of the Lagrangian advection in each direction is considered to restrain the fragmentation caused by the strong interface deformation as the fluids propagate. It is significant to note that the method can be accurately accomplished by a regular structured mesh without any geometrical modifications such as boundary fitted grids. Next, the mass conservation is numerically assessed, thus allowing computations to reach the machine precision. The computational results include widely used benchmarks in 2D and 3D cases, such as the solid-body translations and rotations, the swirled single vortex and the deformation fields of fluid body. Good results are obtained through some numerical tests by using present algorithm as comparing with other numerical solutions. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h m t

Two fundamental one-dimensional (1D) models are proposed and applied to simulate the transient flows with the propagation of an interface in a water-filled duct. The proposed models are developed to simulate the unsteady open channel flows based on finite-volume method (FVM). The models presented herein are based on the continuity and momentum equations of free surface and pressurized flows and the momentum equation of an interface between both flows. However, the highly simplified marker and cell (HSMAC) method with pressure iteration procedures is applied to the pressurized flow region. The numerical simulations are performed under the hydraulic conditions of previous experiments, and then simulated results were compared with the experimental data. It is pointed out that the solitary wave solution is able to reproduce the air cavity profile. In contrast to the hydrostatic model, results of the Boussinesq model compare reasonably well to the experimental observations.

The propagation of viscous, thin gravity currents of non-Newtonian liquids in horizontal
and inclined channels with semicircular and triangular cross-sections is investigated
theoretically and experimentally. The liquid rheology is described by a power-law model
with flow behaviour index n, and the volume released in the channel is taken to be proportional
to tα, where t is time and α is a non-negative constant. Some results are generalised to
power-law cross-sections. These conditions are representative of environmental flows, such
as lava or mud discharges, in a variety of conditions. Theoretical solutions are obtained in
self-similar form for horizontal channels, and with the method of characteristics for inclined
channels. The position of the current front is found to be a function of the current volume,
the liquid rheology, and the channel inclination and geometry. The triangular cross-section
is associated with the fastest or slowest propagation rate depending on whether α < αc or
α > αc. For horizontal channels, αc = n/(n+1) < 1, whereas for inclined channels, αc = 1,
irrespective of the value of n. Experiments were conducted with Newtonian and power-law
liquids by independently measuring the rheological parameters and releasing currents with
constant volume (α = 0) or constant volume flux (α = 1) in right triangular and semicircular
channels. The experimental results validate the model for horizontal channels and inclined
channels with α = 0. For tests in inclined channels with α = 1, the propagation rate of the
current front tended to lower values than predicted, and different flowregimes were observed,
i.e., uniform flow with normal depth or instabilities resembling roll waves at an early stage
of development. The theoretical solution accurately describes current propagation with time
before the transition to longer roll waves. An uncertainty analysis reveals that the rheological
parameters are the main source of uncertainty in the experiments and that the model is most sensitive to their variation. This behaviour supports the use of carefully designed laboratory
experiments as rheometric tests.

A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Other two free surface capturing methods-the original VOF, CIP are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two dimensional (2-D) and three dimensional (3-D) full scale simulations and a large-scale 2-D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

Changes of the susceptibility to lava flow invasion at Mount Etna are quantified by using lava flow simulations on four Digital Elevation Models documenting the morphostructural modifications of the volcano in the time interval 1986–2007. The probabilistic code DOWNFLOW is used to derive the areas invaded by several thousands of lava flows obtaining, for each DEM, maps of the susceptibility to lava flow invasion and of the lava flow hazard. These maps show, for the first time, the evolution of these surficial properties with time, and render a quantitative image of the effects of topographic changes on the preferential lava flow drainage paths. The results illustrate how the emplacement of new lava flows and the growth of scoria cones affect the probability of inundation by lava flows. We conclude that the persistent activity of this volcano requires a frequent updating of the topography for a reliable lava flow hazard
assessment.

