Faster, more accurate, stack-flow measurements.

Exhaust flows from coal-fired electricity-generating plants are determined by averaging flue gas velocities measured at prescribed points in the stack cross section. These velocity measurements are made using EPA-approved differential pressure probes such as the 2-hole S-probe or the 5-hole spherical probe. Measurements using the more accurate 5-hole spherical probes require a time-consuming rotation (or nulling) of the probe to find the yaw angle. We developed a time-saving non-nulling technique using a spherical probe that measures all 3 components of velocity and therefore provides better accuracy than an S-probe. We compared the non-nulling technique with the EPA Method 2F nulling technique at both high (16 m/s) and low (7 m/s) loads in a coal-fired powerplant smokestack. Their excellent mutual agreement (within 0.3% of the flow) demonstrates that the non-nulling technique accurately measures flue gas flows.Implications: Accurate flow measurements are critical for quantifying the levels of greenhouse gases emitted from coal-fired power plant smokestacks. Flow measurement accuracy derives from the annual calibration of stack flow monitors. Calibrations are performed using EPA sanctioned pitot traverse methods called the flow relative accuracy test audit (RATA). This study demonstrates the viability of a new pitot traverse method, herein called the Non-Nulling Method. Testing in a coal-fired power plant stack showed that the new method is 5 times faster to implement than the most accurate EPA pitot traverse method (i.e., Method 2F), yet gives the same or better accuracy.

The Boltzmann project.

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649 × 10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7 × 10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Determination of the molar mass of argon from high-precision acoustic comparisons.

This article describes the accurate determination of the molar mass M of a sample of argon gas used for the determination of the Boltzmann constant. The method of one of the authors (Moldover et al 1988 J. Res. Natl. Bur. Stand.93 85-144) uses the ratio of the square speed of sound in the gas under analysis and in a reference sample of known molar mass. A sample of argon that was isotopically-enriched in 40Ar was used as the reference, whose unreactive impurities had been independently measured. The results for three gas samples are in good agreement with determinations by gravimetric mass spectrometry; (〈Macoustic/Mmass-spec〉 - 1) = (-0.31 ± 0.69) × 10-6, where the indicated uncertainty is one standard deviation that does not account for the uncertainties from the acoustic and mass-spectroscopy references.

Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined.

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys.32 1297, Lin et al 2013 Metrologia50 417, Feng et al 2015 Metrologia52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA's method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean k̂B is 1.380 6484(28) × 10-23 J K-1 with the relative standard uncertainty of 2.0 × 10-6. The corresponding value of the universal gas constant is 8.314 459(17) J K-1 mol-1 with the relative standard uncertainty of 2.0 × 10-6.

Detecting leaks in gas-filled pressure vessels using acoustic resonances.

We demonstrate that a leak from a large, unthermostatted pressure vessel into ambient air can be detected an order of magnitude more effectively by measuring the time dependence of the ratio p/f(2) than by measuring the ratio p/T. Here f is the resonance frequency of an acoustic mode of the gas inside the pressure vessel, p is the pressure of the gas, and T is the kelvin temperature measured at one point in the gas. In general, the resonance frequencies are determined by a mode-dependent, weighted average of the square of the speed-of-sound throughout the volume of the gas. However, the weighting usually has a weak dependence on likely temperature gradients in the gas inside a large pressure vessel. Using the ratio p/f(2), we measured a gas leak (dM/dt)/M ≈ - 1.3 × 10(-5) h(-1) = - 0.11 yr(-1) from a 300-liter pressure vessel filled with argon at 450 kPa that was exposed to sunshine-driven temperature and pressure fluctuations as large as (dT/dt)/T ≈ (dp/dt)/p ≈ 5 × 10(-2) h(-1) using a 24-hour data record. This leak could not be detected in a 72-hour record of p/T. (Here M is the mass of the gas in the vessel and t is the time.).

Perturbations From Ducts on the Modes of Acoustic Thermometers.

We examine the perturbations of the modes of an acoustic thermometer caused by circular ducts used either for gas flow or as acoustic waveguides coupled to remote transducers. We calculate the acoustic admittance of circular ducts using a model based on transmission line theory. The admittance is used to calculate the perturbations to the resonance frequencies and half-widths of the modes of spherical and cylindrical acoustic resonators as functions of the duct's radius, length, and the locations of the transducers along the duct's length. To verify the model, we measured the complex acoustic admittances of a series of circular tubes as a function of length between 200 Hz and 10 kHz using a three-port acoustic coupler. The absolute magnitude of the specific acoustic admittance is approximately one. For a 1.4 mm inside-diameter, 1.4 m long tube, the root mean square difference between the measured and modeled specific admittances (both real and imaginary parts) over this frequency range was 0.018. We conclude by presenting design considerations for ducts connected to acoustic thermometers.

Polarizability of helium and gas metrology.

Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to deduce its molar polarizability A(epsilon) in the limit of zero density. We obtained (A(epsilon,meas) - A(epsilon,theory))/A(epsilon) = (-1.8 +/- 9.1) x 10(-6), where the standard uncertainty (9.1 ppm) is a factor of 3.3 smaller than that of the best previous measurement. If the theoretical value of A(epsilon) is accepted, these data determine a value for the Boltzmann constant that is only 1.8 +/- 9.1 ppm larger than the accepted value. Our techniques will enable a helium-based pressure standard and measurements of thermodynamic temperatures.

Bulk viscosity, thermoacoustic boundary layers, and adsorption near the critical point of xenon.

We present an improved model for the dissipation and dispersion in an acoustic resonator filled with xenon near its critical temperature Tc. We test the model with acoustic measurements in stirred xenon that have a temperature resolution of (T - Tc)/Tc approximately 7 x 10(-6). The model includes the frequency-dependent bulk viscosity calculated numerically from renormalization-group theory and it includes critical-point adsorption. Because the density of adsorbed xenon exceeds the critical density, the bulk viscosity's effect on surface dissipation is reduced, thereby improving the agreement between theory and experiment.

Bulk viscosity of stirred xenon near the critical point.

We deduce the thermophysical properties of near-critical xenon from measurements of the frequencies and half-widths of the acoustic resonances of xenon maintained at its critical density in centimeter-sized cavities. In the reduced temperature range 1 x 10-3<(T-Tc)/Tc<7 x 10 (-6), we measured the resonance frequency and quality factor (Q) for each of six modes spanning a factor of 27 in frequency. As Tc was approached, the frequencies decreased by a factor of 2.2 and the Q's decreased by as much as a factor of 140. Remarkably, these results are predicted (within +/-2% of the frequency and within a factor of 1.4 of Q) by a model for the resonator and a model for the frequency-dependent bulk viscosity zeta(omega) that uses no empirically determined parameters. The resonator model is based on a theory of acoustics in near-critical fluids developed by Gillis, Shinder, and Moldover [Phys. Rev. E 70, 021201 (2004)]. In addition to describing the present low-frequency data (from 120 Hz to 7.5 kHz), the model for zeta(omega) is consistent with ultrasonic (0.4--7 MHz) velocity and attenuation data from the literature. However, the model predicts a peak in the temperature dependence of the dissipation in the boundary layer that we did not detect. This suggests that the model overestimates the effect of the bulk viscosity on the thermal boundary layer. In this work, the acoustic cavities were heated from below to stir the xenon, thereby reducing the density stratification resulting from Earth's gravity. The stirring reduced the apparent equilibration time from several hours to a few minutes, and it reduced the effective temperature resolution from 60 mK to approximately 2 mK, which corresponds to (T-Tc)/Tc approximately =7 x 10(-6).

Thermoacoustic boundary layers near the liquid-vapor critical point.

We measure and calculate the sound attenuation within thermoacoustic boundary layers between solid surfaces and xenon at its critical density rhoc as the reduced temperature tau identical with (T- Tc)/Tc approaches zero. (Tc is the critical temperature.) Using the known thermophysical properties of xenon, we predict that the attenuation at the boundary first increases approximately as tau(-0.6) and then saturates when the effusivity of the xenon exceeds that of the solid. [The effusivity is epsilon identical with (rhoCPlambdaT)(1/2), where CP is the isobaric specific heat and lambdaT is the thermal conductivity.] The model correctly predicts (+/-1.0%) the quality factors Q of resonances measured in a stainless steel resonator (epsilon(ss) =6400 kg K(-1) s(-5/2)); it also predicts the observed increase of the Q, by up to a factor of 8, when the resonator is coated with a polymer (epsilon(pr) =370 kg K(-1) s(-5/2)). The test data span the frequency range 0.1

The Kelvin and Temperature Measurements.

The International Temperature Scale of 1990 (ITS-90) is defined from 0.65 K upwards to the highest temperature measurable by spectral radiation thermometry, the radiation thermometry being based on the Planck radiation law. When it was developed, the ITS-90 represented thermodynamic temperatures as closely as possible. Part I of this paper describes the realization of contact thermometry up to 1234.93 K, the temperature range in which the ITS-90 is defined in terms of calibration of thermometers at 15 fixed points and vapor pressure/temperature relations which are phase equilibrium states of pure substances. The realization is accomplished by using fixed-point devices, containing samples of the highest available purity, and suitable temperature-controlled environments. All components are constructed to achieve the defining equilibrium states of the samples for the calibration of thermometers. The high quality of the temperature realization and measurements is well documented. Various research efforts are described, including research to improve the uncertainty in thermodynamic temperatures by measuring the velocity of sound in gas up to 800 K, research in applying noise thermometry techniques, and research on thermocouples. Thermometer calibration services and high-purity samples and devices suitable for "on-site" thermometer calibration that are available to the thermometry community are described. Part II of the paper describes the realization of temperature above 1234.93 K for which the ITS-90 is defined in terms of the calibration of spectroradiometers using reference blackbody sources that are at the temperature of the equilibrium liquid-solid phase transition of pure silver, gold, or copper. The realization of temperature from absolute spectral or total radiometry over the temperature range from about 60 K to 3000 K is also described. The dissemination of the temperature scale using radiation thermometry from NIST to the customer is achieved by calibration of blackbody sources, tungsten-strip lamps, and pyrometers. As an example of the research efforts in absolute radiometry, which impacts the NIST spectral irradiance and radiance scales, results with filter radiometers and a high-temperature blackbody are summarized.

