Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Large Eddy Simulations of Mixing Time in a Stirred Tank

Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Sma-gorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agree-ment of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes (RANS) approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.

Molecular dynamics simulations for the growth of CH_4-CO_2 mixed hydrate

Molecular dynamics simulations are performed to study the growth mechanism of CH4-CO2 mixed hydrate in xco2 = 75%, xco2 = 50%, and zco2 = 25% systems at T = 250 K, 255 K and 260 K, respectively. Our simulation results show that the growth rate of CH4-CO2 mixed hydrate increases as the CO2 concentration in the initial solution phase increases and the temperature decreases. Via hydrate formation, the composition of CO2 in hydrate phase is higher than that in initial solution phase and the encaging capacity of CO2 in hydrates increases with the decrease in temperature. By analysis of the cage occupancy ratio of CH4 molecules and CO2 molecules in large cages to small cages, we find that CO2 molecules are preferably encaged into the large cages of the hydrate crystal as compared with CH4 molecules. Interestingly, CH4 molecules and CO2 molecules frequently replace with each other in some particular cage sites adjacent to hydrate/solution interface during the crystal growth process. These two species of guest molecules eventually act to stabilize the newly formed hydrates, with CO2 molecules occupying large cages and CH4 molecules occupying small cages in hydrate.

Numerical Simulation of Optimization of Mixing Tank for Residue Upgrading Reactor

For studying the mixing tank for RMAC (residue upgrading to maximize asphaltene conversion) reactor, the CFD simulation was employed to simulate the flow field in the mixing tank. The dispersion of liquid-liquid phase in the mixing tank and the power of turbines were investigated. The simulation results showed that compared with the original doublelayer propeller, the A310-swept double-layer impellers could reduce the liquid heterogeneous degree by 27.5% and the stirring power by 3.25%. The influence of rotation speed on the heterogeneous degree and stirring power was investigated, and the critical rotation speed was obtained. The optimal rotation speed was determined to be 240 r/min. The heterogeneous degree was 0.19 and the minimum stirring power was 10.89 W. By optimizing the impeller selection and process conditions, the overall performance of the mixing tank could be significantly improved.

CFD Simulation of Mixing in a Stirred Tank with Multiple Hydrofoil Impellers

The mixing process in a stirred tank of 0.476 m diameter with single, dual and triple 3-narrow blade hydrofoil CBY impellers was numerically simulated by using computational fluid dynamics (CFD) package FLU-ENT6.1. The multi-reference frame (MRF) and standard k-ε turbulent model were used in the simulation. The shaft power and the mixing time predicted by CFD were in good agreement with the experiment. The effects of tracer feeding and detecting positions on mixing time were investigated. The results are of importance to the optimum design of industrial stirred tank/reactors.

CFD Simulation of Local and Global Mixing Time in an Agitated Tank

The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computational fluid dynamics（CFD） software package Fluent 6.2, the mixing characteristics in a tank agitated by dual six-blade-Rushton-turbines（6-DT） are predicted using the detached eddy simulation（DES） method. A sliding mesh（SM） approach is adopted to solve the rotation of the impeller. The simulated flow patterns and liquid velocities in the agitated tank are verified by experimental data in the literature. The simulation results indicate that the DES method can obtain more flow details than Reynolds-averaged Navier-Stokes（RANS） model. Local and global mixing time in the agitated tank is predicted by solving a tracer concentration scalar transport equation. The simulated results show that feeding points have great influence on mixing process and mixing time. Mixing efficiency is the highest for the feeding point at location of midway of the two impellers. Two methods are used to determine global mixing time and get close result. Dimensionless global mixing time remains unchanged with increasing of impeller speed. Parallel, merging and diverging flow pattern form in the agitated tank, respectively, by changing the impeller spacing and clearance of lower impeller from the bottom of the tank. The global mixing time is the shortest for the merging flow, followed by diverging flow, and the longest for parallel flow. The research presents helpful references for design, optimization and scale-up of agitated tanks with multi-impeller.

Large-eddy simulation of fluid mixing in tee with sintered porous medium

Mixing processes of hot and cold fluids in a tee with and without sin- tered copper spheres are simulated by FLUENT using the large-eddy simulation （LES） turbulent flow model and the sub-grid scale （SGS） Smagorinsky-Lilly （SL） model with buoyancy. Comparisons of numerical results of the two cases with and without sintered copper spheres show that the porous medium significantly reduces velocity and temper- ature fluctuations because the porous medium can effectively restrict the fluid flow and enhance heat transfer. The porous medium obviously increases the pressure drop in the main duct. The porous medium reduces the power spectrum density （PSD） of tempera- ture fluctuations in the frequency range from 1 Hz to 10 Hz.

