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

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At least 1,297 records · Page 72

Review of the Lightning Strike Incident at Launch Complex 37 on July 27, 1967, and Comparison to a Gemini Lightning Strike

The Launch Complex 37 lightning strike of July 27, 1967, was reviewed and compared to a similar incident on the Gemini Program. Available data indicate little likelihood of damaging currents having been present in SA-204 Launch Vehicle or the ground equipment during the July 27th incident. Based on the results of subsystem and system testing after the strike, anticipated results of future testing, the six months elapsed time between the strike-and launch, and the fact that much of the critical airborne electrical/electronic equipment has been removed since the strike for other reasons, no new actions are considered necessary at this time in the Gemini case, significant failures occurred in both airborne and ground circuits. Due to the resultant semi, condlictor uncertainty, and the relatively' short time prior to planned launch, all critical airborne components containing semiconduetors were replaced, and a sophisticated data comparison task was implemented.

Llewellyn, J. A.↗

On local total strain redistribution using a simplified cyclic inelastic analysis based on an elastic solution

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.

Hwang, S. Y.↗

On local total strain redistribution using a simplified cyclic inelastic analysis based on an elastic solution

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.

Hwang, S. Y.↗

Liquid Oxygen (LO2) propellant conditioning concept testing

Marshall Space Flight Center (MSFC) and industry contractors have undertaken activities to develop a simplified liquid oxygen (LO2) propellant conditioning concept for future expendable launch vehicles. The objective of these activities is to reduce operations costs and timelines and to improve safety of these vehicles. The approach followed has been to identify novel concepts through system level studies and demonstrate the feasibility of these concepts through small-scale and full-scale testing. Testing will also provide data for design guidelines and validation of analytical models. Four different concepts are being investigated: no-bleed, low-bleed, use of a recirculation line, and helium (He) bubbling. This investigation is being done under a Joint Institutional Research and Development (JIRAD) program currently in effect between MSFC and General Dynamics Space Systems (GDSS). A full-scale test article, which is a facsimile of a propellant feed duct with an attached section to simulate heat input from a LO2 turbopump, will be tested at the Cold Flow Facility at MSFC's West Test Area. Liquid nitrogen (LN2), which has similar properties to LO2, will be used in place of LO2 for safety and budget reasons. Work to date includes design and fabrication of the test article, design of the test facility and initial fabrication, development of a test matrix and test procedures, initial predictions of test output, and heat leak calibration and heat exchanger tests on the test article. The tests for all propellant conditioning concepts will be conducted in the summer of 1993, with the final report completed by October, 1993.

Perry, Gretchen L. E.↗

NASA Space Flight Vehicle Fault Isolation Challenges

The Space Launch System (SLS) is the new NASA heavy lift launch vehicle and is scheduled for its first mission in 2017. The goal of the first mission, which will be uncrewed, is to demonstrate the integrated system performance of the SLS rocket and spacecraft before a crewed flight in 2021. SLS has many of the same logistics challenges as any other large scale program. Common logistics concerns for SLS include integration of discrete programs geographically separated, multiple prime contractors with distinct and different goals, schedule pressures and funding constraints. However, SLS also faces unique challenges. The new program is a confluence of new hardware and heritage, with heritage hardware constituting seventy-five percent of the program. This unique approach to design makes logistics concerns such as testability of the integrated flight vehicle especially problematic. The cost of fully automated diagnostics can be completely justified for a large fleet, but not so for a single flight vehicle. Fault detection is mandatory to assure the vehicle is capable of a safe launch, but fault isolation is another issue. SLS has considered various methods for fault isolation which can provide a reasonable balance between adequacy, timeliness and cost. This paper will address the analyses and decisions the NASA Logistics engineers are making to mitigate risk while providing a reasonable testability solution for fault isolation.

Bramon, Christopher↗

Towards performance-portability of the Albany Finite Element analysis code using the Kokkos library of Trilinos

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to execute correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The Finite Element Method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industry applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library of Trilinos. We present performance results for two different physics simulations modules in Albany: the Aeras global atmosphere dynamical code and the FELIX land-ice solver. As a result, numerical experiments show that our single code implementation gives reasonable performance across two multi-core/many-core architectures: NVIDIA GPUs and multi-core CPUs.

