Facility for Calibrating Anemometers as a Function of Air Velocity Vector and Turbulence.

NIST calibrates anemometers as a function of airspeed vector and turbulence intensity (Tu). The vector capability (sometimes called "3-D") is particularly important for calibrating multi-hole differential-pressure probes that are often used to quantify pollution emitted by smokestacks of coal-burning electric power plants. Starting with a conventional "1-D" wind tunnel, we achieved vector and Tu capabilities by installing translation/rotation stages and removable turbulence generators (grids or flags). The calibration ranges are: yaw angle ±180°; pitch angle ±45°; airspeed 1 m/s to 30 m/s; turbulence intensity 0.07 ≤ Tu ≤ 0.25; average data collection rate: 300 points/hour at fixed Tu. The system's expanded uncertainties corresponding to 95 % confidence level are: airspeed 0.0045×|V|+(0.036/|V|)2 where |V| is the magnitude of the airspeed in m/s; pitch and yaw angles 0.3°; and turbulence intensity 0.03 Tu. The airspeed working standard is a Laser Doppler Anemometer that is traced to SI unit of velocity via a spinning disk. Calibrations are corrected for blockage by the instrument under test and its supports.

Erratum: Improved First-Principles Calculation of the Third Virial Coeffcient of Helium.

[This corrects the article on p. 729 in vol. 116.].

Refractive-index gas thermometry.

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10-6 to 3.5 × 10-5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10-5 and 4.6 × 10-5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10-5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.

Progress Towards a Gas-Flow Standard using Microwave and Acoustic Resonances.

We describe our progress in developing a novel gas flow standard that utilizes 1) microwave resonances to measure the volume, and 2) acoustic resonances to measure the average gas density of a collection tank / pressure vessel. The collection tank is a 1.85 m3, nearly-spherical, steel vessel used at pressures up to 7 MPa. Previously, using the cavity's microwave resonance frequencies, we determined the cavity's pressure- and temperature-dependent volume V BBB with the expanded uncertainty of 0.022 % (coverage factor k = 2, corresponding to 95 % confidence level). This was the first step in developing a pressure, volume, speed of sound, and time (PVwt) primary standard. In the present work, when the shell was filled with argon, measurements of pressure and acoustic resonance frequencies determined the "acoustic mass" M acst that agreed with gravimetric measurements within 0.04 %, even when temperature gradients were present. Most of these differences were a linear function of pressure; therefore, they can be reduced by further research. We designed and implemented a novel positive feedback system to measure the acoustic resonance frequencies. Using the measurements of V BBB, pressure, and acoustic resonance frequencies of the enclosed gas (nitrogen or argon), we calibrated 3 critical flow venturis that NIST has used as working standards for over 10 years. The two independent flow calibrations agreed within the long-term reproducibility of each CFV, which is less than 0.053 %. Furthermore, the feasibility of a dynamic tracking technique using this feedback loop was tested by comparing ΔM acst computed under no-flow conditions and ΔM acst computed by the rate of fall or rise during a flow. This was done for flows ranging from 0.11 g/s to 3.9 g/s.

Energy accommodation coefficient extracted from acoustic resonator experiments.

We review values of the temperature jump coefficient ζT determined from measurements of the acoustic resonance frequencies facoust of helium-filled and argon-filled, spherical cavities near ambient temperature. We combine these values of ζT with literature data for tangential momentum accommodation coefficient (TMAC) and the Cercignani-Lampis model of the gas-surface interaction to obtain measurement-derived values of the normal energy accommodation coefficient (NEAC). We found that NEAC ranges from 0 to 0.1 for helium and from 0.61 to 0.85 for argon at ambient temperature for several different surfaces. We suggest that measurements of facoust of gas-filled, cylindrical cavities and of the non-radial modes of quasi-spherical cavities might separately determine TMAC and NEAC. Alternatively, TMAC and NEAC could be determined by measuring the heat transfer and momentum transfer between parallel rotating discs at low pressure.

Non-nulling protocols for fast, accurate, 3-D velocity measurements in stacks.

