Scalar Mixing Research Articles

A Multistate Model Incorporating Relative Survival Extrapolation and Mixed Time Scales for Health Technology Assessment.

Multistate models have been widely applied in health technology assessment. However, extrapolating survival in a multistate model setting presents challenges in terms of precision and bias. In this article, we develop an individual-level continuous-time multistate model that integrates relative survival extrapolation and mixed time scales. We illustrate our proposed model using an illness-death model. We model the transition rates using flexible parametric models. We update the hesim package and the microsimulation package in R to simulate event times from models with mixed time scales. This feature allows us to incorporate relative survival extrapolation in a multistate setting. We compare several multistate settings with different parametric models (standard vs. flexible parametric models), and survival frameworks (all-cause vs. relative survival framework) using a previous clinical trial as an illustrative example. Our proposed approach allows relative survival extrapolation to be carried out in a multistate model. In the example case study, the results agreed better with the observed data than did the commonly applied approach using standard parametric models within an all-cause survival framework. We introduce a multistate model that uses flexible parametric models and integrates relative survival extrapolation with mixed time scales. It provides an alternative to combine short-term trial data with long-term external data within a multistate model context in health technology assessment.

Preserving large-scale features in simulations of elastic turbulence

Simulations of elastic turbulence, the chaotic flow of highly elastic and inertialess polymer solutions, are plagued by numerical difficulties: the chaotically advected polymer conformation tensor develops extremely large gradients and can lose its positive-definiteness, which triggers numerical instabilities. While efforts to tackle these issues have produced a plethora of specialized techniques – tensor decompositions, artificial diffusion, and shock-capturing advection schemes – we still lack an unambiguous route to accurate and efficient simulations. In this work, we show that even when a simulation is numerically stable, maintaining positive-definiteness and displaying the expected chaotic fluctuations, it can still suffer from errors significant enough to distort the large-scale dynamics and flow structures. We focus on two-dimensional simulations of the Oldroyd-B and FENE-P equations, driven by a large-scale cellular body forcing. We first compare two positivity-preserving decompositions of the conformation tensor: symmetric square root (SSR) and Cholesky with a logarithmic transformation (Cholesky-log). While both simulations yield chaotic flows, only the latter preserves the pattern of the forcing, i.e. its fluctuating vortical cells remain ordered in a lattice. In contrast, the SSR simulation exhibits distorted vortical cells that shrink, expand and reorient constantly. To identify the accurate simulation, we appeal to a hitherto overlooked mathematical bound on the determinant of the conformation tensor, which unequivocally rejects the SSR simulation. Importantly, the accuracy of the Cholesky-log simulation is shown to arise from the logarithmic transformation. We also consider local artificial diffusion, a potential low-cost alternative to high-order advection schemes. Unfortunately, the artificially enhanced diffusive smearing of polymer stress in regions of intense stretching substantially modifies the global dynamics. We then show how the spurious large-scale motions, identified here, contaminate predictions of scalar mixing. Finally, we discuss the effects of spatial resolution, which controls the steepness of gradients in a non-diffusive simulation.

On the origin of counter-gradient transport in turbulent scalar flux: physics interpretation and adjoint data assimilation

The present study offers a twofold contribution on counter-gradient transport (CGT) of turbulent scalar flux. First, by examining turbulent scalar mixing through synchronized particle image velocimetry and planar laser-induced fluorescence on an inclined jet in cross-flow, we clarify the previously unexplained phenomenon of CGT, revealing key flow structures, their spatial distribution and modelling implications. Statistical analysis identifies two distinct CGT regions: local cross-gradient transport in the windward shear layer and non-local effects near the wall after injection. These behaviours are driven by specific flow structures, namely Kelvin–Helmholtz vortices (local) and wake vortices (non-local), suggesting that scalar flux can be decomposed into a gradient-type term for gradient diffusion and a term for large-eddy stirring. Second, we propose a new approach for reconstruction of turbulent mean flow and scalar fields using continuous adjoint data assimilation (DA). By rectifying model-form errors through anisotropic correction under observational constraints, our DA model minimizes discrepancies between experimental measurements and numerical predictions. As expected, the introduced forcing term effectively identifies regions where traditional models fall short, particularly in the jet centreline and near-wall regions, thereby enhancing the accuracy of the mean scalar field. These enhancements occur not only within the observation region but also in unseen regions, underscoring present DA approach's reliability and practicality for reproducing mean flow behaviours from limited data. These findings lay a solid foundation for adjoint-based model-consistent data-driven methods, offering promising potential for accurately predicting complex flow scenarios like film cooling.

