High-Fidelity Simulations of Shield Assembly Mixed-Convection Flows with Applications Toward Reduced-Resolution Modeling
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Nuclear Science & Technology↗
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Code-to-Code Comparison for a PbLi Mixed-Convection MHD Flow
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Nuclear Science & Technology↗
Measurements of mixed convective heat transfer to low temperature helium in a horizontal channel
A horizontal 2.85 m long, 19 mm i.d. stainless steel heated circular channel was employed to measure coefficients of heat transfer to low temperature helium flow. Experimental parameters range from 6.5 to 15 K, from 0.12 to 0.3 MPa at heat fluxes up to 1000 W/m square and Reynolds numbers from 9,000 to 20,000. A significantly nonuniform distribution of heat transfer coefficients over the tube periphery is observed. Difference between temperatures on the upper and lower surfaces of the stainless steel channel wall was found to reach 9 K. It was noted that the highest temperature on the wall outer surface is displaced from its uppermost point. Measurements of local flow temperatures revealed vortical structure of the flow. The displacement of the point with the highest temperature is attributable to the effect of vortices. The relationships for calculating local and averaged coefficients of heat transfer are proposed.
Yeroshenko, V. M.↗
Efficiency of shear induced entrainment in convectively mixed layers
Lidar data of mixed layer height are used to compare the model of process partitioning to that of Eulerian partitioning. It is found that the Eulerian partitioning model more closely follows the data and that the process partitioning model underpredicts the mixed layer depth. The results suggest that shear production and consumption of turbulent kinetic energy at the mixed layer top are local processes.
Boers, Reinout↗
Savanna burning and convective mixing in southern Africa - Implications for CO emissions and transport
Atmospheric data from both remote and direct measurements were used to compute the carbon monoxide (CO) emissions and mass transport from Africa south of the equator. The Measurement of Air Pollution from Satellites (MAPS) experiment flew on the Space Shuttle during October 5-13, 1984; the highest CO mixing ratios from the entire mission were measured over southern Africa. In addition to the MAPS data, surface CO mixing ratios were measured in the boundary layer at Cape Point, South Africa. A calibration factor for the remote MAPS CO measurements was determined by computing the ratio of the surface measurements from Cape Point during unpolluted periods to coincident MAPS measurements. The adjusted MAPS CO data were then used to compute the mass flux of CO from biomass burning in southern Africa during the MAPS mission. The transport calculations were compared to the estimated CO emissions from biomass burning to examine the efficiency in which the continental tropical clouds redistribute CO in the troposphere.
Connors, Vickie S.↗
Correlation of Normal Gravity Mixed Convection Blowoff Limits with Microgravity Forced Flow Blowoff Limits
The axisymmetric rod geometry in upward axial stagnation flow provides a simple way to measure normal gravity blowoff limits to compare with microgravity Burning and Suppression of Solids - II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (PMMA) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18% by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity 'upward flame spread test' method which extrapolates the linear blowoff boundary to the zero stretch limit in order to resolve microgravity flammability limits-something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.
microgravity↗
Low Pressure Flame Blowoff from the Forward Stagnation Region of a Blunt-Nosed Cast PMMA Cylinder in Axial Mixed Convective Flow
Low-pressure blowoff experiments were conducted with a stagnation flame stabilized on the forward tip of cast PMMA rods in a vertical wind tunnel. Pressure, forced flow velocity, gravity, and ambient oxygen concentration were varied. Stagnation flame blowoff is determined from a time-stamped video recording of the test. The blowoff pressure is determined from test section pressure transducer data that is synchronized with the time stamp. The forced flow velocity is also determined from the choked flow orifice pressure. Most of the tests were performed in normal gravity, but a handful of microgravity tests were also conducted to determine the influence of buoyant flow velocity on the blowoff limits. The blowoff limits are found to have a linear dependence between the partial pressure of oxygen and the total pressure, regardless of forced flow velocity and gravity level. The flow velocity (forced and/or buoyant) affects the blowoff pressure through the critical Damkohler number residence time, which dictates the partial pressure of oxygen at blowoff. This is because the critical stretch rate increases linearly with increasing pressure at low pressure (sub-atmospheric pressures) since a second-order overall reaction rate with two-body reactions dominates in this pressure range.
