Concentration Evolution of Gas Species within a Collapsing Bubble in a Liquid Medium

In this study numerical methods are used to investigate the relationship between chemical concentration of gas species within a cavitating bubble, equilibrium radius of the gas bubble and pressure variations in the ambient liquid. For this purpose, governing equations are developed to describe the dynamic equilibrium of a bubble in a flowing fluid and mass transfer between gas and liquid phases, where it was assumed that gases undergo isothermal compression, obey the ideal gas law, Henry law. It is further assumed that the concentration of each phase within the bubble is uniform. The resulting nonlinear equations are solved using implicit Trapezoidal method with Newton iteration. Four gas species are modeled under various initial and ambient pressure variation conditions. These conditions maybe considered to represent typical cavitation events. The numerical results obtained are presented in terms of dimensionless numbers. These results indicate that chemical damage maybe an important component of cavitation surface damage, since high concentration profiles may develop within a collapsing bubble. Proposed formulation and numerical solutions are simple and cost effective to implement. The results presented in this study maybe used to benchmark experimental investigations or other more complex solutions, which are outside the scope of this study.     

Alternating skimming flow over a stepped spillway

The study of stepped spillways in laboratory scales has been essentially focused on two separated sub-regimes within skimming flow. In this paper we investigate the appearance of an unclassified alternating skimming flow regime in a 0.5 m wide stepped spillway which does not fit on these earlier definitions, and which does not occur in a 0.3 m wide spillway. Our aim is to explain the genesis of this unclassified flow which is visualised in the physical stepped spillway, by using 3D numerical modelling. Flow depths and velocities are measured using an ultrasonic sensor and Bubble Image Velocimetry in the wider flume (0.5 m). The numerical model is validated with the experimental data from the 0.5 m wide spillway. After validation, the channel width of the same numerical model is reduced to 0.3 m wide spillway in order to characterise (compare) the case without (with) alternating skimming flow. Both cases are solved using Reynolds-Averaged Navier–Stokes equations together with the Volume-of-Fluid technique and SST k-\(\omega\) turbulence model. The experimental results reveal that the alternating skimming flow regime is characterised by an evident seesaw pattern of flow properties over consecutive steps. In turn, the numerical modelling clarified that this seesaw pattern is due to the presence of a complex system of cross waves along the spillway. These cross waves are also responsible for a mass and momentum exchange in the transversal direction and for the formation of the alternating skimming flow in the spillway.     

Hydrodynamics of a periodically wind-forced small and narrow stratified basin: a large-eddy simulation experiment

Environmental Fluid Mechanics - We report novel results of a numerical experiment designed for examining the basin-scale hydrodynamics that control the mass, momentum, and energy distribution in a...     

Numerical simulation and optimization study of surface pressure and flow field around a triangular prism behind a porous fence

Environmental Fluid Mechanics - The flow structure around upright porous fences and a triangular prism was numerically investigated by using the RNG k-ε turbulence model. The numerical method...     

Effect of rotational ambient,discharge and inflow density on the formation and evolution of a density-driven current over a steep slope

Environmental Fluid Mechanics - This numerical study investigates the evolution of constant-flux high density fluid introduced vertically to a rotational low-density ambient through a circular...     

Rotational effects on exchange flows across a submerged sill

Environmental Fluid Mechanics - This paper presents new laboratory-scale numerical simulations of density-driven exchange flows generated across an idealised, submerged sill obstruction under both...     

Secondary flow within a river bed and contaminant transport

We have developed a numerical method to simulate the transport of non-sorbing contaminants within the sediment layer of a stream and the leaching of these contaminants in the steam. Typical stream bottom surfaces are uneven with triangularly shaped undulation forms. The flow of the water above such triangular surfaces causes external pressure changes that result in a “pumping effect” and a secondary flow within the sediment. The latter causes a significant contaminant advection within the sediment layer. The flow field in the porous sediment layer is obtained by solving numerically Darcy’s equations. The unsteady mass transfer equation is solved by using a finite-difference method with an up-wind scheme. The effects of parameters, such as channel slope, hydraulic head and dispersion, are studied by quantitatively comparing the numerical results of the total mass flow rate from the contaminant source, the concentration front propagation, and the contaminant mass flow rate into the water column. The “pumping effect,” increases the flow in the vertical direction and, thus, enhances the vertical advective mass transport of the contaminant. This bedform-shape induced flow is largely responsible for the mass transfer of contaminants into the water column. The numerical results also show that the mechanical dispersion inside the sediment bed will significantly increase the contaminant mass flow rate from the source.     

Analytical solution of the system sensitivity equation associated with a linear model

In this paper an analytical derivation of the sensitivity of a linear model to a given parameter is presented. This derivation avoids the numerical solution of the system sensitivity equation associated with the model

$\text{dx/dt=Ax, x(0)=x}{}_0$

and thus reduces the amount of computer time and memory needed to make a comprehensive analysis. Moreover, because of its analytical nature no numerical errors of approximation are made.     

