Turbulent Prandtl Number Research Articles

Direct numerical simulation of sodium in vertical channel flow: From forced convection to natural convection at friction Reynolds number 180

The buoyancy-aided sodium flow in a vertical channel is investigated using direct numerical simulation (DNS) to study turbulent flow and heat transfer at six different Richardson numbers (Ri = 0, Ri = 0.025, Ri = 0.25, Ri = 2.5, Ri = 7.5, and Ri = 15) with a fixed friction Reynolds number (Reτ = 180). The results reveal that the velocity profile shows an “M” shape under buoyancy effect and reverses at the center under strong buoyancy. Additionally, the temperature profile exhibits a thicker boundary layer compared to the velocity profile. Global coefficients, such as the skin friction coefficient and the Nusselt number, are analyzed using Fukagata, Iwamoto, and Kasai (FIK) decomposition to elucidate their respective contributions. Furthermore, anisotropy analysis indicates that buoyancy makes the turbulence more isotropic, and the buoyancy also makes the turbulent Prandtl number (Prt) unpredictable; however, a comparison among the molecular heat flux, the definition of turbulent heat flux, and the calculation of the standard gradient diffusion hypothesis (SGDH) model suggests that the turbulent heat flux can be neglected without significant influence in this study. Finally, the turbulent structures in the viscous layer are presented, and the quadrant analysis is performed to quantitatively analyze the influence of buoyancy on the turbulent structure.

Study of the C-γ-Reθ Transition Model Based on the NNW-HyFLOW Software

Abstract Since the release of hypersonic computational fluid software NNW-HyFLOW in 2023, its computational modules have been continuously expanded for the development needs of hypersonic vehicles. The C-γ-Reθ transition model has been developed based in the framework of the NNW-HyFLOW to expand the prediction of transition in the design of high-speed vehicles. Firstly, the calibration of two basic relations of Re θc and Flength which is originally designed for the low-speed flat plate cases have been realized and expanded to high-speed flows. Secondly, the the empirical formula of Mach number correction has been adjusted by several typical high-speed transition cases. The same correction also has been made to the turbulence Prandtl number correction following the sae procedure. A crossflow transition module has been added with the calibration of the crossflow Reynolds number and validation of the experiment data of the HyTRV lifting body. The numerical tests show that the C-γ-Reθ transition model based on NNW-HyFLOW software has been basically realized with the ability of steamwise transition and crossflow transition prediction.

Simulating Mixed‐Phase Open Cellular Clouds Observed During COMBLE: Evaluation of Parameterized Turbulence Closure

AbstractMarine cold‐air outbreaks, or CAOs, are airmass transformations whereby relatively cold boundary layer (BL) air is transported over relatively warm water. To more deeply understand BL and mixed‐phase cloud properties during CAO conditions, the Cold‐Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) took place from late 2019 into early 2020. During COMBLE, the U.S. Department of Energy's first Atmospheric Radiation Measurement Mobile Facility (AMF1) was deployed to Andenes, Norway, far downstream (∼1,000 km) from the Arctic pack ice. This study examines the two most intense CAOs sampled at the AMF1 site. The observed BL structures are open cellular with high (∼3–5 km) and cold (−30 to −50 C) cloud tops, and they often have pockets of high liquid water paths (LWPs; up to ∼1,000 g ) associated with strong updrafts and enhanced turbulence. We use a high‐resolution mesoscale model to explore how well four turbulence closure methods represent open cellular clouds. After applying a radar simulator to model outputs for direct evaluation, cloud top properties agree well with AMF1 observations (within ∼10%), but radar reflectivity and LWP agreement is more variable. Results suggest that the turbulent Prandtl number may play an important role for the simulated BL and cloud properties. All simulations produce enhanced precipitation rates that are well‐correlated with a cloud transition. Finally, the eddy‐diffusivity/mass‐flux approach produces the deepest cloud layer and therefore the largest and most coherent cellular structures. We recommend the use of a non‐local turbulence closure approach to better capture turbulent processes in intense CAOs.

Determination of Turbulent Prandtl Number for Thermal Fluid Dynamics Simulation of HVAC Unit by Data Assimilation

Abstract Regarding high-precision temperature field prediction of a heating ventilation and air conditioning (HVAC) unit using thermal fluid dynamics simulation, the determination of the turbulent Prandtl number (Prt) was a key issue. In this study, we present an attempt to improve the accuracy of thermal fluid dynamics simulations in HVAC units by adjusting the Prt using data assimilation techniques. First, we simultaneously measured the velocity and temperature in the hot and cold air mixing zone of a simple HVAC model using particle image velocimetry and thermocouples. Second, we coupled data assimilation to the thermal fluid simulation model to determine the Prt in the mixing field. Finally, we proposed two functions of the Prt for high velocity and low velocity regions using multidimensional analysis. In the future, we believe that the Prt functions can be applied to thermal fluid simulations of actual HVAC unit to accurately predict performance without conducting prototype experiments, thereby contributing to reducing development cost and time of HVAC unit.

