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At least 19 records

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantitative assessment of eddy viscosity rans models for turbulent mixed convection in a differentially heated plane channel

Turbulent mixed convection between two vertical, infinite parallel plates at different temperatures is studied using various two-equation turbulence models. The numerical simulations are performed at a turbulent Reynolds number of Re τ = 150 and a Grashof number of Gr = 9.6 × 10 5 . Comparisons are made against the highly trusted DNS results. Consistent with the DNS approach, the current simulations are performed using constant properties and the Boussinesq approximation to predict the influence of buoyancy. Previous studies have provided assessments of two-equation turbulence models for various scenarios, but often rely on a qualitative “eye” test in order to determine the most appropriate model to predict a given flow. This study aims to provide a new form of quantitative assessment that accounts for both the physics captured by the turbulence model as well as the magnitude of the system response quantities (SRQ) using a modified symmetric mean absolute percent error (SMAPE) method. This method is designed to be approachable to researchers at any level and can be applied to system response quantities from multiple research fields. Uncertainty quantification is also performed to determine the discretization error for each turbulence model. Recommendations are made as to which turbulence models best capture the physics – hydrodynamically and thermally – using both local and global validation metrics. Lastly, a sensitivity analysis is performed on the damping functions used in the most accurate models. This underpins the potential of model developments and adjustments most worth pursuing for buoyant flows. Finally, this framework provides a more physics-based comparative analysis of the selected turbulence models.

42 ENGINEERING↗

3D modelling of MHD mixed convection flow in a vertical duct with transverse magnetic field and volumetric or surface heating

Understanding phenomena associated with the multiple effects/interactions of the fusion nuclear environment on liquid metal flow is required to correctly design liquid metal (LM) blankets for fusion facilities. These effects are investigated in the present work by numerically simulating 3D LM MHD flow. The simulated geometry consists of a straight, vertical duct which runs perpendicular to a strong, fringing applied magnetic field. There is also a region of applied heating as the primary goal is to explore buoyancy effects in MHD duct flows. Results are presented for both buoyancy assisted (upwards) and buoyancy opposed (downwards) flows in conducting and insulating ducts for a range of Hartmann numbers (Ha) up to 100, Reynolds numbers (Re) from 10 3 to 10 4 and Grashof (Gr) numbers from 10 7 to 10 8 . While increasing Gr or decreasing Re increases buoyancy effects, increasing Ha was shown to increase maximum temperature through turbulence reduction. The extent to which the MHD mixed convection flows are quasi-2D is analyzed and buoyant effects, in competition with electromagnetic forces, are shown to bring about 3D flow features not seen in purely MHD flows. Volumetric nuclear heating with steep gradients is applied to the vertical MHD flows for comparison to flows with surface heating only. Finally, surface heating generates stronger buoyancy effects than volumetric heating of the same total power; however, many of the same phenomena occur. Therefore, surface heating, the only option for lab experiments, can provide indication of the effects of volumetric heating in MHD flows.

42 ENGINEERING↗

High-Fidelity CFD Simulation of Mixed Convection and Forced Convection in a Pebble Bed Test Reactor Core

The Hermes low-power [35-MW(thermal)] reactor will be built and operated by Kairos Power LLC (KP) to demonstrate its fluoride salt-cooled high-temperature reactor (FHR) technology. In the KP FHR, the reactor core is composed of randomly packed pebbles with TRISO fuel particles inside with FLiBe flow upward through the core acting as a coolant. Previous numerical and experimental studies have been limited to either a small-size bed or to a lack of detailed measurements for heat transfer. Here, to address the lack of high-fidelity heat transfer data in a real-size FHR core, in this study, we simulated a pebble bed core with 34 374 pebbles randomly packed, similar to the Hermes reactor's size. The core radius was 14 times that of the pebble diameter, while the core height was 45 times. In this work, we were particularly interested in a mixed convection regime, where buoyancy is important. Therefore, we performed several large-eddy simulations at different Reynolds numbers (160 to 1000) with gravitational force included. The spectral element computational fluid dynamics code NekRS with graphics processing unit acceleration was used for this study. The low-Mach number approximation was applied to address property changes in the FLiBe and to account for buoyancy. A pure hexahedral mesh with 60 million elements was generated by the Voronoi cell method. At the polynomial order of 5, the total degrees of freedom was 7.5 billion. The developed case in this work is the first of its kind in terms of size and complexity. The local numerical data across the domain were obtained and compared with empirical correlations. After examining the data, we found the following conclusions. For pressure drop, the Reger correlation predicted less than a 5% error. On the other hand, for heat transfer, the Wakao correlation outperformed the others. Based on our findings, we recommend the use of the Wakao correlation for the Nusselt number calculation, and for pressure drop, the KTA (Kerntechnischer Ausschuss) correclation, among the available experimental correlations. In conclusion, the Reger direct numerical simulation-driven correlation for pressure drops should also be considered, given its best agreement with our calculations.

