@article{iskhakov_leite_merzari_dinh_2023, title={Data-Driven High-to-Low for Coarse Grid System Thermal Hydraulics}, volume={4}, ISSN={["1943-748X"]}, url={https://publons.com/wos-op/publon/55933581/}, DOI={10.1080/00295639.2023.2180987}, abstractNote={Traditional one-dimensional system thermal-hydraulic analysis has been widely applied in the nuclear industry for licensing purposes because of its numerical efficiency. However, such tools have inherently limited opportunities for modeling multiscale multidimensional flows in large reactor enclosures. Recent interest in three-dimensional coarse grid (CG) simulations has shown their potential in improving the predictive capability of system-level analysis. At the same time, CGs do not allow one to accurately resolve and capture turbulent mixing and stratification, whereas implemented in CG solvers relatively simple turbulence models exhibit large model form uncertainties. Therefore, there is a strong interest in further advances in CG modeling techniques. In this work, two high-to-low data-driven (DD) methodologies (and their combination) are explored to reduce grid and model-induced errors using a case study based on the Texas A&M upper plenum of a high-temperature gas-cooled reactor facility. The first approach relies on the use of a DD turbulence closure [eddy viscosity predicted by a neural network (NN)]. A novel training framework is suggested to consider the influence of grid cell size on closure. The second methodology uses a NN to predict velocity errors to improve low-fidelity results. Both methodologies and their combination have shown the potential to improve CG simulation results by using data with higher fidelity.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Iskhakov, Arsen S. and Leite, Victor Coppo and Merzari, Elia and Dinh, Nam T.}, year={2023}, month={Apr} }
 @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://publons.com/wos-op/publon/58758847/}, 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{iskhakov_dinh_leite_merzari_2023, title={Machine learning from RANS and LES to inform coarse grid simulations}, volume={163}, ISSN={["1878-4224"]}, DOI={10.1016/j.pnucene.2023.104809}, abstractNote={Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. The performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility.}, journal={PROGRESS IN NUCLEAR ENERGY}, author={Iskhakov, Arsen S. and Dinh, Nam T. and Leite, Victor Coppo and Merzari, Elia}, year={2023}, month={Sep} }
 @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={http://dx.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} }
 @book{wiser_baglietto_iskhakov_dinh_tai_bolotnov_nguyen_merzari_shaver_2022, title={Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches}, url={https://www.osti.gov/biblio/1881860}, DOI={10.2172/1881860}, abstractNote={plenum of Texas A&M University’s 1/16th scaled very-high-temperature gas-cooled reactor (VHTR), and (2) development of wall heat-transfer correlation for laminar flow in a wall-heated pipe. The CFD tool validation exercises can be helpful to choose the models and CFD tools to simulate and design specific components of the HTRGs such as upper plenum where jet mixing is a complex phenomenon. In a loss of forced circulation event, the laminar flow can be observed during the development of natural circulation flow. This work includes the development and validation of heat transfer correlations for laminar flow using the Nek5000 CFD code due to limited available experimental data for laminar flow conditions to guide low-order models (1D). In this report, the flow characteristics of a single isothermal jet discharging into the upper plenum was investigated using the Nek5000 Large-Eddy Simulation (LES) CFD tool. Several numerical simulations were performed for various jet-discharged Reynolds numbers ranging from 3,413 to 12,819. A grid-independent study was performed. The numerical results of mean velocity, root-mean-square fluctuating velocity, and Reynolds stress were compared against the benchmark data. Good agreement was obtained between simulated and measured data for axial mean velocities, except near the upper plenum hemisphere. The maximum predicted errors for axial mean velocities at various normalized coolant channel diameter heights of 1, 5, and 10 are 1.56%, 1.88%, and 3.82%, respectively. In addition, the predicted root-mean-square fluctuating velocity and Reynolds stress are qualitatively in agreement with the experimental data. The Nek5000 code was used to develop wall-heat transfer correlation for laminar flow in a cylindrical tube. Several simulations were performed for various Reynolds flow and wall-heat fluxes. A new heat transfer correlation was developed using data from Nek5000 simulation results and regression functions in Matlab. The developed heat transfer correlation is valid for various Reynolds flows from 200 to 2000. The predicted R² value for model fit was 0.875, which ensures that 87.5% of the model data lies on the Nek5000 data. Moreover, a machine learning (ML) tool was used to train and test the Nek5000 data. A good fit of the ML-based model was observed with the test data.}, author={Wiser, Ralph; and Baglietto, Emilio; and Iskhakov, Arsen; and Dinh, Nam T.; and Tai, Cheng-Kai; and Bolotnov, Igor; and Nguyen, Tri; and Merzari, Elia; and Shaver, Dillon}, year={2022}, month={Jun} }
