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At least 181 records · Page 10

Grid-Integrated Production of Fischer-Tropsch Synfuels from Nuclear Power

Idaho National Laboratory (INL) investigates the relative economic profitability of an integrated energy system (IES) coupling an NPP with a synfuel production process at selected case study locations across the United States. In the synfuel IES, a high-temperature steam electrolysis (HTSE) plant is thermally and electrically coupled with an NPP to produce zero-carbon hydrogen. The synthetic fuel is produced from this H 2 combined with a CO 2 supply using the reverse water gas shift process followed by the Fischer-Tropsch (FT) reaction. This analysis considers a system in which the CO 2 is sourced from regional CO 2 emitters via the construction and operation of pipeline-based CO 2 supply networks. Locating the FT plant at the same site as the NPP and HTSE plants enables the NPP to provide zero-carbon heat and power to the HTSE plant and zero-carbon power to the FT plant as well as avoid the requirement for long-distance H 2 product transport from the HTSE plant to the FT plant. Hydrogen storage is used to enable the NPP to dispatch power to the electrical grid (instead of the HTSE plant) when grid demand increases, thus enabling the FT plant to continue to operate in a steady-state production mode. The ability to cease hydrogen production for several hours within each day enables the NPP to provide power to the grid to balance the electricity market during peak periods and maximize revenues for the nuclear synfuel IES. The FT process design considered has a 99% carbon conversion efficiency. The use of nuclear energy and nuclear energy-derived hydrogen enables synfuel production to achieve this high level of carbon utilization. Additionally, the life-cycle carbon emissions of the nuclear-based synfuel production process are very low, with WTW emissions of approximately 25 gCO 2 e/MJ, including steam credits (generated from FT process excess heat), and approximately 7 gCO 2 e/MJ, if steam credits are excluded. This compares favorably with the WTW emissions of 90.5 gCO 2 e/MJ for a compression-ignition, direct injection (CIDI) vehicle with a fuel economy of 31.6 miles per gallon gasoline equivalent (MPGGE), using low-sulfur diesel produced using conventional petroleum production and refining processes. Several NPPs in various regions of the U.S. are considered as case study analyses. Supply locations and transportation via pipeline of the CO 2 feedstock to the NPP site are analyzed through the National Energy Technology Laboratory (NETL) CO 2 Transport Cost model. The team finds that the amount of CO 2 generated by different sectors is sufficient for the synfuel production process at all locations considered. The CO 2 transportation costs are functions of the distance of the source to the NPP location, the CO 2 capture cost at the source, and the quantity of CO 2 transported. Historical electricity prices for the NPP case study locations are collected and analyzed. Monthly average prices, price range, and duration of negative-price periods vary among these locations. For each location, an auto-regressive moving average (ARMA) model is trained on historical electricity price data. ARMA validation is done to ensure the synthetic price distributions represent one of historical prices with high fidelity. Synthetic time series from these ARMA models are used in a coupled dispatch and system optimization in the Holistic Energy Resource Optimization Network (HERON) to compute the differential net present value (NPV) of the IES. The team finds that this econometric is positive, ranging from $14M–1.3bn (2020) depending on the location. The optimal synfuel IES configuration to obtain this increase in NPV often maximizes the size of the synfuel production process with regards to the size of the NPP. However, the team shows that the NPP still plays a stabilizing role for the grid: In periods of high prices and high loads, more electricity from the NPP is sent to the grid. A high variability of electricity prices and extreme maximum prices tend to drive up electricity production. While it requires significant investment, the synfuel IES could increase the economic profitability for the existing fleet of LWRs across the country while still maintaining the grid stabilizer role of NPPs. During its lifetime, the main costs for the nuclear synfuel IES are the carbon feedstock transportation costs, followed by the capital expenses (CAPEX) and operation and maintenance (O&M) costs while the revenue comes first from the IRA H 2 production tax credit (PTC) and then from the sales of synfuel products. The profitability of the synfuel IES is most sensitive to the value of the hydrogen PTC and the synfuel products as well as the cost of the carbon feedstock, highlighting the importance of governmental incentives regarding hydrogen, carbon emissions, and synfuel in driving the deployment of future nuclear synfuel IESs.

