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At least 721 records · Page 40

1/3-Octave Analysis of Core/Combustor-Noise Measurements for the DGEN Aeropropulsion Research Turbofan with Application to Noise Prediction

This work continues the analysis of data obtained during a 2017 NASA DGEN Aeropropulsion Research Turbofan (DART) core/combustor-noise baseline test in the NASA GRC Aero-Acoustic Propulsion Laboratory (AAPL). The DART is a cost-efficient testbed for the study of core-noise physics and mitigation. Acoustic data were simultaneously acquired using the AAPL overhead microphone array in the engine aft-quadrant farfield, a single midfield microphone, and two infinite-tube-probe sensors for unsteady pressures at the core-nozzle exit. The data are here examined on an 1/3-octave basis as a first step in extending and improving core-noise prediction capability.

Hultgren, Lennart S.↗

SERFE Thermal Performance Results

NASA has been developing a new spacesuit, called the Exploration Extravehicular Mobility Unit (xEMU) for over a decade. This spacesuit is underdevelopment to support missions to the International Space Station (ISS) and also to the Moon. Improvements in the life and robustness of the Portable Life Support System (PLSS) has been a major objective of these efforts. The Suit Water Membrance Evaporator (SWME) was chosen as the technology to provide cooling to the xEMU and has undergone several iterations of development over this period. An ISS flight experiment centered around the SWME and other thermal loop technologies was developed and has been under test in an ISS EXpedite PRocessing of Experiments to the Space Station (EXPRESS) rack since November of 2020. In addition to the SWME, The SWME EXPRESS Rack Flight Experiment (SERFE) contains several technology demonstrations from the xEMU project and has been demonstrating their performance in micro-gravity and over an extended duration. In addition to the SWME, these include two dissimilar water pumps, custom check valves, custom bypass relieve valves, a custom thermal control valve, development pressure and temperature sensors, and the Thermal Loop Controller. This paper presents thermal and fluids testing results of the system as a whole and of key components.

SERFE↗

SERFE PLSS Component Lessons Learned from ISS

NASA has been developing a new spacesuit, called the Exploration Extravehicular Mobility Unit (xEMU) for over a decade. This spacesuit is under development to support missions to the International Space Station (ISS) and also to the Moon. Improvements in the life and robustness of the Portable Life Support System (PLSS) has been a major objective of these efforts. The Suit Water Membrane Evaporator (SWME) was chosen as the technology to provide cooling to the xEMU and has undergone several iterations of development over this period. An ISS flight experiment centered around the SWME and other thermal control loop (TCL) technologies was developed and tested in an ISS EXpedite PRocessing of Experiments to the Space Station (EXPRESS) rack from November of 2020 to August of 2022. In addition to the SWME, the SWME EXPRESS Rack Flight Experiment (SERFE) contains several technologies from the xEMU project and demonstrated their performance in micro-gravity and over an extended duration. These included two dissimilar water pumps, custom check valves, custom bypass relieve valves, a custom thermal control valve, development pressure and temperature sensors, and the thermal loop controller. This paper presents PLSS component lessons learned after return of the SERFE flight unit in August of 2022. The SERFE team took the flight unit apart and handed hardware components over to hardware owners to see how parts of the TCL managed after almost 2 years on the ISS and 25 simulated EVAs (Exploration Extravehicular Activity) on orbit. The team performed inspection, testing, and analysis and provided lessons learned on PLSS components for NASA’s prototype spacesuit. This analysis included how well SWME maintained its heat rejection capability, as well as looked at the robustness of the other TCL hardware.

