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Modeling and Analysis of Stirling Power Convertors

Modeling and Analysis of Stirling Power Convertors Luis A. Rodriguez1 Steven M. Geng, Terry V. Reid, Scott D. Wilson NASA Glenn Research Center, Cleveland, OH, 44135, USA NASA Glenn’s Thermal Energy Conversion Branch is supporting the development of the next generation free-piston Stirling power convertors. American Superconductor (AMSC) and Sunpower Inc. are the two firms under contract to develop the Flexure Isotope Stirling Convertor (FISC) and the Sunpower Robust Stirling Convertor (SRSC), respectively. To comprehend and forecast convertor performance, Sage, ANSYS® Maxwell, and ANSYS® Fluent were used to model the Stirling thermodynamic cycle, alternator electromagnetics, and piston and displacer dynamics. I. Introduction Stirling convertors are being developed by NASA as a potential steady source of electrical power for NASA’s future scientific space missions. Currently, NASA Glenn Research Center has two corporations under contract, American Superconductor (AMSC) and Sunpower Inc., for the development of the next generation of free-piston Stirling convertors for dynamic radioisotope power systems. AMSC is developing the Flexure Isotope Stirling Convertor (FISC), which uses flexures to prevent side motion and rubbing of the piston. Similarly, Sunpower Inc, is developing the Sunpower Robust Stirling Convertor (SRSC). The SRSC uses gas bearings to prevent radial contact of the moving piston. As convertor development continues, it is increasingly important to understand and predict the interactions of components in the system, how they respond to one another, and how they perform as a response to changes in operating conditions. A suitable and enlightening way to demonstrate and foresee these interactions is with the use of accurate modeling software. Sage, ANSYS® Maxwell, and ANSYS® Fluent are the current modeling tools used by NASA to analytically determine convertor performance. Sage is a one-dimensional object-oriented commercial software package used for modeling and optimizing Stirling convertors for Dynamic Radioisotope Power Systems (DRPS) and it is one of the most accurate Stirling convertor codes in use by NASA. This code is the successor to GLIMPS (Globally-Implicit Stirling Cycle Simulation) and GLOP (GLIMPS Optimization) software created by Gedeon Associates [1]. Model input parameters are typically material/gas type, component physical dimensions, temperatures, frequency, charge pressure, and number of time/space nodes. Sage is used to model both the FISC’s and SRSC’s Stirling cycle thermodynamics and piston/displacer dynamics. Performance maps were created and analyzed for both power systems to better understand the relationship between the following conditions: cold-end temperature, hot-end temperature, piston/displacer amplitudes, pressure drop, and thermal input power. The synergy between these conditions will help determine parameter sensitivity. ANSYS® Maxwell was used to create a three-dimensional (3-D) axisymmetric model for both FISC and SRSC alternators. The significant physical components included in each model are the magnets, magnet carrier, outer/inner laminations, and the coil. Inputs to the model are piston amplitude, piston frequency, alternator load, coil resistance, tuning capacitance, and specific material properties. The alternator models calculate terminal voltage, current, piston/current phase, voltage/current phase, coil inductance, terminal power and efficiency. The RI2 losses, core (hysteresis and eddy) losses, and magnet/can eddy losses are also a part of the final results. ANSYS® Fluent is used to build 3-D computational fluid dynamic (CFD) models to examine the Stirling cycle thermodynamics for both the FISC and SRSC systems. Three-dimensional Computer Aided Design (CAD) models were used to create the physical components of each convertor. Steady-state simulations were conducted for hardware testing, prediction of environmental losses during testing, and generation of radiation look-up tables. The model inputs to the aforementioned analysis are the material properties and boundary thermal conditions. The steady-state model calculates temperature and heat flow distributions. Transient 3-D calculations were also part of the CFD analysis. In this study a physically reduced version of the FISC is used to obtain a prediction of available engine power. For the gas bearing SRSC, the transient effort is used to obtain a prediction of bearing pad performance and its sensitivity to micro-channel geometric variation. The model inputs to the transient simulations are the piston amplitude, displacer amplitude, frequency, displacer/piston phase angle, dynamic deforming CFD grid, temperature boundary conditions, and user defined files describing motion profile of piston/displacer. The results of the model are temperature distributions, heat distributions, and PV power produced at pre-determined conditions.