 @article{iskhakov_dinh_leite_merzari_2022, title={Data-driven Hi2Lo for Coarse-grid System Thermal Hydraulic Modeling}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85126815096&partnerID=MN8TOARS}, journal={arXiv}, author={Iskhakov, A.S. and Dinh, N.T. and Leite, V.C. and Merzari, E.}, year={2022} }
 @article{tai_nguyen_iskhakov_merzari_dinh_bolotnov_2022, title={Direct Numerical Simulation of Low and Unitary Prandtl Number Fluids in Reactor Downcomer Geometry}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85128839982&partnerID=MN8TOARS}, journal={arXiv}, author={Tai, C.-K. and Nguyen, T. and Iskhakov, A.S. and Merzari, E. and Dinh, N. and Bolotnov, I.A.}, year={2022} }
 @book{bolotnov_dihn_iskhakov_tai_merzari_nguyen_baglietto_wiser_hassan_hu_et al._2021, title={Challenge Problem 1: Benchmark Specifications for the Direct Numerical Simulation of Canonical Flows}, url={https://www.osti.gov/biblio/1873405}, DOI={10.2172/1873405}, abstractNote={In this report detailed specifications for the canonical problems to study the heat transfer in different coolants, geometries and conditions are presented. The scope has been chosen with industry input and will address the outstanding challenges in predictive capabilities of coolant flows in advanced reactor-relevant conditions.}, author={Bolotnov, Igor; and Dihn, Nam; and Iskhakov, Arsen; and Tai, Cheng-Kai; and Merzari, Elia; and Nguyen, Tri; and Baglietto, Emilio; and Wiser, Ralph; and Hassan, Yassin; and Hu, Rui; and et al.}, year={2021}, month={May} }
 @article{iskhakov_dinh_chen_2021, title={Integration of neural networks with numerical solution of PDEs for closure models development}, volume={406}, ISSN={["1873-2429"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85107023012&partnerID=MN8TOARS}, DOI={10.1016/j.physleta.2021.127456}, abstractNote={The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1] physics-integrated (or PDE-integrated (partial differential equation)) machine learning (ML) framework is furtherly investigated. The Navier-Stokes equations are solved using the Tensorflow ML library for Python programming language via the Chorin's projection method. The Tensorflow solution is integrated with a deep feedforward neural network (DFNN). Such integration allows one to train a DFNN embedded in the Navier-Stokes equations without having the target (labeled training) data for the direct outputs from the DFNN; instead, the DFNN is trained on the field variables (quantities of interest), which are solutions for the Navier-Stokes equations (velocity and pressure fields). To demonstrate performance of the framework, two additional case studies are formulated: 2D turbulent lid-driven cavities with predicted by a DFNN (a) turbulent viscosity and (b) derivatives of the Reynolds stresses. Despite its complexity and computational cost, the proposed physics-integrated ML shows a potential to develop a "PDE-integrated" closure relations for turbulent models and offers principal advantages, namely: (i) the target outputs (labeled training data) for a DFNN might be unknown and can be recovered using the knowledge base (PDEs); (ii) it is not necessary to extract and preprocess information (training targets) from big data, instead it can be extracted by PDEs; (iii) there is no need to employ a physics- or scale-separation assumptions to build a closure model for PDEs. The advantage (i) is demonstrated in the Part I paper [1], while the advantage (ii) is the subject of the current paper.}, journal={PHYSICS LETTERS A}, author={Iskhakov, Arsen S. and Dinh, Nam T. and Chen, Edward}, year={2021}, month={Aug} }
 @article{review of physics-based and data-driven multiscale simulation methods for computational fluid dynamics and nuclear thermal hydraulics_2021, url={https://publons.com/wos-op/publon/58758834/}, journal={ArXiv}, year={2021} }
 @article{iskhakov_dinh_2021, title={Review of physics-based and data-driven multiscale simulation methods for computational fluid dynamics and nuclear thermal hydraulics}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85102858814&partnerID=MN8TOARS}, journal={arXiv}, author={Iskhakov, A.S. and Dinh, N.T.}, year={2021} }
 @article{iskhakov_dinh_2020, title={Physics-integrated machine learning: Embedding a neural network in the navier-stokes equations. Part II}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85108266968&partnerID=MN8TOARS}, journal={arXiv}, author={Iskhakov, A.S. and Dinh, N.T.}, year={2020} }
