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At least 397 records · Page 22

PolarMERRA: A collaborative effort for NASA’s polar reanalysis

The polar atmosphere is often poorly represented in global models, adversely impacting analyses in these regions and forecasts on much larger scales. PolarMERRA is an initiative that brings together the modeling expertise from NASA’s global modeling and assimilation office (GMAO) and observational expertise from NASA’s Cryospheric sciences lab to assess and improve the representation of polar processes in the NASA’s modelling system in preparation for upcoming and next generation reanalyses. Model improvements in resolution, physics, and data assimilation have been guided by assessment of model skill in the polar regions. Preliminary results from a novel validation framework indicate a reduction in near surface air temperature, turbulent fluxes, and precipitation biases.

Chelsea Parker↗

Parametrized uncertainties in the spectral function model of neutrino charged-current quasielastic interactions for oscillation analyses

A substantial fraction of systematic uncertainties in neutrino oscillation experiments stem from the lack of precision in modeling the nuclear target in neutrino-nucleus interactions. Whilst this has driven significant progress in the development of improved nuclear models for neutrino scattering, it is crucial that the models used in neutrino data analyses be accompanied by parameters and associated uncertainties that allow the coverage of plausible nuclear physics. Based on constraints from electron scattering data, we propose such a set of parameters, which can be applied to nuclear shell models, and test their application to the Benhar [] spectral function model. The parametrization is validated through a series of maximum likelihood fits to cross section measurements made by the T2K and MINERvA experiments, which also permit an exploration of the power of near-detector data to provide constraints on the parameters in neutrino oscillation analyses. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Preliminary Convective-Radiative Heating Environments for a Neptune Aerocapture Mission

Convective and radiative heating environments have been computed for a three-dimensional ellipsled configuration which would perform an aerocapture maneuver at Neptune. This work was performed as part of a one-year Neptune aerocapture spacecraft systems study that also included analyses of trajectories, atmospheric modeling, aerodynamics, structural design, and other disciplines. Complementary heating analyses were conducted by separate teams using independent sets of aerothermodynamic modeling tools (i.e. Navier-Stokes and radiation transport codes). Environments were generated for a large 5.50 m length ellipsled and a small 2.88 m length ellipsled. Radiative heating was found to contribute up to 80% of the total heating rate at the ellipsled nose depending on the trajectory point. Good agreement between convective heating predictions from the two Navier-Stokes solvers was obtained. However, the radiation analysis revealed several uncertainties in the computational models employed in both sets of codes, as well as large differences between the predicted radiative heating rates.

Hollis, Brian R.↗

TransPlatformer

We propose TransPlatformer for translating toxicogenomics from one platform to another. Transcriptomic profiling has evolved through multiple generations of technology, from microarrays (e.g., Affymetrix, CodeLink) to more recent high-throughput sequencing and targeted panels such as S1500+. Microarrays, which dominated gene expression studies in the early 2000s, provided affordable and high-throughput transcript quantification but suffered from cross-hybridization issues and limited dynamic range . RNA-Seq, introduced in the late 2000s, revolutionized transcriptomics by enabling unbiased and comprehensive gene expression analysis, albeit at higher costs and computational demands . Despite advances, many studies rely on historical microarray data, necessitating the translation of legacy data into modern platforms to ensure continuity and comparability. This translation is complicated by factors such as platform-specific probe design, differences in transcript coverage, and batch effects . Existing methods for cross-platform mapping include statistical normalization, machine learning models, and biological anchoring approaches. The ability to translate transcriptomic data between platforms has broad implications, including enhanced meta-analyses, improved toxicological modeling, and better integration of historical datasets with contemporary research. TransPlatformer seeks to contribute to this effort by evaluating translation methodologies and proposing novel strategies to improve cross-platform gene expression harmonization. In this repository there are code examples for TransPlatformer implementation

Cong, Guojing↗

Cation Data for the East River Watershed, Colorado (2014-2025)