Abstract
In urban areas the impacts of flash floods can be very high due to these regions being generally densely populated and containing vital infrastructure. Parts of the UK have been particularly prone to such serious urban flooding in recent years, such as the 2004 Boscastle flood. Due to climate change the occurrence of urban flooding is predicted to increase in the future, which is likely to lead to increasing flood risk to people and property in urban areas. Therefore, it is appropriate to estimate the potential flood risk to people and property for improved flood risk management. In the current study, an integrated numerical model for estimating the flood risk in urban areas is outlined herein, including the module for predicting the 2D hydrodynamic characteristics of urban floods, together with a new module for predicting the flood risk to people (including children and adults) and property (including vehicles and buildings). The hydrodynamic module of this model was then verified against laboratory experimental data and real flood tracks in urban areas. Finally, the integrated model was applied to predict the flood risk to people and property for the Boscastle floods, with different reoccurrence frequencies. The predicted results for different flood scenarios indicated that: (i) people would be swept away in the majority of the flooded area for a flood with P = 1% (a return period of 100 years) , while they would be in danger almost in all the flooded area for a high flood, with P = 0.25% (a return period of 400 years) or 0.1% (a return period of 1000 years); (ii) vehicles would be washed away from the parking area in the centre of a car park during a flood with P = 1%, while they would also be flushed on the main road and main street, and in the car park during a flood with P = 0.25 or 0.1% ; and (iii) there would be no damage to buildings during a flood with P = 1%, but severe damage to buildings would be likely to occur during high floods. Therefore, the developed integrated model can be used to predict the potential flood risk to people and property in urban areas, and these predictions can be used for improved flood risk management.

This research aims to evaluate the influence of air on the water surface and pressure profiles in two-phase (air–water) flow. In previous studies, the authors used the continuity and momentum equations for water in a one-dimensional finite volume model. In the present study, the authors additionally incorporate both the mass conservation and momentum equations for incompressible fluids as basic equations for the air portion. Momentum equations were integrated for the free surface and pressurized flow regions after interface observations made at each time step. To correct velocity and pressure in the pressurized portion, the authors used the highly simplified mark-and-cell method. A pressure drop equation is used at the interface of pressurized and free surface flows to deduce the pressure. The Harten total variation diminishing scheme was used to avoid numerical oscillations. The results were compared with experimental data and numerical simulations without considering the air effect.

The paper reports a study of the water surface profile of an entrapped air cavity while emptying water in an initially filled inclined duct. A one-dimensional (1D) model, which consists of the continuity and momentum equations applicable for open channel flow, pipe flow and air–water interface flow, is developed based on the finite volume method. A pressure drop model is proposed to reproduce a better profile around the cavity front, with a particular focus on air pressure changes inside the confined cavity to simulate a kind of transient flow with an entrapped air cavity. In contrast to the previous studies, the application of the model shows that when the pressure drop is not considered and the air pressure is not changed, the confined cavity soon vanishes. A comparison between the simulated and experimental results shows that the model is able to accurately reproduce the water surface profile of an entrapped air cavity while emptying inclined ducts.

Capillary driven surface oscillations of liquid argon (Tsat = 87.3 K at 1,013 hPa) have been investigated in a partly filled right circular cylinder under non-isothermal boundary conditions. The oscillations take place during the reorientation from the normal gravity surface position towards a new position upon step reduction of gravity. The situation is similar to the end of thrust in a rocket tank when the cold propellant moves along the warmer tank wall driven by capillary forces. The aim was to investigate the influence of the temperature difference between the slightly subcooled cryogenic liquid and the superheated cylinder wall on the oscillations and their characteristics in a single-component, two-phase system. Axial wall temperature gradients of averaged 0.15 K/mm − 1.93 K/mm above the normal gravity surface position were implemented. A general dependence of the reorientation behavior on the gradient value was observed, concerning the apparent contact line behavior, the frequency and damping of the oscillations of the free surface center point, and the apparent contact angle. The behavior of the ullage pressure was found to follow the behavior of the contact line.

