Experimental characterization of mixing and flow field in the liquid plugs of gas–liquid flow in a helically coiled reactor

Flow mixing of two miscible liquids with the addition of gas bubbles is a process often found in industrial chemical apparatus for the production of primary matter. The ongoing optimization of such processes also involves the transformation of batch to continuous mode operation. In that case, the use of helically coiled tubes is an interesting alternative, since those reactors have narrow residence time distributions, very good radial mixing properties and excellent mass transfer can be realized between gases and liquids. For these reasons, in this study the mixing of two miscible liquids with addition of air bubbles in gas–liquid flows has been characterized in a horizontal helically coiled reactor in the laminar flow regime at $${\text{Re}}_{{{\text{total}}}} = 300 \ldots 1088$$ Re total = 300 … 1088 . Eight different superficial liquid velocities and five superficial gas velocities were investigated. In order to characterize mixing in the liquid plugs between two bubbles, laser-induced fluorescence of resorufin was used and particle image velocimetry has been employed to characterize the flow field. Pseudo-3D-visualizations of the resorufin concentration and the Q-criterion, representing the mixing efficiency and vorticity, respectively, were established for individual liquid plugs from the time-resolved measurement results. A time-resolved mixing coefficient, as well as a mean mixing coefficient obtained from multiple liquid plugs, is calculated from the fluorescence images for all examined flow conditions. The experimental results clearly show an increase in the mixing coefficient compared to single-phase conditions, caused by the bubbles. However, distinct mixing pattern, depending on the flow structure, can be recognized on different locations inside the liquid plug. Compared to a stationary case without air bubbles, mixing is worse behind the bubbles and increases inside the plug, reaching a maximum mixing coefficient in front of the next bubble. Overall the mixing coefficient is always increased by the presence of the bubbles. Pseudo-3D-visualizations of the Q-criterion and the vorticity show the presence of secondary vortices right in front of the bubbles, shifted to the outer tube walls, and in addition to the steady Dean vortices. In small plugs, these secondary vortices appear in the whole plug and increase the mixing coefficient drastically. Graphical Abstract

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

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 of turbulent mixing rate in simulated subchannels of a reactor rod bundle

Subchannel analysis codes are widely used for the thermal-hydraulic design of nuclear reactor rod bundle. The effectiveness of subchannel analysis codes depends on turbulent mixing between these subchannels. Turbulent mixing has no direct contribution to the axial mass flow rate through subchannel but it will cause exchange of momentum and energy between the neighboring subchannels. Thus, it is important to evaluate the turbulent mixing coefficient for reactor rod bundle as it is a significant factor in the lateral energy and momentum equation for subchannel analysis codes like COBRA IIIC, COBRA-IV and MATRA LMR-FB. With the rapid developments in computational fluid dynamics and computer performance, three-dimensional analyses of turbulent flows occurring in the nuclear rod bundle have become more prominent. Several numerical analyses have already been attempted to investigate the flow behavior in rod bundles of different reactors. Much of these are dedicated to find out the structure of turbulence in rod bundle but a few analyses has been done to evaluate the magnitude of the turbulent mixing coefficient. In view of this, CFD analyses were carried out to determine the turbulent mixing coefficient in the simulated sub-channels of the reactor rod bundle. Previous studies on the structure of turbulence reveals that it is highly anisotropic. Hence, the Reynolds Stress Model (RSM), finer mesh and near wall distance ( y + ≤ 2) is required to capture turbulent mixing phenomena. The validation of results is done by comparing with subchannel mixing experiments.

Modeling Water-Mass Distributions in the Modern and LGM Ocean: Circulation Change and Isopycnal and Diapycnal Mixing

Paleoproxy observations suggest that deep-ocean water-mass distributions were different at the Last Glacial Maximum than they are today. However, even modern deep-ocean water-mass distributions are not completely explained by observations of the modern ocean circulation. This paper investigates two processes that influence deep-ocean water-mass distributions: 1) interior downwelling caused by vertical mixing that increases in the downward direction and 2) isopycnal mixing. Passive tracers are used to assess how changes in the circulation and in the isopycnal-mixing coefficient impact deep-ocean water-mass distributions in an idealized two-basin model. We compare two circulations, one in which the upper cell of the overturning reaches to 4000-m depth and one in which it shoals to 2500-m depth. Previous work suggests that in the latter case the upper cell and the abyssal cell of the overturning are separate structures. Nonetheless, high concentrations of North Atlantic Water (NAW) are found in our model’s abyssal cell: these tracers are advected into the abyssal cell by interior downwelling caused by our vertical mixing profile, which increases in the downward direction. Further experiments suggest that the NAW concentration in the deep South Atlantic Ocean and in the deep Pacific Ocean is influenced by the isopycnal-mixing coefficient in the top 2000 m of the Southern Ocean. Both the strength and the vertical profile of isopycnal mixing are important for setting deep-ocean tracer concentrations. A 1D advection–diffusion model elucidates how NAW concentration depends on advective and diffusive processes.