08 HYDROGEN↗

Defining a Platform Approach and Market Participation: Data Driven Business Models for Solid State Transformer-Based Synthetic Inertia and Voltage Stability Controls (CRADA Final Report, Project 1, Mod 1)

The primary objective of this project is to determine the incremental value created with the medium voltage solid-state transformer (MV SST) technology to different stakeholders in view of the updated DER grid regulations. This includes studying the benefits of the MV SST technology in a range of use cases for EV and DER penetration including (1) “corridor charging” for EVs and (2) solar plus storage (FERC 2222). The potential customers of this technology include utilities for EV charging, DER installers who must meet utility interconnection requirements, balancing authorities, and DER aggregators. The traditional transformers on the grid could be a limiting factor for the EV-grid integration as the distribution transformers were not designed to handle the dynamic and fluctuating EV charging loads. Thus, the issues such as voltage fluctuations, increased losses and reduced efficiency [1] can negatively impact the grid operation. To address these challenges, transformers with flexibility and adaptability become imperative to meet the evolving energy demands. In this regard, the concept of Medium Voltage Solid-State Transformers.

14 SOLAR ENERGY↗

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗

WFPC2 photometry from subtraction of TinyTim PSFs

Based upon the subtraction of TinyTim Point Spread Function (PSFs) from Principle Component Image (PC1) point-like objects, a method has been developed to determine the optimal values for the telescope jitter and the Z4 relative focus during calibration or science observations. Using these jitter and focus values, an optimal TinyTim PSF, computed over a resampled grid, is then iteratively fitted to the object, yielding an improvement in the PSF centering, more accurate photometric results and a better detection of underlying structures. Preliminary results seem to indicate that appropriate synthetic TinyTim PSFs perform as well as observed PSFs.

Remy, M.↗

Achieving Accuracy Requirements for Forest Biomass Mapping: A Spaceborne Data Fusion Method for Estimating Forest Biomass and Lidar Sampling Error

The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission (+/-20 Mg/ha or 20%, the greater of the two, for at least 80% of grid cells). A data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional-global extents. A general framework for mapping above ground live forest biomass density (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify contiguous areas (>0.5 ha) that are relatively homogenous in remote sensing metrics (forest patches). We used this image-derived data with simulated spaceborne LiDAR derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (LVIS) to compute AGB and estimate LiDAR sampling error for forest patches and 100 m, 250 m, 500 m, and 1 km grid cells. At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. First, this data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting. Second, a data fusion approach for estimating AGB using simulated spaceborne LiDAR with SAR and passive optical image combinations reduced forest AGB sampling errors 12%-38% from those where LiDAR is used with SAR or passive optical alone. In absolute terms, sampling errors were reduced from 14-40 Mg/ha to 11-28 Mg/ha across all grid scales and prediction methods, where minimum sampling errors were 11, 15, 18, and 22 Mg/ha for 1 km, 500 m, 250 m, and 100 m grid scales, respectively. Third, spaceborne global scale accuracy requirements were achieved whereby at least 80% of the grid cells at 100 m, 250 m, 500 m, and 1 km grid levels met AGB accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500 m and 250 m grid level, respectively..

LiDAR↗

Advancing Grid Resilience through Smart Charge Management: Findings from Maryland’s Pilot