In this paper, we propose a Radial Basis Function (RBF) based grid free scheme for capturing the interface which is passively advected by the underlying velocity field and present some preliminary results. The level set function is used to capture the interface and reinitialization algorithm is applied to maintain its signed distance property. The presented scheme is validated with two examples.

In this study, an interface-tracking method, NS-PFM, combining Navier-Stokes (NS) equations with a phase-field model (PFM) is applied to an incompressible two-phase free surface flow problem at a high density ratio equivalent to that of an air-water system, for examining the computational capability. Based on the Cahn-Hilliard free energy theory, PFM describes an interface as a finite volumetric zone across which physical properties vary steeply but continuously. Surface tension is defined as an excessive free energy per unit area induced by local density gradient. Consequently, PFM simplifies the interface-tracking procedure on a fixed spatial grid without any elaborating techniques in conventional numerical methods. It was confirmed through the numerical simulation that (1) the NS-PFM conducts self-organizing reconstruction of the interface with a certain thickness using volume flux driven by chemical potential gradient and (2) predicted collapse of two-dimensional liquid column in a gas under gravity agreed well with available data.

A spiral separator is one of the commonly-used gravity-concentration devices. It has been widely used in the mineral processing of coal. Also, it is used for the inexpensive pre-concentration of low grade ores. Spiral separator consists of an open trough that twists downward in helical configuration about a central axis. The aim of the present study is the simulation of the flow of water in spiral separators. The study is based on volume of Fluid (VOF) approach and turbulence modeling. The results focus on waterflow characteristics such as the depth of water as well as the turbulence intensity. The results demonstrated that the water depth and turbulence intensity on spiral trough increase smoothly outward. Predicted results are compared with the experimental findings from LD9 coal spiral. Comparison between the predicted and the measured values show good agreement and the most accurate turbulence model is RSM.

In this study the results of Baseline Explicit Algebraic Reynolds Stress model (BSL EARSM), Baseline Reynolds Stress model (BSL RSM) and Speziale-Sarkar-Gatski Reynolds Stress model (SSG RSM) of turbulent flow in an asymmetric compound channel are presented. The numerical results are validated with experi-mental measurements of Tominaga & Nezu (1991).

A part of non-Newtonian fluids are yield stress fluids. They require a minimum stress to flow. Below this minimum value, yield stress fluids remain solid. To date, 1D and 2D numerical models have been used predominantly to study free surface flows. However, some phenomena have three-dimensional behaviour such as the appearance of the limit between the liquid regime and the solid regime. Here the aim is to use a Computational Fluid Dynamics (CFD) to reproduce the properties of the free surface flow of yield stress fluids in an open channel. Modelling the behaviour of the yield stress fluid is also expected. The numerical study is driven with the software OpenFOAM. Numerical outcomes are compared with experimental results from model experiment and theorical predictions based on the rheological constitutive law. The 3D model is validated by evaluating its capacity to reproduce reliably flow patterns. The depth, the local velocity and the stress are quantified for different numerical configurations (grid level, rheological parameters). Then numerical results are used to detect the presence of rigid and sheared zones within the flow.

The effect of free surface height on the submerged synthetic jet parallel to the surface in quiescent flow is studied experimentally. The purpose of the study is to understand the vortex ring structure of synthetic jet and their effects on the free surface. Flow visualization using Laser Induced Fluorescence (LIF) and measurement of time-averaged streamwise and crossstream velocities carried out using Laser Doppler Velocimetry (LDV) are reported. Due to change in free surface height (H), vortex ring drifts from centerline and surface perturbations are observed. Analysis of the velocity field reveals that the velocity normal to the surface reduces while the velocity parallel to the surface increases as the vortex ring approaches the free surface. Previous studies also suggest similar phenomenon for submerged continuous jets.

Die Ausbreitung eines runden Düsenfreistrahls bei verschiedenen Auftreffwinkeln auf eine
ebene Wand wird in einem großen Wasserbecken experimentell untersucht. Die Wechsel-
wirkungen zwischen Freistrahl und Wand werden bei den unterschiedlichen Konfigurationen
anhand des mit einer tauchbaren 3D-LDA-Sonde gemessenen Strömungsfeldes charakteri-
siert. Das radiale Ausbreitungsverhalten sowie der Volumenstrom über die Strahlquer-
schnitte stehen dabei im Mittelpunkt der Auswertung.