 @article{physics-integrated machine learning: embedding a neural network in the navier-stokes equations. part i_2020, url={https://publons.com/wos-op/publon/58758828/}, journal={ArXiv}, year={2020} }
 @article{iskhakov_melikhov_melikhov_2019, title={Hugoniot analysis of energetic molten lead-water interaction}, volume={129}, url={http://dx.doi.org/10.1016/j.anucene.2019.02.018}, DOI={10.1016/j.anucene.2019.02.018}, abstractNote={Steam generator tube rupture and/or leakage (SGTR/L) is one of the least studied and dangerous safety issues in pool-type lead-cooled fast reactors (LFRs). During this accident, high-pressure water from the secondary circuit is injected into the primary circuit with relatively low-pressure molten lead. One of the possible consequences of SGTR/L is multiphase flow formation consisting water droplets inside vapor bubbles in lead, which could engender a potential explosive coolant-coolant interaction (CCI). The present paper is devoted to the analysis of energetic molten lead-water interaction during SGTR/L in LFRs using Hugoniot adiabats. A review of literature addressing multiphase thermal detonations using Hugoniot adiabats is carried out. Calculations for CCIs are performed which are compared with earlier works and experimental data. Hugoniot analysis is applied to the case of SGTR/L in Russian BREST reactor and detonation velocities and pressures in the Chapman-Jouguet plane are estimated. The mechanical expansion work of the explosion products and the conversion ratios are calculated for typical values of initial void fractions in two-phase water-steam mixture; lead volume fractions and temperatures. Dependencies of the expansion work potential on the void fraction, initial melt volume fraction, and melt temperature are addressed. It is shown that for typical low void fractions for the case of SGTR/L in LFRs the expansion work has a limited value.}, journal={Annals of Nuclear Energy}, publisher={Elsevier BV}, author={Iskhakov, A.S. and Melikhov, V.I. and Melikhov, O.I.}, year={2019}, month={Jul}, pages={437–449} }
 @article{iskhakov_melikhov_melikhov_yakush_chung_2019, title={Hugoniot analysis of experimental data on steam explosion in stratified melt-coolant configuration}, volume={347}, url={http://dx.doi.org/10.1016/j.nucengdes.2019.04.004}, DOI={10.1016/j.nucengdes.2019.04.004}, abstractNote={Recent experimental results on stratified steam explosion are analyzed by the model of “non-ideal” thermal detonation based upon Hugoniot relations, with factors taking into account incomplete melt fragmentation and participation of liquid coolant. The pressure behind the shock wave and conversion ratio are obtained as functions of the mass fraction of melt undergoing fragmentation and mass fraction of coolant in the explosion zone. Calculations are performed for one of the recent experiments on stratified steam explosion carried out with simulant oxidic materials. It is confirmed that the idealized scheme for thermal detonation overestimates significantly the conversion ratio, while predicting very low pressure levels. Taking into account incomplete melt fragmentation and limited participation of coolant improved the agreement between the predictions and experiments. Ranges for the melt fragmentation fraction and mass fraction of participating coolant where the model predictions agree with experimental values are obtained.}, journal={Nuclear Engineering and Design}, publisher={Elsevier BV}, author={Iskhakov, A.S. and Melikhov, V.I. and Melikhov, O.I. and Yakush, S.E. and Chung, L.T.}, year={2019}, month={Jun}, pages={151–157} }
 @article{iskhakov_melikhov_melikhov_yakush_2019, title={Steam generator tube rupture in lead-cooled fast reactors: Estimation of impact on neighboring tubes}, volume={341}, url={http://dx.doi.org/10.1016/j.nucengdes.2018.11.001}, DOI={10.1016/j.nucengdes.2018.11.001}, abstractNote={Lead-cooled fast reactors have several advantages in comparison to thermal neutron reactors and sodium-cooled fast reactors. Despite the considerable interest of international nuclear power community to this technology, safety issues associated with possible chain rupture of steam generator tubes initiated by rupture of a single tube in the tube bundle have not been completely resolved so far. Such initiating events can cause large dynamic loads on the neighboring tubes, and methods for evaluation of their consequences are to be developed. In this work, approaches are proposed for the estimation of forces acting on neighboring tubes at the initial stage of an accident initiated by tube rupture in a lead-heated steam generator. The forces considered include the shock impact caused by pressure wave propagating in liquid lead, and subsequent hydrodynamic impact caused by high-speed flow of heavy lead around the neighboring tubes. The shock impact is calculated from a model for water droplet evaporation and expansion in liquid lead based on the assumptions that two-phase water mixture is in thermodynamic and mechanical equilibrium, while liquid lead is an inviscid compressible fluid. The hydrodynamic impact is estimated using a simplified model with incompressible liquid lead and volume-averaged two-phase water-vapor mixture properties. Both models are implemented in 1D spherical coordinates. Estimates for the shock and hydrodynamic impact of tube rupture on the neighboring tubes are obtained for the conditions of BREST-OD-300 steam generator.}, journal={Nuclear Engineering and Design}, publisher={Elsevier BV}, author={Iskhakov, A.S. and Melikhov, V.I. and Melikhov, O.I. and Yakush, S.E.}, year={2019}, month={Jan}, pages={198–208} }
