Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “computation time”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Time-dependent Computational Studies of Premixed Flames in Microgravity

This report describes the research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of NASA Microgravity Science and Applications Program. The primary focus of this research is on investigating fundamental questions concerning the propagation and extinction of premixed flames in earth gravity and in microgravity environments. Our approach is to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. Recently more advanced wall boundary conditions such as isothermal and no-slip have been added to the model. This enables the simulation of flames propagating in more practical systems than before. We have used the numerical simulations to investigate the effects of heat losses and buoyancy forces on the structure and stability of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the interaction between the various processes leading to flame instabilities and extinguishment, and to study the dynamics of cell formation and splitting. Our studies have been able to bring out the differences between upward- and downward-propagating flames and predict the zero-gravity behavior of these flames. The simulations have also highlighted the dominant role of wall heat losses in the case of downward-propagating flames. The simulations have been able to qualitatively predict the formation of multiple cells and the cessation of cell-splitting. Our studies have also shown that some flames in a microgravity environment can be extinguished due to a chemical instability and without any external losses. However, further simulations are needed to more completely understand upward-propagating and zero-gravity flames as well as to understand the potential effect of radiative heat losses.

Kailasanath, K.↗

Accelerated deep self-supervised ptycho-laminography for three-dimensional nanoscale imaging of integrated circuits

Three-dimensional inspection of nanostructures such as integrated circuits is important for security and reliability assurance. Two scanning operations are required: ptychographic to recover the complex transmissivity of the specimen, and rotation of the specimen to acquire multiple projections covering the 3D spatial frequency domain. Two types of rotational scanning are possible: tomographic and laminographic. For flat, extended samples, for which the full 180° coverage is not possible, the latter is preferable because it provides better coverage of the 3D spatial frequency domain compared to limited-angle tomography. It is also because the amount of attenuation through the sample is approximately the same for all projections. However, both techniques are time consuming because of extensive acquisition and computation time. Here, we demonstrate the acceleration of ptycho-laminographic reconstruction of integrated circuits with 16 times fewer angular samples and 4.67 times faster computation by using a physics-regularized deep self-supervised learning architecture. We check the fidelity of our reconstruction against a densely sampled reconstruction that uses full scanning and no learning. As already reported elsewhere [ Opt. Express 28 , 12872 ( 2020 ) OPEXFF 1094-4087 10.1364/OE.379200 ], we observe improvement of reconstruction quality even over the densely sampled reconstruction, due to the ability of the self-supervised learning kernel to fill the missing cone.

47 OTHER INSTRUMENTATION↗

A Novel Framework for Performance Evaluation and Design Optimization of PCM Embedded Heat Exchangers for the Built Environment

This research sheds light on the performance evaluation and design optimization of PCM-HXs for the built environment, addressing several barriers to practical issues to PCM-HX commercialization such as modeling aspects (i.e., modeling expertise and computational / time investment, etc.), manufacturing aspects (i.e., at-scale manufacturing, cost assessments, etc.) and experimental performance assessment (i.e., reliable experimental data, assessment of multiple PCM-working fluid combinations, etc.). We present a novel, comprehensive, and experimentally-validated design optimization framework for PCM-HXs capable of simulating any PCM-HX geometry with reasonable accuracy and significant computational time savings when compared to traditional CFD-based design practices. The framework was validated for a wide range of PCM-HX configurations, including a design optimization for a domestic hot water heater application where TES partially replaces electrical heating input. The resulting PCM-HXs were found to deliver 34-68% of the total daily hot water supply with only 5-10% package volume increase from the water heater, thus within U.S. DOE targets for TES systems. To identify the most promising HXs for PCM applications, first-order geometry and cost analyses were conducted based on off-the-shelf HX products. As part of this work, 9 PCM-HX prototypes were manufactured using additive and conventional manufacturing methods. Detailed economy-of-scale assessments were conducted for the most promising PCM-HXs and were found to have a good outlook for the next 5-10 years. The PCM-HX design optimization framework was validated through comprehensive in-house experimental testing using newly-developed PCM-to-fluid test facilities. In total,10 total in-house component-level experiments were conducted using these prototypes, including 9 with water and 1 with refrigerant (R410A) as the working fluid. It was found that the framework can successfully predict experimental thermal-hydraulic performance within ±10-20% the first time without manual design changes, eliminating the need for time-consuming and expensive prototyping efforts as part of the design process. As part of this work, a publicly-available PCM web tool was released which includes a PCM property database (531 PCMs) and PCM-HX modeling tool to assist the design community on common PCM-HX use-cases, e.g., single/multiple flow path(s) fluid-to-PCM and air-to-fluid-to-PCM configurations (https://ceeeweb.umd.edu/pcmapp/). This work will accelerate the design and time to market for next generation PCM-HXs.