SERFE↗

SERFE PLSS Component Lessons Learned from ISS

NASA has been developing a new spacesuit, called the Exploration Extravehicular Mobility Unit (xEMU) for over a decade. This spacesuit is under development to support missions to the International Space Station (ISS) and also to the Moon. Improvements in the life and robustness of the Portable Life Support System (PLSS) has been a major objective of these efforts. The Suit Water Membrane Evaporator (SWME) was chosen as the technology to provide cooling to the xEMU and has undergone several iterations of development over this period. An ISS flight experiment centered around the SWME and other thermal control loop (TCL) technologies was developed and tested in an ISS EXpedite PRocessing of Experiments to the Space Station (EXPRESS) rack from November of 2020 to August of 2022. In addition to the SWME, the SWME EXPRESS Rack Flight Experiment (SERFE) contains several technologies from the xEMU project and demonstrated their performance in micro-gravity and over an extended duration. These included two dissimilar water pumps, custom check valves, custom bypass relieve valves, a custom thermal control valve, development pressure and temperature sensors, and the thermal loop controller. This paper presents PLSS component lessons learned after return of the SERFE flight unit in August of 2022. The SERFE team took the flight unit apart and handed hardware components over to hardware owners to see how parts of the TCL managed after almost 2 years on the ISS and 25 simulated EVAs (Exploration Extravehicular Activity) on orbit. The team performed inspection, testing, and analysis and provided lessons learned on PLSS components for NASA’s prototype spacesuit. This analysis included how well SWME maintained its heat rejection capability, as well as looked at the robustness of the other TCL hardware.

SERFE↗

HDG-1 Experiment Irradiation Monitoring Data Qualification Final Report

SUMMARY The U.S. Department of Energy (DOE) Advanced Reactor Technologies (ART) Graphite Research and Development (GRD) Program is conducting a series of six experiments to quantify the effects of irradiation on nuclear-grade graphite. This report documents the qualification of irradiation monitoring data for the fifth experiment, High Dose Graphite-1 (HDG-1). Qualified monitoring data are required by the ART program to support the design and licensing of the first high-temperature reactor (HTR) nuclear plant. Data are classified as Qualified if they meet the usage requirements described in the experiment planning and quality assurance (QA) documents, Failed if they do not meet those requirements and provide no usable information, or Trend if they do not fully meet all requirements but still provide useful information subject to an assessment of how any deficiencies may affect a particular use of the data. HDG-1 irradiation began with Advanced Test Reactor (ATR) Cycle 168B on August 24, 2020, and concluded after Cycle 173C on January 27, 2025. The HDG-1 capsule was removed from the reactor core twice—during core internal change (CIC) Cycle 170A and powered axial locator mechanism (PALM) Cycle 172A—to prevent overheating of the graphite specimens during high-power PALM cycles. The capsule was therefore irradiated during a total of seven normal ATR cycles: 168B, 169A, 171A, 171B, 173A, 173B, and 173C. Irradiation monitoring data evaluated in this report include thermocouple (TC) temperature, gas flow rate, gas moisture, gas pressure, specimen load, and graphite stack displacement. Temperature. A total of 14,508,065 TC temperature records were captured. Of these, 13,901,785 (95.8%) are Qualified and 606,280 (4.2%) are Failed. The principal source of failed temperature data was the instrument failure of TC-9 (Zone 2) on June 24, 2024, and TC-10 (Zone 1) on July 5, 2024, near the end of Cycle 173A, which resulted in 595,554 Failed readings. An additional 379 missing values and 10,347 slightly negative values from TC-13 during ATR outages are also Failed. Neither TC-9 nor TC-10 was used as a temperature-control TC, and their failures did not compromise capsule condition monitoring. Correlation analysis of all 13 TCs found no evidence of virtual junction formation. Control chart analysis revealed clear downward drift of approximately 80°C for TC-6 (Zone 3) relative to other stable TCs, and possible downward drift of approximately 60°C for TC-13 relative to the Zone 5 control TC (TC-1), though TC-13 remained consistent with the Zone 2 control TC (TC-12). Gas flow. A total of 20,088,090 gas flow rate records were captured. Of these, 19,941,463 (99.3%) are Qualified and 146,627 (0.7%) are Failed due to missing values. All argon, helium, and total gas flow data were within expected ranges throughout the irradiation. Gas moisture. A total of 1,116,005 outlet gas moisture values were captured. Of these, 1,101,421 (98.7%) are Qualified and 14,584 (1.3%) are Failed, comprising 14,556 out-of-range values and 28 missing values. The out-of-range moisture values exceeded 22,000 ppmv for approximately 1 week at the beginning of Cycle 173A, when accumulated moisture evaporated after the capsule was retrieved from water storage during PALM Cycle 172A and reinserted into the east flux trap. Moisture levels returned to below 25 ppmv for the remaining three cycles, and the transient high-moisture event did not affect the integrity of specimen irradiation. Gas pressure. A total of 7,812,035 gas pressure values were captured. Of these, 6,642,048 (85.0%) are Qualified and 1,169,987 (15.0%) outlet pressure values are Failed, comprising 718,537 zero outlet pressure values due to sensor failure from Cycle 168B through Cycle 171B, 54,550 missing values, and 396,900 too-low outlet pressure values, ranging from 1.1 to 1.6 psia after sensor replacement during Cycle 173A. Load. A total of 6,696,030 load values were captured. Of these, 6,694,580 (99.98%) are Qualified and 1,450 (0.02%) are Failed due to missing values. Applied loads to the six specimen stacks were stable throughout the irradiation. Stack displacement. A total of 6,696,030 displacement values were captured. Of these, 5,713,297 (85.32%) are Qualified and 3,781 (0.06%) are Failed due to missing values. Stack displacement increased consistently throughout the irradiation, reaching approximately 3.08 in. for Channels 5 and 6 by the end of irradiation. 978,952 (14.62%) substantially elevated displacements observed for Channel 6 beginning in Cycle 171A and for Channel 5 beginning in Cycle 173A are assigned Trend status. Raising pressure. A total of 1,115,999 raising pressure values were captured. Of these, 1,115,430 (99.95%) are Qualified and 569 (0.05%) are Failed due to missing values. Ram pressure. A total of 6,696,030 ram pressure values were captured. Of these, 6,692,249 (99.95%) are Qualified and 3,484 (0.05%) are Failed due to missing values. Stack raising was perf