Investigation on numerical simulation models for heat transfer characteristics of lead-bismuth eutectic

The liquid lead-bismuth eutectic (LBE) has distinct thermal and physical properties that challenge the effectiveness of traditional RANS turbulence models and turbulent Prandtl number (Prt) models for accurately simulating its flow and heat transfer characteristics. This study aims to investigate numerical simulation models of LBE based on existing experimental data. Simulations are conducted using different combinations of three turbulence models and four Prt models, and comparisons are made with experimental data. The local and overall heat transfer characteristics of LBE are analyzed, and the applicability of each model combination is evaluated. Results indicate that for simulating local heat transfer characteristics, the SST k-ω turbulence model combined with the Prt model proposed by Cheng et al. yields the highest accuracy. Additionally, the empirical correlation for heat transfer proposed by Kutateladze provides the best prediction of the local Nusselt number. For overall heat transfer characteristics, the combination of the SST k-ω turbulence model and the Prt model introduced by Reynolds et al. demonstrates the highest accuracy and applicability. This investigation might offer a pivotal benchmark for the discernment of appropriate computational fluid dynamics (CFD) models for liquid metal breeder reactor (LMBR) applications utilizing lead-bismuth eutectic (LBE) as coolant.

Enhancing thermal field prediction in a jet in cross flow through turbulent heat flux model optimization by using large eddy simulation

High fidelity big data obtained from highly accurate large eddy simulation (LES) was utilized to enhance current models for turbulent heat transfer, boosting the precision of the realizable Reynolds averaged Navier Stokes (RANS) k-ε model in forecasting film cooling thermal field. The LES analysis was conducted on a flat plate with a jet in crossflow, at a primary flow Reynolds number (Re) of around 17382. Post-validation of the LES outcomes, a data analysis, and a numerical optimization (gradient descent algorithm) technique were employed to fine-tune three chosen models for turbulent Prandtl number using data near the coolant wall. In order to demonstrate the effectiveness of these refined models for RANS simulations of various film cooling setups with distinct shapes and flow situations, a series of simulations were executed, encompassing two curved surfaces to simulate flow around leading-edge and over the blade suction side. The optimized models exhibited marked enhancement in forecasting film cooling effectiveness in both averaged lateral and longitudinal directions (achieving reductions in numerical errors of up to 68.0 % and 43.67 % respectively). These fine-tuned models were proven suitable for use across different geometries and flow conditions according to their performance in three analyzed problems.

Thermal-hydraulic investigation of liquid metal cross flow different arrangements of tube bundles under pulsating

The topic of this paper is to couple the passive and active approaches to enhance the heat transfer performance in the inline tube bundle heat exchanger. Firstly, the k-kl-ω turbulence model and Kays turbulent Prandtl number model are validated by liquid metal cross flow tube bundle experiments and rectangular groove pulsating flow experimental results. Then the numerical studies were carried out for pulsating velocity amplitude of 0.5, frequency of 10, and Re of 20,000 with transverse and streamwise pitch-to-diameter ratios of 1.5, 1.65, and 1.8. The introduction of pulsating flow effectively improves the turbulence characteristics between the tube bundles, especially at the first three rows, where the velocity fluctuation is enhanced by about 1.5–2 times. The tube heat transfer performances are all improved. The performance evaluation criterion (PEC) variation ranges from 1.04 to 1.32, which signifies that the introduction of pulsating flow can enhance the comprehensive heat transfer performance. The per unit flow rate thermal entropy generation decreased by about 9.7–33.3 %, in addition, a phase difference between the transient thermal entropy production and pulsating velocity was found. The correlation equations about Nu and f factor within the scope of this paper are presented.