This data package contains mean values for cation concentration for water samples taken from the East River Watershed in Colorado. Inductively coupled plasma mass spectrometry (ICP-MS) has been used to measure the concentrations of elements of interest simultaneously for the East River Watershed, Colorado groundwater and surface water samples to inform insights on the biogeochemistry processes within the watershed. The East River is part of the Watershed Function Scientific Focus Area (WFSFA) located in the Upper Colorado River Basin, United States. For samples collected prior to 06-16-2021, the instrumentation, Elan DRC II, PerkinElmer SCIEX, automatically switches among the three models necessary to analyze all 37 elements. These 37 elements include: (1) Lithium (Li), Beryllium (Be), Boron (B), Sodium (Na), Magnesium (Mg), Aluminium (Al), Silicon (Si), Phosphorus (P), Titanium (Ti), Cobalt (Co), Nickel (Ni), Copper (Cu), Zinc (Zn), Germanium (Ge), Arsenic (As), Rubidium (Rb), Strontium (Sr), Zirconium (Zr), Molybdenum (Mo), Silver (Ag), Cadmium (Cd), Tin (Sn), Antimony (Sb), Caesium (Cs), Barium (Ba), Europium (Eu), Lead (Pb), Thorium (Th), Uranium (U) using standard model, argon Ar as reaction gas, (2) Potassium (K), Calcium (Ca), Vanadium (V), Chromium (Cr), Manganese (Mn), Iron (Fe) using dynamic reaction cell (DRC) model, ammonia NH3 as reaction gas, and (3) Phosphorus (P) and Selenium (Se) using DRC model, oxygen O2 as reaction gas. Note for the samples with higher concentrations of chloride (Cl-), asenic (As) concentrations were analysed with DRC model (oxygen O2 as reaction gas) to avoid the interference of chloride. For samples collected on and after 06-16-2021, an advanced Agilent 8900 triple quadrupole inductively coupled plasma mass spectrometry system (Agilent 8900 QQQ ICP-MS, Agilent Technologies) has been used to measure the concentrations of interested 36 elements simultaneously for environmental samples, including (1) Lithium (Li), Beryllium (Be) and Boron (B) using standard no gas mode, (2) Sodium (Na), Magnesium (Mg), Aluminium (Al) Phosphorus (P), Potassium (K), Chromium (Cr), Manganese (Mn), Iron (Fe), Cobalt (Co), Nickel (Ni), Copper (Cu), Zinc (Zn), Germanium (Ge), Arsenic (As), Rubidium (Rb), Strontium (Sr), Zirconium (Zr), Molybdenum (Mo), Silver (Ag), Cadmium (Cd), Tin (Sn), Antimony (Sb), Cesium (Cs), Barium (Ba), Europium (Eu), Lead (Pb), Thorium (Th) and Uranium (U) using standard helium (He) collision mode, (3) Titanium (Ti) and Vanadium (V) using high Energy (HEHe) helium (He) collision mode, and (4) Silicon (Si), Calcium (Ca) and Selenium (Se) using standard H2 reaction mode. All samples were prepared/diluted with 2% (v/v) ultrapure nitric acid in Milli-Q water (18.2 mega ohm-cm), and analyzed under a rigorous quality assurance and quality control (QA/QC) process. This data package contains (1) a zip file (cation_data_2014_2025.zip) containing a total of 5,849 files: 5.848 data files of cation data from across the Lawrence Berkeley National Laboratory (LBNL) Watershed Function Scientific Focus Area (SFA) which is reported in .csv files per location and a locations.csv (1 file) with latitude and longitude for each location; (2) a file-level metadata (v6_20260901_flmd.csv) file that