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Wireless Instrumented RB Experiment Preliminary Design and Analysis

The ability to deploy new nuclear fuels for current or future reactor concepts requires carefully designed experiments to generate data to support fuel qualification. Ideally these experiments would include state of-the-art sensing to maximize the amount of in situ data that can be collected during operation. Furthermore, advanced reactor systems can take advantage of integrated in-core sensing technologies to maximize fuel utilization, reduce unnecessary conservativism in design margins, and improve operator’s understanding of limiting peaking factors. Before any novel sensing technologies can be readily adopted for nuclear applications, they must first demonstrate acceptable performance in test reactors. This report summarizes the preliminary design and analysis of the most highly instrumented irradiation experiment ever performed in the removable beryllium (RB) positions of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL). The Wireless Instrumented RB Experiment 2021 (WIRE-21) will test a wide range of sensors including wireless sensors being developed by Westinghouse Electric Company (WEC) that could provide in situ measurements of peak fuel temperatures and fuel rod pressurization due to fission gas release. The ability to wirelessly transmit a signal through the fuel rod’s cladding is critical to improving fuel monitoring capabilities without requiring signal penetrations through the cladding pressure boundary, which would significantly impact fuel fabrication, handling, and operation. Other sensors that will be tested in WIRE-21 include an array of thermocouples, self-powered neutron detectors (SPNDs), and spatially distributed fiber-optic temperature sensors. More generally, WIRE-21 will establish a flexible irradiation vehicle design to allow accelerated, economical testing of advanced sensor technologies while leveraging the extremely high neutron flux that is available in HFIR. This report summarizes the mechanical design for WIRE-21, the experimental test matrix, initial neutronic and thermal design analyses, and the active monitoring and control system enhancements necessary to support testing of advanced sensor technologies. The containment for WIRE-21 is similar to previous RB irradiation vehicles but includes a few modifications, most notably the use of integrated compression seals to pass a larger number of sensor leads through the experiment’s pressure boundary. In addition to the sensor leads, inert gas lines are passed into the experiment to enable active temperature control and the ability to pneumatically actuate a bellows-driven pressure sensor. WIRE-21 is targeting temperatures (300–350°C) and neutron fluence levels (~10 22 n/cm 2 ) relevant to light water reactors (LWRs), but the flexible design of the experiment vehicle allows much higher operating temperatures (>1,100°C). Neutronic calculations determine the neutron flux conditions as well as the nuclear heating within the experiments. These results are used as inputs to detailed thermal finite element calculations, which are required to evaluate the complex, three-dimensional heat transfer that occurs within WEC’s wireless sensor enclosures. Initial results show that the temperatures of the sensors’ enclosures and the metal bellows can be operated near the temperature range of LWR coolants and cladding while simultaneously increasing the temperature of a surrogate fuel material to values in the range of 800–1200°C to simulate centerline fuel temperatures during LWR operation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hydrogen Mitigation Process Installation at Nevada Solar One