The authors present protocols for making fast, accurate, 3D velocity measurements in the stacks of coal-fired power plants. The measurements are traceable to internationally-recognized standards; therefore, they provide a rigorous basis for measuring and/or regulating the emissions from stacks. The authors used novel, five-hole, hemispherical, differential-pressure probes optimized for non-nulling (no-probe rotation) measurements. The probes resist plugging from ash and water droplets. Integrating the differential pressures for only 5 seconds determined the axial velocity Va with an expanded relative uncertainty Ur(Va) ≤ 2% of the axial velocity at the probe's location, the flow's pitch (α) and yaw (ß) angles with expanded uncertainties U(α) = U(ß) = 1 °, and the static pressure ps with Ur(ps) = 0.1% of the static pressure. This accuracy was achieved 1) by calibrating each probe in a wind tunnel at 130, strategically-chosen values of (Va, α, ß) spanning the conditions found in the majority of stacks (|α| ≤ 20 °; |ß| ≤ 40 °; 4.5 m/s ≤ Va ≤27 m/s), and 2) by using a long-forgotten definition of the pseudo-dynamic pressure that scales with the dynamic pressure. The resulting calibration functions span the probe-diameter Reynolds number range from 7,600 to 45,000.Implications: The continuous emissions monitoring systems (CEMS) that measure the flue gas flow rate in coal-fired power plant smokestacks are calibrated (at least) annually by a velocity profiling method. The stack axial velocity profile is measured by traversing S-type pitot probes (or one of the other EPA-sanctioned pitot probes) across two orthogonal, diametric chords in the stack cross-section. The average area-weighted axial velocity calculated from the pitot traverse quantifies the accuracy of the CEMS flow monitor. Therefore, the flow measurement accuracy of coal-fired power plants greenhouse gas (GHG) emissions depends on the accuracy of pitot probe velocity measurements. Coal-fired power plants overwhelmingly calibrate CEMS flow monitors using S-type pitot probes. Almost always, stack testers measure the velocity without rotating or nulling the probe (i.e., the non-nulling method). These 1D non-nulling velocity measurements take significantly less time than the corresponding 2D nulling measurements (or 3D nulling measurements for other probe types). However, the accuracy of the 1D non-nulling velocity measurements made using S-type probes depends on the pitch and yaw angles of the flow. Measured axial velocities are accurate at pitch and yaw angles near zero, but the accuracy degrades at larger pitch and yaw angles.The authors developed a 5-hole hemispherical pitot probe that accurately measures the velocity vector in coal-fired smokestacks without needing to rotate or null the probe. This non-nulling, 3D probe is designed with large diameter pressure ports to prevent water droplets (or particulates) from obstructing its pressure ports when applied in stack flow measurement applications. This manuscript presents a wind tunnel calibration procedure to determine the non-nulling calibration curves for 1) dynamic pressure; 2) pitch angle; 3) yaw angle; and 4) static pressure. These calibration curves are used to determine axial velocities from 6 m/s to 27 m/s, yaw angles between ±40°, and pitch angles between ±20°. The uncertainties at the 95% confidence limit for axial velocity, yaw angle, and pitch angle are 2% (or less), 1°, and 1°, respectively. Therefore, in contrast to existing EPA-sanctioned probes, the non-nulling hemispherical probe provides fast, low uncertainty velocity measurements independent of the pitch and yaw angles of the stack flow.

Improved First-Principles Calculation of the Third Virial Coefficient of Helium.

We employ state-of-the-art pair and three-body potentials with path-integral Monte Carlo (PIMC) methods to calculate the third density virial coefficient C(T) for helium. The uncertainties are much smaller than those of the best experimental results, and approximately one-fourth the uncertainty of our previous work. We have extended our results in temperature down to 2.6 K, incorporating the effect of spin statistics that become important below approximately 7 K. Results are given for both the (3)He and (4)He isotopes. We have also performed PIMC calculations of the third acoustic virial coefficient γ a; our calculated values compare well with the limited experimental data available. A correlating equation for C(T) of (4)He is presented; differentiation of this equation provides a reliable and simpler way of calculating γ a.

Shear thinning near the critical point of xenon.