lists each file contained in the dataset with associated metadata; (3) a data dictionary (v6_20260901_dd.csv) file that contains terms/column_headers used throughout the files along with a definition, units, and data type; (4) PDF and docx files for the detemination of Method Detection Limits (MDLs) for ICP-MS PerkinElmer DRC II instrumentation (Detemination_of_Method_Detection_Limits__MDLs__for_ICP_MS__PerkinElmer_Elan_DRC_II__LBL_Bldg74_Lab214D) for samples before November 2021; (5) PDF and docx files for the determination of MDLs for ICP-MS Agilent 8900 QQQ instrumentation (ICP_MS_Analysis_detection_limits_and_QA_QC_WenmingDong_updated_2026-08-06) for samples November 2021 and onward. Missing values within the anion data files are noted as either "-9999" or "0.0" for not detectable (N.D.) data. There are a total of 113 locations containing cation data. Update on 2021-04-11: Added Detemination of Method Detection Limits (MDLs) for ICP-MS document, which can be accessed as a PDF or with Microsoft Word. Update on 2022-06-10: versioned updates to this dataset was made along with these changes: (1) updated cation data for all locations up to 2021-12-31, (2) removal of units from column headers in datafiles, (3) added row underneath headers to contain units of variables, (4) removed suffix and prefix on two variables (“aqberylliumion_asberyllium” and “aqlithiumion_aslithium”), (5) added -9999 for empty numerical cells, and (6) the addition of the file-level metadata (flmd.csv) and data dictionary (dd.csv) were added to comply with the File-Level Metadata Reporting Format. Update on 2022-09-09: Updates were made to reporting format specific files (file-level metadata and data dictionary) to correct swapped file names, add additional details on metadata descriptions on both files, add a header_row column to enable parsing, and add version number and date to file names (v2_20220909_flmd.csv and v2_20220909_dd.csv). Update on 2023-08-08: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2023-01-05. The file level metadata and data dictionary files were updated to reflect the additional data added. Update on 2024-03-11: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2023-10-16. Further, revisions to the data files were made to remove incorrect data points (from 1970 and 2001). The reporting format specific files were updated to reflect the additional data added. Updated versions of the PDF and docx files for determination of MDLs for ICP-MS data were added to this dataset for samples starting in November 2021. Update on 2025-05-15: Updates were made to both the data files and reporting format specific files. New available cation data was added, up until the end of WY2024 (September 30, 2024). International Generic Sample Numbers (IGSNs), when registered, were added to the data files. The reporting format specific files were updated to reflect the additional data added. Update on 2026-09-01: Updates were made to both the data files and reporting format specific files. New available cation data was added, up until the end of WY2025 (September 30, 2025). Updated versions, as of 2026-08-06, of the PDF and docx files for determination of MDLs for ICP-MS data were added to this dataset for samples starting in November 2021.