This report presents research findings from a four-year Smart Charge Management (SCM) pilot program conducted by Maryland’s largest electric utilities—Baltimore Gas and Electric (BGE), Potomac Electric Power Company (Pepco), and Delmarva Power & Light (DPL)—to evaluate strategies for optimizing electric vehicle (EV) charging loads and enhancing grid stability. Supported by the U.S. Department of Energy (DOE), Argonne National Laboratory collaborated with all project partners and examined the effectiveness of Time-of-Use (TOU) and Load Balancing (LB) strategies in managing peak demand, deferring costly infrastructure upgrades, and reducing grid constraints at the feeder level. Using charging data from over 4,600 EV drivers, the study analyzed SCM’s impact on the distribution systems of BGE and Pepco, which consists of over 2000 feeders. Unlike prior research that focused on system-wide trends or synthetic feeders, this analysis offers granular, feeder-level insights based on real-world operational data. It highlights how transformer density, load profiles, and infrastructure constraints influence smart charging performance. Results show feeder-level conditions play a crucial role in SCM effectiveness, with most feeders benefiting more from LB, while TOU-based SCM may be sufficient for others. By 2035, LB reduced peak charging loads by 27% on average, compared to 23% under TOU-based SCM, though some feeders saw reductions exceeding 35%, while others experienced minimal impact. Feeders with higher transformer utilization and limited capacity benefited more from LB, which more effectively distributed charging demand during off-peak hours. Beyond reducing grid constraints, SCM offers long-term operational and financial benefits. By shifting EV charging demand strategically, utilities can optimize asset utilization, delay infrastructure investments, and enhance grid performance. In terms of infrastructure upgrade deferrals, at the feeder level, LB consistently reduced peak charging loads and resulting infrastructure upgrade costs, particularly in high EV enrollment areas, decreasing the number of overloaded transformers by up to 35%, while TOU-based SCM achieved 20-30% reductions depending on feeder characteristics. At the system level, LB has the potential to defer total upgrade costs by $\$$186 million for BGE, compared to $\$$159 million under TOU-based SCM. For Pepco, TOU-based SCM performed slightly better, deferring upgrade costs by $\$$30 million, compared to $\$$29 million under LB. Section 4.5 reviews some of the system differences between BGE and Pepco. However, as EV adoption scales, TOU-based SCM will introduce secondary peak charging loads, reinforcing the need for more advanced, adaptive SCM approaches to prevent new grid challenges. As EV adoption continues to grow, feeder-level managed charging strategies will be essential for mitigating grid stress, improving infrastructure efficiency, and maintaining energy affordability for consumers. This report provides critical insights for utilities, Public Utility Commissions (PUCs), and state agencies on the role of feeder-specific smart charging in infrastructure planning, policy development, and grid modernization. The findings underscore the importance of tailored, data-driven SCM solutions that align with local grid conditions, ensuring a resilient, cost-effective transition to increasing EV adoption while safeguarding distribution system performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Feasibility of sea ice typing with synthetic aperture radar (SAR): Merging of Landsat thematic mapper and ERS 1 SAR satellite imagery

Earth Remote-Sensing Satellite (ERS) 1 synthetic aperture radar (SAR) and Landsat thematic mapper (TM) images were acquired for the same area in the Beaufort Sea, April 16 and 18, 1992. The two image pairs were colocated to the same grid (25-m resolution), and a supervised ice type classification was performed on the TM images in order to classify ice free, nilas, gray ice, gray-white ice, thin first-year ice, medium and thick first-year ice, and old ice. Comparison of the collocated SAR pixels showed that ice-free areas can only be classified under calm wind conditions (less than 3 m/s) and for surface winds greater than 10 m/s based on the backscattering coefficient alone. This is true for pack ice regions during the cold months of the year where ice-free areas are spatially limited and where the capillary waves that cause SAR backscatter are dampened by entrained ice crystals. For nilas, two distinct backscatter classes were found at -17 dB and at -10 dB. The higher backscattering coefficient is attributed to the presence of frost flowers on light nilas. Gray and gray-white ice have a backscatter signature similar to first-year ice and therefore cannot be distinguished by SAR alone. First-year and old ice can be clearly separated based on their backscattering coefficient. The performance of the Geophysical Processor System ice classifier was tested against the Landsat derived ice products. It was found that smooth first-year ice and rough first-year ice were not significantly different in the backscatter domain. Ice concentration estimates based on ERS 1 C band SAR showed an error range of 5 to 8% for high ice concentration regions, mainly due to misclassified ice-free and smooth first-year ice areas. This error is expected to increase for areas of lower ice concentration. The combination of C band SAR and TM channels 2, 4, and 6 resulted in ice typing performance with an estimated accuracy of 90% for all seven ice classes.

Steffen, Konrad↗

An improved land mask for the SSM/I grid

This paper discusses the development of a new land/ocean/coastline mask for use with Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I) data, and other types of data which are mapped to the polar stereographic SSM/I grid. Pre-existing land masks were found to disagree, to lack certain land features, and to disagree with land boundaries that are visible in high resolution sensor imagery, such as imagery from the Synthetic Aperture Radar (SAR) on the Earth Resources Satellite (ERS-1). The Digital Chart of the World (DCW) database was initially selected as a source of shoreline data for this effort. Techniques for developing a land mask from these shoreline data are discussed. The resulting land mask, although not perfect, is seen to exhibit significant improvement over previous land mask products.

Martino, Michael G.↗

State-of-the-Art Techniques for Large-Scale Stochastic Unit Commitment

Recent advances in deterministic unit commitment, both formulaic and algorithmic, along with modern algorithmic approaches for stochastic programming, have enabled the solution of stochastic unit commitment problems with hundreds of scenarios on large-scale transmission networks. In this presentation, we will give an overview of these methods, including lazy transmission constraint generation, lower-bounding techniques, and heuristics, all of which can be executed in concert with customized decomposition approaches for optimization under uncertainty. We demonstrate the effectiveness of these techniques on the TAMU Texas7K synthetic transmission network, leveraging realistic high-resolution forecasts based on NREL renewable resource availability data. The software leveraged for these demonstrations is available via the open-source software packages EGRET (for electrical grid optimization) and mpi-sppy (for optimization under uncertainty).