 @article{yakush_iskhakov_melikhov_melikhov_2018, title={Pressure Waves due to Rapid Evaporation of Water Droplet in Liquid Lead Coolant}, volume={2018}, url={http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000427223200001&KeyUID=WOS:000427223200001}, DOI={10.1155/2018/3087051}, abstractNote={Flash evaporation of a superheated water droplet in heavy liquid metal coolant (lead) is considered, in application to the analysis of a lead-cooled fast reactor steam generator tube rupture accident. The model is based on thermodynamic equilibrium formulation for the expanding water-steam mixture and inviscid compressible formulation for the surrounding liquid lead, with the interface conditions determined from the solution of the Riemann problem. Numerical solution is performed in the spherically symmetric geometry using a conservative numerical scheme with a moving sharp interface. Transient pressure and velocity profiles in each phase are presented for the parameters typical of the steam generator tube rupture accidents, demonstrating the process of boiling water expansion and pressure wave formation in the coolant. The results obtained are compared with a simplified model which considers the volume-averaged parameters of boiling water droplets and considers coolant as an incompressible liquid. Good agreement between the full and simplified models is demonstrated. Impacts of coolant flow on structures caused by pressure wave propagation and subsequent coolant flow are discussed.}, journal={Science and Technology of Nuclear Installations}, publisher={Hindawi Limited}, author={Yakush, S. E. and Iskhakov, A. S. and Melikhov, V. I. and Melikhov, O. I.}, year={2018}, pages={10} }
 @article{numerical modeling of the hydrodynamic loads applied on the «brest-300» reactor steam generator tubes during a primary-to-secondary leak accident_2017, url={http://dx.doi.org/10.24160/1993-6982-2017-3-33-40}, DOI={10.24160/1993-6982-2017-3-33-40}, abstractNote={The article considers the flashing of water in liquid lead and the hydrodynamic processes caused by this phenomenon initially in the emergency mode involving primary-to-secondary leak in the steam generator used as part of the «BREST-OD-300» fast-neutron lead-cooled nuclear reactor plant. The analysis was carried out using an integral equilibrium thermodynamic model for water describing the flashing of a single droplet. In the analysis, uniform distributions of the physical parameters (pressure, void fraction, etc.) inside the droplet are assumed. The liquid lead hydrodynamics is described by a system of nonsteady equations of continuity and motion for ideal incompressible fluid in a spherical system of coordinates. Mathematical descriptions of the “equilibrium” model and semi-implicit numerical method for solving the differential equations used in the model are given. Time dependences of the droplet expansion radius and droplet pressure are obtained. Spatial distributions of lead velocity and pressure for different moments of time are calculated and presented. Transitions of one kind of energy to another are analyzed. The numerical results obtained from the equilibrium model are compared with similar results calculated from an “explosion” model, the main assumption of which is that the initial excess energy of the droplet instantaneously transforms into the liquid lead mechanical energy. The article presents a short description of the explosion model developed proceeding from generalization of the model of instantaneous point energy release (explosion) in ideal incompressible liquid for the case of instantaneous energy release in a finite volume. The liquid lead velocity field is calculated, based on which the hydrodynamic force applied to the steam generator tube located in close vicinity of the rupture place is estimated. The calculation results have shown that this force is insufficient for causing damage to the nearest steam generator tubes. It has been shown that the hydrodynamic impact force calculated taking into account a finite rate of energy transfer from the droplet to the lead (the equilibrium model) is lower than that obtained from using the explosion model.}, number={3}, journal={Vestnik MEI}, publisher={Moscow Power Engineering Institute (MPEI)}, year={2017}, pages={33–40} }