97 MATHEMATICS AND COMPUTING↗

High-performance epistasis detection in quantitative trait GWAS

epiSNP is a program for identifying pairwise single nucleotide polymorphism (SNP) interactions (epistasis) in quantitative-trait genome-wide association studies (GWAS). A parallel MPI version (EPISNPmpi) was created in 2008 to address this computationally expensive analysis on large data sets with many quantitative traits and SNP markers. However, the falling cost of genotyping has led to an explosion of large-scale GWAS data sets that challenge EPISNPmpi’s ability to compute results in a reasonable amount of time. Therefore, we optimized epiSNP for modern multi-core and highly parallel many-core processors to efficiently handle these large data sets. This paper describes the serial optimizations, dynamic load balancing using MPI-3 RMA operations, and shared-memory parallelization with OpenMP to further enhance load balancing and allow execution on the Intel Xeon Phi coprocessor (MIC). For a large GWAS data set, our optimizations provided a 38.43× speedup over EPISNPmpi on 126 nodes using 2 MICs on TACC’s Stampede Supercomputer. We also describe a Coarray Fortran (CAF) version that demonstrates the suitability of PGAS languages for problems with this computational pattern. We show that the Coarray version performs competitively with the MPI version on the NERSC Edison Cray XC30 supercomputer. Finally, the performance benefits of hyper-threading for this application on Edison (average 1.35× speedup) are demonstrated.

97 MATHEMATICS AND COMPUTING↗

Field Demonstration of The Krauklis Seismic Wave In A Novel Mva Method For Geologic CO 2 Storage

The Energy & Environmental Research Center (EERC) conducted a feasibility study of a new, low-impact geophysics monitoring method designed to incrementally track the saturation front of CO 2 injected into a reservoir. The method leverages a new way of transmitting energy from the surface to the reservoir and employs a new subsurface signal called the Krauklis wave (K-wave) and other guided waves for seismic monitoring. The EERC partnered with Seismos, Inc., the company that holds the exclusive technology license for this method, to advance development of K-wave technology, and Denbury Onshore, LLC, to field-test the system. The system was field-tested at Denbury’s Bell Creek oil field, currently undergoing CO 2 -based enhanced oil recovery (EOR) in southeastern Montana. The K-wave system uses a wellhead-mounted source to propagate energy down the wellbore in the form of a tube wave and through the well perforations into the reservoir. Part of the energy transmitted through the perforations into the reservoir converts to slow moving K-waves and/or other guided waves that are expected to propagate through the formation to neighboring wells. The propagated signal would induce tube waves in the neighboring wells that return to the surface to be recorded with a wellhead-mounted receiver. The propagation time of the signal is directly affected by the presence of CO 2 between the wells, so the difference in transit time of the returning signal between pre- and postinjection data sets could be used to help define the lateral extent of a CO 2 saturation front. Objectives of the study were to demonstrate, validate, and evaluate the K-wave method’s ability to monitor the morphology of injected CO 2 and estimate saturation distribution. Results from the demonstration were to be compared to conventional 4-D surface seismic methods, dynamic reservoir simulations, and CO 2 breakthrough data to validate the technology and provide useful information that may result in improvements. Prior to mobilizing for the full-scale K-wave baseline survey, a field test was conducted to better understand wellhead hardware configurations and test the response from the Bell Creek reservoir using three wells. Useful operational information resulted but signal from the first-generation gas release/gas injection source was not recorded in neighboring wells. After the initial field test, numerical modeling of the K-wave method was initiated using parameters specific to the Bell Creek Field. Modeling results indicated that the fundamental concepts behind the K-wave method exhibited problems and revealed a significantly greater attenuation of the signal at the wellbore perforations than expected, totaling on the order of 10-8 from source well to receiver well over a 400-m well spacing. Modeling also showed that greater source frequency bandwidth was needed to produce guided waves within a 30-foot-thick reservoir layer such as that at Bell Creek and that reservoir layer seismic velocity would need to be slower than the velocities of the bounding layers in order to act as a wave guide opposite to what exists at Bell Creek. Modeling results prompted a second field test with a stronger, second-generation displacement source developed in the interim. Concurrent with the second field test, a 3-D seismic survey was acquired to serve as a baseline for project validation and to serve as a monitor data set for the portion of the project area where CO 2 injection had already commenced. The new source was tested using a four-well geometry and failed to produce a detectable signal, which appeared to confirm modeling results and indicated that the Bell Creek Field is not an ideal site for the K-wave test. It was concluded that a source with sufficient strength and bandwidth could not be built to overcome the factors discovered by the modeling within a reasonable amount of time. Several other sites undergoing CO 2 -based EOR were also evaluated; however, none of these sites was amenable because of geology, limitations of source and receiver hardware, or the advanced state of the CO 2 flood. In addition, two other configurations of the source and receiver layout were considered; however, these design modifications either changed the scope of the project or did not meet the goals of the Carbon Storage Program. In consultation with the U.S. Department of Energy (DOE) Project Manager and Technology Manager, a no-go decision was invoked to forego additional expenditures as the technology would not meet current project objectives. Project activities to date have moved the technology forward by developing modeling equations that can be applied elsewhere, advanced the state of wellhead sensors and sources, and spurred improvements to field operations. The 3-D seismic survey in the project area and the dynamic reservoir simulations done as part of this study have provided value for ongoing and future synergistic activities at Bell Creek related to DOE carbon storage goals.