Luis A Rodriguez↗

Two-Way Coupled CFD/DEM Simulation of Electromagnetic Heating in a Fluidized Bed Reactor - Extended Abstract

A set of tools has been developed to couple a multiphase reacting computational fluid dynamics solver (MFIX) with two computational electromagnetic solvers (COMSOL and Elmer). In contrast to several recent investigations, which calculate a single static EM field prior to the CFD calculation, in the present work the electromagnetic field is periodically updated during the simulation. This enables the EM field and associated EM heating predictions to reflect the effects of evolving material properties (temperature, composition, size etc.) and the evolving distribution of material in the system. The present work uses effective medium theory (EMT) for the electromagnetic field calculations since the goal is to apply the tool for industrial scale reacting systems. Predictions using MFIX/COMSOL and MFIX/Elmer are compared to in bed thermocouple measurements from a fluidized bed experiment and recent simulation predictions and recent experiments performed at NETL. The NETL experiments also include packed bed operating conditions. Coupled MFIX/COMSOL simulations at these conditions are compared with similar simulations using only COMSOL to measure errors due to the solver coupling approach.

CFD↗

Resilience-Oriented DG Siting and Sizing Considering Stochastic Scenario Reduction

In this paper, a fuel-based distributed generator (DG) allocation strategy is proposed to enhance the distribution system resilience against extreme weather. The long-term planning problem is formulated as a two-stage stochastic mixed-integer programming (SMIP). The first stage is to make decisions of DG siting and sizing under the given budget constraint. In the second stage, a post-extreme-event-restoration (PEER) is employed to minimize the operating cost in an uncertain fault scenario. In particular, this study proposes a method to select the most representative scenarios for the SMIP. First, a Monte Carlo Simulation (MCS) is introduced to generate sufficient scenarios considering random fault locations and load profiles. Then, the number of scenarios is reduced by the K-means clustering algorithm. The advantage of scenario reduction is to make a trade-off between accuracy and computational efficiency. Finally, the SMIP is solved by the progressive hedging algorithm. Here, the case studies of the IEEE 33-bus and 123-bus test systems demonstrate the effectiveness of the proposed algorithm in reducing the expected energy not served (EENS), which is a critical criterion of resilience.

42 ENGINEERING↗

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

Data-driven surrogate modeling of hPIC ion energy-angle distributions for high-dimensional sensitivity analysis of plasma parameters' uncertainty

In this work, we present a data-driven strategy for effective construction of a surrogate model in high-dimensional parameter space for the ion energy-angle distribution (IEAD) output of hPIC simulations of plasma-surface interactions. The methodology is based on a bin-by-bin least-squares fitting of the IEAD in the parameter space. The fitting is performed in a transformed coordinate system to normalize the IEAD, and it employs sparse grids for sampling the parameter space to overcome sampling challenges in high dimensions. The surrogate model is significantly cheaper computationally than direct hPIC simulations yet maintains high fidelity to them, providing a fast emulator for hPIC simulations. Sensitivity analysis based on the surrogate model is utilized to characterize the dependence of the ion impact angle and energy moments on the physical parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Distribution of blackouts in the power grid and the Motter and Lai model

Carreras, Dobson, and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them with computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts changes with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. Finally, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Digital Twin + AI: Control Room of the Future [Slides]

The control room functions as the central brain of the grid, essential for balancing supply and demand and ensuring moment-to-moment grid reliability. Like the human brain, which processes sensory data to make decisions, control room operators analyze operational data from power generation, transmission, and distribution to make informed decisions. Currently, decision-making primarily rests with operators due to hardware and software limitations. However, with technological advancements, Digital Twins and AI are becoming high interest points in the control room's decision-making pilot programs. NREL is developing a comprehensive decision-making platform that integrates Digital Twins, AI, and advanced visualization techniques. As this integration progresses, the role of Digital Twins will evolve from conducting automated simulations to serving as a Trustworthy AI enabler, offering verification and validation of AI-generated response for power systems or providing physics-aware synthetic data of AI pre-training.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Controls and guidance: Space