EXTENDING CTF MODELING CAPABILITIES TO SFRs AND VALIDATION AGAINST SHRT TESTS

The utilization of liquid metals as coolants for fast reactors brings several economical and practical advantages that lead to a sustainable future for nuclear energy. Molten sodium is used as a coolant in Sodium Fast Reactors (SFRs). Sodium is relatively cheaper than other metal coolants. It requires lower pumping power, causes less neutron moderation and it is non-corrosive to the fuel cladding. The SFR hexagonal subassemblies are relatively smaller than Light Water Reactors (LWRs) subassemblies. The differences in the geometrical design of SFRs compared to LWRs lead to different physical behavior of the coolant. Several models and correlations particular to sodium were implemented in thermal-hydraulics (TH) computer codes in order to model the coolant behavior accurately. CTF is a subchannel TH code that was designed and validated for LWRs. In this work, the capabilities of the code were extended to SFRs by incorporating sodium coolant properties and correlations for friction factor, flow mixing coefficient and conduction heat transfer. The code was then validated against selected steady state data from the Experimental Breeder Reactor II Shutdown Heat Removal Tests SHRT-17 and SHRT-45R. CTF was used to simulate the instrumented subassemblies XX09 and XX10. The results demonstrate the capability of CTF to model SFRs. Code validation is currently being extended to the transient phases of the SHRT experiments.

Mixing characterization in different helically coiled configurations by laser-induced fluorescence

Flow Mixing of two miscible liquids has been characterized experimentally in three different helically coiled reactor configurations of two different lengths in the laminar flow regime at Re = 50…1000. A straight helical coil, a coiled flow inverter, and a new coiled flow reverser have been built, each in a 3-turn and a 6-turn configuration. Laser-induced fluorescence of resorufin has been used to visualize and quantify mixing in cross-sections throughout the reactors. A mixing coefficient is derived from the fluorescence images to allow for a quantitative measure and comparison of the six configurations. It becomes obvious from these experimental results, that an early flow redirection in the helical configuration is beneficial to mixing. The 3-turn reactors achieve nearly the same mixing coefficients as the 6-turn reactors with the double length. This can be explained by the stabilizing effect of the Dean vortices in the helix, which develop during the first two turns. After that, the liquid is trapped inside the vortices and further mixing is inhibited. Accordingly, the coiled flow inverter and coiled flow reverser configurations lead to much higher mixing coefficients than the straight helical coil. The results of these measurements are now used for validation of numerical simulations, which reproduce the geometrical and flow conditions of the experiments. Some exemplary results of these calculations are also shown in this article. Graphic abstract Mass fractions of tracer fluid at Re = 500 in the six examined helix configurations.

Chi-Square and Student Bridge Distributions and the Behrens–Fisher Statistic

We prove that the Behrens–Fisher statistic follows a Student bridge distribution, the mixing coefficient of which depends on the two sample variances only through their ratio. To this end, it is first shown that a weighted sum of two independent normalized chi-square distributed random variables is chi-square bridge distributed, and secondly that the Behrens–Fisher statistic is based on such a variable and a standard normally distributed one that is independent of the former. In case of a known variance ratio, exact standard statistical testing and confidence estimation methods apply without the need for any additional approximations. In addition, a three pillar bridges explanation is given for the choice of degrees of freedom in Welch’s approximation to the exact distribution of the Behrens–Fisher statistic.

Age distribution and organic matter degradation in bioturbated sediment

<p>Bioturbation is an important process in the early diagenesis of soft marine sediment. Benthic infaunal activity, such as feeding, burrowing and ploughing redistributes particles within the topmost layers of the sediment. Recently deposited particles are mixed into deeper sediment depth layers and old material remains longer near the surface. A sediment layer thus contains an assemblage of particles from young to very old ages. Under certain assumptions, bioturbational mixing can be modelled as a diffusive process with the macroscopic mixing coefficient D<sub>B</sub>. Here we model the age distribution of the bioturbated sedimentary record with a depth dependent mixing coefficient D<sub>B</sub>(z). The potential age bias introduced by mixing is typically higher than multiples of the mean mixed layer residence time, which scales linearly with the ratio of mixed layer depth and sediment accumulation rate. Scaling the mixing intensity has only a minor effect, as most marine environments are mixing dominated.</p><p>The rate of organic matter degradation can been modelled empirically as an age dependent process, with recently deposited, fresh organic matter having higher reactivities than older and more refractory material. With insights into the age distribution, this allows to couple the degradation of organic matter with bioturbation and estimate the burial of carbon.</p>