54 ENVIRONMENTAL SCIENCES↗

Accelerator Real-time Edge AI for Distributed Systems (READS) (Proposal)

Over the last decade, Machine Learning (ML) technologies have slowly made their way into the accelerator community. Rapid advances in recent years in deep learning, particularly reinforcement learning for control system applications and the accessibility of deep learning in embedded hardware, have generated renewed interest and spawned a number of applications. The Fermilab Accelerator Complex, shown in Fig. 1, has provided High Energy Physics (HEP) experiments with proton beams for nearly fifty years. The current focus of the laboratory is its world-class experimental program at the intensity frontier. While increasing beam intensity certainly presents its own challenges, preserving beam size while minimizing beam losses – particles lost through interactions with the beam vacuum pipe – turns out to be, in many ways, the main challenge. The accelerator is controlled via a complex system of hundreds of thousands of devices. Enabling fine tuning and real-time optimization of their parameters using ML methods and stepping beyond experience-based reasoning of human operators are key to the success of future intensity upgrades. Our objective will be to integrate ML into accelerator operations and furthermore, provide an accessible framework, which can also be used by a broad range of other accelerator systems with dynamic tuning needs.

43 PARTICLE ACCELERATORS↗

Practical aspects of modeling aircraft dynamics from flight data

The purpose of parameter estimation, a subset of system identification, is to estimate the coefficients (such as stability and control derivatives) of the aircraft differential equations of motion from sampled measured dynamic responses. In the past, the primary reason for estimating stability and control derivatives from flight tests was to make comparisons with wind tunnel estimates. As aircraft became more complex, and as flight envelopes were expanded to include flight regimes that were not well understood, new requirements for the derivative estimates evolved. For many years, the flight determined derivatives were used in simulations to aid in flight planning and in pilot training. The simulations were particularly important in research flight test programs in which an envelope expansion into new flight regimes was required. Parameter estimation techniques for estimating stability and control derivatives from flight data became more sophisticated to support the flight test programs. As knowledge of these new flight regimes increased, more complex aircraft were flown. Much of this increased complexity was in sophisticated flight control systems. The design and refinement of the control system required higher fidelity simulations than were previously required.

Iliff, K. W.↗

Multigrid with Overlapping Patches

Solving boundary value problems with optimal efficiency requires adaptivity and multilevel techniques. Previously, an implementation of the AFACx algorithm is presented that is based on rectangular Cartesian grids. This implementation does not allow for the over]ap of grids that lie on the same level of refinement. We investigate the case in which these grids overlap. A standard technique for overlapping grids is the Schwarz algorithm. Some ways of using the Schwarz algorithm in a standard multigrid scheme are presented. Also, a problem that arises in some situations with non-aligned, overlapping grids is described. This situation comes up in a natural way when the Schwarz algorithm is used as a relaxation scheme within a multilevel algorithm. We identify the reason for the bad convergence and show that by more sophisticated interpolation the difficulties can be overcome. Then we present a multiplicative Schwarz algorithm for a large number of grids that has a high potential for parallelization. Finally we give some numerical results for the FACx algorithm with overlapping grids on each refinement level. The implementation of the described codes uses C++ and the array class libraries A++ and P++. Using the A++/P++ programming environment, it was possible to move from a serial code to a parallel code within a few days.