Large eddy simulation of a supersonic lifted hydrogen flame: Impacts of Lewis, turbulent Schmidt and Prandtl numbers

Parametric large eddy simulations (LES) of a supersonic lifted hydrogen flame are reported. The emphases are on two aspects: impacts of (1) Lewis number (Lei of the ith species) and (2) turbulent Schmidt and Prandtl numbers (Sct and Prt) on supersonic turbulent flame and flow structures. Five cases are considered: species-specific Lei, Sct=Prt=1.0 (C0); unity Lei, Sct=Prt=1.0 (C1); species-specific Lei, Sct=0.5, Prt=1.0 (C2); species-specific Lei, Sct=1.0, Prt=0.5 (C3); and species-specific Lei, Sct=Prt=0.5 (C4). Numerical results of instantaneous and/or time-averaged species mole fractions, mixture fraction, heat release rate, flame base location, and mixed modes of premixed and diffusion combustion are compared between cases C0 and C1. Differences in auto-ignition locations and strengths and flame structures and stabilization specify the impacts of Lewis number. They are triggered by different predictions of species mass and thermal diffusions at fuel-coflow and/or coflow-ambient air mixing layers. These differences are rationalized by a scale analysis of mass/thermal diffusion and convection for case C0, which suggests the relatively low but non-negligible former against the latter. Cases C0 and C2–C4 barely see differences in terms of instantaneous and/or time-averaged temperature, velocity, and mixed combustion modes except for further downstream areas where combustion occurs. Both Sct and Prt impose less significant influences than Lewis number, as sub-grid scale mass/thermal diffusion is subordinate to its resolved counterpart according to their scale analysis for case C4.

Investigation on turbulent heat transfer to lead-bismuth eutectic flows in rough rod bundles for nuclear applications

Liquid lead-bismuth eutectic corrosion and the deposition of corrosion particles can lead to surface roughening of rod bundles, which impacts the convective heat transfer characteristics of the rod bundles. In this study, the Kays turbulent Prandtl number model and the SSTk‐ω turbulence model were validated using the existing models. Then, the validated model was used to simulate the convective heat transfer in different rough rod bundles. Based on the numerical simulation results, a new Nusselt number correlation for liquid lead-bismuth eutectic within the rough rod bundle was developed. The applicable range of the new correlation is P/D = 1.1–1.5, Pe = 400–4000, and ε/De = 0.0015–0.009. The error between the Nusselt number obtained from the correlation and the numerical simulation results is within 20 %.

Enhancing the SST turbulence model for predicting heat flux in hypersonic flows through symbolic regression

In the context of hypersonic flows, shock-wave/turbulent boundary-layer interactions (SWTBLIs) can lead to substantial aerodynamic heating. The commonly used Reynolds-averaged Navier–Stokes (RANS) method in engineering applications faces challenges in accurately predicting heat transfer in these conditions, as the assumptions made by Morkovin’s assumption in the RANS method are not applicable in hypersonic SWTBLI flows. This article addresses these challenges by introducing a variable turbulent Prandtl number (Prt) model for non-adiabatic walls, established through field inversion and symbolic regression (SR) techniques. The methodology begins with field inversion for an oblique SWTBLI case at Mach 5. The corrected field, denoted as β(x), obtained from this inversion, is integrated with selected local flow characteristics to derive a corrected expression using SR. Following the necessary adjustments, this expression is incorporated into the RANS solver. Various cases with different wall cooling ratios, Mach numbers, and Reynolds numbers are chosen to assess the generalization ability of the variable Prt model. The outcomes demonstrate a substantial improvement in the model’s ability to predict heat transfer in hypersonic SWTBLI flows without compromising the baseline model’s performance in predicting the undisturbed boundary layer. The correction effect remains notably enhanced even in complex three-dimensional cases.

Usage of high-fidelity large eddy simulation to improve the turbulence modeling of Reynolds averaged navier stokes simulation in film cooling applications via a neural network

In this study, high-Fidelity Large eddy simulation (LES) data was used to create a surrogate turbulence model to enhance the estimation of turbulent heat flux in a Reynolds averaged Navier Stokes (RANS) solver for film cooling applications. The LES simulation (A flat plate film cooling application with a Reynolds number of 17,382, a blowing ratio of 1 and a density ratio of 2) was validated by comparison with experimental data. A correlation analysis was performed to identify the most influential parameters, and temperature gradient, velocity gradient, turbulent dissipation rate, shear strain rate, and turbulent viscosity ratio were selected as the most effective parameters. A second model was developed to create a Galilean-invariant model that remains unaffected by changes in the coordinate system. Neural network was applied to the LES training data to propose a modified surrogate dynamic turbulent Prandtl number to be applied to the k − ε realizable RANS simulation. The first surrogate model was implemented to two different geometries, one geometry was a flat plate film cooling similar to the training data but with different flow conditions, and another one was a more complex geometry with pressure gradient. The second model was only implemented on the second geometry and produced similar results. The surrogate models predicted a more accurate thermal field near the cooling wall (up-to 58 % error reduction) with a computational time complexity similar to the base RANS solver.