25 ENERGY STORAGE↗

Generating Skeletal Chemical Reaction Mechanisms for Post-Detonation Flows

This report documents the generation of a skeletal chemical reaction mechanism for use with hemispherical pentaerythritol tetranitrate charges. Skeletal mechanisms can substantially reduce computation time while maintaining accuracy. The methodology within uses faster running sample simulations to build a representative thermodynamic state space. These thermodynamic states are used with a constant-volume reactor analysis and a reaction flow analysis to remove unimportant species and reactions from a full chemical reaction mechanism. For the given test case, this results in a 6x speedup in computation time for directly comparable simulations in 2D axisymmetric simulations. We see a 30x speedup in simulations in 3D Cartesian coordainates when compared to a prior full kinetics simulation. There is strong agreement between temperature and species mass fraction profiles between the full and skeletal chemical reaction mechanisms. These methodologies can be applied to any explosive, given the availability of sample simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore network model

In this work, a hybrid method coupling a pseudo-potential lattice Boltzmann model (LBM) and a pore network model (PNM) to simulate drying in porous media is proposed. Based on the watershed method, the porous medium is firstly decomposed into pore regions. According to the liquid–vapor phase distribution at a given time, the pore regions are further divided into four pore types, namely two-phase pores where a liquid–vapor interface exists, buffer pores next to the two-phase pores, single-liquid and single-vapor phase pores. The pseudo-potential LBM is used in the two-phase and buffer pores to simulate liquid drying and track the movement of the interfaces, while the single-phase PNM simulations are conducted in the buffer and single-phase pores to simulate vapor or liquid flow. LBM and PNM are coupled in the buffer pores through exchange of boundary information. The hybrid method is applied to simulate liquid drying in a porous medium. The whole-domain LBM simulation is considered as the reference solution to validate the hybrid method. Liquid saturation variation during the drying process and detailed phase and pressure distributions obtained by the two methods match quite well, demonstrating the accuracy of the hybrid method. For the specific case studied, the hybrid method saves more than 60% computational time compared to the whole-domain LBM simulation. In addition, the speedup of the hybrid method becomes more significant for a larger computational domain. In summary, the hybrid method developed in this work combines the accuracy of LBM and the efficiency of PNM to simulate drying in porous media at pore scale and can lead to significant reduction of computation time, thus allowing the pore-scale consideration of drying in larger porous systems.

36 MATERIALS SCIENCE↗

Analysis of Hydrocyclone Geometry via Rapid Optimization Based on Computational Fluid Dynamics

Abstract Hydrocyclones exploit density gradients for the centrifugal separation of dispersions in a continuous liquid. Selection of the geometrics for optimal separation is case specific, like the media characteristics. The existing optimization method based on computational fluid dynamics (CFD) provides a powerful analytical tool but requires long computational times. The most common praxis for CFD optimization is via the single‐factor optimization method (SFOM). In this study, a novel approach is presented as an improved rapid optimization method that implements a dynamic‐mesh and user‐defined function optimization method (DUOM). The DUOM adapts the dynamic‐mesh approach from other applications to the optimization analysis of hydrocyclones. The DUOM reduced the computational time by 31.1 %, compared to the SFOM.

