Transverse Mixing Research Articles

A genetic algorithm-based support vector machine to estimate the transverse mixing coefficient in streams

Abstract Transverse mixing coefficient (TMC) is known as one of the most effective parameters in the two-dimensional simulation of water pollution, and increasing the accuracy of estimating this coefficient will improve the modeling process. In the present study, genetic algorithm (GA)-based support vector machine (SVM) was used to estimate TMC in streams. There are three principal parameters in SVM which need to be adjusted during the estimating procedure. GA helps SVM and optimizes these three parameters automatically in the best way. The accuracy of the SVM and GA-SVM algorithms along with previous models were discussed in TMC estimation by using a wide range of hydraulic and geometrical data from field and laboratory experiments. According to statistical analysis, the performance of the mentioned models in both straight and meandering streams was more accurate than the regression-based models. Sensitivity analysis showed that the accuracy of the GA-SVM algorithm in TMC estimation significantly correlated with the number of input parameters. Eliminating the uncorrelated parameters and reducing the number of input parameters will reduce the complexity of the problem and improve the TMC estimation by GA-SVM.

Simulation study of turbulent mixing characteristics of tight lattice with triangular arrangement under blockage condition

The study of turbulent mixing in the gaps of fluid sub-channels in the tight lattice under blockage conditions is of great significance to the prediction of the thermal-hydraulic behavior of fuel assemblies under accident conditions. The CFD method was used to simulate the fluid flow phenomenon in the blockage condition in the tight lattice, and the velocity field and the turbulent mixing coefficient distribution in the section and downstream of the blockage under different blockage conditions were further compared and analyzed. The analysis results show that the blockage mainly affects the flow field of the sub-channel where it is located and the adjacent sub-channels. The turbulent mixing coefficient in these channels will increase significantly; when the sub-channel blockage rate is small, the turbulent mixing coefficient downstream of the blockage will be reduced; the short length will make the flow field near the top of blockage segment more complicated. The obtained changes of transverse and axial turbulent mixing coefficients under different blockage conditions can provide a reference for the parameter setting of the sub-channel analysis program.

Experimental investigation of solute transport in variably saturated porous media using x-ray computed tomography

Solute transport through variably saturated porous media is ubiquitous in multiple subsurface flows, piquing the geoscience community's interest. This study adopts a novel experimental approach using microfocus x-ray computed tomography for real-time imaging of a three-dimensional NaI tracer plume in a partially saturated packing column. A stabilized two-phase flow field is achievable through continuous co-injection of two-phase fluids: NaCl solvent and pump oil. Thus, the critical role of the NaCl saturation Sw and Péclet number on dispersion can be fully studied by controlling the NaCl fractional flow rate and the total flow rate from the Buckley–Leverett theory. Furthermore, we study solute transport behavior based on statistical moments, the dispersion coefficient, the dilution index, and the mean scalar dissipation rate. Experimental results indicate that the solute transport is Fickian for high Sw ≥ 0.34. In contrast, anomalous transport behavior is found for Sw < 0.34, where the concentration distribution is initially left-tailed and leptokurtic before reaching a well-dispersed regime. The dispersion coefficient is 2–10 times larger for partially saturated cases compared with the fully saturated case and shows a non-monotonical dependency on Sw. Finally, the analysis of the dilution index indicates that the overall mixing strength increases when Sw decreases, whereas the mean scalar dissipation rate reveals that the time scaling of transverse mixing is the largest at an intermediate Sw. The results can be used to elucidate the solute transport behavior in a two-phase system.