The Space Controls and Guidance Research and Technology Program is directed toward enabling the next generation of space transportation systems, large future spacecraft, and space systems such as the Space Station to have large communication antennas and high precision segmented reflector astrophysical telescopes. The new generation of transportation vehicles has demanding requirements to provide for an order of magnitude reduction in cost as well as an increase in capability. The future orbital facilities have demanding control requirements for pointing and stabilization, momentum management, build-up and growth accomodation, and disturbance management. To address these advanced requirements, the research and development program is designed to provide the generic technology base to support the implementation of advanced guidance, navigation, and control. The area of computational controls will be stressed in order to develop cost effective, high speed, high fidelity control system simulation and analysis and synthesis tools. The trust of this work will be to develop methods and software to enable analysis and real-time hardware-in-the-loop simulation of complex spacecraft for control design certification. To address future orbital facilities requirements, an advanced technology program is underway in system identification, distributed control, integrated controls/structures design methods, and advanced sensors and actuators. Because the behavior of large, light weight per unit area deployable/assembled spacecraft is greatly influenced by the ground environment, the testing and verification activity is both ground- and space-based.

Dibattista, John D.↗

Natural Ocean Carbon Cycle Sensitivity to Parameterizations of the Recycling in a Climate Model

Sensitivities of the oceanic biological pump within the GISS (Goddard Institute for Space Studies ) climate modeling system are explored here. Results are presented from twin control simulations of the air-sea CO2 gas exchange using two different ocean models coupled to the same atmosphere. The two ocean models (Russell ocean model and Hybrid Coordinate Ocean Model, HYCOM) use different vertical coordinate systems, and therefore different representations of column physics. Both variants of the GISS climate model are coupled to the same ocean biogeochemistry module (the NASA Ocean Biogeochemistry Model, NOBM), which computes prognostic distributions for biotic and abiotic fields that influence the air-sea flux of CO2 and the deep ocean carbon transport and storage. In particular, the model differences due to remineralization rate changes are compared to differences attributed to physical processes modeled differently in the two ocean models such as ventilation, mixing, eddy stirring and vertical advection. GISSEH(GISSER) is found to underestimate mixed layer depth compared to observations by about 55% (10 %) in the Southern Ocean and overestimate it by about 17% (underestimate by 2%) in the northern high latitudes. Everywhere else in the global ocean, the two models underestimate the surface mixing by about 12-34 %, which prevents deep nutrients from reaching the surface and promoting primary production there. Consequently, carbon export is reduced because of reduced production at the surface. Furthermore, carbon export is particularly sensitive to remineralization rate changes in the frontal regions of the subtropical gyres and at the Equator and this sensitivity in the model is much higher than the sensitivity to physical processes such as vertical mixing, vertical advection and mesoscale eddy transport. At depth, GISSER, which has a significant warm bias, remineralizes nutrients and carbon faster thereby producing more nutrients and carbon at depth, which eventually resurfaces with the global thermohaline circulation especially in the Southern Ocean. Because of the reduced primary production and carbon export in GISSEH compared to GISSER, the biological pump efficiency, i.e., the ratio of primary production and carbon export at 75 m, is half in the GISSEH of that in GISSER, The Southern Ocean emerges as a key region where the CO2 flux is as sensitive to biological parameterizations as it is to physical parameterizations. The fidelity of ocean mixing in the Southern Ocean compared to observations is shown to be a good indicator of the magnitude of the biological pump efficiency regardless of physical model choice.

Antarctic Ocean↗

Health Management Applications for International Space Station

Traditional mission and vehicle management involves teams of highly trained specialists monitoring vehicle status and crew activities, responding rapidly to any anomalies encountered during operations. These teams work from the Mission Control Center and have access to engineering support teams with specialized expertise in International Space Station (ISS) subsystems. Integrated System Health Management (ISHM) applications can significantly augment these capabilities by providing enhanced monitoring, prognostic and diagnostic tools for critical decision support and mission management. The Intelligent Systems Division of NASA Ames Research Center is developing many prototype applications using model-based reasoning, data mining and simulation, working with Mission Control through the ISHM Testbed and Prototypes Project. This paper will briefly describe information technology that supports current mission management practice, and will extend this to a vision for future mission control workflow incorporating new ISHM applications. It will describe ISHM applications currently under development at NASA and will define technical approaches for implementing our vision of future human exploration mission management incorporating artificial intelligence and distributed web service architectures using specific examples. Several prototypes are under development, each highlighting a different computational approach. The ISStrider application allows in-depth analysis of Caution and Warning (C&W) events by correlating real-time telemetry with the logical fault trees used to define off-nominal events. The application uses live telemetry data and the Livingstone diagnostic inference engine to display the specific parameters and fault trees that generated the C&W event, allowing a flight controller to identify the root cause of the event from thousands of possibilities by simply navigating animated fault tree models on their workstation. SimStation models the functional power flow for the ISS Electrical Power System and can predict power balance for nominal and off-nominal conditions. SimStation uses realtime telemetry data to keep detailed computational physics models synchronized with actual ISS power system state. In the event of failure, the application can then rapidly diagnose root cause, predict future resource levels and even correlate technical documents relevant to the specific failure. These advanced computational models will allow better insight and more precise control of ISS subsystems, increasing safety margins by speeding up anomaly resolution and reducing,engineering team effort and cost. This technology will make operating ISS more efficient and is directly applicable to next-generation exploration missions and Crew Exploration Vehicles.