Mixed Convection↗

Heat transfer and pseudo phase transition for low-Reynolds, mixed-convection channel flow in the supercritical thermodynamic regime

Fluids at supercritical thermodynamic conditions are inherently complex due to the large variations in thermodynamic and transport properties. Multiple recent numerical and experimental investigations indicate ongoing interest for these fluids, especially supercritical CO and supercritical water, for a variety of applications. The potential heat transfer benefits in this regime are directly influenced by the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. Limited studies have been conducted for low-Reynolds/intermediate-Rayleigh numbers mixed-convection channel flow of supercritical water, which is the focus of this study. To investigate the thermally driven hydrodynamic instabilities in this regime, we use a high-order fully-implicit numerical method. As expected, in this channel configuration and flow regime, a competition arises between the forced and the natural convection. Buoyancy, driven by the thermal gradient at the wall, pushes the fluid upwards in the channel, while inertial forces drive the fluid from inlet to outlet. We observe significant differences in the heat transfer coefficient between the top and bottom walls of the channel flow, due to natural convection, and unstable plumes. We further quantify the buoyancy forces along the channel flow through evaluation of the Richardson number. Simulations show that with a higher negative Richardson number, there are more unstable structures along the channel, resulting in enhanced mixing. Furthermore, we demonstrate the existence of gas-like, liquid-like, and the possibility of pseudo-two-phase regimes in the supercritical fluid. The pseudo-two-phase regime occurs when the range of fluid temperatures is crossing the pseudo-critical line, also known as the Widom line. The density of the fluid varies significantly near the Widom line, and further influences the natural convection and heat transfer in the flow.

42 ENGINEERING↗

From hydrogen to helium: the spectral evolution of white dwarfs as evidence for convective mixing

ABSTRACT We present a study of the hypothesis that white dwarfs undergo a spectral change from hydrogen- to helium-dominated atmospheres using a volume-limited photometric sample drawn from the Gaia-DR2 catalogue, the Sloan Digital Sky Survey (SDSS), and the Galaxy Evolution Explorer (GALEX). We exploit the strength of the Balmer jump in hydrogen-atmosphere DA white dwarfs to separate them from helium-dominated objects in SDSS colour space. Across the effective temperature range from 20 000 to 9000 K, we find that 22 per cent of white dwarfs will undergo a spectral change, with no spectral evolution being ruled out at 5σ. The most likely explanation is that the increase in He-rich objects is caused by the convective mixing of DA stars with thin hydrogen layers, in which helium is dredged up from deeper layers by a surface hydrogen convection zone. The rate of change in the fraction of He-rich objects as a function of temperature, coupled with a recent grid of 3D radiation-hydrodynamic simulations of convective DA white dwarfs – which include the full overshoot region – lead to a discussion on the distribution of total hydrogen mass in white dwarfs. We find that 60 per cent of white dwarfs must have a hydrogen mass larger than MH/MWD = 10−10, another 25 per cent have masses in the range MH/MWD = 10−14–10−10, and 15 per cent have less hydrogen than MH/MWD = 10−14. These results have implications for white dwarf asteroseismology, stellar evolution through the asymptotic giant branch and accretion of planetesimals on to white dwarfs.