The National Renewable Energy Laboratory (NREL) and Acciona Solar Power (ASP) have developed and are implementing a process that addresses the issue of hydrogen buildup in parabolic trough power plants. Our method selectively removes hydrogen from the expansion tanks of the power plant to control hydrogen levels in the circulating heat-transfer fluid (HTF). During previous work, we developed a sensor that measures hydrogen partial pressure in the expansion-tank headspace gas. We demonstrated that our sensor measures hydrogen levels over a wide range of partial pressure—from 1.33 mbar down to 0.003 mbar. More recently, we conceived and developed an integrated process module that performs both hydrogen sensing and separating functions. The sensor/separator measures hydrogen partial pressure in the headspace gas in the same way as our original sensor design. Additionally, the integrated module separates hydrogen from the headspace gas to reduce hydrogen to the level needed to maintain the performance of receivers in the collector field. We demonstrated the performance of a laboratory-scale version of this module. Testing showed that the module performed as expected: the accuracy of the sensing function was ±7%, and the hydrogen extraction rate for the separating mode was consistent with our modeling predictions. The primary benefit of this module is its simple design, both in terms of function and incorporation into the HTF subsystem of the power plant. Most recently, NREL and ASP planned, specified, and designed a mitigation process that is based on the integrated module. We are currently completing installation of this process at ASP's Nevada Solar One power plant in Boulder City, Nevada, USA. The mitigation process is being installed at ground level below the HTF expansion tanks, where it draws headspace gas from the tanks, removes hydrogen, and returns the treated gas back to the tanks. In this paper, we report progress on the installation and describe some of the many design details and challenges that we addressed during the past year. We will generate initial performance data from the Nevada Solar One mitigation process in early 2020.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Hydrogen Mitigation Process Testing at Nevada Solar One

The National Renewable Energy Laboratory (NREL) and Acciona Solar Power (ASP) developed and installed a process that addresses the issue of hydrogen buildup in Acciona's Nevada Solar One power plant. Our method selectively removes hydrogen from the expansion tanks of the power plant to control hydrogen levels in the circulating heat-transfer fluid (HTF). During previous work, we developed a sensor that measures hydrogen partial pressure in the expansion-tank headspace gas. We demonstrated that our sensor measures hydrogen levels over a wide range of partial pressure from 10 mbar down to 0.003 mbar. More recently, we conceived and developed an integrated process module that performs both hydrogen sensing and separating functions. The sensor/separator measures hydrogen partial pressure in the headspace gas in the same way as our original sensor design. Additionally, the integrated module separates hydrogen from the headspace gas to reduce hydrogen to the level needed to maintain the performance of receivers in the collector field. Laboratory testing at NREL showed that the sensor function had an accuracy of +/-7%, and the hydrogen extraction rate for separator function was consistent with our modeling predictions. The primary benefit of this module is its simple design, both in terms of function and incorporation into the HTF subsystem of the power plant. Most recently, NREL and ASP completed installation and initial testing of a mitigation process at ASP's Nevada Solar One power plant in Boulder City, Nevada. In this paper, we report on the completed installation, initial testing, and plans to bring the process to full automation, so that it can be operated unattended on a daily schedule.

chemical elements↗

Propellant Feed System Leak Detection: Lessons Learned From the Linear Aerospike SR-71 Experiment (LASRE)

This paper presents pertinent results and assessment of propellant feed system leak detection as applied to the Linear Aerospike SR-71 Experiment (LASRE) program flown at the NASA Dryden Flight Research Center, Edwards, California. The LASRE was a flight test of an aerospike rocket engine using liquid oxygen and high-pressure gaseous hydrogen as propellants. The flight safety of the crew and the experiment demanded proven technologies and techniques that could detect leaks and assess the integrity of hazardous propellant feed systems. Point source detection and systematic detection were used. Point source detection was adequate for catching gross leakage from components of the propellant feed systems, but insufficient for clearing LASRE to levels of acceptability. Systematic detection, which used high-resolution instrumentation to evaluate the health of the system within a closed volume, provided a better means for assessing leak hazards. Oxygen sensors detected a leak rate of approximately 0.04 cubic inches per second of liquid oxygen. Pressure sensor data revealed speculated cryogenic boiloff through the fittings of the oxygen system, but location of the source(s) was indeterminable. Ultimately, LASRE was cancelled because leak detection techniques were unable to verify that oxygen levels could be maintained below flammability limits.