Flux‐gradient relations and their dependence on turbulence anisotropy

AbstractMonin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.

An improved Baldwin–Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

Effects of turbulent Prandtl number on supercritical carbon dioxide turbulent flow with high heat flux in vertical round tube

Supercritical carbon dioxide (sCO2) is a promising working medium for coal-fired power plants, high-temperature solar power systems, nuclear reactor systems, and fuel cells owing to its high efficiency and inertness. In these cases, the sCO2 is in a round tube under high temperature and pressure, far from the pseudo-critical point. Here, the thermophysical properties of sCO2 changes, resulting in large prediction errors. In this study, a conjugate heat transfer model with the k-ε turbulent model was created to analyze the tube performance of the sCO2, and the effects of turbulent Prandtl number (Prt) on the sCO2 turbulent flow with high heat flux were examined through experimental and numerical investigations. Prt had a considerable effect on the performance of the sCO2 turbulent flow far from the pseudo-critical point. The mean relative errors of the inner wall temperature and convective heat transfer coefficient were reduced by approximately 13% and 27%, respectively, when Prt was decreased from 1 to 0.55. For the sCO2 turbulent flow with a high heat flux, constant Prt values of 0.55–0.6 were applicable. The findings afford key insights for the development of sCO2 turbulent flow with high heat flux.

Study on the turbulent Prandtl number model for liquid metal flow and heat transfer in a narrow rectangular channel

In order to improve the core power density of liquid metal reactors, plate-type fuel assemblies are typically used, which have obvious advantages in heat transfer capacity. For the low Prandtl number fluid, the RANS turbulence model-based CFD method needs to be modified by inserting the turbulent Prandtl number model. This paper investigated the turbulent Prandtl number model for the turbulent heat transfer of liquid metal flow in a narrow rectangular channel. First, the existing turbulent Prandtl number models were summarized and classified as the local turbulence Prandtl number model and the global turbulence Prandtl number model. They were evaluated based on the experimental data. The results showed that the prediction results of each model are not ideal. Then, a typical numerical example was used to analyze the temperature field and flow field in the narrow gap of a narrow rectangular channel. It was shown that the entire flow region only includes the near-wall region and the transition region, and the transition region accounts for the main proportion. A semi-empirical local turbulence Prandtl number model was obtained by solving the turbulent transport equation, and the unknown coefficients were determined iteratively with the experimental data. The error was controlled within ±20%. Finally, the applicability of the newly proposed turbulent Prandtl number model was explored, and the results showed that it has good applicability for the different runner sizes and different liquid metal types. This study can provide a reference for the numerical simulation of turbulent heat transfer of metal liquid in the narrow rectangular channel.

Countergradient turbulent transport in a plume with a crossflow

AbstractDirect numerical simulation of a turbulent forced buoyant plume in a crossflow is performed at a source Reynolds number $${\text{ Re }}_0=1000$$ Re 0 = 1000 , Richardson number $$\mathrm{{Ri}}_0=1$$ Ri 0 = 1 , Prandtl number $$\mathrm{{Pr}}=1$$ Pr = 1 and source-to-crossflow velocity ratio $$R_0=1$$ R 0 = 1 . The instantaneous and temporally averaged flow fields are assessed in detail, providing an overview of the flow dynamics. The velocity, temperature and pressure fields are used together with enstrophy fields to describe qualitatively the evolution of the plume as it is swept downstream by the crossflow, and the mechanisms involved in its evolution are outlined. The plume trajectory is determined quantitatively in a number of ways, and it is shown that the central streamline and the centre of buoyancy of the plume differ significantly—as with jets in crossflow, the central streamline is seen to follow the top of the plume, whereas the centre of buoyancy, by definition, describes the plume as a whole. We then investigate the turbulence properties inside the plume; in particular the eddy viscosity and diffusivity are presented, which are significant parameters in turbulence modelling. Assessment of turbulence production demonstrates the presence of regions where turbulence kinetic energy is redistributed to the kinetic energy of the mean flow, implying a negative eddy viscosity within certain regions of the domain. Similarly, the observation that the buoyancy flux and buoyancy gradient are anti-parallel in specific regions of the flow implies a negative eddy diffusivity in said regions, which must be realised in models of such flows in order to capture the countergradient transport of thermal properties. A characteristic eddy viscosity and diffusivity are presented, and shown to be approximately constant in the fully developed regime, resulting in a constant characteristic turbulent Prandtl number, in turn signifying self-similarity.