54 ENVIRONMENTAL SCIENCES↗

Low-frequency oscillations in radiative-convective systems. Part 2: An idealized model

A simple model is used to examine the hypothesis that nonlinear interactions among atmospheric radiation, cumulus convection, and the surface moisture flux can result in a stationary, low-frequency (30-60 day period) oscillating heat source in the tropical atmosphere. The model produces low-frequency oscillations of temperature, moisture, and precipitation. The mechanism that produces these oscillations is identified through analyses of the model and its results. The relevance of this mechanism to understand the observed Madden-Julian oscillation in the tropical atmosphere over the Indian and western Pacific Oceans is discussed.

Hu, QI↗

Programmatic effects of utilizing various space tug options

The results are summarized of the computerized (DORCA) analyses of a number of NASA/Non-NASA and DoD payload mission models that have been used in conjunction with studies of the Space Transportation System (STS). The first analysis performed was on the 1971 NASA/Non-NASA and DoD mission models. Subsequent to that, analyses of the June 1972 excursion to the 1971 NASA/Non-NASA mission models were performed. The mission models have two basic versions; i.e., one employing expendable payloads and another employing a best mix of expendable and reusable payloads. Both versions of the models have the same payload deployment schedule. However, in the best mix version, payloads are retrieved from orbit and whenever possible, refurbished payloads are deployed. The analyses were performed to determine the relative merits to different Tug configurations and of Tug combinations employed in several phased development schemes.

