Fiber Bundle Topology Optimization for Surface Flows

This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.

The Effect of Baffled Surface Flow Wetlands on Water Purification

[Objective] The effect of baffled surface flow wetlands on water purification was studied in order to provide a reference for the ecological restoration of polluted river.[Method] Contents of some indexes like DO,TN,TP,NH＋4-N,CODCr,SS,SD,etc.were determined in the band baffled surface flow wetlands with total area of 7 400 m2 at JiaLu riverside.[Result] Baffled surface flow wetlands could improve the effluent quality significantly,could enhance transparency and dissolved oxygen content and also could decrease SS content.The removal rate of TN was kept at more than 73% in summer and decreased to 23% in early winter;The removal rate of TP was little influenced by temperature,and it was kept at more than 77% in summer and still kept at more than 69% in autumn and winter;The removal rate of NH＋4-N was kept at more than 83% in summer and decreased slightly in autumn and winter,but still kept at more than 75%;The removal rate of CODCr ranged from 14% to 50%.[Conclusion] Baffled surface flow wetlands could effectively improve the purification effect of surface flow wetlands,which is a feasible way for ecological restoration.

Exploration of regional surface average heat flow from meteorological and geothermal series

We attempt to compute the Surface Average Heat Flow （SAHF） from long-term temperature observations of one hundred seventy-seven observational points at the depths of 0.8, 1.6, and 3.2 m, which were relatively evenly distributed in China's Mainland. We first employ Fourier transformation to remove the influence of atmospheric temperature variations from the observation series, which are classified into the type of the steady-state temperature monotonously increasing with depth （type I） and other three types. Then we compare our results obtained from the data of type I, of which the values are thought to equal to those of the mean borehole heat flow, with those obtained from traditional heat flow observations mainly distributed in North China Craton. In computations of the SAHF at the observation stations, we deduce the thermal diffusivity and volumetric specific heat of the soil by employing harmonic solutions of the heat conduction equation for the same moisture group as the first step, and then we determine the SAHF using Fourier＇s law. Our results indicate that the SAHF derived from shallow earth geothermal data can reflect the heat flow field to a large extent.

Vertical 2D Modeling of Free Surface Flow with Hydrodynamic Pressure Using SIMPLE Arithmetic in σ Coordinates

A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k-ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.

Validation of a CIP-based tank for numerical simulation of free surface flows

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.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

A proposed surface resistance model for the Penman-Monteith formula to estimate evapotranspiration in a solar greenhouse

Greenhousing is a technique to bridge season gap in vegetable production and has been widely used worldwide. Calculation of water requirement of crops grown in greenhouse and determination of their irrigation schedules in arid and semi-arid regions are essential for greenhouse maintenance and have thus attracted increased attention over the past decades. The most common method used in the literature to estimate crop evapotranspiration（ET） is the Penman-Monteith（PM） formula. When applied to greenhouse, however, it often uses canopy resistance instead of surface resistance. It is understood that the surface resistance in greenhouse is the result of a combined effect of canopy restriction and soil-surface restriction to water vapor flow, and the relative dominance of one restriction over another depends on crop canopy. In this paper, we developed a surface resistance model in a way similar to two parallel resistances in an electrical circuit to account for both restrictions. Also, considering that wind speed in greenhouse is normally rather small, we compared three methods available in the literature to calculate the aerodynamic resistance, which are the r_a^1 method proposed by Perrier（1975a, b）, the r_a^2 method proposed by Thom and Oliver（1977）, and the r_a^3 method proposed by Zhang and Lemeu（1992）. We validated the model against ET of tomatoes in a greenhouse measured from sap flow system combined with micro-lysimeter in 2015 and with weighing lysimeter in 2016. The results showed that the proposed surface resistance model improved the accuracy of the PM model, especially when the leaf area index was low and the greenhouse was being irrigated. We also found that the aerodynamic resistance calculated from the r_a^1 and r_a^3 methods is applicable to the greenhouse although the latter is slightly more accurate than the former. The proposed surface resistance model, together with the r_a^3 method for aerodynamic resistance, offers an improved approach to estimate ET in greenhouse using the PM formula.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

The Surface Friction and the Flow over Mountain

The flow over mountain is quite complicated. There are a lot of papers on this problem and a lot of progresses have been made. However, in the most of these papers, just the dynamics contributions of mountain have been analysed; the effect of the friction is often neglected. Since the frictional effect is always associated with flow, especially when it flows over the mountain. The study shows that the friction is small in the magnitude but it is not a negligible effect because it changes the features of the flow. In the case of super-or sub-critical flow, there are two extremes: one maximum, one minimum of the fluid surface on the lee-side of the mountain, while in the inviscid fluid, there is just one extreme. The frictional effect should neither be too strong nor too weak to make the situation happened according to the investigation of this paper.