The actual fluid flow in the waterways is in contrast to the ideal fluid flow with the creation of shear stresses and on the one hand the amount of these stresses depends on the physical properties of the fluid and the flow behavior and on the other hand depends on the physical characteristics of the waterway, So, these characteristics affect the environmental resistance against the fluid passing through the environment. The exact measurement of the frictional force of the source of the shear stresses is not feasible, and this has led to many investigators to approximate estimate the resistance level. As a result, investigations were applied to optimize the coefficients in transactions governing the flow of open and close channels. Although the experiments showed that the use of uniform flow resistance coefficients for non-uniform flows are usable, But they all confirmed the necessity of modulating the coefficients for non-uniform flows and here, assuming that the being non-uniform in the passing flow on smooth surfaces or interstitial surfaces is hydraulically the formation and growth of the boundary layer, It was attempted to investigate the probable deviation of the manning resistance coefficient in non-uniform flows relative to their amount in uniform flows and The result of the research showed that the  resistance coefficients in non-uniform flows were less than uniform flows and the necessity of correction of the resistance coefficients  in culverts and dewatering channels.

Keywords: Boundary Layer, Resistance Coefficient, Manning Coefficient, Non-Uniform Flow

The proposed research work presents the development and application of an implicit finite-volume numerical scheme capable of simulating 3D, steady, free-surface flows in irregular geometry channels with shockwave presence. The Navier-Stokes equations are used together with the utilization of the pseudocompressibility technique to calculate the pressure from the continuity equation. The position of the free surface is determined by applying a moving boundary condition through the inclusion of the two-dimensional depthaveraged mass continuity equation. All of the mentioned equations are transformed into non-orthogonal bodyfitted coordinate system and approximated using a second order implicit scheme resulting from the linearization of the governing equations. To deal with significant numerical instabilities, resulting from dispersion errors appearing during the abrupt change of the free-surface position, an alternative numerical technique is presented leading to the utilization of two nested iteration steps. The resulting numerical model is used to simulate super-critical free-surface flows including discontinuous flow featured with shock waves. The comparisons are remarkably satisfactory.

Transom stern flow is a complicated fluid flow phenomenon especially at high speed
regime. Therefore, various authors have studied the transom stern flow, both numerically and
experimentally. Smoothed Particle Hydrodynamics method can be considered as a good
choice for simulation of nonlinear physics related to the transom flow. Accordingly, SPH as a
meshless, Lagrangian, and particle method is presented in this article and SPS turbulent
model is also included for more accurate solution. For density modification, a second order
density filter scheme is employed. For validation of numerical setup, several draft based
Froude numbers are considered and it is shown that SPH solution is in good agreement with
available experimental data. Furthermore, three longitudinal Froude number are investigated
for high speed transom flow simulation. High speed cases are compared with Savitsky’s
formula and it is observed that at high speeds, SPH solutions are also reasonable.

In this paper we derive a finite-volume algorithm for simulating two-fluid flows in porous media. The algorithm handles arbitrary heterogeneous porosity fields containing discontinuities without introducing instabilities or oscillations into the solution. For the two-fluid (free-surface) modelling the volume of fluid (VoF) method is used with the HiRAC interface capturing algorithm. The developed scheme is evaluated by comparison with high-fidelity experimental results and found to agree well. The scheme is implemented in the OpenFOAM R code and extends upon the capabilities contained therein.