Competitive influence of interface effect, scale effect and mixed salt ratio on thermal conductivity of mesoporous complex nitrate

The rising prominence of energy security and climate change issues necessitates the advancement of sustainable energy development and energy storage technologies. Enhancing the capabilities of mesoporous composite phase change materials (CPCMs) has gained considerable research interest. CPCM’s heat storage and release performance is largely determined by its thermal conductivity. While the existing literature has documented the individual effects of the composition ratio of mixed molten salts, scale effects, and interfacial effects on thermal conductivity, no studies have been found that investigate the competitive interplay among these three factors with respect to their impact on thermal conductivity. This study aims to gain a deeper insight into the thermal conductivity changes of CPCM consisting of mixed molten salts as the phase change material (PCM) and mesoporous skeleton. A combination of molecular dynamics simulations and experimental investigations was employed to explore how interface effects, scale effects, and the proportion of mixed salts contribute to the thermal conductivity of CPCM. The findings indicate that augmented thermal conductivity, resulting from interface effects, supersedes the diminishing effects of interionic interactions. Compared to mixed salt ratios, interface effects primarily result in variations in the thermal conductivity of CPCM. The thermal conductivity of mixed nitrates escalates alongside scale increases. In the 3–4 nm range, the scale effect and mixed nitrate proportions do not notably compete in terms of influence on thermal conductivity, interface effects are more profound than scale effects. In the 4–9.5 nm range, the scale effect is more profound than mixed nitrate ratios. If the skeleton transitions from SiO2 to Al2O3, the impact of the interface effect on thermal conductivity is greater influential than the scale effect. While transitioning the interface from Al2O3 to ceramic, the effect of the interface is less than or equal to that of the scale effect on the thermal conductivity.

Co-evolutionary dynamics for two adaptively coupled Theta neurons.

Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple network of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of adaptivity in the coupling strength, a, influences the dynamics. We first investigate the dynamics possible in the non-adaptive limit; our bifurcation analysis reveals stability regions of quiescence and spiking behaviors, where the spiking frequencies mode-lock in a variety of configurations. Second, as we increase the adaptivity a, we observe a widening of the associated Arnol'd tongues, which may overlap and give room for multi-stable configurations. For larger adaptivity, the mode-locked regions may further undergo a period-doubling cascade into chaos. Our findings contribute to the mathematical theory of adaptive networks and offer insights into the potential mechanisms underlying neuronal communication and synchronization.

Scalar mixing and entrainment in an axisymmetric jet subjected to external turbulence

The present study aims to understand the process of turbulent entrainment into a jet, as affected by background turbulence, using scalar statistics. Planar laser-induced fluorescence was employed to capture the orthogonal cross sections of the jet at a fixed downstream station with varying background turbulence intensities and length scales. The conditional scalar profiles revealed that the thickness of the scalar turbulent/turbulent interface is greater than that of the traditional turbulent/non-turbulent interface, and the interfacial thickness is an increasing function of the background turbulence intensity. Although nibbling remains the primary entrainment mechanism in the far field, increased occurrence of concentration “holes” within the interfacial layer in the presence of ambient turbulence suggests a more significant role of large-scale engulfment in the turbulent/turbulent entrainment process (although still below 1% of the total mass flux). Enhanced contribution of the area of detached jet patches (i.e., “islands”) to that of the main jet is hypothesized to be evidence of intense detrainment events in the background turbulence. This can potentially contribute to a reduced net entrainment into the jet, which manifests as less negative values of scalar skewness within the jet core.