Transverse Mixing in Rivers With Longitudinally Varied Morphology

AbstractImproving the quantification of the transverse mixing coefficient in rivers is essential for a better estimation of pollutant dispersion. This coefficient is evaluated from tracing experiments or from semi‐empirical equations assuming uniform flow conditions. This assumption, verified for laboratory experiments, is questionable for river studies. For example, piedmont rivers exhibit nonuniform flows due to their longitudinal morphological variations. This work aims at studying the longitudinal variability of the transverse mixing coefficient in a river with longitudinally varied morphology and the overlooked impact of the flow nonuniformity on the coefficient’s values. Tracing experiments were conducted in the Durance River in France using slug injections and concentration measurements made at the cross‐sections delineating homogeneous sub‐reaches. Using the well‐known 1D transverse diffusion model, values of the transverse mixing coefficient are determined for all consecutive sub‐reaches. These values substantially vary along the studied river, with stronger mixing efficiency at pools and complex riffles and weaker mixing efficiency in straight sub‐reaches with emerging obstacles. The dimensionless transverse mixing coefficient is strongly related to a parameter quantifying the deviation from flow‐uniformity, i.e., indicating flow acceleration, deceleration or a succession of both within the sub‐reaches. While usual formulas from the literature fail to predict our empirical results, a new equation including the flow nonuniformity parameter fits our experimental data with high accuracy. After further validation, such equation may be used for predicting the transverse mixing coefficient in rivers with longitudinally varied morphology.

Effect of tabs on transverse jet instabilities, structure, vorticity dynamics and mixing

Abstract

Subchannel analysis of thermal-hydraulic performance in rod bundle with spacer grid considering anisotropic turbulent mixing

Combined with the relationship between the time averaged parameters of flow field and the inter-subchannel transverse turbulent mixing velocity, a method for solving the mixing velocity between adjacent subchannels is presented in this paper. Then an anisotropic mixing model, which is based on subchannel-wise inhomogeneous turbulent mixing, is presented to reflect the three-dimensional mixing effect in rod bundle with spacer grid. By comparing the anisotropic mixing model with isotropic mixing model, it is found that the anisotropic mixing model agrees well with the experimental data from literature. In addition, based on the anisotropic mixing model, analysis on the subchannels with different spacer grids is also performed, including configurations with or without the mixing vanes and different arrangements of mixing vanes. It is found that the forced mixing effect between subchannels is mainly caused by the mixing vanes of the spacer grid. Besides, the continuous change of the flow and temperature fields is also caused by mixing vanes, which improves the Departure from Nucleate Boiling Ratio (DNBR) of the rod bundle channel. Also, the effect of different mixing vane arrangements on flow and heat transfer in the rod bundle is analyzed in detail.

Large-Eddy Simulations of Transverse Jet Mixing and Flame Stability in Supersonic Crossflow

Large-eddy simulations (LES) combined with the partially stirred reactor (PaSR) combustion model are employed to investigate the turbulent mixing, combustion mode, and flame stability of a sonic hydrogen jet injecting into high-enthalpy supersonic crossflow at three momentum flux ratios , in other words, 0.71, 2.11, and 4.00, respectively. The LES accuracy in terms of the turbulent kinetic energy, power spectra density, and subgrid Damköhler number is carefully addressed against various LES resolution criteria and the experimental mean pressure distribution on the upper wall. The ignition processes with autoignition and shock compression effects are identified and analyzed. At , the shock-induced ignition occurs behind the reflected shock wave, and the combustion heat release is dominated by the premixed combustion. While for the high jet-to-crossflow momentum flux ratios, for example, and 4.00, ignition happens around the jet orifice due to the strong bow shock and reflected shock effects, and the combustion heat releases are dominated by the nonpremixed combustion. Furthermore, the mechanisms of flame stabilization, local extinction, and reignition in the transverse jet combustion in supersonic crossflow are further analyzed with the chemical explosive mode analysis.

Effective Chemical Delivery Through Multi‐Screen Wells to Enhance Mixing and Reaction of Solute Plumes in Porous Media

AbstractIn‐situ groundwater remediation is usually limited by the incomplete mixing of reactive species due to creeping flow characteristics and limited dispersion in porous media. In this study, we propose a novel approach to deliver chemicals through a multi‐screen well (MSW) to enhance the in‐situ remediation efficiency without extra energy or labor costs. The basic idea is to separate the injected solution into several plumes to enlarge the contact area between injected chemical compounds and ambient contaminants and enhance the mass exchange flux and reactive mixing. We perform laboratory experiments and numerical simulations of steady‐state instantaneous reactive transport in two‐dimensional porous media. We consider three separate screens in an MSW for the injection of treatment solutions and compare its plume distributions with a classical single‐screen well system. The experimental results confirm our conjecture and demonstrate the reliability of the numerical model. Furthermore, we derive an optimal injection interval of the MSW system by comparing analytical and numerical methods and demonstrate its capability to achieve effective transverse mixing and reaction enhancement. An interval that is smaller than the optimal injection interval leads to the exhaustion of contaminants between the injected plumes and the coalescence of the separate injected plumes at the downgradient portion along the travel distance, which reduces the effectiveness of the MSW system. We also investigate the sensitivity of the injected concentration, individual screen length, transverse dispersivity, and seepage rate on the determination of the optimal injection interval and provide suggestions about the design of an MSW system.