Stricker, L. T.↗

Low Speed Analysis of Mission Adaptive Flaps on a High Speed Civil Transport Configuration

Thin-layer Navier-Stokes analyses were done on a high speed civil transport configuration with mission adaptive leading-edge flaps. The flow conditions simulated were Mach = 0.22 and Reynolds number of 4.27 million for angles-of-attack ranging from 0 to 18 degrees. Two turbulence closure models were used. Analyses were done exclusively with the Baldwin-Lomax turbulence model at low angle-of-attack conditions. At high angles-of-attack where considerable flow separation and vortices occurred the Spalart-Allmaras turbulence model was also considered. The effects of flow transition were studied. Predicted aerodynamic forces, moment, and pressure are compared to experimental data obtained in the 14- by 22-Foot Subsonic Tunnel at NASA Langley. The forces and moments correlated well with experimental data in terms of trends. Drag and pitching moment were consistently underpredicted. Predicted surface pressures compared well with experiment at low angles-of-attack. Above 10 angle-of-attack the pressure comparisons were not as favorable. The two turbulent models affected the pressures on the flap considerably and neither produced correct results at the high angles-of-attack.

Lessard, Victor R.↗

Adaptive Protection and Validated Models to Enable Deployment of High Penetrations of Solar PV (PV-MOD)

The availability and validation of various PV models in commercial tools differ, with some models not yet thoroughly validated for advanced inverter functionalities and reliable performance under weak system conditions. Many existing models do not fully incorporate new inverter control functions, which can affect system stability. The increasing deployment of solar PV and other inverter-based resources (IBRs), including distributed energy resources (DERs), is influencing the reliable operation of protection schemes in distribution systems and microgrids. Emerging adaptive protection schemes (APS) offer new opportunities for protecting these systems during varying configurations and DER operating conditions, though their demonstration and validation remain limited. Adaptive protection schemes face similar challenges, as they are typically designed for specific configurations. There is a growing need for tools and methodologies to streamline the deployment of adaptive protection for safe and reliable DER integration. The project main objective was to develop and validate high-fidelity generic models of solar PV facilities for stability, protection, EMT, and QSTS analyses. This objective was achieved, and these models can now be integrated into commercial software tools, enabling utilities, vendors, and developers to study high-penetration PV systems more confidently. The project also demonstrated advanced applications of these models, including the design and deployment of adaptive protection schemes in high-penetration field applications and microgrids, supporting grid safety and reliability. Several milestones were reached by the end of the project. A sophisticated inverter test plan was developed, and inverters representative of the North American marketplace were selected. EPRI and NREL tested various inverters, conforming to IEEE standards. Improvements were made to existing generic models of IBR units, IBR plants, and aggregated feeders for various analyses. The first generic electromagnetic transient (EMT) model for a solar PV plant was developed, conforming to IEEE Std 2800™-2022 and validated against laboratory measurements of a 2.2 MVA large-scale battery energy storage system (BESS) inverter. That model was then used to produce reference responses illustrating examples of validated and verified IBR plant models that pass or fail tests for technical minimum capability and performance as specified in the IEEE standard. The developed, tested, and validated generic models can be used for transmission planning, stability assessments, expansion planning, and evaluating potential future IBR interconnection requirements. They can also support interconnection screens and conformity assessments of IBR plants, including solar PV. The project significantly contributed to the ongoing standardization and model-based representation and verification of IBR responses. The project further addressed challenges of common distribution protection schemes with increasing deployment of DER by developing, validating, and demonstrating adaptive protection schemes (APS) that can improve the reliable and safe integration of DER into distribution systems. New APS were designed using improved DER models for three common distribution systems: a radial feeder, a meshed network, and a microgrid. Modeling and hardware-in-the-loop (HIL) testing of the APS were conducted, successfully showing their effectiveness and selectivity. Proof-of-concept field demonstration was achieved for two APS, i.e., one on a radial feeder and another one in a microgrid. Field demonstration could not be achieved for the APS on a meshed network, primarily due apprehension of one utility partner and also due to limited access to the protective algorithms in the network protectors. Guidelines developed from the lessons learned in the project lay out the general process followed in the design, installation, and commissioning of APS for various distribution systems. Distribution utility partners’ apprehension about field demonstration of the new APS were addressed—with varying success—by taking a stepped risk-management approach of modeling of a wide range of sensitivities first, performing in-depth proof-of-concept testing in the laboratory including HIL next, and finally deliberately implementing and commissioning the actual protection equipment and algorithms into parts of—or in parallel operation to—the three real distribution systems. Future work should include pilot projects that further show the acceptable performance of the developed APS before these schemes be rolled out more widely. Inclusion of both utility and original equipment manufacturers (OEMs) in future projects could increase chances of successful field demonstration. Despite challenges in achieving the field demonstration goal of the project for all three APS, the research significantly contributed to the innovation of adaptive protection solutions for scalable and reliable DER integration into distribution systems. This project significantly enhances the understanding of the impact of using appropriate inverter models on distribution and transmission (T&D) systems. By addressing the limitations of existing generic models, the project introduces high-fidelity models for stability, protection, electromagnetic transient (EMT), and quasi-static time series (QSTS) analyses. These models, integrated into commercial software tools, enable utilities, vendors, and developers to confidently study high-penetration PV systems. The project also demonstrates advanced applications, including adaptive protection schemes (APS) for distribution systems and microgrids, ensuring grid safety and reliability. The technical effectiveness and economic feasibility of the methods are evident through the development and validation of sophisticated inverter test plans and the selection of representative inverters. Testing by EPRI and NREL on retail, commercial, and utility-scale inverters, conforming to IEEE standards, underscores the robustness of the models. Improvements to existing generic models for various analyses further enhance their validity and applicability. The project also identifies gaps in common distribution protection schemes and designed new APS using improved DER models, demonstrating their effectiveness through modeling and hardware-in-the-loop (HIL) testing. The project’s benefits to the public are manifold. By advancing the standardization and model-based representation of IBR response, it supports transmission planning, stability assessments, and future IBR interconnection requirements. The generic models can facilitate better communication between transmission planners and developers, supporting expected IBR plant capability and performance. Additionally, the development of APS for radial feeders, meshed networks, and microgrids supports the integration of distributed energy resources (DERs) into distribution systems, enhancing grid reliability and safety. The project’s emphasis on thorough testing and simplicity in design ensures practical and scalable solutions for DER integration.