Large Eddy Simulation of an impinging Jet for Cooling of Blades

Abstract The impinging jet shows extremely high performance in local blade cooling and has been widely applied. In this study, high precision Large Eddy Simulation (LES) was employed to simulate compressible fully turbulent impinging jet under specific conditions, using three subgrid-scale (SGS) models - the Smagorinsky model (SM), the Coherent-structure Smagorinsky Model (CSM), and the Selective Mixed Scale Model (SMSM). The predictive accuracy and computational efficiency of the three SGS models were evaluated. Compared with existing DNS and experimental results, the results indicate that there is no significant difference among the three models in computational efficiency. However, subgrid models have a crucial impact on heat transfer. The SMSM model, which utilizes small-scale turbulence information, can better simulate the heat transfer in the impingement region compared with the SM model and the CSM model.

Glaciation of mixed-phase clouds: insights from bulk model and bin-microphysics large-eddy simulation informed by laboratory experiment

Abstract. Mixed-phase clouds affect precipitation and radiation differently from liquid and ice clouds, posing greater challenges to their representation in numerical simulations. Recent laboratory experiments using the Pi Cloud Chamber explored cloud glaciation conditions based on increased injection of ice-nucleating particles. In this study, we use two approaches to reproduce the results of the laboratory experiments: a bulk scalar mixing model and large-eddy simulation (LES) with bin microphysics. The first approach assumes a well-mixed domain to provide an efficient assessment of the mean cloud properties for a wide range of conditions. The second approach resolves the energy-carrying turbulence, the particle size distribution, and their spatial distribution to provide more details. These modeling approaches enable a separate and detailed examination of liquid and ice properties, which is challenging in the laboratory. Both approaches demonstrate that, with an increased ice number concentration, the flow and microphysical properties exhibit the same changes in trends. Additionally, both approaches show that the ice integral radius reaches the theoretical glaciation threshold when the cloud is subsaturated with respect to liquid water. The main difference between the results of the two approaches is that the bulk model allows for the complete glaciation of the cloud. However, LES reveals that, in a dynamic system, the cloud is not completely glaciated as liquid water droplets are continuously produced near the warm lower boundary and subsequently mixed into the chamber interior. These results highlight the importance of the ice mass fraction in distinguishing the mixed-phase clouds and ice clouds.

Synthesis, performance and application of environmental protection scale inhibitorβ-CD-MA-SSS copolymer——in electric power industry

The issue of water scaling in the treatment of cooling water has become an imperative problem that should be solved urgently for the sake of safe operation in large-scale flexible DC converter stations. However, the coexistence of Ca2+ and Mg2+ in high content in this sort of pending raw water is quite hard to tackle. β-CD-MA-SSS, an eco-friendly ternary co-polymer antiscalant with good performance of inhibiting the formation of scale, was applied to address this conundrum in this paper. The efficacy of the antiscalant β-CD-MA-SSS was investigated in cooling water systems under the conditions of low hardness, low alkalinity, a temperature not exceeding 80 °C, and a pH range of 6–8. After optimization, this reagent dem onstrated an excellent scale inhibition rate up to 80% for both calcium carbonate and calcium-magnesium mixed scales. Scanning electron microscopy (SEM) analysis revealed a noticeable reduction in the size of CaCO3 particles when subjected to the action of β-CD-MA-SSS. It was postulated from FTIR analysis that nanoinpurity and chelation effects mainly contributed to the mixed scale inhibition. Further, the effect of β-CD-MA-SSS on the actual production wastewater was comprehensively evaluated from the technical, economic and environmental aspects.

Prevalence, Symptom Profiles, and Correlates of Mixed Anxiety-Depression in Male and Female Autistic Youth.

Relatively little attention has been given to mixed anxiety and depression in autistic youth, particularly how this differs between males and females. This study investigated sex-based differences in the prevalence and correlates of mixed anxiety and depression in a sample of 51 autistic males (M age = 10.16 yr, SD = 2.81 yr, and range = 6 yr to 17 yr) and 51 autistic females (M age = - 10.07 yr, SD = 2.76 yr, and range = 6 yr to 17 yr), matched for age, IQ, and autism severity. Self-reports on generalised anxiety disorder and major depressive disorder, morning salivary cortisol, ADOS-2 scores, and WASI-II full-scale scores were collected from these autistic youth, and data on the ASD-related symptoms of these youth were collected from their parents. The data were analysed for total anxiety-depression score levels, for the underlying components of this scale, and for the individual items used in the scale. The results indicate no significant sex differences for the prevalence of mixed anxiety and depression total scores or the underlying components of anxiety and depression or for the individual items of the mixed anxiety-depression scale. There were sex differences in the significant correlates of mixed anxiety and depression: morning cortisol and ASD-related difficulties in social interaction for females, and ASD-related behaviour for males. Males' feelings of being restless or edgy were correlated with their social interaction and repetitive and restricted behaviour. Females' difficulties in social interaction were correlated with their concerns about their abilities and their sleeping problems. Females' sleeping problems, their tendency to talk about dying, and feeling worthless, were correlated with their morning cortisol. These findings suggest that, while mixed anxiety and depression is experienced similarly by autistic males and females at the global, component, and individual item levels, specific aspects of the symptomatology of mixed anxiety and depression are differently associated with aspects of their ASD-related symptomatology and their levels of chronic physiological stress for males and females.