Numerical simulations of the transverse injection and mixing with a Mach 3 supersonic cross-flow

Numerical simulations of the transverse injection of helium (surrogate for hydrogen) into a Mach 3 cross-flow through circular and wedge injectors have been carried out. Three-dimensional, compress...

Numerical simulations of the transverse injection and mixing with a Mach 3 supersonic cross-flow

Numerical simulations of the transverse injection and mixing with a Mach 3 supersonic cross-flow

Mixing effects in the river downstream from pollution discharge point

This paper follows the propagation of pollution in a river with a rectangular cross-section of the river bed and a variable cross-sectional velocity. The calculations were made for steady flows and steady pollutant concentrations. To approximate the velocity distribution in the river bed a set of equations for current and vorticity functions was solved. The distribution of pollutant concentrations in the river was calculated from a bidirectional advection and turbulent diffusion equation. Analysis of the distribution of concentrations leads to the conclusion that the effects of transverse advection associated with a lateral inflow of pollutants disappear relatively quickly. Therefore, the distribution of concentrations in cross sections further downstream from the point of pollutant discharge can be determined quite accurately just from an advection-diffusion model, with no transverse advection effects included. Such a level of accuracy is usually sufficient to assess the impact of a pollution source on the aquatic environment. The transverse mixing of pollutants in the stream proceeds slowly and creates a large mixing zone in which the concentrations of pollutants (low but still significant for water quality) can be detected in cross-sections that are remote from the pollutant discharge point. Transverse advection may be ignored while calculating concentrations in remote cross sections at straight watercourse sections and in steady state conditions.

Enhancing transverse mixing by using triangular vane in the straight channel

The transport of pollutants in the large rivers especially in the lowest downstream reach of a river, in which the velocity and the intensity of flow turbulent become very low, is performed to a great extent by dispersion. Any measure to enhance the level of turbulence in the flow field will increase the mixing of pollutants. The main goal of the present study is to investigate how the transverse mixing is increased by using a triangular vane (TV). TV is a hydraulic structure used for bank protection and habitat restoration and is suitable for fish and other aquatic organisms. Experiments were carried out in a flume of 10m long and 0.8m wide. Two different conditions of with and no vane were tested under four different flow conditions. A salt solution was used as a tracer. An electronic concentration measuring equipment consisted of conductivity probes was used which can measure the concentration at 49 nodes in four cross-sections downstream simultaneously. The three-dimensional velocity components were also measured by using the electromagnetic velocity meter and the characteristics of three-dimensional flow patterns including turbulent kinetic energy (TKE) and the vertical distribution of the transverse velocity were analyzed. The result showed that the TV by deviating the velocity vectors to the transverse direction, by developing the secondary flows and by displacing the position of the rotating cells in different transverse sections, causes the transverse mixing to increase 3.2 times and to reduce the complete mixing length by as much as 76% compare to the case of no vane. The average values of the TKE found to be increased by as much as 3 times. Finally, a new dimensionless parameter has been proposed to correlate dimensionless transverse mixing to the flow parameters.

Modelling transverse solute mixing across a vegetation generated shear layer

ABSTRACT Transverse solute mixing across a vegetation generated horizontal shear layer was quantified using laser induced fluorometry techniques for artificial and real vegetation. A two-dimensional finite difference model (FDM) was developed to describe transverse concentration profiles for flows containing transverse variations in velocity and transverse dispersion, from a steady solute input. The FDM was employed inversely, to optimize the parameters describing the transverse distribution of the transverse dispersion coefficient for vegetation generated shear layers. When laboratory data are available, continuous function descriptions produce slightly improved FDM modelled solute concentration profiles compared with simplified step discontinuity velocity and dispersion inputs. When laboratory data are not available, estimates of step or continuous transverse distributions from other work enable concentration profiles to be predicted with a similar goodness of fit. This paper presents a validated, simple, robust finite difference model to describe the mixing of solutes in a channel containing marginal vegetation.