Hass, Neal↗

Thermocouples of tantalum and rhenium alloys for more stable vacuum-high temperature performance

Thermocouples of the present invention provide stability and performance reliability in systems involving high temperatures and vacuums by employing a bimetallic thermocouple sensor wherein each metal of the sensor is selected from a group of metals comprising tantalum and rhenium and alloys containing only those two metals. The tantalum, rhenium thermocouple sensor alloys provide bare metal thermocouple sensors having advantageous vapor pressure compatibilities and performance characteristics. The compatibility and physical characteristics of the thermocouple sensor alloys of the present invention result in improved emf, temperature properties and thermocouple hot junction performance. The thermocouples formed of the tantalum, rhenium alloys exhibit reliability and performance stability in systems involving high temperatures and vacuums and are adaptable to space propulsion and power systems and nuclear environments.

Morris, J. F.↗

Thermocouples of molybdenum and iridium alloys for more stable vacuum-high temperature performance

Thermocouples providing stability and performance reliability in systems involving high temperatures and vacuums by employing a bimetallic thermocouple sensor are described. Each metal of the sensor is selected from a group of metals comprising molybdenum and iridium and alloys containing only those two metals. The molybdenum, iridium thermocouple sensor alloys provide bare metal thermocouple sensors having advantageous vapor pressure compatibility and performance characteristics. The compatibility and physical characteristics of the thermocouple sensor alloys result in improved emf, temperature properties and thermocouple hot junction performance.

Morris, J. F.↗

Summary of Activities for Health Monitoring of Composite Overwrapped Pressure Vessels

This three-year project (FY12-14) will design and demonstrate the ability of new Magnetic Stress Gages for the measurement of stresses on the inner diameter of a Composite Overwrapped Pressure Vessel overwrap. The sensors are being tested at White Sands Testing Facility (WSTF) where the results will be correlated with a known nondestructive technique acoustic emission. The gages will be produced utilizing Meandering Winding Magnetometer (MWM) and/or MWM array eddy current technology. The ultimate goal is to utilize this technology for the health monitoring of Composite Overwrapped Pressure Vessels for all future flight programs. The first full-scale pressurization test was performed at WSTF in June 2012. The goals of this test were to determine adaptations of the magnetic stress gauge instrumentation that would be necessary to allow multiple sensors to monitor the vessel's condition simultaneously and to determine how the sensor response changes with sensor selection and orientation. The second full scale pressurization test was performed at WSTF in August 2012. The goals of this test were to monitor the vessel's condition with multiple sensors simultaneously, to determine the viability of the multiplexing units (MUX) for the application, and to determine if the sensor responses in different orientations are repeatable. For both sets of tests the vessel was pressured up to 6,000 psi to simulate maximum operating pressure. Acoustic events were observed during the first pressurization cycle. This suggested that the extended storage period prior to use of this bottle led to a relaxation of the residual stresses imparted during auto-frettage. The pressurization tests successfully demonstrated the use of multiplexers with multiple MWM arrays to monitor a vessel. It was discovered that depending upon the sensor orientation, the frequencies, and the sense element, the MWM arrays can provide a variety of complementary information about the composite overwrapped pressure vessel load conditions. For example, low frequency measurements can be used to monitor the overwrap thickness and changes associated with pressure level. High frequency data is dominated by the properties of the overwrap, including the fiber orientations and lay-up of the layers.

Russell, Rick↗

Turbine blade and vane heat flux sensor development, phase 1

Heat flux sensors available for installation in the hot section airfoils of advanced aircraft gas turbine engines were developed. Two heat flux sensors were designed, fabricated, calibrated, and tested. Measurement techniques are compared in an atmospheric pressure combustor rig test. Sensors, embedded thermocouple and the Gordon gauge, were fabricated that met the geometric and fabricability requirements and could withstand the hot section environmental conditions. Calibration data indicate that these sensors yielded repeatable results and have the potential to meet the accuracy goal of measuring local heat flux to within 5%. Thermal cycle tests and thermal soak tests indicated that the sensors are capable of surviving extended periods of exposure to the environment conditions in the turbine. Problems in calibration of the sensors caused by severe non-one dimensional heat flow were encountered. Modifications to the calibration techniques are needed to minimize this problem and proof testing of the sensors in an engine is needed to verify the designs.