A variable turbulent Schmidt number model in Jet-in-Crossflow simulation and its applications

This study proposes a variable turbulent Schmidt number (Sct) model to improve the precision of Reynolds-Averaged Navier-Stokes (RANS) simulations for Jet-in-Crossflow (JICF) scalar mixing phenomena, with a particular focus on hydrogen/air mixing characterized by strong density variations. By incorporating a correction term associated with turbulent kinetic energy based on a selected Sct value, the model aims to amplify the diffusion rate of the jet, particularly in regions where the interaction between the mainstream flow and the jet is significant. This enhancement in simulation accuracy is validated against Large Eddy Simulation (LES) results, which serve as the benchmark for analysis. Statistical analysis of LES results reveals a notable increase in the turbulent diffusion coefficient in regions characterized by strong interactions between the jet and mainstream flow. Meanwhile, minimal variation in turbulent viscosity is observed, resulting in a reduced Sct in areas with high turbulent kinetic energy. The proposed model is validated within a open-space JICF case, a micro-tube JICF case and a free jet case. In micro-tube JICF scenarios, initial simulations with a fixed Sct value were conducted. Following comparison, a value of 0.7 was identified as the basis for correction. Subsequently, the variable Sct model was implemented, thereby enhancing the accuracy of RANS simulations in micro-tubes.

Software application profile: tpc and micd-R packages for causal discovery with incomplete cohort data.

The Peter Clark (PC) algorithm is a popular causal discovery method to learn causal graphs in a data-driven way. Until recently, existing PC algorithm implementations in R had important limitations regarding missing values, temporal structure or mixed measurement scales (categorical/continuous), which are all common features of cohort data. The new R packages presented here, micd and tpc, fill these gaps. micd and tpc packages are R packages. The micd package provides add-on functionality for dealing with missing values to the existing pcalg R package, including methods for multiple imputations relying on the Missing At Random assumption. Also, micd allows for mixed measurement scales assuming conditional Gaussianity. The tpc package efficiently exploits temporal information in a way that results in a more informative output that is less prone to statistical errors. The tpc and micd packages are freely available on the Comprehensive R Archive Network (CRAN). Their source code is also available on GitHub (https://github.com/bips-hb/micd; https://github.com/bips-hb/tpc).

Mixing in two-dimensional shear flow with smooth fluctuations.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar mixing, e.g., inside a large-scale coherent vortex forming in two-dimensional turbulence or in elastic turbulence in a microchannel. We examine both the decaying case and the case of the continuous forcing of the scalar variances. In both cases dynamics possesses strong intermittency, which can be characterized via the single-point moments and correlation functions calculated in our work. We present general qualitative properties of pair correlation function as well as certain quantitative results obtained in the framework of the model with fluctuations that are short correlated in time.

Vortical structures and passive scalar transport in starting process of annular purging jet

The evolution of vortical structures and passive scalar transport in the starting process of annular purging jets are numerically investigated by large eddy simulation. Three flow configurations with different nozzle-to-plate distances at a fixed radius ratio of 0.71 and the Reynolds number of 13 750 are simulated. The numerical results are validated against documented experimental data. Three stages during the evolution are proposed based on instantaneous flow visualizations and assessed by calculating the circulation changes of the annular jets and vortex rings. The vortical structures are identified to understand the three-dimensional characteristics. The entrainment process is analyzed focusing on the passive scalar transport in the flow fields and is correlated with the cleaning performance of annular purging jets. The flow structures dominate the process of scalar mixing, especially the inner and outer vortex rings. The large-scale motions of trailing jets cause the intermittent events of scalar transport. During the starting process, the cleaning performance is better with a smaller nozzle-to-plate distance, while the cleaning efficiency may reach the optimum at a moderate distance. The cleaning process is limited by the scalar diffusion and entrainment process. These findings highlight the significance of flow structures for effective cleanness of temperature and contaminations in the purging systems.