Multispecies Reactive Transport in a Microporous Rock: Impact of Flow Heterogeneity and Reversibility of Reaction

AbstractWe study the impact of pore space heterogeneity on mixing and reaction in porous media. We simulate the parallel injection of two streams of reactants at different pH in a three‐dimensional microporous consolidated rock whose pore space was resolved by differential micro‐CT imaging. As an exemplar of a heterogeneous medium, we consider the pore structure obtained from a Portland carbonate sample. We use direct numerical simulation to study the coupled impact of flow heterogeneity, characterized by a wide distribution of velocities and chemical reversibility on multispecies reaction. The flow field is found from the Darcy‐Brinkman equation while the advection‐diffusion equation describes transport, which is coupled to a general multispecies geochemical solver for homogeneous reactions; precipitation, and dissolution are ignored. We observe a highly nonuniform spatial distribution of concentration and rates of formation and consumption. For advection‐dominated transport, the heterogeneous flow field leads to significant transverse mixing in macropores at early times, followed by a slower mixing driven by diffusion between macropore and micropore regions. The effective rates of formation and consumption are species‐dependent and distinct in macroporosity and microporosity: while some species reach an asymptotic rate in well‐mixed regions, others still show a transient nonmonotonic behavior as a consequence of incomplete mixing. Our findings have important implications for the understanding of time‐ and space‐dependent reaction rate behavior: the coupled impact of pore space heterogeneity and reversible reactions need to be taken into account as key determinants to describe multispecies reactive transport.

A Numerical Study of the Influence of Channel-Scale Secondary Circulation on Mixing Processes Downstream of River Junctions

A rapid downstream weakening of the processes that drive the intensity of transverse mixing at the confluence of large rivers has been identified in the literature and attributed to the progressive reduction in channel scale secondary circulation and shear-driven mixing with distance downstream from the junction. These processes are investigated in this paper using a three-dimensional computation of the Reynolds averaged Navier Stokes equations combined with a Reynolds stress turbulence model for the confluence of the Kama and Vishera rivers in the Russian Urals. Simulations were carried out for three different configurations: an idealized planform with a rectangular cross-section (R), the natural planform with a rectangular cross-section (P), and the natural planform with the measured bathymetry (N), each one for three different discharge ratios. Results show that in the idealized configuration (R), the initial vortices that form due to channel-scale pressure gradients decline rapidly with distance downstream. Mixing is slow and incomplete at more than 10 multiples of channel width downstream from the junction corner. However, when the natural planform and bathymetry are introduced (N), rates of mixing increase dramatically at the junction corner and are maintained with distance downstream. Comparison with the P case suggests that it is the bathymetry that drives the most rapid mixing and notably when the discharge ratio is such that a single channel-scale vortex develops aided by curvature in the post junction channel. This effect is strongest when the discharge of the tributary that has the same direction of curvature as the post junction channel is greatest. A comprehensive set of field data are required to test this conclusion. If it holds, theoretical models of mixing processes in rivers will need to take into account the effects of bathymetry upon the interaction between river discharge ratio, secondary circulation development, and mixing rates.

Predicting Transverse Mixing Efficiency Downstream of a River Confluence

AbstractPredicting mixing processes, especially transverse mixing, downstream of river confluences, is necessary for assessing and modeling the fate of pollutants transported in river networks, but it is still challenging. Typically, there is a lack of transverse mixing solutions implemented in 1‐D hydrodynamical models widely used in river engineering applications. To investigate the mixing processes developing downstream of a medium‐sized river confluence, three high‐resolution in situ surveys are conducted at the Rhône‐Saône confluence in France, based on geolocated specific conductivity and hydroacoustic measurements. Contrasting mixing situations are observed depending on hydrological conditions. In some cases, the two flows mix slowly due to turbulent shear at their vertical interface. This can be modeled by an analytical solution of the advection‐diffusion equation. In other cases, the waters from one of the two tributaries move under the waters of the other tributary. The induced local circulation enhances transverse mixing but not vertical mixing and the flow remains stratified vertically, which may be missed when surface or satellite images are analyzed qualitatively. Stratification may be predicted by comparing the time scales for shear and density‐driven adjustment. Shear‐dominated transverse mixing of depth‐averaged concentrations can be predicted analytically and implemented in 1‐D hydrodynamical models. However, the initiation of apparently rapid transverse mixing due to density‐driven circulation remains to be better understood and quantified.