The Young Dong Coal Mine site in northeastern South Korea was closed in the early 1990s and initial reclamation was finished in 1995. Even though the adit was filled with limestone, there is still significant acid rock drainage (ARD) flowing from the site. An assessment that was started in March 2008 revealed that there were three types of water flowing from various sources on the site. ARD still flowed from the adit; which carried an average of 500 mg CaCO 3 / L of mineral acidity primarily in the form of Fe(II) with a flow that reached 2.8 m3 / min in spring runoff. This water is the focus of this paper. The hydrology is complex because there are at least two periods of high surface flow during the year, one in the spring and one during monsoon season. The water issuing from the adit is from a diffuse aquifer where concentrations increase when flow increases. In addition, the terrain is quite steep with few level spots. One other factor in the assessment of treatment is that a limestone quarry is only a few kilometers from the site. All of these factors have led to the conclusion that none of the traditional methods of passive treatment can be applied to this site. Instead, it is proposed to use an upgrade of a diversion well that is called a pulsed passive limestone reactor (PPLR). With maximizing all of the parameters that can be changed on a PPLR, it is anticipated that a one stage PPLR system could generate up to 250 mg CaCO 3 / L and so there would be a set of reactors needed to treat the complete flow.

www.asmr.us/Publications/Conference%20Proceedings/2009/1069-Ranville-CO.pdf

The Contingent Valuation Method was used to elicit willingness to pay an annual tax to preserve the Region of Veneto (Italy) wetlands. The Total Economic Value(TEV) of the wetlands was arrived at by means of responses from a wide spectrum of representative levels of society of the Region of Veneto, considering their spatial contiguity to these ecosystems, their socio-cultural membership, their rural/urban distribution, and demographic and socio-economic characteristics. The mean value obtained was 62,12 €/year/family. The analyses of the social awareness of the multiple wetland functions suggested a clear perception of some functions (recreation and habitat), and a less clear perception of other "environmental based" functions (water depuration, flood protection, etc.). Several expected descriptors of the willingness to pay were detected (income level, training level, urbanity, association), which did not correspond to the variables concerned for eliciting a higher awareness of the landscape management role of wetlands.

A comparative study of the numerical treatments that are commonly used in Smoothed Particle Hydrodynamics (SPH) together with relatively a new one, namely Artificial Particle Displacement algorithm is presented. As a benchmark study, two-dimensional dam-break problem is investigated by means of weakly compressible SPH approximation using Euler's equation of motion with artificial viscosity. After adopting standard SPH discretization schemes and equations without any numerical remedies, three different treatments are sequentially tested on the dam-break problem. In weakly compressible SPH approximation, the precise calculation of the densities of the particles is vital for the overall accuracy of the solution. In order to have an improved density field, a density correction algorithm is incorporated into the numerical algorithm as a basic numerical treatment. Subsequently, XSPH velocity variant algorithm [1] and artificial particle displacement (APD) algorithm [2] are implemented concurrently in conjunction with the density correction algorithm. The effects of each treatment on the calculated free surface profiles, pressure values and the total mechanical energy of the system are compared methodically. The effects of the numerical treatments particularly on the dynamic characteristics of the free surface flow in the dam-break test case are shown. The outcomes of the simulations show that density correction algorithm to large extent circumvents density fluctuation induced numerical issues in dam-breaking problem. It is further noted that the combined usage of the APD treatment and the density correction algorithm gives the most compatible results with those of the experimental studies.

The effects of stratification and rotation in mixing are apparent in the environment, the body forcesinvolved produce a strong anysotropy in the behaviour of scalars in the fluid leading to the relaminarization of turbulent patches, to anomalous diffusion and to propagation of internal waves. Basic aspects of stratification in turbulent flows are reviewed, providing some background on the interesting problem of mixing in stratified fluids as well as some of the techniques used to investigate stratified turbulent flows in the laboratory. Stratification reduces vertical transport of scalars by up to several orders of magnitude. In both the ocean and the atmosphere, the existence of many relatively sharp density interfaces produces most of the control of the global vertical mixing. Horizontal transport, on the other hand, is at a maximum near density interfaces. The ways in which stratification affects, and some of the previous attempts to understand flow structure and mixing near density interfaces are reviewed. We show experimental results to relate the different experimental approaches used in the laboratory to model mixing across density interfaces. The effect of density stratification on vertical diffusion and the different behaviour that the mixing efficiency has for different circumstances is discussed in the light of previous experimental observations.