Liu, Lin↗

Mobiliti v1.0

Mobiliti is a software platform designed to emulate the dynamics of a regional transportation road network. It is built on open-source software that provides parallel discrete-event simulation. The software is transformative in the area of transportation network simulation because of the geospatial scale and fidelity of the network model and the computational time it takes to model a full day of travel demand. For example, it runs a simulation of the entire San Francisco Bay Area, with a network model of ~1M links and a population that completes ~19M trips in ~5 minutes. This scale of simulation has not been attempted with existing simulation models due to the complexity of the model and the computational time it would take to complete. The intent of the software is to create a digital twin capability for cities to evaluate consequences of infrastructure or policy changes on road network dynamics.

Macfarlane, Jane↗

Nuclear reactor descriptions for space power systems analysis

For the small, high performance reactors required for space electric applications, adequate neutronic analysis is of crucial importance, but in terms of computational time consumed, nuclear calculations probably yield the least amount of detail for mission analysis study. It has been found possible, after generation of only a few designs of a reactor family in elaborate thermomechanical and nuclear detail to use simple curve fitting techniques to assure desired neutronic performance while still performing the thermomechanical analysis in explicit detail. The resulting speed-up in computation time permits a broad detailed examination of constraints by the mission analyst.

Mccauley, E. W.↗

Deep learning for NLTE spectral opacities

Computer simulations of high energy density science experiments are computationally challenging, consisting of multiple physics calculations including radiation transport, hydrodynamics, atomic physics, nuclear reactions, laser–plasma interactions, and more. To simulate inertial confinement fusion (ICF) experiments at high fidelity, each of these physics calculations should be as detailed as possible. However, this quickly becomes too computationally expensive even for modern supercomputers, and thus many simplifying assumptions are made to reduce the required computational time. Much of the research has focused on acceleration techniques for the various packages in multiphysics codes. In this work, we explore a novel method for accelerating physics packages via machine learning. The non-local thermodynamic equilibrium (NLTE) package is one of the most expensive calculations in the simulations of indirect drive inertial confinement fusion, taking several tens of percent of the total wall clock time. We explore the use of machine learning to accelerate this package, by essentially replacing the physics calculation with a deep neural network that has been trained to emulate the physics code. Overall, we demonstrate the feasibility of this approach on a simple problem and perform a side-by-side comparison of the physics calculation and the neural network inline in an ICF Hohlraum simulation. We show that the neural network achieves a 10× speed up in NLTE computational time while achieving good agreement with the physics code for several quantities of interest.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reliability enhancement of Navier-Stokes codes through convergence enhancement