Berndt, Markus↗

A Search for the Solar Sources of High-Speed Streams

The original Grant was intended to support backward mapping of the stream structures observed at 1 AU by the WIND spacecraft using the observed wind speeds so that solar sources of the streams could be explored. Realizing that backwards mapping was unlikely to produce reasonable results inside of about 30 Rs, we let a subcontract to Mikic and Linker at SAIC who had developed a MHD code to cover the distance between the lower corona and 30 Rs. We used IPS measurements made by our Co-I Andy Breen to try to establish a correlation between the mapped-back streams and IPS determinations of the stream sources. We report the results of these portions of the program and then explain the progress on studies which were proposed to give insight into stream sources by exploiting the alpha/proton abundance ratios observed from WIND.

Source record↗

Low-GWP HVAC System with Ultra-small Centrifugal Compression

Mechanical Solutions, Incorporated (MSI) was awarded a contract from the United States Department of Energy under Contract DE-EE0007042 to advance the potential of vapor compression utilizing an advanced high speed centrifugal compressor with an advanced heat exchanger design. The design was mandated to maintain high efficiency while utilizing a low GWP refrigerant. The specific goal of this program was to develop an advanced 5 ton air conditioning system. The target of the air conditioner is residential and commercial. To accomplish these goals, MSI teamed with Lennox International, a leading air conditioning manufacturer. MSI would design, oversee manufacturing, assemble, and test the compressor, while Lennox designed the heat exchanger and tested the overall air conditioner. Lennox initiated the project with a detailed cycle analysis that examined systems and refrigerants. At various break points, MSI performed a preliminary compressor design to identify realizable targets. Initially, the refrigerant that was targeted was R1234ze(E), but this was subsequently rejected over concerns of flammability. R515a was ultimately accepted as a qualified fluid based upon its GWP and flammability rating. MSI performed a complete design of the centrifugal compressor based upon the cycle system design and analysis. The design was based upon advanced aerodynamics utilizing transient Computational Fluid Dynamics (CFD), as well as mechanical and rotordynamic analysis. A detailed materials investigation was conducted to ensure mechanical integrity and refrigerant compatibility. To achieve the high rotational speed required by the compressor (105,300 rpm), foil bearings were designed by MSI, as was a high speed motor to provide the required torque for the compressor. All elements of the design complied with Design for Manufacturing and Assembly (DFMA) principles. The compressor was manufactured in components, utilizing specializing subcontractors throughout the country. The components were assembled into an operational compressor in MSI’s Albany facility, where it was tested in the MSI refrigeration test loop. The compressor achieved 90% of its maximum speed during testing at MSI. The interaction between the inverter and the high speed motor was the reason that full speed could not be attained. The compressor operated smoothly and quietly at all speeds, with the bearings performing as expected. The compressor was then shipped to Lennox’s facilities in Texas, where it was tested in the entire air conditioning system. Lennox was able to achieve 95% of the maximum rotational speed. They employed the same inverter as MSI. Lennox compiled the results of the testing and based upon the results, a go forward plan has been developed to correct the issues with the inverter, as well as redesign some parts that proved to be a challenge during the program. The consensus of the team is that a fully functional air conditioning system can be developed to achieve all of the goals identified in this program.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Investigations on RELAP5-3D to RELAP5-3D coupling methodology by PVMEXEC