27 ARPA - Advanced Research Projects Agency-Energy↗

Dynamics Informed Optimization for Resilient Energy Systems

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Distributed Model Identification Algorithm for Multi-Agent Systems: Preprint

In this study, we investigate agent-based approach for system model identification with emphasis on power distribution system applications. Departing from conventional practices of relying on historical data for offline model identification, we adopt online update approach utilizing real-time data by employing the latest data points for gradient computation. This methodology offers advantages including a large reduction in the communication network's bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt in real-time to disturbances. Furthermore, we extend our model identification process from linear frameworks to more complex non-linear convex models. This extension is validated through numerical studies demonstrating improved control performance for a synthetic IEEE test case.

data-driven control↗

Inlet Flow Control and Prediction Technologies for Embedded Propulsion Systems

Fail-safe inlet flow control may enable high-speed cruise efficiency, low noise signature, and reduced fuel-burn goals for hybrid wing-body aircraft. The objectives of this program are to develop flow control and prediction methodologies for boundary-layer ingesting (BLI) inlets used in these aircraft. This report covers the second of a three year program. The approach integrates experiments and numerical simulations. Both passive and active flow-control devices were tested in a small-scale wind tunnel. Hybrid actuation approaches, combining a passive microvane and active synthetic jet, were tested in various geometric arrangements. Detailed flow measurements were taken to provide insight into the flow physics. Results of the numerical simulations were correlated against experimental data. The sensitivity of results to grid resolution and turbulence models was examined. Aerodynamic benefits from microvanes and microramps were assessed when installed in an offset BLI inlet. Benefits were quantified in terms of recovery and distortion changes. Microvanes were more effective than microramps at improving recovery and distortion.

McMillan, Michelle L.↗

High-energy and low-cost membrane-free chlorine flow battery

Abstract Grid-scale energy storage is essential for reliable electricity transmission and renewable energy integration. Redox flow batteries (RFB) provide affordable and scalable solutions for stationary energy storage. However, most of the current RFB chemistries are based on expensive transition metal ions or synthetic organics. Here, we report a reversible chlorine redox flow battery starting from the electrolysis of aqueous NaCl electrolyte and the as-produced Cl 2 is extracted and stored in the carbon tetrachloride (CCl 4 ) or mineral spirit flow. The immiscibility between the CCl 4 or mineral spirit and NaCl electrolyte enables a membrane-free design with an energy efficiency of >91% at 10 mA/cm 2 and an energy density of 125.7 Wh/L. The chlorine flow battery can meet the stringent price and reliability target for stationary energy storage with the inherently low-cost active materials (~$5/kWh) and the highly reversible Cl 2 /Cl − redox reaction.

25 ENERGY STORAGE↗

Towards Improved Decision Making for the Smarter Grid: Geomagnetic Disturbance Implicit Modeling Uncertainty Quantification

Geomagnetic disturbances can greatly disrupt the power grid operation. This is caused by low-frequency changes in the earth’s magnetic field, which upon interaction with the deep earth conductivity induces a changing electric field at the earth’s surface. This in turn induces quasi-direct currents which have the potential to cause protective devices to operate, widespread damage to high-voltage transformers, or voltage collapse due to induced reactive power losses. While these impacts have been known since the 1940s, only recently have standards for GMD response been implemented. Because these standards are heavily based on models, it is important to understand when it is appropriate to make certain modeling assumptions. In this work, implicit modeling uncertainty is quantified for the purpose of enhanced decision making for disturbance impact mitigation. Considering electromagnetic models, modeling assumptions of non-uniform grounding, imbalanced operation, transformer saturation, and geomagnetically induced currents, voltage estimation values are analyzed. Statistical characteristics of modeling uncertainty are obtained by analysis of synthetically generated data. Results statistically characterize geomagnetic disturbances modeling uncertainty, providing an important tool for impact mitigation.

grid analysis↗

A multi-scale time-series dataset with benchmark for machine learning in decarbonized energy grids