Effects on the mixing process of a coiled tube after a T-junction:Simulation and correlation

Simulations were performed to examine the effects of a coiled tube after a T-junction on the mixing and flow characteristics. A coiled tube was found to have two effects: inducing a radial flow and flattening the axial velocity distribution, which enhances and weakens the mixing, respectively. In the straight tube section connecting the Tjunction and coiled tube, the latter may dominate and cause the mixing to deteriorate. An experiment was performed with the Villermaux/Dushman method to verify the simulation results. Based on a mixing performance simulation with various fluid and geometric structure parameters, a dimensionless correlation was obtained that can be used to determine the mixing intensity along the coiled tube with a deviation of less than 1.5%.These results provide guidance for designing a coiled tube or optimizing the operating conditions to meet the mixing requirements of specific chemical processes.

Numerical Simulation of the Scalar Mixing Characteristics in Three-dimensional Microchannels

Based on the transport phenomena theory, the passive mixing of water and ethanol in different threedimensional microchannels is simulated numerically. The average variance of water volume fraction is used to index the mixing efficiency in the cases with different Reynolds number and different fabricated mixers. The results show that the efficiency of liquid mixing is progressively dependent on the convective transport as the Reynolds number increases. The efficiency of serpentine microchannel decreases with the increasing Reynolds number in the laminar regime. Altering the aspect ratio of channel inlet section has no significant effect on the mixing efficiency. Increasing the area of channel inlet section will cause the decrease of the mixing efficiency. The mixing in serpentine channels is the most efficient among three different mixers because of the existence of second flow introduced by its special structure.

Large eddy simulation of hot and cold fluids mixing in a T-junction for predicting thermal fluctuations

Temperature fluctuations in a mixing T-junction have been simulated on the FLUENT platform using the large eddy simulation （LES） turbulent flow model and a sub-grid scale Smagorinsky-Lilly model. The normalized mean and root mean square temperatures for describing time-averaged temperature and temperature fluctuation intensity, and the velocity are obtained. The power spectrum densities of temperature fluctuations, which are key parameters for thermal fatigue analysis and lifetime evaluation, are analyzed. Simulation results are consistent with experimental data published in the literature, showing that the LES is reliable. Several mixing processes under different conditions are simulated in order to analyze the effects of varying Reynolds number and Richardson number on the mixing course and thermal fluctuations.

A Mixed-Depth Visual Rendering Method for Bleeding Simulation

The visual fidelity of bleeding simulation in a surgical simulator is critical since it will affect not only the degree of visual realism,but also the user’s medical judgment and treatment in real-life settings.The conventional marching cubes surface rendering algorithm provides excellent visual effect in rendering gushing blood,however,it is insufficient for blood flow,which is very common in surgical procedures,since in this case the rendered surface and depth textures of blood are rough.In this paper,we propose a new method called the mixed depth rendering for rendering blood flow in surgical simulation.A smooth height field is created to minimize the height difference between neighboring particles on the bleeding surface.The color and transparency of each bleeding area are determined by the number of bleeding particles,which is consistent with the real visual effect.In addition,there is no much extra computational cost.The rendering of blood flow in a variety of surgical scenarios shows that visual feedback is much improved.The proposed mixed depth rendering method is also used in a neurosurgery simulator that we developed.

Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.

Numerical Simulation of Double Diffusive Mixed Convection in a Horizontal Annulus with Finned Inner Cylinder

The present work relates to a numerical investigation of double diffusive mixed convection around a horizontal annulus with a finned inner cylinder.The solutal and thermal buoyancy forces are sustained by maintaining the inner and outer cylinders at uniform temperatures and concentrations.Buoyancy effects are also considered,with the Boussinesq approximation.The forced convection effect is induced by the outer cylinder rotating with an angular velocity(ω)in an anti-clockwise direction.The studies are made for various combinations of dimensionless numbers;buoyancy ratio number(N),Lewis number(Le),Richardson number(Ri)and Grashof number(Gr).The isotherms,isoconcentrations and streamlines as well as both average and local Nusselt and Sherwood numbers were studied.A finite volume scheme is adopted to solve the transport equations for continuity,momentum,energy and mass transfer.The results indicate that the use of fins on the inner cylinder with outer cylinder rotation,significantly improves the heat and mass transfer in the annulus.

NUMERICAL SIMULATION OF SUPERSONIC REACTING MIXING LAYER

In this paper, the supersonic chemically reacting mixing layer is simulated with the third order ENN scheme, based on the Navier-Stokes equations, containing transport equations of all species. The numerical results show that the thickness of mixing layer increases gradually along the flow direction, and that the Kelvin-Helmholtz, instabilities may not exist in mixing layer flows.

Simulation of random mixed packing of different density particles

This paper presents the effects of density difference on the three-dimensional （3D） distribution of random mixed packing. The random mixed packing dynamics of particles of two different densities are simulated. The initial state is homogeneous, but the final packing state is inhomogeneous. The segregation phenomenon （inhomogeneous distribution） is also observed. In the final state, the top layers are composed of mostly light particles. The several layers beneath the top contain more heavy particles than light particles. At the bottom, they also contain more heavy particles than light particles. Furthermore, at both the top and the bottom, particle clustering is observed. The current study also analyses the cause of this inhomogeneity in detail. The main cause of this phenomenon is the velocity difference after collision of these two types of particles induced by the density difference. The present study reveals that even if particles were perfectly mixed, the packing process would lead to the final inhomogeneous mixture. It suggests that special treatment may be required to get the true homogeneous packing.

