@article{iskhakov_tai_bolotnov_nguyen_merzari_shaver_dinh_2023, title={Data-Driven RANS Turbulence Closures for Forced Convection Flow in Reactor Downcomer Geometry}, volume={3}, ISSN={["1943-7471"]}, url={https://doi.org/10.1080/00295450.2023.2185056}, DOI={10.1080/00295450.2023.2185056}, abstractNote={Recent progress in data-driven turbulence modeling has shown its potential to enhance or replace traditional equation-based Reynolds-averaged Navier-Stokes (RANS) turbulence models. This work utilizes invariant neural network (NN) architectures to model Reynolds stresses and turbulent heat fluxes in forced convection flows (when the models can be decoupled). As the considered flow is statistically one dimensional, the invariant NN architecture for the Reynolds stress model reduces to the linear eddy viscosity model. To develop the data-driven models, direct numerical and RANS simulations in vertical planar channel geometry mimicking a part of the reactor downcomer are performed. Different conditions and fluids relevant to advanced reactors (sodium, lead, unitary-Prandtl number fluid, and molten salt) constitute the training database. The models enabled accurate predictions of velocity and temperature, and compared to the baseline k−τ turbulence model with the simple gradient diffusion hypothesis, do not require tuning of the turbulent Prandtl number. The data-driven framework is implemented in the open-source graphics processing unit–accelerated spectral element solver nekRS and has shown the potential for future developments and consideration of more complex mixed convection flows.}, journal={NUCLEAR TECHNOLOGY}, author={Iskhakov, Arsen S. and Tai, Cheng-Kai and Bolotnov, Igor A. and Nguyen, Tri and Merzari, Elia and Shaver, Dillon R. and Dinh, Nam T.}, year={2023}, month={Mar} }
 @article{tai_nguyen_iskhakov_merzari_dinh_bolotnov_2023, title={Direct Numerical Simulation of Low and Unitary Prandtl Number Fluids in Reactor Downcomer Geometry}, volume={6}, ISSN={["1943-7471"]}, DOI={10.1080/00295450.2023.2213286}, abstractNote={Mixed convection of low and unitary Prandtl fluids in a vertical passage is fundamental to passive heat removal in liquid metal and gas-cooled advanced reactor designs. Capturing the influence of buoyancy in flow and heat transfer in engineering analysis is hence a cornerstone to the safety of the next-generation reactor. However, accurate prediction of the mixed convection phenomenon has eluded current turbulence and heat transfer modeling approaches, yet further development and validation of modeling methods is limited by a scarcity of high-fidelity data pertaining to reactor heat transfer. In this work, a series of direct numerical simulations was conducted to investigate the influence of buoyancy on descending flow of liquid sodium, lead, and unitary Prandtl fluid in a differentially heated channel that represents the reactor downcomer region. From time-averaged statistics, flow-opposing/aiding buoyant plumes near the heated/cooled wall distort the mean velocity distribution, which gives rise to promotion/suppression of turbulence intensity and modification of turbulent shear stress and heat flux distribution. Frequency analysis of time series also suggests the existence of large-scale convective and thermal structures rising from the heated wall. As a general trend, fluids of lower Prandtl number were found to be more susceptible to the buoyancy effect due to stronger differential buoyancy across the channel. On the other hand, the effectiveness of convective heat transfer of the three studied fluids showed a distinct trend against the influence of buoyancy. Physical reasoning on observation of the Nusselt number trend is also discussed.}, journal={NUCLEAR TECHNOLOGY}, author={Tai, Cheng-Kai and Nguyen, Tri and Iskhakov, Arsen S. and Merzari, Elia and Dinh, Nam T. and Bolotnov, Igor A.}, year={2023}, month={Jun} }