Determination of Slip Length in Couette Flow Based on an Analytical Simulation Incorporating Surface Interaction

An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect, as they contribute to the achieve- ment of the slip length. The calculated results are compared with those obtained from the molecular dynamics simulation, showing an excellent agreement. Further, the effect of the shear rate on the slip is investigated. The results can well predict the fluid flow behaviors on a solid substrate, but has to be proved by experiment.

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.

Eddy formation and surface flow field in the Luzon Strait area during the summer of 2009

The formation of mesoscale eddies and the structure of the surface flow field in the Luzon Strait area were examined using in-situ CTD data, Argo float data, and multi-satellite remote sensing data collected from May to August 2009. The results show that vigorous water exchange between Kuroshio water and South China Sea （SCS） water began to emerge over the 200 m water column throughout the strait. Based on an objective definition of surface currents, float A69 tracked an anti-cyclonic eddy southwest of Taiwan Island under a Lagrangian current measurement. The salinity inside the anti-cyclonic eddy was higher than in typical SCS water but lower than in Kuroshio mainstream water, indicating that this eddy was induced by Kuroshio frontal intrusion through the Luzun Strait and into the SCS. From hydrographic data, we propose that continuous horizontal diffusion with high-salinity characteristics in the subsurface layer could extend to 119°E or even further west. The high-temperature filament, large positive sea level anomaly and clockwise geostrophic current all confirmed the existence of this warm eddy in May and June. A strongly negative wind stress curl maintained the eddy until it died. The surface flow field during July and August was rather complicated. Float A83 described an east-west orientated shuttle run in the 20°N section that was not reported by previous studies. At the same time, float A80 indicated a Kuroshio bend into the north-central region of Luzon Strait but it did not cross 120.5°E. The water mass rejoining the Kuroshio mainstream from the southern tip of Taiwan Island was less saline, indicating an entrainment of water from SCS by the Kuroshio bend.

Simulation of Free Surface Flows Based on MapReduce in Cloud Computing

Simulating turbulent liquids with breaking waves and splashes is among the most desired features in fluid animation. Lagrangian methods such as Smoothed Particle Hydrodynamics method (SPH) are a promising way to capture such properties. However, the Particle-based liquid surface simulation has not been applied very well since its consumption is way too large. This paper derives the governing equations in SPH approaches and parallelizes the dynamics-based surface simulation with the MapReduce program models which apply the SPH approach in Cloud Computing. Compared to the serial methods, this approach obtained a 3.11 times speedup on the experimental platform.

Free Surface Flow Generated by Submerged Twin-cylinders in Forward Motion Using a Fully Nonlinear Method

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume.This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms.The presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element.The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations.Furthermore,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be passive.The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is known.The new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.

Surface flow constructed wetland with composite plant bed for pretreatment of micro-polluted Yellow River raw water in China

In order to investigate the feasibility of pretreating the micro-polluted Yellow River raw water by constructed wetland, an experiment was conducted using a surface flow constructed wetland with composite plant bed. The contamination removal efficiency and their trends in the wetland treatment system were studied under different hydraulic loading rates(HLR). The contamination removal efficiencies were compared according to the seasonal change under optimum HLR. The result shows that in the same season, under different hydraulic loadings ranging from 2 to 6 m3/(m2·d) at the same period, the best HLR is 4 m3/(m2·d) in the experimental system. The average removal rates of COD, TN, ammoniacal nitrogen(NH4+-N), and TP in the constructed wetland are 38.37%, 45.97%, 39.86% and 41.69%, respectively. According to China Standard for Surface Water Resources (GB3838-2002), mean effluent of COD, TN, NH4+-N and TP can nearly reach Grade Ⅲ, GradeⅤ, GradeⅠand GradeⅠ, respectively. Furthermore, treatment efficiency of the system in summer is obvious higher than that in other seasons. The expenditure of constructing the constructed wetland with the average treating capacity of 176 m3/d and lifetime of 20 years is 17075.00 RMB. The average disposal cost is summed up to 0.17 RMB/m3, which shows that the pretreatment of the micro-polluted Yellow River raw water by constructed wetland is feasible.

Analysis on MHD Stability of Free Surface Jet flow in a Gradient Magnetic Fields

The simplified modeling for analysis on MHD stability of free surface jet flow in a gradient magnetic fields is based on the theoretical and experimental results on channel liquid metal MHD flow, especially, the results of MHD flow velocity distribution in cross-section of channels (rectangular duct and circular pipe), and the expected results from the modeling are well agreed with the recent experimental data obtained. It is the first modeling which can efficiently explain the experimental results of liquid-metal free surface jet flow.

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.