Automatic sensitivity analysis of a finite volume model for two-dimensional shallow water flows

Given a numerical model for solving two-dimensional shallow water equations, we are interested in the robustness of the simulation by identifying the rate of change of the water depths and discharges with respect to a change in the bottom friction coefficients. Such a sensitivity analysis can be carried out by computing the corresponding derivatives. Automatic differentiation (AD) is an efficient numerical method, free of approximation errors, to evaluate derivatives of the objective function specified by the computer program, Rubar20 for example. In this paper AD software tool Tapenade is used to compute forward derivatives. Numerical tests were done to show the robustness of the model and to demonstrate the efficiency of these AD-derivatives.     

Nitrobenzene contamination of groundwater in a petrochemical industry site

The contaminant transport distance is predicted using numerical model. Zero-valent iron can be used to effectively transform nitrobenzene to aniline. Experiment shows that two-layer PRB systems have a very good treatment effect. Organic contamination of groundwater is a major concern in China. However, remediation technology for groundwater contamination to address the potential harm and danger brought by the above-mentioned serious issue is still in the research stage. This study aims to improve the current research findings. In the research project, drilling, soil, and groundwater sampling and analysis were conducted in a contamination site of a petrochemical plant, migration of contaminants to the river was predicted using a numerical model, the sequence permeable reactive barrier (PRB) for treating nitrobenzene (NB) and benzene was proposed, and simulation was carried out. Research findings demonstrated that three leaking locations had been identified in the plant, the major pollutants were NB and benzene, and the groundwater contamination area was around 640000 m². Computation results of the numerical model indicated that, in the worst case, the groundwater plume would reach the river after migration for nearly 9 years, which would endanger the safety of surface water supply. Furthermore, the two-PRB system with the filling of zero-valent iron (ZVI) and granular activated carbon attached with biofilm exerted strong remediation effects. Experimental results indicated that ZVI could transform NB to aniline effectively with a rate of approximately 93%. Meanwhile, aniline, benzene, and other organic pollutants could easily be biodegraded.     

Modelling nature-like fishway flow around unsubmerged obstacles using a 2D shallow water model

In the scope to create efficient nature like fish ramps using large-scale roughness elements, the present study is an audit of modelling such complex 3D free surface flows using an industrial 2D code solving shallow water equations. Validation procedure is based upon the comparison between numerous experimental measurements and numerical runs around large-scale roughness patterns disposed on the flume bottom in order to determine what 2D reliable numerical results can be expected. In this paper, we focused on cases of unsubmerged obstacles. The results demonstrate that 2D shallow water modelling using an industrial code such as TELEMAC-2D can be a convenient way for the hydraulic engineer to help design a nature-like fishway. This article emphasizes the limitations due to 2D depth integration of velocities and turbulence modelling and gives the domain of validity of the method.     

Characterization of turbulence statistics on the non-aerated skimming flow over stepped spillways: a numerical study

Environmental Fluid Mechanics - In this work we address the mean flow and turbulence statistics in the non-aerated region of a stepped spillway by using two different numerical strategies in two...     

Integration of a fish bioenergetics model into a spatially explicit water quality model: Application to menhaden in Chesapeake Bay

Although fish are usually thought of as victims of water quality degradation, it has been proposed that some planktivorous species may improve water quality through consumption of algae and sequestering of nutrients via growth. Within most numerical water quality models, the highest trophic level modeled explicitly is zooplankton, prohibiting an investigation of the effect a fish species may be having on its environment. Conversely, numerical models of fish consumption do not typically include feedback mechanisms to capture the effects of fish on primary production and nutrient recycling. In the present study, a fish bioenergetics model is incorporated into CE-QUAL-ICM, a spatially explicit eutrophication model. In addition to fish consumption of algae, zooplankton, and detritus, fish biomass accumulation and nutrient recycling to the water column are explicitly accounted for. These developments advance prior modeling efforts of the impact of fish on water quality, many of which are based on integrated estimates over an entire system and which omit the feedback the fish have through nutrient recycling and excretion. To validate the developments, a pilot application was undertaken for Atlantic menhaden (Brevoortia tyrannus) in Chesapeake Bay. The model indicates menhaden may reduce the algal biomass while simultaneously increasing primary productivity.     

Nested numerical scheme in a polar coordinate shallow water model for the coast of Bangladesh

This study is concerned with the development of storm surge model to predict water level accurately due to surge associated with a cyclone along the coast of Bangladesh. Considering the funnel shape of the Bay of Bengal, coastal bending and the existence of off-shore islands, a vertically integrated model in cylindrical polar coordinate system is developed using nested numerical scheme. A fine mesh scheme capable of incorporating coastal bending and offshore islands properly in the numerical scheme is nested into a coarse mesh scheme covering up to 15° N latitude of the Bay of Bengal. The developed model is used to estimate water levels at different coastal and island stations associated with a few storms that hit the coast of Bangladesh. The computed surge levels compared well with observed ones and predicted surge levels investigated with different approaches.     

Numerical behavior of a zooplankton,phytoplankton and phosphorus system

Several numerical features of a three-dimensional dynamical system which models the three species system made up of phytoplankton, zooplankton and organic phosphorus nutrient in a lake environment are presented. Certain properties of this system, such as the existence of limit cycles, are demonstrated numerically. It is shown that in certain time domains the system may be stiff, thus requiring the use of suitable algorithms.     