 @article{tai_mao_petrov_manera_bolotnov_2023, title={Study of Stable Stratification in HiRJET Facility With Direct Numerical Simulation}, volume={6}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2023.2197656}, abstractNote={Stable density stratification in a large enclosure could significantly hamper the effectiveness of natural convection cooling in pool-type liquid metal or gas-cooled advanced reactors. In addition, accurate prediction of stratified front behavior remains to be a challenging task for turbulence modeling. With the rapid growth of high-performance-computing capabilities in recent years, conducting high-fidelity simulations for a large-timescale transient has become more affordable and hence a valuable data source to support turbulence modeling as well as to gain further physical insights. In this work, direct numerical simulation is performed at experiment-consistent conditions to simulate the density stratification transient High-Resolution Jet (HiRJET) facility. Specifically, we focus on the case where an injected aqueous sugar solution has 1.5% density higher than that in the enclosure. In the early stage of the transient, the impingement of the denser jet to the bottom surface of the enclosure promoted turbulent mixing locally. This rendered the establishment of the mixture layer, formation and swift upward propagation of the stratified front, and elevation with (locally) the highest vertical concentration gradient. As the front rose, the diminishing turbulent mass flux slowed down the propagation, and a larger vertical concentration gradient was established. In this stage, both the velocity and the concentration scalar showed large-timescale fluctuation behavior around the stratified front. For the concentration time signal, the characteristic frequency in the power spectral density was found to agree well with the Brunt-Väisällä frequency. The preliminary validation endeavor showed that the stratified front location and the corresponding concentration gradient magnitude in the simulation agreed well with the experiment data. Further validation will mainly revolve around benchmarking against high-resolution density measurement and high-order flow statistics.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Tai, Cheng-Kai and Mao, Jiaxin and Petrov, Victor and Manera, Annalisa and Bolotnov, Igor A.}, year={2023}, month={Jun} }
 @article{nguyen_merzari_tai_bolotnov_jackson_2023, title={Toward Improved Correlations for Mixed Convection in the Downcomer of Molten Salt Reactors}, volume={7}, ISSN={["1943-7471"]}, DOI={10.1080/00295450.2023.2223036}, abstractNote={Developing heat transfer correlations for buoyancy-driven flows and mixed convection is challenging, especially if the fluid’s Prandtl (Pr) number is not close to 1. For advanced nuclear reactor (Generation IV) designs, the downcomer plays a crucial role in normal operation and loss-of-power scenarios. The fluid-flow behavior in the downcomer can involve forced, mixed, or natural convection. Characterizing the heat transfer for these changing regimes is a serious challenge, especially in the heat transfer deterioration region. In this paper, the downcomer is simplified to heated parallel plates. The high–Pr number fluid FLiBe (a mixture of lithium fluoride and beryllium fluoride) is considered for all simulations. Direct numerical simulations using the graphics processing unit–based spectral element code NekRS are performed for a wide range of the Richardson number, from 0 to 400, at two different FLiBe Pr numbers (12 and 24). This results in an unprecedented 74 cases in total. Each case’s Nusselt number is calculated to evaluate existing heat transfer correlations.Moreover, we propose several new modifications for cases without satisfactory choice. As a result, several novel mixed-convection heat transfer correlations have been built for high–Pr number fluids. The correlations are expressed as a function of the buoyancy number, covering several mixed-convection regimes. The Pr number effect on the Nusselt number behavior is also analyzed in detail. We also propose a novel method to evaluate the heat transfer deterioration region. Modified Reynolds-Gnielinski forced-convection correlations are defined for the laminarization region, and a free-convection correlation is used for the natural-convection-dominated region. These correlations can describe well the trend in the heat transfer–deficient region.}, journal={NUCLEAR TECHNOLOGY}, author={Nguyen, Tri and Merzari, Elia and Tai, Cheng-Kai and Bolotnov, Igor A. and Jackson, Brian}, year={2023}, month={Jul} }