Validation of a Hybrid Domain Overlapping Coupling Between SAM and CFD Against the TALL-3D Transients

The system thermal-hydraulic (STH) code SAM has been coupled to the computational fluid dynamics (CFD) code Simcenter STARCCM+ utilizing a hybrid domain overlapping coupling method in space and an explicit coupling in time. The coupling aims to extend the STH code’s applicability to scenarios where local momentum and energy transfers are important yet difficult for STH standalone models to capture, such as three-dimensional (3D) mixing and thermal stratification. The coupling method’s numerical stability was previously verified against multiple test cases including two closed-loop configurations, and it was validated against a double T-junction experiment with 3D scalar mixing. In the present work, the method is validated against the TALL-3D STH/CFD coupling benchmark facility. TALL-3D is a liquid-metal facility with a large, pool-type enclosure (test section) that exhibits 3D flow effects to be modeled by a CFD code. The rest of the system exhibits approximately one-dimensional behavior that is well predicted by a STH code. First, a STAR-CCM+ CFD model of the 3D test section is validated against experimental temperature data. Then a SAM-STARCCM+ coupled model is validated against six different TALL-3D steady states and includes SAM standalone results for comparison. Last, the coupled model is validated against two TALL-3D transients: one exhibiting flow reversal in the test section and one exhibiting nonlinear, limit cycle oscillations (LCOs). For the first transient, the SAM-STARCCM+ coupled model properly predicts an increase in the test section’s inlet temperature during flow reversal, and this increase is not predicted by the SAM standalone model. The coupled model also better predicts initial flow recovery and subsequent oscillations as the system approaches a final natural circulation state. For the second transient, no true final steady state is observed due to LCOs. Neither the SAM-STARCCM+ coupled model nor the SAM standalone model can perfectly capture the experiment’s changing oscillation frequency during the transient. Nevertheless, the coupled model does reproduce the general oscillatory feedback observed. This is a significant achievement because the present coupling only uses an explicit coupling in time, as opposed to a tighter, semi-implicit coupling. In comparison, STH/CFD coupling efforts previously performed by other authors required a semi-implicit coupling to obtain similar results to this work. The strengths of the novel coupling scheme validated in the present paper lie in the superior convergence characteristics and the much simpler, nonintrusive implementation.

Numerical Investigation of Observational Flux Partitioning Methods for Water Vapor and Carbon Dioxide

AbstractWhile yearly budgets of CO2 flux (Fc) and evapotranspiration (ET) above vegetation can be readily obtained from eddy‐covariance measurements, the separate quantification of their soil (respiration and evaporation) and canopy (photosynthesis and transpiration) components remains an elusive yet critical research objective. In this work, we investigate four methods to partition observed total fluxes into soil and plant sources: two new and two existing approaches that are based solely on analysis of conventional high frequency eddy‐covariance (EC) data. The physical validity of the assumptions of all four methods, as well as their performance under different scenarios, are tested with the aid of large‐eddy simulations, which are used to replicate eddy‐covariance field experiments. Our results indicate that canopies with large, exposed soil patches increase the mixing and correlation of scalars; this negatively impacts the performance of the partitioning methods, all of which require some degree of uncorrelatedness between CO2 and water vapor. In addition, best performances for all partitioning methods were found when all four flux components are non‐negligible, and measurements are collected close to the canopy top. Methods relying on the water‐use efficiency (W) perform better when W is known a priori, but are shown to be very sensitive to uncertainties in this input variable especially when canopy fluxes dominate. We conclude by showing how the correlation coefficient between CO2 and water vapor can be used to infer the reliability of different W parameterizations.