Alena, Richard↗

SCUC-DER Integration Report: Integrating Distributed Energy Resources (DER) Using Advanced Unit Commitment Models and DER Aggregation Methodologies

Distributed energy resources (DERs) are continuing to grow due to regulatory, policy, and market shifts, and it needs to be ensured that small DERs are given a level playing field with traditional resources. Legacy market processes such as unit-commitment problems were designed for a power grid consisting largely of centralized power plants. In contrast, DERs consist of many small devices with distinct operating characteristics that may or may not be connected at the transmission interconnection points, limiting their visibility to the independent system operators (ISOs) who operate wholesale electricity markets. This report details the development and initial results from a simulation platform that integrates state-of-the-art security-constrained unit commitment software, detailed feeder models, and a DER aggregator model to quantify potential DER integration issues. Quantitative results to date illustrate potential infeasible scheduling solutions from SCUC when the DERA includes aggregations of energy-limited energy storage resources. Likewise, if aggregations are not penalized for dispatch deviations, they may have incentives to deviate from the SCUC-determined resource schedules. Assumptions about the amount of aggregated demand response resources (DRRs) and the ability of DERAs to follow profit incentives have an important impact – DRRs have significant flexibility and can typically feasibly meet their SCUC schedule, but on the other hand, their profit incentives can cause unscheduled increases in load before and after DRR dispatch. Computation time results on the SCUC solver and simulation platform only show a modest increase in SCUC solution time as the number of DERAs is increased, but results to date only reflect the RTS-GMLC test system; results may show more significant solver slowdown in larger transmission systems. The largest contribution to simulation time is attributed to the DERA offer generation method, which is suggested for future improvements.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Computer simulations of planetary accretion dynamics: Sensitivity to initial conditions

The implications and limitations of program ACRETE were tested. The program is a scheme based on Newtonian physics and accretion with unit sticking efficiency, devised to simulate the origin of the planets. The dependence of the results on a variety of radial and vertical density distribution laws, the ratio of gas to dust in the solar nebula, the total nebular mass, and the orbital eccentricity of the accreting grains was explored. Only for a small subset of conceivable cases are planetary systems closely like our own generated. Many models have tendencies towards one of two preferred configurations: multiple star systems, or planetary systems in which Jovian planets either have substantially smaller masses than in our system or are absent altogether. But for a wide range of cases recognizable planetary systems are generated - ranging from multiple star systems with accompanying planets, to systems with Jovian planets at several hundred AU, to single stars surrounded only by asteroids.

Isaacman, R.↗

Large-scale offshore wind farm effects on weather and climate in Puerto Rico (Final Technical Report)

Puerto Rico’s current electricity generation heavily relies on imported fossil fuels. This results in an average cost of electricity higher than the U.S. mainland average in all sectors (residential, commercial, and industrial), despite abundant local offshore wind resources, which have the potential to provide secure, low-cost energy generation and consequent economic prosperity. However, effects on atmospheric and oceanic circulation resulting from large-scale deployments of offshore wind farms have not been previously studied at tropical latitude. This project addressed this knowledge gap through a computational modeling effort designed to capture the coupled dynamics of the atmosphere and the ocean in presence of offshore wind farms. Results indicate that wind farm wakes can alter wind stress, generate Ekman-driven vertical transport, and potentially affect nutrient distribution. While full model coupling remains challenging, progress in parameterization and large-eddy simulations provides a foundation for future research. The project contributes to DOE’s Earth System modeling efforts and supports STEM workforce development.