Cunningham, Tim↗

On the Departure from Monin–Obukhov Surface Similarity and Transition to the Convective Mixed Layer

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients Φ for wind speed and air temperature generally align with Monin–Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in Φ to first-order approximation, yielding improved similarity from approximately 0.05z i to above 0.3z i , where z i is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin–Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1 z i .

54 ENVIRONMENTAL SCIENCES↗

Long‐Term Observations of Turbulence Vertical Velocity Spectra in a Convective Mixed Layer: Dependence on Land‐Surface Forcing in the U.S. Southern Great Plains

Doppler lidar vertical velocity retrievals were analyzed for the scale and structure of mixed-layer turbulence over a 7-year period, on fair-weather warm season days (442 cases) in the U.S. Southern Great Plains. Based on the hypothesized influence of land-surface forcing and updraft size on convective boundary layer clouds, a spectral analysis was performed to quantify effects of surface forcing (surface buoyancy flux, friction velocity, and evaporative fraction) on turbulence scale. Significant (order-of-magnitude) variations in spectral density were found in the energy-production subrange and mesoscale regimes. Integral scale decreased with increasing buoyancy flux (and Monin-Obukhov stability parameter), while spectral density in the energy-production subrange increased, implying a transition to buoyancy-driven cellular structures with narrower updrafts. The influence of stability parameter was limited to the neutral to convective transition, and could not explain the wide variation in spectral density in the mesoscale regime. However, high friction velocity (u* > 0.5 m s –1 ) was associated with larger integral scale (updraft width), and a greater portion of spectral density in the mesoscale regime. Lidar profiles and radar reflectivity for individual cases revealed evidence of roll and wave-like structures contributing to mesoscale variability on high friction velocity days, suggesting shear instabilities on days with wetter land surface conditions and smaller buoyancy flux. The role of friction velocity emphasizes the multivariate nature of surface influences on turbulence, and implies that variance-based turbulence closures may not be adequate for capturing effects of surface forcing on updraft size.

54 ENVIRONMENTAL SCIENCES↗

Hydrodynamic instabilities and heat transfer characteristics in the duct flow of a fluid in the supercritical thermodynamic regime

The behavior of fluids at supercritical thermodynamic conditions is inherently complex due to large variations in thermodynamic and transport properties. Recent numerical and experimental investigations illustrate ongoing interest for these fluids, especially supercritical CO 2 and supercritical water, for a variety of applications. For example, supercritical water reactors (SCWR) operate in this extreme condition of high-pressure and temperature, resulting in highly dynamic flow fields and unexpected heat transfer regimes. The potential heat transfer benefits in this regime are directly associated with the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. This work characterizes the hydrodynamic instabilities that arise for fluids at supercritical thermodynamic conditions when buoyancy forces are significant. Two specific configurations are considered, a natural convection cavity flow, and a mixed convection, heated, horizontal channel flow. Natural convection flow in a cavity is a classical configuration with expected behavior below the critical point. This configuration aids in characterizing the effect of the variable properties in the supercritical thermodynamic regime. Further, limited studies in the existing literature have been conducted for low-Reynolds and intermediate-Rayleigh numbers, mixed-convection channel flows for supercritical water, which is the focus of the channel flow configuration. To investigate the thermally driven hydrodynamic instabilities in this regime, a high-order fully-implicit numerical method is used. Such strong variations in thermophysical properties (in particular, density) are difficult to simulate and an altogether compressible framework is needed. Therefore, the compressible Navier-Stokes equations are solved without any additional assumptions. The fully implicit, high-order in space and time, reconstructed discontinuous Galerkin method as implemented within the multi-physics code called ALE3D (Arbitrary Lagrangian and Eulerian in 2D and 3D), developed at Lawrence Livermore National Laboratory (LLNL), is used. This fully implicit, L-stable method accurately captures the compressible nature of the ow in the limit of very low Mach number. It has been widely accepted that above the critical point, only one phase is observed. However, recent research has indicated the existence of the distinct gas-like and liquid-like regions separated by the Widom line, the locus of the maxima of the specific heat. Along the Widom line, density decreases 6-fold, viscosity drops by a factor of 2, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film boiling. A pseudo-film at the heated wall of the cavity and the horizontal channel is observed where buoyancy forces induce mixing through the specific configurations. Further the local Rayleigh and Richardson numbers provide maps of the flow field and the buoyancy forces driving the microscopic mixing. In the first chapter, I describe a background of supercritical fluid and the various applications. The second chapter focuses on the mathematical model and numerical method used for simulations, where a description of the equation of state for supercritical water is described. The third chapter focuses on the natural convection cavity with a heated bottom wall. In this cavity a gas-like and a liquid-like flow within the supercritical thermodynamic regime are observed. The fourth chapter focuses on a forced convection, horizontal channel, distinguishing between the gas-like, liquid-like, and mixed flow regimes. Mixed convection flow, with the addition of gravitational forces in the horizontal channel show the influence of variable properties on the hydrodynamic development, heat transfer, and rising instabilities. The last chapter of this research focuses on characterizing the unstable hydrodynamics through time-averaging processes and analysis of the movement of energy through the developing plumes.