Numerical study of turbulent heat transfer of annular fuel assembly in a sodium-cooled fast reactor by a SST k-ω-kθ-εθ model

ABSTRACT The annular fuel has two cooling surfaces inside and outside, which can fully take away the heat of the fuel assemblies. It is urgent to conduct research on sodium-cooled fast reactor annular fuel assemblies. The Prandtl number Pr of liquid sodium is much less than 1 (Pr ˂˂ 1). The problem is that using the traditional constant turbulent Prandtl number Pr t of 0.85 ~ 0.9, which will greatly affect the accuracy of the numerical prediction of the thermal-hydraulic properties of liquid sodium. In order to address this issue, the turbulent heat transfer characteristics of the bare and wire spacers 7-pin annular fuel assembly for a sodium-cooled fast reactor are investigated by a SST k-ω-k θ -ε θ model. The open-source CFD software OpenFOAM is used for this calculation. In order to verify the validity of the present calculation method, some classical liquid metal heat transfer correlations are used to compare and analyze the results of the present calculation method (k θ -ε θ model), the results of the Reynolds analogy hypothesis (Pr t = 0.85 model), and the results of the turbulent Prandtl number correlation (Pr t = kays model). It is shown that the SST k-ω-Pr t = 0.85 model overestimates the Nusselt number Nu of the annular fuel assembly. The SST k-ω-k θ -ε θ model agrees well with the SST k-ω-Pr t = Kays model of the bare and wire spacers 7-pin annular fuel assembly . It suggests that the numerical calculation results of the SST k-ω-k θ -ε θ model are reliable in both the simple and complex fuel assembly models. In brief, the SST k-ω-k θ -ε θ model is more capable of predicting the turbulent heat transfer characteristics of the bare and wire spacers 7-pin annular fuel assembly in sodium-cooled fast reactors. In addition, the thermal-hydraulic characteristics of annular fuel assemblies with wire spacers for sodium-cooled fast reactors have been investigated. This research can provide a reference for the study of turbulent heat transfer characteristics of annular fuel assemblies in sodium-cooled fast reactor.

Effects of Viscosity Law on High-Temperature Supersonic Turbulent Channel Flow for Chemical Equilibrium

Direct numerical simulations of temporally evolving high-temperature supersonic turbulent channel flow for chemical equilibrium were conducted with a Mach number of 3.0, a Reynolds number of 4880, and a wall temperature of 1733.2 K to investigate the influence of the viscosity law. The mean and fluctuating viscosity for the mixture rule is higher than that for Sutherland’s law, whereas an opposite trend is observed in the mean temperature, mean pressure, and dissociation degree. The Trettel and Larsson transformed mean velocity, the Reynolds shear stress, the turbulent kinetic energy budget, and the turbulent Prandtl number are insensitive to the viscosity law. The semilocal scaling that take into account local variation of fluid characteristics better collapses the turbulent kinetic energy budget. The modified strong Reynolds analogies provide reasonably good results for the mixture rule, which are better than those for Sutherland’s law. The streamwise and spanwise coherencies for the mixture rule are stronger and weaker than those for Sutherland’s law, respectively. The relationship between viscosity and species components can help to identify the traveling wave packet.

Numerical heat transfer to LBE flow in a wire-wrapped 19-rod bundle using an OpenFOAM-based solver: fourParameterFoam

The LBE-cooled fast reactor (LFR) has received significant attention due to its diverse applications. However, numerical heat transfer simulations encounter challenges with lead-bismuth eutectic (LBE) due to its low Prandtl number and high molecular thermal diffusion, often resulting in an overestimation of heat transfer using the simple gradient diffusion hypothesis (SGDH). This study aims to improve the prediction accuracy of heat transfer to LBE in numerical models by developing a solver, named fourParameterFoam, based on the turbulent model SST k-ω and algebraic heat flux model (AHFM) kθ-ɛθ within the OpenFOAM framework. The performance of SGDH models and AHFMs is compared based on heat transfer experiments in vertical tube flow with LBE. The behavior of the turbulent Prandtl number (Prt) under various flow conditions is concluded based on the SST k-ω-kθ-ɛθ model. Additionally, the applicability of the SST k-ω-kθ-ɛθ model in complex flow is validated through heat transfer experiments in a wire-wrapped 19-rod bundle with LBE flow. Local temperature variations on the heated rod surface and sub-channels are analyzed to elucidate the thermal development process in the bundle. The impact of wire spacers on flow behavior is summarized using visualization techniques, and the suitability of corresponding empirical Nusselt number correlations in LBE flow is evaluated.