 @article{mao_vishwakarma_welker_tai_bolotnov_petrov_manera_2023, title={Validation of RANS-Based Turbulence Models Against High-Resolution Experiments and DNS for Buoyancy-Driven Flow with Stratified Fronts}, volume={8}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2023.2241800}, abstractNote={AbstractTo provide computational fluid dynamics (CFD)–grade experimental data for studying stratification, measurements on the High-Resolution Jet (HiRJet) facility at the University of Michigan have been conducted with density differences of 1.5% and −1.5%, respectively. Fluid with a density different from the fluid initially present in the HiRJet tank was injected, and the propagation of the time-dependent density stratification was captured on a two-dimensional plane with the aid of the wire-mesh sensor technique for Reynolds numbers near 5000 and Richardson numbers near 0.29. Direct numerical simulations (DNSs) of the two cases have also been conducted to expand the multifidelity database. The novel experimental and DNS data were then used to assess the predictive capabilities of the Standard k−ε (SKE) model and the Reynolds Stress Transport (RST) model. In particular, the propagation speed and thickness of the stratification fronts were assessed by comparing the CFD results against the experimental and DNS data. It was found that the general trends of the stratified density fronts were well predicted by the CFD simulations; however, slight overprediction of the thickness of the stratification layer was found with the SKE model while the RST model gave a larger overprediction of the mixing. Examination of the turbulent statistics showed that the turbulent viscosity was largely overpredicted by the RST model compared to the SKE model.Keywords: StratificationexperimentsDNSCFD RANS, HiRJet Disclosure StatementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was cofunded by the NEUP and the IRP entitled “Center of Excellence for Thermal-Fluids Applications in Nuclear Energy: Establishing the Knowledgebase for Thermal-Hydraulic Multiscale Simulation to Accelerate the Deployment of Advanced Reactors,” IRP-NEAMS-1.1, “Thermal-Fluids Applications in Nuclear Energy,” from DOE. The authors are thankful for the financial support from the DOE office and appreciate the insightful suggestions from all colleagues under these two projects.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Mao, J. and Vishwakarma, V. and Welker, Z. and Tai, C. K. and Bolotnov, I. A. and Petrov, V. and Manera, A.}, year={2023}, month={Aug} }
 @article{iskhakov_tai_bolotnov_dinh_2022, title={A Perspective on Data-Driven Coarse Grid Modeling for System Level Thermal Hydraulics}, volume={9}, ISSN={["1943-748X"]}, url={https://doi.org/10.1080/00295639.2022.2107864}, DOI={10.1080/00295639.2022.2107864}, abstractNote={Abstract In the future, advanced reactors are expected to play an important role in nuclear power. However, their development and deployment are hindered by the absence of reliable and efficient models for analysis of system thermal hydraulics (TH). For instance, mixing and thermal stratification in reactor enclosures cannot be captured by traditional one-dimensional system codes, yet usage of high-resolution solvers is computationally expensive. Recent developments of coarse grid (CG) and system codes with three-dimensional capabilities have shown that they are promising tools for system-level analysis. However, these codes feature large turbulence model form and discretization errors and require further improvements to capture turbulent effects during complex transients. Improvements can be achieved by using data-driven (DD) approaches. This paper provides an overview of recent applications of DD methods in the areas of fluid dynamics and TH. It is demonstrated that they are being widely applied for engineering-scale analysis (e.g., closures for large eddy simulations/Reynolds-averaged Navier-Stokes using direct numerical simulation data). However, they cannot be directly employed for the system scale because of some features of the latter: usage of CG, transient nature of the considered phenomena, nonlinear interaction of multiple closures, etc. At the same time, accumulated experience allows outlining of potential frameworks for further developments in DD CG modeling of system-level TH.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, publisher={Informa UK Limited}, author={Iskhakov, Arsen S. and Tai, Cheng-Kai and Bolotnov, Igor A. and Dinh, Nam T.}, year={2022}, month={Sep} }
 @article{tai_evdokimov_schlegel_bolotnov_lucas_2022, title={Development of machine learning framework for interface force closures based on bubble tracking data}, volume={399}, ISSN={["1872-759X"]}, DOI={10.1016/j.nucengdes.2022.112032}, abstractNote={Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. Discussion and further plans of investigation are provided.}, journal={NUCLEAR ENGINEERING AND DESIGN}, author={Tai, Cheng-Kai and Evdokimov, Ilya and Schlegel, Fabian and Bolotnov, Igor A. and Lucas, Dirk}, year={2022}, month={Dec} }