42 ENGINEERING↗

Radiative Heat Transport and Optical Characterization of High Temperature Molten Salts

The goal of this project was to advance the field of molten fluoride radiative heat transfer (RHT), through optical property measurements, heat transfer loop construction and operation, and computational fluid dynamics simulations. The following outcomes have been accomplished. A comprehensive review has been conducted to compile all available RHT-relevant optical absorption data for molten fluorides. The various measurement methods have also been compiled and critiqued. Thermal emission measurement methods have been refined and documented. A unique thermal emissivity measurement facility has been constructed and used to measure the emissivity of flowing FLiBe-exposed SS316 samples. A slight increase has been observed in the emissivity compared to unexposed SS316. A dual reflectance-emission setup was partially demonstrated for the purpose of molten fluoride absorption measurement. Preliminary infrared edge data for FLiNaK was obtained. A visible near-infrared (NIR) measurement setup has been constructed and will be used to measure absorption of corrosion products in FLiBe. A new multi-band thermal radiation method using blackbody-weighted spectral bands for the absorption-coefficient was deployed to investigate the thermal performance of the UW Natural Circulation FLiBe Loop under various power levels and operating conditions. The results showed an increasing and decreasing trend in the overall heat transfer with optical thickness with a maximum at optical thickness τ D ≈Ο(1). A forced convection FLiBe loop was constructed for the purpose of studying corrosion and thermal hydraulic phenomena. A vertical cantilever pump is used to achieve up to 5 gpm and 5 m/s flow velocity in hot and cold test sections. A methodology has been established for modeling radiative heat transfer (RHT) in molten salt coolants for the purpose of quantifying the contribution of thermal radiation in conditions relevant to FHR or MSR systems. The comparison between the results obtained for forced and mixed convection showed that in the studied ranges of optical thickness, the maximum effect of RHT on overall heat transfer was 60% improvement observed at z/D = 250 for forced convection; whereas for mixed convection, that value was higher at 170% observed at z/D = 30. The highest effect of RHT on the overall energy distribution was observed at τ D ≈3.4. Negligible effect (<20%) was observed above τ D =18 and below τ D ≈0.002. A CFD code-to-code comparison was conducted using COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT, for a forced and mixed convection laminar flow for a grey medium in a vertical heated using both COMSOL Multiphysics at UW-Madison and STAR-CCM at MIT. The relative error was the largest at τ D =40 for the radiative heat flux, bulk temperature, and Nusselt number. On the other hand, the relative error was the least at τ D =0.002 for the conductive heat flux, bulk temperature, and Nusselt number.