Harvest policies and nonmarket valuation in a predator — prey system

Although prey may not have commercial value, their economic value can be ascertained in a predator-prey model if the predator has a harvest value. The economic optimal (recovery) path of the predator and prey are carefully described when growth is quadratic in the predator (prey) and linear in prey (predator). Parameter values, in part, resembling Pacific halibut are used to provide numerical illustrations.     

Numerical simulations of intrusive gravity currents interacting with a bottom-mounted obstacle in a continuously stratified ambient

In this study, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle were investigated using highly resolved numerical simulations. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of \(\tilde{D}=D/H\), where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-springback phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: (1) a retarding regime (\(\tilde{D}\) \(\approx \) 0–0.3) where a 30 % increase in obstacle height leads to a 20 % reduction in propagation speed, simply due to the obstacle’s retarding effect; (2) an impounding regime (\(\tilde{D}\) \(\approx \) 0.3–0.6) where the additional 30 % increase in obstacle height only leads to a further (negligible) 5 % reduction in propagation speed, due to the accelerating effect of upstream impoundment and downstream enhanced mixing; and (3) a choking regime (\(\tilde{D}\) \(\approx \) 0.6–1.0) where the propagation speed is dramatically reduced due to the dominance of the obstacle’s blocking effect. The obstacle thickness was found to be irrelevant in determining the downstream propagation speed at least for the parameter range explored in this study. The present work highlights the significance of topographic effects in stratified flows with horizontal pressure forcing.     

Suspended particulate matter dynamics in a particle framework

Suspended particulate matter (SPM) dynamics in ocean models are usually treated with an advection–diffusion equation for one or more sediment size classes coupled to the hydrodynamical part of the model. Numerical solution of these additional partial differential equations unavoidably introduces numerical diffusion, i.e. in the case of sharp gradients the possible occurrence of artificial oscillations and non-positivity. A Lagrangian particle-tracking model has been developed to simulate short-term SPM dynamics. Modelling individual sediment particles allows a straightforward physical interpretation of the processes. The tracking of large numbers of individual and independent particles (up to 25 million in total in a single sediment class) can be achieved on high performance computer clusters, due to efficient parallelisation of particle tracking. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the 3D velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field. To account for erosion a new parameterisation is proposed. Three numerical particle tracking schemes (EULER, MILSTEIN and HEUN) are presented and validated in idealised test cases. Finally, the particle tracking algorithms are applied to a realistic scenario, a severe winter storm in the East Frisian Wadden Sea (southern North Sea). The comparison with observations and an Eulerian SPM transport model seems to indicate a somewhat better fidelity of the Lagrangian approach.     

Wave hydrodynamics around a multi-functional artificial reef at Leirosa

This paper describes an application of the Boussinesq-type COULWAVE model to study the wave hydrodynamics in the vicinity of a multi-functional artificial reef (MFAR). This reef is under investigation and consists of a supplementary protection solution for the Leirosa sand dune system located at South of Figueira da Foz, on the Portuguese West coast. Such installation near the coastline is expected to contribute to enhance the surfing conditions in the area, protect the sand dune system in the surroundings of Leirosa beach, and increase its environmental value. Numerical calculations with the COULWAVE model were performed for four test cases, considering two reef geometries (differing in the reef angle) and two incident wave conditions (storm condition and a common wave condition). Comparisons between the results obtained, in terms of wave heights and breaking line positions allow us to assess the influence of the reef on the hydrodynamics near the beach and around the reef. Moreover, the reef performance was analysed in terms of surfability and coastal protection. The surfability parameters (breaker height, Iribarren number and peel angle) were calculated for each test case using the numerical wave heights, wave directions and wave breaking positions. Comparisons of parameters allow characterizing the most appropriate configuration of the reef to improve the surfing conditions in the study area. A methodology based on numerical free surface elevations and horizontal velocity components was developed to calculate wave directions, since this is not a direct output of the COULWAVE model. Concerning coastal protection, analyses of the mean currents around the reef were used together with observations of the velocity cells near the shoreline as an indication of the sediment transport.     

Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model

Dam failures usually cause huge economic and life losses , especially in urban areas where there is a high concentration of inhabitants and economic actors. In order to understand the physical mechanisms of the formation and development of dam-break flooding, lots of efforts have been put into different types of modelling techniques. However, most of existing models are 1D (one-dimensional) or 2D models based on the shallow water equations. In this paper, we present a 3D numerical modelling investigation of dam-break flow hydrodynamics in an open L-shape channel. A newly developed 3D unstructured mesh finite element model is used here. An absorption-like term is introduced to the Navier–Stokes equations in order to control the conditioning of the matrix equation in the numerical solution process and thus improve the stability. A wetting and drying algorithm is used here to allow the free surface height to be treated with a high level of implicitness and stability. The 3D model has been validated by comparing the results with the published experimental data. Good agreement has been achieved at six selected locations. This study shows that the 3D unstructured mesh model is capable of capturing the 3D hydraulic aspects and complicated local flows around structures in simulation of dam-break flows.