Atkinson, W. H.↗

Fluctuating pressures measured beneath a high-temperature, turbulent boundary layer on a flat plate at Mach number of 5

Fluctuating pressures were measured beneath a Mach 5, turbulent boundary layer on a flat plate with an array of piezoresistive sensors. The data were obtained with a digital signal acquisition system during a test run of 4 seconds. Data sampling rate was such that frequency analysis up to 62.5 kHz could be performed. To assess in situ frequency response of the sensors, a specially designed waveguide calibration system was employed to measure transfer functions of all sensors and related instrumentation. Pressure time histories were approximated well by a Gaussian prohibiting distribution. Pressure spectra were very repeatable over the array span of 76 mm. Total rms pressures ranged from 0.0017 to 0.0046 of the freestream dynamic pressure. Streamwise, space-time correlations exhibited expected decaying behavior of a turbulence generated pressure field. Average convection speed was 0.87 of freestream velocity. The trendless behavior with sensor separation indicated possible systematic errors.

Parrott, Tony L.↗

Air pressure measurement

The pressure measurement was made by a Model 830J Rosemont sensor which utilized the principle of a changing pressure to change correspondingly the capacitance of the pressure sensitive element. The sensor's range was stated to be from zero to 100 Torr (14 km); however, the sensor was not activated until an altitude of 20 km (41 Torr) was reached during the balloon ascent. The resolution of the sensor was specified by the manufacturer as infinitesimal; however, associated electronic and pressure readout systems limit the resolution to .044 Torr. Thus in the vicinity of an altitude of 30 km the pressure resolution corresponded to an altitude resolution of approximately 33 meters.

Ballard, H. N.↗

Sensor capsule for diagnosis of gastric disorders

Motility and pH sensor capsule is developed to monitor gastric acidity, pressure, and temperature. Capsule does not interfere with digestion. Sensor is capsule which includes pH electrode, Pitran pressure transducer, and thermistor temperature sensor all potted in epoxy and enclosed in high density polyethylene sheath.

Holen, J. T.↗

Pneumatic distortion compensation for aircraft surface pressure sensing devices

In this paper a technique of compensating for pneumatic distortion in aircraft surface pressure sensing devices is developed. The compensation allows conventional pressure sensing technology to obtain improved unsteady pressure measurements. Pressure distortion caused by frictional attenuation and pneumatic resonance within the sensing system makes obtaining unsteady pressure measurements by conventional sensors difficult. Typically, most of the distortion occurs within the pneumatic tubing used to transmit pressure impulses from the surface of the aircraft to the measurement transducer. This paper develops a second-order distortion model that accurately describes the behavior of the primary wave harmonic of the pneumatic tubing. The model is expressed in state-variable form and is coupled with standard results from minimum-variance estimation theory to develop an algorithm to compensate for the effects of pneumatic distortion. Both postflight and real-time algorithms are developed and evaluated using simulated and flight data. Covariance selection and filter-tuning examples are presented. Results presented verify that, given appropriate covariance magnitudes, the algorithms accurately reconstruct surface pressure values from remotely sensed pressure measurements.

Whitmore, Stephen A.↗

Fluidic angular velocity sensor

A fluidic sensor providing a differential pressure signal proportional to the angular velocity of a rotary input is described. In one embodiment the sensor includes a fluid pump having an impeller coupled to a rotary input. A housing forming a constricting fluid flow chamber is connected to the fluid input of the pump. The housing is provided with a fluid flow restrictive input to the flow chamber and a port communicating with the interior of the flow chamber. The differential pressure signal measured across the flow restrictive input is relatively noise free and proportional to the square of the angular velocity of the impeller. In an alternative embodiment, the flow chamber has a generally cylindrical configuration and plates having flow restrictive apertures are disposed within the chamber downstream from the housing port. In this embodiment, the differential pressure signal is found to be approximately linear with the angular velocity of the impeller.

Berdahl, C. M.↗