Anderson, Mark↗

Comparative study with two reduced test facilities for air-cooled RCCS scaling law

Korea Atomic Energy Research Institute (KAERI) and Argonne National Laboratory (ANL) conducted steady-state tests at constant heat flux conditions to investigate the scale effect on heat removal behavior of the air-cooled Reactor Cavity Cooling System (RCCS). Two differently scaled-down test facilities were used in this study, KAERI’s ¼ scale with 4.0-m cavity height, and ANL’s ½ scale with 6.8-m cavity height. Two scaling laws were proposed to simulate the radiation across the cavity and the buoyancy-driven duct flow in the riser, respectively. The test matrix for KAERI and ANL test facilities focused on the scaling effect of the heated riser length with constant heat flux at the PMR200 RCCS design. The test results showed that mixed convection in the riser duct is an important factor for accurately extrapolating the thermo-fluid behavior in the prototype from the test results in the scale-down facilities. The system analysis code, GAMMA+, with improved heat transfer models predicted fairly well the air-cooled RCCS test data from two facilities. GAMMA+ analysis results showed that the predicted radiation fractions on the heated plate in the scale-down test conditions were larger than those on the reactor vessel in the prototype. The scaling law for air-cooled RCCS was improved by considering the mixed convection in the riser duct and the same radiation fraction on the heated plate. The mixed convection effect was calculated by the height ratio. The same radiation fraction provided a conservative extrapolation from the scale-down test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

This report presents the modeling progress of a university consortium studying flexible modeling for turbulent heat transfer. In the context of advanced nuclear reactor design, where challenges include non-unity Prandtl fluids, free and mixed convection, and transitional flow, computational fluid dynamics methods are underutilized due to low confidence in modeling approaches and high computational cost. This report evaluates the performance of engineering CFD models in diabatic, buoyant turbulent flow. It finds that all turbulence models including several variants of the k-ε and k-ω models struggle to predict accurate turbulent momentum and heat transfer in such flows. The Nusselt numbers have been compared between the models and the DNS data, where calculations have been performed for each case and trends have shown a good agreement between DNS estimated Nusselt numbers and available correlations as well as experimental data. A novel DNS correlation for high Pr cases as they are transitioning from mixed convection to natural convection has been proposed. While Nusselt number errors relative to DNS range from 20% to 50%, the models capture similar trends to DNS with respect to Nusselt suppression and amplification under varying levels of buoyancy effect. This report also highlights model form error as a significant contributor to CFD predictions and proposes a framework for quantifying model error and improving confidence in CFD calculations. To improve the predictive capability of engineering CFD models, data-driven approaches for turbulence models are investigated. Theoretical frameworks based on the invariant tensor / vector basis neural networks for prediction of Reynolds stresses and turbulent heat fluxes are employed. The models are developed using direct numerical simulations data for forced convection flows of different fluids in vertical planar channel domain. The framework is implemented in spectral element solvers Nek5000 / nekRS and has shown a potential for future development and consideration of mixed convection flows.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On the Spectral Evolution of Hot White Dwarf Stars. II. Time-dependent Simulations of Element Transport in Evolving White Dwarfs with STELUM

White dwarf stars are subject to various element transport mechanisms that can cause their surface composition to change radically as they cool, a phenomenon known as spectral evolution. In this paper, we undertake a comprehensive theoretical investigation of the spectral evolution of white dwarfs. First, we introduce STELUM, a new implementation of the stellar evolutionary code developed at the Université de Montréal. We provide a thorough description of the physical content and numerical techniques of the code, covering the treatment of both stellar evolution and chemical transport. Then, we present two state-of-the-art numerical simulations of element transport in evolving white dwarfs. Atomic diffusion, convective mixing, and mass loss are considered simultaneously as time-dependent diffusive processes and are fully coupled to the cooling. We first model the PG 1159-DO-DB-DQ evolutionary channel: a helium-, carbon-, and oxygen-rich PG 1159 star transforms into a pure-helium DB white dwarf due to gravitational settling and then into a helium-dominated, carbon-polluted DQ white dwarf through convective dredge-up. We also compute for the first time the full DO-DA-DC evolutionary channel: a helium-rich DO white dwarf harboring residual hydrogen becomes a pure-hydrogen DA star through the float-up process and then a helium-dominated, hydrogen-bearing DC star due to convective mixing. We demonstrate that our results are in excellent agreement with available empirical constraints. In particular, our DO-DA-DC simulation perfectly reproduces the lower branch of the bifurcation observed in the Gaia color–magnitude diagram, which can therefore be interpreted as a signature of spectral evolution.

79 ASTRONOMY AND ASTROPHYSICS↗