Bottom-charmed meson spectrum from a QCD approach based on the Tamm-Dancoff approximation

The bottom-charmed meson spectrum is studied in this work via an effective version of the Coulomb gauge QCD Hamiltonian. The Tamm-Dancoff approximation is employed to estimate the energies of the low-lying and radial-excited $B_c$ states with quantum numbers $J^P = 0^{-}, 0^{+}, 1^{-}, 1^{+}, 2^{+}, 2^{-}$. In particular, we analyze the effects of incorporating an effective transverse hyperfine interaction and spin mixing. The Regge trajectories and hyperfine splitting of both $S$- and $P$-wave states are also examined. The numerical results are compared with available experimental data and theoretical predictions of other models.

Viscoplastic displacements in axially rotating pipes

We investigate experimentally the effects of a pipe axial rotation on buoyant miscible displacement flows in an inclined pipe. The displacing Newtonian fluid (salt-water solution) is heavier than the displaced viscoplastic one (Carbopol solution). Via image processing techniques and ultrasound Doppler velocity measurements, we analyze the key flow features such as the flow patterns, the velocity and concentration fields, and the leading front velocity (Vˆf) as well as the trailing front velocity (Vˆt) of the displacement flow. The main flow parameters in our experiments are the pipe inclination angle, the small density difference between the two fluids, the yield stress of the displaced fluid, the imposed mean flow velocity (Vˆ0), and most importantly the pipe rotation speed. We find that increasing the pipe rotation speed enhances the transverse mixing between the two fluids and, above a critical transition, leads to a complete removal of the displaced viscoplastic fluid. We classify the flow regimes into efficient and inefficient displacement flows, using appropriate dimensionless groups, i.e. the Rossby number (Rb) and the Froude number (Fr). We find that the critical transition between the two flow regimes can be roughly described by a critical Rossby number (Rbc), as a function of Fr, independent of the other flow dimensionless numbers. For Rb≤Rbc, we find that Vˆf≈1.6Vˆ0 and Vˆt≈Vˆ0, while for Rb>Rbc we propose an empirical relation for the leading front velocity versus the Rossby number. These findings can offer new insight to control viscoplastic displacement flows using rotational motion.

Exchange flows in axially rotating pipes

Buoyancy-induced flows in many industrial and natural processes are significantly affected by rotation. The effects of pipe axial rotation on flow patterns and front dynamics of buoyant miscible exchange flows are studied experimentally and numerically. With increasing rotation speed, the flow pattern is experimentally shown to transition from a slumping interface to complete transverse mixing. To complement experimental observations, specific simulations provide a cross-sectional view of the pipe, in which the front dynamics is shown to change as the rotation speed increases.

Effects of Sinusoidal Excitation on Transverse Jet Dynamics, Structure, and Mixing

This experimental study explored the effects of axisymmetric sinusoidal excitation on structural and mixing characteristics in the equidensity jet in crossflow (JICF). Planar laser-induced fluorescence imaging of acetone seeded in the jet fluid was used in this quantification, where the jet Reynolds number was fixed at and crossflow velocity was varied. Jet-to-crossflow momentum-flux ratios ranged from , with a convectively unstable upstream shear layer (USL) in the absence of forcing, to , with a globally unstable USL. Sinusoidal excitation had a relatively significant influence on the convectively unstable JICF at larger values, especially when the USL was locked-in to the forcing frequency, causing the jet cross section to become more symmetric and causing molecular mixing, quantified in both centerplane and cross-sectional planes, to improve. For a globally unstable JICF, only sinusoidal forcing corresponding to clear lock-in conditions, close to the fundamental shear-layer frequency and/or at very high amplitudes, affected jet structure, with somewhat moderate improvements in molecular mixing. Typically, excitation conditions creating enhanced jet penetration and spread did not correlate directly with improved molecular mixing; there was a stronger correlation of improved mixing with creation of a more symmetric jet cross section, in some cases with a counter-rotating vortex pair structure.