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Choi, K.-Y.↗

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗

Analysis of Sample Acquisition Dynamics Using Discrete Element Method

The analysis presented in this paper is conducted in the framework of the Ocean Worlds Autonomy Testbed for Exploration Research and Simulation (OceanWATERS) project, currently under development at NASA Ames Research Center. OceanWATERS aims at designing a simulation environment which allows for testing autonomy of scientific lander missions to the icy moons of our solar system. Mainly focused on reproducing the end effector interaction with the inherent terrain, this paper introduces a novel discrete element method (DEM)-based approach to determine forces and torques acting on the lander’s scoop during the sample acquisition process. An accurate force feedback from the terrain on the scoop is required by fault-detection and autonomous decision-making algorithms to identify when the requested torque on the robotic arm’s joints exceeds the maximum available torque. Knowledge of the terrain force feedback significantly helps evaluating the arm’s links structural properties and properly selecting actuators for the joints. Models available in literature constitute a partial representation of the dynamics of the interaction. As an example, Balovnev derived an analytical expression of the vertical and horizontal force acting on a bucket while collecting a sample as a function of its geometry and velocity, soil parameters and reached depth. Although the model represents an adequate approximation of the two force components, it ignores the direction orthogonal to the scoop motion and neglects the torque. This work relies on DEM analysis to compensate for analytical models’ deficiencies and inaccuracies, i. e. provide force and torque 3D vectors, defined in the moving reference (body) frame attached to the scoop, at each instant of the sample collection process. Results from the first presented analysis relate to the specific OceanWATERS sampling strategy, which consists of collecting the sample through five consecutive passes with increasing depth, each pass following the same circularlinear- circular trajectory. Data is collected given a specific scoop design interacting with two types of bulk materials, which may characterize the surface of icy planetary bodies: snow and ice. Although specifically concerned with the OceanWATERS design, this first analysis provides the expected force trends for similar sampling strategies and allows to deduce phenomenological information about the general scooping process. In order to further instruct the community on the use of DEM tools as a solution to the sampling collection problem, two more analyses have been carried out, mainly focused on reducing the DEM computation time, which increases with a decrease in particle size. After running a set of identical simulations, where the only changing parameter is the size of the spherical particle, it is observed that the resulting force trajectories, starting from a given particle size, converge to the true trend. It is deducible that a further decrease in size yields negligible improvements in the accuracy, while it sensibly increases computation time. A final analysis aims at discussing limitations of approximating bulk material particles having a complex shape, e. g. ice fragments, with spheres, by comparing force trends resulting in the two cases for the same simulation scenario.

Catanoso, Damiana↗

Convergence acceleration of viscous and inviscid hypersonic flow calculations

The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presented for various cases; and a 50 percent savings in computer time is usually achieved. An analytical formula for the overrelaxation factor is derived, and the performance of this scheme is confirmed numerically. Moreover, application of this overrelaxation scheme produces a favorable preconditioning for Wynn's epsilon-algorithm. Both techniques have been extended to viscous three-dimensional flows and applied to accelerate the convergence of the compressible Navier-Stokes code. A savings of 40 percent in computer time is achieved in this case.

Cheer, A.↗

Performance Study of Distance-Weighting Approach with Loopy Sum-Product Algorithm for Multi-Object Tracking in Clutter

In this paper, we explore the performance of the distance-weighting probabilistic data association (DWPDA) approach in conjunction with the loopy sum-product algorithm (LSPA) for tracking multiple objects in clutter. First, we discuss the problem of data association (DA), which is to infer the correspondence between targets and measurements. DA plays an important role when tracking multiple targets using measurements of uncertain origin. Second, we describe three methods of data association: probabilistic data association (PDA), joint probabilistic data association (JPDA), and LSPA. We then apply these three DA methods for tracking multiple crossing targets in cluttered environments, e.g., radar detection with false alarms and missed detections. We are interested in two performance metrics: tracking accuracy and computation time. LSPA is known to be superior to PDA in terms of the former and to dominate JPDA in terms of the latter. Last, we consider an additional DA method that is a modification of PDA by incorporating a weighting scheme based on distances between position estimates and measurements. This distance-weighting approach, when combined with PDA, has been shown to enhance the tracking accuracy of PDA without significant change in the computation burden. Since PDA constitutes a crucial building block of LSPA, we hypothesize that DWPDA, when integrated with LSPA, would perform better under the two performance metrics above. Contrary to expectations, the distance-weighting approach does not enhance the performance of LSPA, whether in terms of tracking accuracy or computation time.

47 OTHER INSTRUMENTATION↗

Parametric Analysis of Aircraft WingWeight Using Low-Order Physics-Based Analysis