flammability↗
Mixed Convection Blowoff Limits as a Function of Oxygen Concentration and Upward Forced Stretch Rate for Burning Pmma Rods of Various Sizes
Normal gravity flame blowoff limits in an axisymmetric pmma rod geometry in upward axial stagnation flow are compared with microgravity Burning and Suppression of Solids II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (pmma) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18 by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity upward flame spread test method which extrapolates the linear blowoff boundary to the zero stretch limit to resolve microgravity flammability limits, something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.
blowoff↗
A review of turbulent-boundary-layer heat transfer research at Stanford, 1958-1983
For the past 25 years, there has existed in the Thermosciences Laboratory of the Mechanical Engineering Department of Stanford University a research program, primarily experimental, concerned with heat transfer through turbulent boundary layers. In the early phases of the program, the topics considered were the simple zero-pressure-gradient turbulent boundary layer with constant and with varying surface temperature, and the accelerated boundary layer. Later equilibrium boundary layers were considered along with factors affecting the boundary layer, taking into account transpired flows, flows with axial pressure gradients, transpiration, acceleration, deceleration, roughness, full-coverage film cooling, surface curvature, free convection, and mixed convection. A description is provided of the apparatus and techniques used, giving attention to the smooth plate rig, the rough plate rig, the full-coverage film cooling rig, the curvature rig, the concave wall rig, the mixed convection tunnel, and aspects of data reduction and uncertainty analysis.
Moffat, R. J.↗
A theory of nonlocal mixing-length convection. I - The moment formalism
A flexible and potentially powerful theory of convection, based on the mixing length picture, is developed to make unbiased self-consistent predictions about overshooting and other complicated phenomena in convection. The basic formalism is set up, and the method's power is demonstrated by showing that a simplified version of the theory reproduces all the standard results of local convection. The second-order equations of the theory are considered in the limit of a steady state and vanishing third moments, and it is shown that they reproduce all the standard results of local mixing-length convection. There is a particular value of the superadiabatic gradient, below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. Two distinct regimes of convection, which are identified as efficient and inefficient convection, are determined.
Grossman, Scott A.↗
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↗
Trace element and isotopic effects arising from magma migration beneath mid-ocean ridges
The trace element concentrations and isotopic ratios in the magma erupted on mid-ocean ridges may differ from those in the source material due to physical effects such as porous flow dispersion, exchange of trace elements between the fluid and solid phases during magma migration, and convective mixing in magma chambers. These differences are in addition to those produced by better known processes such as fractional crystallization and partial melting. The effects of the three former processes are described. It is predicted that magma typically reaches the subridge magma chambers with a spatial heterogeneity only slightly reduced from that of the source material, but with a subdued variation in time. Convective mixing then further reduces the spatial heterogeneity. Application of the results for convective mixing to a recent Fourier analysis of Sr-87/Sr-86 variations along the Mid-Atlantic Ridge suggests that the falloff in amplitude of variation observed with decreasing wavelength in the Mid-Atlantic Ridge data cannot be explained by convective mixing in magma chambers. Instead, it is postulated that this falloff is due to the mechanics of the production and/or the solid-state convective mixing of chemical and isotopic heterogeneities in the solid mantle.
Kenyon, Patricia M.↗
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↗
A convective model for turbulent mixing in rotating convection zones
The effects of rotation are included in an analytical model for the convective motions in a plane-parallel layer of an ideal fluid. The turbulent stress tensor, formed by taking products and averages of the various velocity components, is calculated for an arbitrary eddy size and shape. Heuristic formulae presented for determining the size and shape of the dominant eddy then give a fully specified stress tensor. Applications for this stress tensor in problems of stellar internal dynamics, heat flow, scalar diffusion, and dynamo theory are suggested. The resultant stresses tend to produce differential rotation profiles with rapidly rotating equators and interiors. The dynamo activity associated with these convective motions tends to occur near the lower boundary of the convection zone.
Hathaway, D. H.↗
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↗
Along-strike magma mixing beneath mid-ocean ridges - Effects on isotopic ratios
The effects of mixing processes on the isotopic variability of midocean ridge basalts are studied. The processes considered are porous flow dispersion and convective mixing in magma chambers. Porous flow dispersion is capable of mixing magmas over distances of only a few tens of meters. Convective mixing, on the other hand, is found to produce continuous magma chambers, where mixing is limited by convective processes, and for discontinuous chambers, where mixing is limited by chamber size. Preliminary comparison of the calculations with observations along the midocean ridges shows that the calculations are consistent with the existence of a correlation between bathymetry and isotopic ratio at long, but not at short, wavelengths. They are also capable of explaining a decrease in isotopic variability with increasing spreading rate.
Kenyon, P. M.↗