Two Film Approach to Continuum Scale Mixing and Dispersion with Equilibrium Bimolecular Reaction

Reliable reactive transport models require careful separation of mixing and dispersion processes. Here we treat displacing and displaced fluids as two separate fluid phases and invoke Whitman’s classical two-film theory to model mass transfer between the two phases. We use experimental data from Gramling’s bimolecular reaction experiment to assess model performance. Gramling’s original model involved just three coupled PDEs. In this context, our new formulation leads to a set of seven coupled PDEs but only requires the specification of two extra parameters, associated with the mass transfer coefficient and its dependence on time. The two film mass transfer model provides a simple and theoretically based method for separating mixing from dispersion in Eulerian continuum-scale methods. The advantage of this approach over existing methods is that it enables the simulation of equilibrium chemical reactions without having to invoke unrealistically small reaction rate coefficients. The comparison with Gramling’s experimental data confirms that our proposed method is suitable for simulating realistic and complicated bimolecular reaction behaviour. However, further work is needed to explore alternative methods for avoiding the need of a time-dependent mass transfer rate coefficient.

MARKET INDICATORS OF CHARUTINHO (Hemiodus spp.) PICKLE

Fresh samples of charutinho (Hemiodus spp.) were used to prepare four fish pickles formulations: F1 = 55v4s, F2 = 55v5s, F3 = 45v4s e F4 = 45v5s), which differ in the percentual content of alcohol vinegar and common iodized salt, indicated by numbers before the letters “v” and “s” of formulations code. They were analyzed by 78 untrained judges as following indicators and hedonic scale: acceptability (seven points), purchase intention (five points), and consumption frequency (mixed scale). Mostly, the judges accepted the formulations with minor vinegar content (F3 and F4). Of them, that with more salt content had the highest average. This same formulation has the best notes as purchase intention and consumption frequency. The charutinho pickle showed promising results by market indicators. The formulation with minor vinegar and more salt is better for entrepreneurial initiatives.

Shear Coaxial Methane–Oxygen Injector Mixing and Combustion Examined by Laser Absorption Tomography

Mixing length scales for methane–oxygen shear-coaxial single-element rocket injectors were experimentally assessed using laser absorption tomography. The laser spectroscopy technique enables quantitative and spatially resolved measurements of carbon monoxide (CO) and temperature within the near-field region, probing rovibrational absorption lines of CO near 5 μm. Multiple injector designs were examined with differing oxidizer post recess depths to compare mixing characteristics. All tests were performed at an oxidizer-to-fuel ratio of 3 with a total propellant flow rate of 0.350 g/s. Planar measurements were taken at 16 axial positions, which collectively captured the first 57 mm of each flame. A tomographic inversion method was applied to obtain radially resolved distributions of temperature and CO mole fraction for each axial position, from which two-dimensional images of the thermochemical structure were generated. Characteristic mixing parameters are defined and extracted from features within the species and temperature profiles to visualize the spatial evolution of CO production. Increasing oxidizer post recess improved mixing due to enhanced shear-induced turbulence and associated radial diffusion of species and temperature; however, the enhancement was nonlinear. This work establishes the first use of laser absorption tomography to directly measure mixing length scales associated with temperature and species profiles in coaxial flames.

A draft tube to improve mixing in swirling flow-based solid–liquid mixing reactors

The Swirl Flow Reactor (SFR) is a recently proposed specially designed reactor to address challenges of solid–liquid mixing for high-temperature and high-pressure processes. Previous research has shown that the mixing homogeneity of the SFR is not yet optimal and has still potential for improvement. To enhance the homogeneity of the SFR and to optimize the utilization of the previously identified Precessing Vortex Core at the nozzle, an improvement is proposed by the inclusion of a draft tube in the reactor center. Computational Fluid Dynamics is used to study the flow structure, particle distribution, and large-scale coherent structures in the SFR. The improved SFR has been validated for its more homogeneous mixing, where the homogeneity is improved from 0.945 for the original reactor to 0.991 in the new proposed design. Also, the influence of the draft tube on the fluctuating velocities and turbulence within the improved SFR has been indicated. In addition, Spectral Proper Orthogonal Decomposition (SPOD) is used to identify and reconstruct the coherent structures in the reactor. A flattened double-layer helical precessing vortex core (PVC) and its second-order harmonic at frequencies of 35.8 Hz and 71 Hz have been identified, which introduce extra large scale mixing near the nozzle of the reactor.