In the framework of a BEPU (Best Estimate Plus Uncertainty) approach within the licensing process of a nuclear power plant, the need to extend the resources of nuclear system thermal-hydraulics codes, such as RELAP5-3D, arises to allow more detailed simulations of the complex 3D reality of Nuclear Power Plants (NPPs), either under normal steady-state or during various accident scenarios. Currently, it is not possible to achieve the same degree of detail for a whole nuclear system when it is simulated with RELAP5-3D and this is due to the inherent limitations in the number of components and volumes to be used for the analysis. For this reason, it is of extreme interest the use of tools for codes coupling that enable the use of different codes for the simulation of different portions of a system in a unified analysis. In this paper the attention will be focused on the decomposition of the thermal-hydraulic domain of a system into subsystems to be simulated by different instances of the same code (e.g. RELAP5-3D) coupled together by means of PVMEXEC program and parallel virtual machine (PVM) technology. Explicit and semi-implicit solution algorithms were used for the analyses. Among the analyzed cases, the following will be discussed in detail with the aim to provide additional guidelines for the use of the PVMEXEC tool: (i) the Edward's pipe blowdown test, (ii) a simplified countercurrent heat exchanger, (iii) different hydraulics and heat structure coupling schemes for a shell-tube heat exchanger and (iv) a three-task coupled model of an adaptation of the Christensen subcooled boiling experiment. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development and Validation of a Two-Phase Thermal-Hydraulic CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance Computational Fluid Dynamics (CFD) code NEK5000. The goal of this work is to verify and validate the two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) previously developed at Argonne but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2020. This report focuses on verification and validation of the water-steam boiling model NEK-2P Two-Phase, CFD code. The NEK-2P was validated with Nuclear Power Engineering Corporation (NUPEC) Pressurized Water Reactor (PWR) Sub-channel and Bundle Test (PSBT) void distribution benchmark. Three different simulations were performed and analyzed for various operating conditions such as wall-heat flux and sub-cooled inlet temperatures. Reasonably good agreement with measured data was obtained in predicting the measured void distributions. Simulations were performed for Virginia Tech. (VT) 3x3 rod bundle geometry with and without spacers. The preliminary results were presented for Simplified Spacer Grid (SSG). In addition, the implementation of interface reconstruction model was tested with one of the Becker benchmark Critical Heat Flux (CHF) experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Development of a Beam Halo Monitor

Muons, Inc. proposed improved Residual-Gas luminescent Beam Profile Monitors for Intense Beams by adding novel features including a mirascope, a light collecting device devised in the 16th century by an inventor of the telescope. A modern mirascope consists of 2 paraboloids. Light generated by the beam is collected by the paraboloids and creates a beam image. By placing a lens near the image it is possible to collect almost 100% of the emitted light, up to ten times better than existing fluorescence profilometers. Intense (multi-MW) proton beams pose a challenge for beam profile measurements. Solid-based beam intercepting instrumentation produces unallowable levels of radiation at these high powers. An alternative is to use a zero-or-low mass device such as a residual-gas profile monitor, either through collection of ionization or fluorescence. Fluorescence has an intrinsic advantage over the usual collection of ionized electrons in that it is not affected by the strong and variable electric and magnetic fields created by the beam that can distort profiles and make calibration difficult. For this reason, we proposed the fluorescence technique using the mirascope and other methods to enhance light collection and versatility by modifying the residual gas and its spatial distribution. In Phase I, we designed a mirascope and its electronics for commissioning and beam tests in a proposed Phase II. The design was based on optical simulations done in Phase I, and a physics run plan was developed for optimizing and testing. The Phase II experimental site and program have been planned and our goal is to produce a universal low cost Mirascope Residual-Gas Luminescent Beam Profile Monitor that can replace all other profile monitors currently used in accelerators.

43 PARTICLE ACCELERATORS↗

Local strain redistribution corrections for a simplified inelastic analysis procedure based on an elastic finite-element analysis

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction proposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite-element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure predicts stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load-cycled problems. Neuber-type corrections were derived and incorporated in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was used on a mechanically load-cycled benchmark notched-plate problem. The predicted material response agrees well with the nonlinear finite-element solutions for the problem. The simplified analysis computer program was 0.3% of the central processor unit time required for a nonlinear finite-element analysis.

Kaufman, A.↗

The effect of sensor sheltering and averaging techniques on wind measurements at the Shuttle Landing Facility

This document presents results of a field study of the effect of sheltering of wind sensors by nearby foliage on the validity of wind measurements at the Space Shuttle Landing Facility (SLF). Standard measurements are made at one second intervals from 30-feet (9.1-m) towers located 500 feet (152 m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. A companion study, Merceret (1995), quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. This work examines the effect of nearby foliage on the accuracy of the measurements made by any one sensor, and the effects of averaging on interpretation of the measurements. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions as a function of distance from the obstructing foliage. Appropriate statistics were computed. The results suggest that accurate measurements require foliage be cut back to OFCM standards. Analysis of averaging techniques showed that there is no significant difference between vector and scalar averages. Longer averaging periods reduce measurement error but do not otherwise change the measurement in reasonably steady flow regimes. In rapidly changing conditions, shorter averaging periods may be required to capture trends.

Merceret, Francis J.↗