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(-3)gamma tau , C gamma depends also on both x 0 and omega . The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma)/eta(0)=[1+A gamma|gamma tau|]-x eta/(3+x eta) , where x eta=0.069 is the critical exponent for viscosity and mode-coupling theory predicts A gamma=0.121 . For xenon we find A gamma=0.137+/-0.029 , in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature Tc were independent of the cooling rate (both above and below Tc ) and these data were symmetric about Tc to within a temperature scale factor. The scale factors for the magnitude of the oscillator's response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below Tc .

Advances in thermometry.

The last 25 years have seen tremendous progress in thermometry in the moderate temperature range (1 K to 1235 K). Various primary thermometers - based on different physics -have uncovered errors in the International Temperature Scale of 1990 and set the stage for the planned redefinition of the kelvin.

Can a Pressure Standard be Based on Capacitance Measurements?

We consider the feasibility of basing a pressure standard on measurements of the dielectric constant ϵ and the thermodynamic temperature T of helium near 0 °C. The pressure p of the helium would be calculated from fundamental constants, quantum mechanics, and statistical mechanics. At present, the relative standard uncertainty of the pressure ur(p) would exceed 20 × 10-6, the relative uncertainty of the value of the molar polarizability of helium Aϵ calculated ab initio. If the relativistic corrections to Aϵ were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain ur(p) < 6 × 10-6 for pressures near 1 MPa, a result of considerable interest for pressure metrology. One obtains p by eliminating the density from the virial expansions for p and ϵ - 1. If ϵ - 1 were measured with a very stable, 0.5 pF toroidal cross capacitor, the small capacitance and the small values of ϵ - 1 would require state-of-the-art capacitance measurements to achieve a useful pressure standard.

Design and Uncertainty Analysis for a PVTt Gas Flow Standard.

A new pressure, volume, temperature, and, time (PVTt) primary gas flow standard at the National Institute of Standards and Technology has an expanded uncertainty (k = 2) of between 0.02 % and 0.05 %. The standard spans the flow range of 1 L/min to 2000 L/min using two collection tanks and two diverter valve systems. The standard measures flow by collecting gas in a tank of known volume during a measured time interval. We describe the significant and novel features of the standard and analyze its uncertainty. The gas collection tanks have a small diameter and are immersed in a uniform, stable, thermostatted water bath. The collected gas achieves thermal equilibrium rapidly and the uncertainty of the average gas temperature is only 7 mK (22 × 10(-6) T). A novel operating method leads to essentially zero mass change in and very low uncertainty contributions from the inventory volume. Gravimetric and volume expansion techniques were used to determine the tank and the inventory volumes. Gravimetric determinations of collection tank volume made with nitrogen and argon agree with a standard deviation of 16 × 10(-6) VT . The largest source of uncertainty in the flow measurement is drift of the pressure sensor over time, which contributes relative standard uncertainty of 60 × 10(-6) to the determinations of the volumes of the collection tanks and to the flow measurements. Throughout the range 3 L/min to 110 L/min, flows were measured independently using the 34 L and the 677 L collection systems, and the two systems agreed within a relative difference of 150 × 10(-6). Double diversions were used to evaluate the 677 L system over a range of 300 L/min to 1600 L/min, and the relative differences between single and double diversions were less than 75 × 10(-6).

Theory of the Greenspan viscometer.

We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rd. In the lowest order, eta=pi f rho(rd/Q)2, where f and Q are the frequency and quality factor of the isolated Greenspan mode, and rho is the gas density. In this level of approximation, the viscosity can be determined by measuring the duct radius and frequency response of the resonator. In the full acoustic model of the resonator, the duct is represented by a T-equivalent circuit, the chambers as lumped impedances, and the effects of the diverging fields at the duct ends by lumped end impedances with inertial and resistive components. The model accounts for contributions to 1/Q from thermal dissipation (primarily localized in the chambers) and from a capillary used for filling and evacuating the resonator. A robust, prototype instrument is being used for measuring the viscosity of reactive gases used in semiconductor processing. For well-characterized surrogate gases, the prototype viscometer generated values of eta that were within +/-0.8% of published reference values throughout the pressure range 0.2-3.2 MPa. Remarkably, we achieved this level of agreement by only slight adjustment of the numerically calculated inertial and resistive end effect parameters to improve the agreement with helium reference values. No other parameters were adjusted.