The electric grid is a key enabling infrastructure for the ambitious transition towards carbon neutrality as we grapple with climate change. With deepening penetration of renewable resources, the reliable operation of the electric grid becomes increasingly challenging. In this paper, we present PSML, a first-of-its-kind open-access multi-scale time-series dataset, to aid in the development of data-driven machine learning (ML)-based approaches towards reliable operation of future electric grids. The dataset is synthesized from a joint transmission and distribution electric grid to capture the increasingly important interactions and uncertainties of the grid dynamics, containing power, voltage and current measurements over multiple spatio-temporal scales. Using PSML, we provide state-of-the-art ML benchmarks on three challenging use cases of critical importance to achieve: (i) early detection, accurate classification and localization of dynamic disturbances; (ii) robust hierarchical forecasting of load and renewable energy; and (iii) realistic synthetic generation of physical-law-constrained measurements. We envision that this dataset will provide use-inspired ML research in safety-critical systems, while simultaneously enabling ML researchers to contribute towards decarbonization of energy sectors.

54 ENVIRONMENTAL SCIENCES↗

Federated Machine Learning-Based Anomaly Detection System for Synchrophasor Network Using Heterogeneous Data Sets: Preprint

Synchrophasor technology is widely deployed in the energy management system to monitor the grid health at micro level and perform necessary corrective actions in real time; however, integrated phasor devices and data aggregators are exposed to several cybersecurity threats. This paper proposes a federated ML(FML)-based ADS to detect several data integrity attacks in the synchrophasor network. The proposed approach integrates the horizontal FML technique and consists of substation-based local models and a control center-based global model. The proposed methodology includes training local models using heterogeneous data sets that include network and grid information and updating the global model through multiple iterations by sharing model gradients. Finally, the trained global model is applied to identify cyberattacks, normal operation, and physical events. To validate the proof of concept, we used synthetic data sets generated by Mississippi State University and Oak Ridge National Laboratory for training and testing the classification models using the National Renewable Energy Laboratory's high performance computing resources. Our experimental results, computed through several performance measures, reveal that the proposed approach shows consistent performance during the binary, three-class, and multiclass classifications while ensuring privacy of synchrophasor data.

anomaly detection system↗

Techno-Economic Analysis of Synthetic Fuels Pathways Integrated with Light Water Reactors

The purpose of this work is to identify, model, perform techno-economic analysis, and compare two possible synfuel production routes utilizing CO 2 as the feedstock. Heat from an LWR nuclear plant is integrated wherever possible to positively affect the economics of the LWR by converting power to fuels during times of low grid electricity demand. Process and economic modeling for a conceptual synfuel production plant co-located (or in near proximity) with an LWR is presented, including the cost of CO 2 captured from an ethanol plant, compressed, and transported to the LWR hybrid plant, co-electrolysis of the CO 2 with water in a solid oxide electrolyzing cell (SOEC) system to produce syngas, and thermocatalytic conversion of the syngas to transportation fuel. The hybrid LWR/synfuels plant is assumed to be located within 50–150 miles of an ethanol plant (e.g., located in the midwest region of the United States). Performance and nth-plant economics for the co-electrolysis-based processes are evaluated and compared with biomass-gasification-based technology for the synfuel routes considered. Sensitivity analysis around the price of CO 2 and electricity, two of the major cost drivers, is presented for each case. Consideration of a carbon credit is also included in the sensitivity analysis.

10 SYNTHETIC FUELS↗

Simulation of a Synthetic Jet in Quiescent Air Using TLNS3D Flow Code

Although the actuator geometry is highly three-dimensional, the outer flowfield is nominally two-dimensional because of the high aspect ratio of the rectangular slot. For the present study, this configuration is modeled as a two-dimensional problem. A multi-block structured grid available at the CFDVAL2004 website is used as a baseline grid. The periodic motion of the diaphragm is simulated by specifying a sinusoidal velocity at the diaphragm surface with a frequency of 450 Hz, corresponding to the experimental setup. The amplitude is chosen so that the maximum Mach number at the jet exit is approximately 0.1, to replicate the experimental conditions. At the solid walls zero slip, zero injection, adiabatic temperature and zero pressure gradient conditions are imposed. In the external region, symmetry conditions are imposed on the side (vertical) boundaries and far-field conditions are imposed on the top boundary. A nominal free-stream Mach number of 0.001 is imposed in the free stream to simulate incompressible flow conditions in the TLNS3D code, which solves compressible flow equations. The code was run in unsteady (URANS) mode until the periodicity was established. The time-mean quantities were obtained by running the code for at least another 15 periods and averaging the flow quantities over these periods. The phase-locked average of flow quantities were assumed to be coincident with their values during the last full time period.

Vatsa, Veer N.↗