Investigation of gravity influence on EOR and CO_(2) geological storage based on pore-scale simulation

Gravity assistance is a critical factor influencing CO_(2)-Oil mixing and miscible flow during EOR and CO_(2)geological storage.Based on the Navier-Stokes equation,component mass conservation equation,and fluid property-composition relationship,a mathematical model for pore-scale CO_(2) injection in oilsaturated porous media was developed in this study.The model can reflect the effects of gravity assistance,component diffusion,fluid density variation,and velocity change on EOR and CO_(2) storage.For nonhomogeneous porous media,the gravity influence and large density difference help to minimize the velocity difference between the main flow path and the surrounding area,thus improving the oil recovery and CO_(2) storage.Large CO_(2) injection angles and oil-CO_(2) density differences can increase the oil recovery by 22.6% and 4.2%,respectively,and increase CO_(2) storage by 37.9% and 4.7%,respectively.Component diffusion facilitates the transportation of the oil components from the low-velocity region to the main flow path,thereby reducing the oil/CO_(2) concentration difference within the porous media.Component diffusion can increase oil recovery and CO_(2) storage by 5.7% and 6.9%,respectively.In addition,combined with the component diffusion,a low CO_(2) injection rate creates a more uniform spatial distribution of the oil/CO_(2) component,resulting in increases of 9.5% oil recovery and 15.7% CO_(2) storage,respectively.This study provides theoretical support for improving the geological CO_(2) storage and EOR processes.

Numerical Simulation of Flow Field and Flow State Division in Thin-Film Evaporators

The flow field and flow state of thin-film evaporators are complex,and it is significant to effectively divide and quantify the flow field and flow state,as well as to study the internal flow field distribution and material mixing characteristics to improve the efficiency of thin-film evaporators.By using computational fluid dynamics(CFD)numerical simulation,the distribution pattern of the high-viscosity fluid flow field in the thin-film evaporators was obtained.It was found that the staggered interrupted blades could greatly promote material mixing and transportation,and impact the film formation of high-viscosity materials on the evaporator wall.Furthermore,a flow field state recognition method based on radial volume fraction statistics was proposed,and could quantitatively describe the internal flow field of thin-film evaporators.The method divides the high-viscosity materials in the thin-film evaporators into three flow states,the liquid film state,the exchange state and the liquid mass state.The three states of materials could be quantitatively described.The results show that the materials in the exchange state can connect the liquid film and the liquid mass,complete the material mixing and exchange,renew the liquid film,and maintain continuous and efficient liquid film evaporation.

Numerical simulation of micromixing effect on the reactive flow in a co-rotating twin screw extruder

To control the multicomponent reactions in extrusion, reactive-mixing flow in a co-rotating twin screw extruder was numerically studied in the present paper. Effects of initial species distribution, rotating speed and flow rate on a competitive-parallel reaction were investigated and the relationship between mixing and reactions was discussed from the view of chemical reaction engineering. The simulation results show the studied operational parameters, which determine residence time distribution, earliness of mixing and segregation degree of reactive-mixing flows, affect the local species concentration and reaction time and hence have significant influences on the reaction extent. Orthogonal test was adopted to clarify the significance of operational parameters.The analysis shows that initial species distribution and flow rate are the most important factors in the control of reaction extent, and effect of rotating speed is conditional depending on the micro-mixing status of the fluid.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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Influence of Coriolis Parameter Variation on Langmuir Turbulence in the Ocean Upper Mixed Layer with Large Eddy Simulation

Langmuir turbulence is a complex turbulent process in the ocean upper mixed layer.The Coriolis parameter has an important effect on Langmuir turbulence through the Coriolis-Stokes force and Ekman effect,however,this effect on Langmuir turbulence has not been systematically investigated.Here,the impact of the Coriolis parameter on Langmuir turbulence with a change of latitude(LAT)from 20°N to 80°N is studied using a non-hydrostatic large eddy simulation model under an ideal condition.The results show that the ratio of the upper mixed layer depth to Ekman depth scale(RME)RME=0.266(LAT=50°N)is a key value(latitude)for the modulation effect of the Coriolis parameter on the mean and turbulent statistics of Langmuir turbulence.It is found that the rate of change of the sea surface temperature,upper mixed layer depth,entrainment flux,crosswind velocity,downwind vertical momentum flux,and turbulent kinetic energy budget terms associated with Langmuir turbulence are more evident at RME≤0.266(LAT≤50°N)than at RME≥0.266(LAT≥50°N).However,the rate of change of the depth-averaged crosswind vertical momentum flux does not have a clear variation between RME≤0.266 and RME≥0.266.The complex changes of both Langmuir turbulence characteristics and influence of Langmuir turbulence on the upper mixed layer with latitude presented here may provide more information for further improving Langmuir turbulence parameterization.