In the conceptual aircraft design phase, prediction of the empty weight typically relies on empirically-based regression equations which execute quickly and require little detailed information about the internal structural layout. Since they are based on existing aircraft, however, empirical methods can lose their validity for newer technologies and unconventional configurations. Designers can transition to higher-order, physics-based analysis methods to improve the accuracy of the weight prediction, but at the cost of complex model setup and increased computational time. This paper describes a methodology for low-order aero-structural analysis of conceptual aircraft configurations that increases the use of physics-based analysis in conceptual design, but is less complex and time-consuming than higher-order methods such as finite-element analysis. The methodology uses Vehicle Sketch Pad (OpenVSP) to model the aircraft geometry, and ASWING to perform the aero-structural analysis. The internal forces and moments from the ASWING analysis are post-processed to calculate the resulting direct and shear stresses in the structure, and the thickness distributions of the aircraft components are varied to match the maximum von Mises stress at each cross section to the material allowable. To offset the increased computational time relative to empirical weight equations, a process is studied which uses parametric variation to develop a regression equation relating the weight of the aircraft wing to major design variables. This new weight equation is similar to existing empirical equations, but is built using the more physics-based methodology; the new equation could be used to augment or replace portions of the empirical database to improve the validity of the wing weight prediction for unconventional configurations and advanced technologies.

Olson, Erik D.↗

Monitoring by Use of Clusters of Sensor-Data Vectors

The inductive monitoring system (IMS) is a system of computer hardware and software for automated monitoring of the performance, operational condition, physical integrity, and other aspects of the health of a complex engineering system (e.g., an industrial process line or a spacecraft). The input to the IMS consists of streams of digitized readings from sensors in the monitored system. The IMS determines the type and amount of any deviation of the monitored system from a nominal or normal ( healthy ) condition on the basis of a comparison between (1) vectors constructed from the incoming sensor data and (2) corresponding vectors in a database of nominal or normal behavior. The term inductive reflects the use of a process reminiscent of traditional mathematical induction to learn about normal operation and build the nominal-condition database. The IMS offers two major advantages over prior computational monitoring systems: The computational burden of the IMS is significantly smaller, and there is no need for abnormal-condition sensor data for training the IMS to recognize abnormal conditions. The figure schematically depicts the relationships among the computational processes effected by the IMS. Training sensor data are gathered during normal operation of the monitored system, detailed computational simulation of operation of the monitored system, or both. The training data are formed into vectors that are used to generate the database. The vectors in the database are clustered into regions that represent normal or nominal operation. Once the database has been generated, the IMS compares the vectors of incoming sensor data with vectors representative of the clusters. The monitored system is deemed to be operating normally or abnormally, depending on whether the vector of incoming sensor data is or is not, respectively, sufficiently close to one of the clusters. For this purpose, a distance between two vectors is calculated by a suitable metric (e.g., Euclidean distance) and "sufficiently close" signifies lying at a distance less than a specified threshold value. It must be emphasized that although the IMS is intended to detect off-nominal or abnormal performance or health, it is not necessarily capable of performing a thorough or detailed diagnosis. Limited diagnostic information may be available under some circumstances. For example, the distance of a vector of incoming sensor data from the nearest cluster could serve as an indication of the severity of a malfunction. The identity of the nearest cluster may be a clue as to the identity of the malfunctioning component or subsystem. It is possible to decrease the IMS computation time by use of a combination of cluster-indexing and -retrieval methods. For example, in one method, the distances between each cluster and two or more reference vectors can be used for the purpose of indexing and retrieval. The clusters are sorted into a list according to these distance values, typically in ascending order of distance. When a set of input data arrives and is to be tested, the data are first arranged as an ordered set (that is, a vector). The distances from the input vector to the reference points are computed. The search of clusters from the list can then be limited to those clusters lying within a certain distance range from the input vector; the computation time is reduced by not searching the clusters at a greater distance.

Iverson, David L.↗

Towards Efficient Alternating Current Optimal Power Flow Analysis on Graphical Processing Units

We present a solution of sparse ACOPF analysis on GPU. In particular, we discuss the performance bottlenecks and detail our efforts to accelerate the linear solver, a core component of ACOPF that dominates the computational time. ACOPF solutions of two large-scale systems, synthetic Northeast (25,000 buses) and Eastern (70,000 buses) \cite{birchfield2017tamu-cases} on GPU show promising speed-up compared to CPU based solution using a state-of-the-art solver. To our knowledge, this is the first result demonstrating acceleration of sparse ACOPF on GPUs.

Power grid analysis, GPU↗

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