14 SOLAR ENERGY↗

Models Extracted from Text for System-Software Safety Analyses

This presentation describes extraction and integration of requirements information and safety information in visualizations to support early review of completeness, correctness, and consistency of lengthy and diverse system safety analyses. Software tools have been developed and extended to perform the following tasks: 1) extract model parts and safety information from text in interface requirements documents, failure modes and effects analyses and hazard reports; 2) map and integrate the information to develop system architecture models and visualizations for safety analysts; and 3) provide model output to support virtual system integration testing. This presentation illustrates the methods and products with a rocket motor initiation case.

Malin, Jane T.↗

System cost performance analysis (study 2.3). Volume 1: Executive summary

A study is described which was initiated to identify and quantify the interrelationships between and within the performance, safety, cost, and schedule parameters for unmanned, automated payload programs. The result of the investigation was a systems cost/performance model which was implemented as a digital computer program and could be used to perform initial program planning, cost/performance tradeoffs, and sensitivity analyses for mission model and advanced payload studies. Program objectives and results are described briefly.

Campbell, B. H.↗

Basic Diagnosis and Prediction of Persistent Contrail Occurrence using High-resolution Numerical Weather Analyses/Forecasts and Logistic Regression. Part I: Effects of Random Error

Straightforward application of the Schmidt-Appleman contrail formation criteria to diagnose persistent contrail occurrence from numerical weather prediction data is hindered by significant bias errors in the upper tropospheric humidity. Logistic models of contrail occurrence have been proposed to overcome this problem, but basic questions remain about how random measurement error may affect their accuracy. A set of 5000 synthetic contrail observations is created to study the effects of random error in these probabilistic models. The simulated observations are based on distributions of temperature, humidity, and vertical velocity derived from Advanced Regional Prediction System (ARPS) weather analyses. The logistic models created from the simulated observations were evaluated using two common statistical measures of model accuracy, the percent correct (PC) and the Hanssen-Kuipers discriminant (HKD). To convert the probabilistic results of the logistic models into a dichotomous yes/no choice suitable for the statistical measures, two critical probability thresholds are considered. The HKD scores are higher when the climatological frequency of contrail occurrence is used as the critical threshold, while the PC scores are higher when the critical probability threshold is 0.5. For both thresholds, typical random errors in temperature, relative humidity, and vertical velocity are found to be small enough to allow for accurate logistic models of contrail occurrence. The accuracy of the models developed from synthetic data is over 85 percent for both the prediction of contrail occurrence and non-occurrence, although in practice, larger errors would be anticipated.

Duda, David P.↗

Thermal Integration of a Liquid Acquisition Device into a Cryogenic Feed System

Primary objectives of this effort were to define the following: (1) Approaches for quantification of the accumulation of thermal energy within a capillary screen liquid acquisition device (LAD) for a lunar lander upper stage during periods of up to 210 days on the lunar surface, (2) techniques for mitigating heat entrapment, and (3) perform initial testing, data evaluation. The technical effort was divided into the following categories: (1) Detailed thermal modeling of the LAD/feed system interactions using both COMSOL computational fluid device and standard codes, (2) FLOW-3D modeling of bulk liquid to provide interfacing conditions for the LAD thermal modeling, (3) condensation conditioning of capillary screens to stabilize surface tension retention capability, and (4) subscale testing of an integrated LAD/feed system. Substantial progress was achieved in the following technical areas: (1) Thermal modeling and experimental approaches for evaluating integrated cryogen LAD/feed systems, at both the system and component levels, (2) reduced gravity pressure control analyses, (3) analytical modeling and testing for capillary screen conditioning using condensation and wicking, and (4) development of rapid turnaround testing techniques for evaluating LAD/feed system thermal and fluid integration. A comprehensive effort, participants included a diverse cross section of representatives from academia, contractors, and multiple Marshall Space Flight Center organizations.

Hastings, L. J.↗

The virtual front end: Towards better management of solid geometric data

Throughout the last decade, Computer Aided Design was seen as a Great Promise. Much was accomplished, but that pales in comparison with what was promised. Ultimate achievement has always seemed just a step away. During the era of the early turnkey system, the one step was limited by modeling geometry through a wire frame. Besides being cumbersome to deal with in three dimensions, it was continually shown that a wire frame is ambiguous. This made the modeling of geometry for engineering purposes even more frustrating. The fundamentals of computer aided engineering design rest on the ability to do various analyses. Presently, solid modeling is taking the mechanical engineering CAD world by storm. There are no fewer than 20 solid modeling packages around the world, and more appearing with each vendor show. The question of integration, that is, the combination of elements of the CAD process into unified and easily usable design tools still exists.

Charlesworth, W. W.↗

Shielding requirements for the Space Station habitability modules

The design, analysis, development, and tests of the total meteoroid/debris protection system for the Space Station Freedom habitability modules, such as the habitation module, the laboratory module, and the node structures, are described. Design requirements are discussed along with development efforts, including a combination of hypervelocity testing and analyses. Computer hydrocode analysis of hypervelocity impact phenomena associated with Space Station habitability structures is covered and the use of optimization techniques, engineering models, and parametric analyses is assessed. Explosive rail gun development efforts and protective capability and damage tolerance of multilayer insulation due to meteoroid/debris impact are considered. It is concluded that anticipated changes in the debris environment definition and requirements will require rescoping the tests and analysis required to develop a protection system.

Avans, Sherman L.↗

ISAC - A tool for aeroservoelastic modeling and analysis

This paper discusses the capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrate some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

ISAC: A tool for aeroservoelastic modeling and analysis

The capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules is discussed. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrates some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

An extension of Thwaites’ method for turbulent boundary layers

Thwaites developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations. The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

17 WIND ENERGY↗