17 WIND ENERGY↗

Modelling the solution growth of TGS crystals in low gravity

The experimental growth of triglycine sulfate (TGS) crystals from aqueous solution is modeled here in two dimensions using the PHOENICS finite volume code. Simulations are carried out for steady, impulsive, and periodic accelerations in order to determine tolerable acceleration levels. Scaling arguments are used to estimate the times required for thermal and solutal variations from the initial equilibrium state to be diffusively transported throughout the system, and to obtain order of magnitude information on the relative magnitudes of diffusive and convective transport. The computed concentration fields reflect the features of the concentration distributions found experimentally during experiments conducted aboard Spacelab 3 in 1985.

Nadarajah, Arunan↗

Charging of interplanetary grains

The objective of this program is to quantify, by laboratory experiments, the charging of ices and other insulators subject to irradiation with electrons, ions and ultraviolet photons and to model special conditions based on the data. The system and conditions to be studied are those relevant for charging of dust in magnetospheric plasmas. The measurements are supplemented by computer simulations of charging or grains under a variety of conditions. Our work for this period involved experiments on water ice, improved models of charging of ice grains for Saturn's E-ring, and the construction of apparatus for electron impact studies and measurements of electron energy distributions.

Baragiola, R. A.↗

Effect of a Nonplanar Melt-Solid Interface On Lateral Compositional Distribution During Unidirectional Solidification of a Binary Alloy with a Constant Growth Velocity V: Theory - Pt. 1

Infrared detected materials, such as Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te have energy gaps almost linearly proportional to their composition. Due to the wide separation of liquidus and solidus curves of their phase diagram, there are compositional segregation in both of the axial and radial directions of these crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms, which affect lateral segregation such that large radially uniform composition crystal can be produced. Following Coriel, etc's treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on lateral composition distribution. The model is considered to be a cylindrical system with azimuthal symmetry and a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessell's functions. The results show that melt-solid interface shape has a dominant effect on the lateral composition distribution of these systems. For small values of beta, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the produce of beta and (1 -k), where beta = VR/D, with V as growth velocity, R as the sample radius, D as the diffusion constant and k as the distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.

Wang, Jai-Ching↗

Assessment of Microphysical Models in the National Combustion Code (NCC) for Aircraft Particulate Emissions: Particle Loss in Sampling Lines

This paper at first describes the fluid network approach recently implemented into the National Combustion Code (NCC) for the simulation of transport of aerosols (volatile particles and soot) in the particulate sampling systems. This network-based approach complements the other two approaches already in the NCC, namely, the lower-order temporal approach and the CFD-based approach. The accuracy and the computational costs of these three approaches are then investigated in terms of their application to the prediction of particle losses through sample transmission and distribution lines. Their predictive capabilities are assessed by comparing the computed results with the experimental data. The present work will help establish standard methodologies for measuring the size and concentration of particles in high-temperature, high-velocity jet engine exhaust. Furthermore, the present work also represents the first step of a long term effort of validating physics-based tools for the prediction of aircraft particulate emissions.

Wey, Thomas↗

Development of a Grid-Independent Geos-Chem Chemical Transport Model (v9-02) as an Atmospheric Chemistry Module for Earth System Models

The GEOS-Chem global chemical transport model (CTM), used by a large atmospheric chemistry research community, has been re-engineered to also serve as an atmospheric chemistry module for Earth system models (ESMs). This was done using an Earth System Modeling Framework (ESMF) interface that operates independently of the GEOSChem scientific code, permitting the exact same GEOSChem code to be used as an ESM module or as a standalone CTM. In this manner, the continual stream of updates contributed by the CTM user community is automatically passed on to the ESM module, which remains state of science and referenced to the latest version of the standard GEOS-Chem CTM. A major step in this re-engineering was to make GEOS-Chem grid independent, i.e., capable of using any geophysical grid specified at run time. GEOS-Chem data sockets were also created for communication between modules and with external ESM code. The grid-independent, ESMF-compatible GEOS-Chem is now the standard version of the GEOS-Chem CTM. It has been implemented as an atmospheric chemistry module into the NASA GEOS- 5 ESM. The coupled GEOS-5-GEOS-Chem system was tested for scalability and performance with a tropospheric oxidant-aerosol simulation (120 coupled species, 66 transported tracers) using 48-240 cores and message-passing interface (MPI) distributed-memory parallelization. Numerical experiments demonstrate that the GEOS-Chem chemistry module scales efficiently for the number of cores tested, with no degradation as the number of cores increases. Although inclusion of atmospheric chemistry in ESMs is computationally expensive, the excellent scalability of the chemistry module means that the relative cost goes down with increasing number of cores in a massively parallel environment.

CTM↗