Ab Initio Values of the Thermophysical Properties of Helium as Standards.

Recent quantum mechanical calculations of the interaction energy of pairs of helium atoms are accurate and some include reliable estimates of their uncertainty. We combined these ab initio results with earlier published results to obtain a helium-helium interatomic potential that includes relativistic retardation effects over all ranges of interaction. From this potential, we calculated the thermophysical properties of helium, i.e., the second virial coefficients, the dilute-gas viscosities, and the dilute-gas thermal conductivities of (3)He, (4)He, and their equimolar mixture from 1 K to 10(4) K. We also calculated the diffusion and thermal diffusion coefficients of mixtures of (3)He and (4)He. For the pure fluids, the uncertainties of the calculated values are dominated by the uncertainties of the potential; for the mixtures, the uncertainties of the transport properties also include contributions from approximations in the transport theory. In all cases, the uncertainties are smaller than the corresponding experimental uncertainties; therefore, we recommend the ab initio results be used as standards for calibrating instruments relying on these thermophysical properties. We present the calculated thermophysical properties in easy-to-use tabular form.

Electrostriction of a near-critical fluid in microgravity.

We used interferometry to measure the electric-field-induced (i.e., electrostrictive) increase of the density of sulfur hexafluoride (SF6) near its critical point. The results at three temperatures (T(c)+5.0 mK, T(c)+10.0 mK, T(c)+30.0 mK with T(c)=319 K) agree with a calculation based on the Clausius-Mossotti relation and the restricted cubic model equation of state. To measure electrostriction, an inhomogeneous electric field (< or =26 kV/cm) was applied to the SF6 sample by charging a fine wire that passed through it. These measurements were performed in microgravity so that the small electrostrictive density changes (< or =3.5% in this paper) would not be complicated by stratification of the fluid's density induced by the Earth's gravity. The predicted shifts of the critical temperature and density resulting from the electric field were too small to detect.

Frequency-dependent viscosity of xenon near the critical point.

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity eta of xenon near its critical density rho(c) and temperature Tc. In microgravity, useful data were obtained within 0.1 mK of Tc, corresponding to a reduced temperature t=(T-Tc)/Tc=3 x 10(-7). Because they avoid the detrimental effects of gravity at temperatures two decades closer to T(c) than the best ground measurements, the data directly reveal the expected power-law behavior eta proportional, variant t(-nuz(eta)). Here nu is the correlation length exponent, and our result for the viscosity exponent is z(eta)=0.0690+/-0.0006. (All uncertainties are one standard uncertainty.) Our value for z(eta) depends only weakly on the form of the viscosity crossover function, and it agrees with the value 0.067+/-0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)]. The measurements spanned the frequency range 2 Hz< or = f < or =12 Hz and revealed viscoelasticity when t < or = 10(-5), further from Tc than predicted. The viscoelasticity's frequency dependence scales as Aftau, where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0+/-0.3 times the result of a one-loop perturbation calculation. Near Tc, the xenon's calculated time constant for thermal diffusion exceeded days. Nevertheless, the viscosity results were independent of the xenon's temperature history, indicating that the density was kept near rho(c) by judicious choices of the temperature versus time program. Deliberately bad choices led to large density inhomogeneities. At t>10(-5), the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.

An interface phase transition: complete to partial wetting.

When two fluid phases are near a critical point, one of them will be excluded from contact with any third phase that happens to be present by a wetting film of the other critical phase. A simple and quite general strategy that may be used to induce a phase transition from complete wetting of the third phase to incomplete wetting is to add a new component to the fluid phases chosen to drive the two phases away from their critical point. This strategy is illustrated for methanol-cyclohexane mixtures.

Implementation of Scaling and Extended Scaling Equations of State for the Critical Point of Fluids.

An explicit, practical procedure is suggested for transforming from the laboratory variables density (ρ) and temperature (T) into the parametric variables r and θ, which occur in various scaled representations of equations of state and of transport properties of fluids near critical points. A reasonably efficient and versatile computer program illustrating this procedure is provided. With this program, the parametric equations of state which occur in several formulations of simple, extended, and/or revised scaling are as easy to use as any other equation of state for which T and ρ are the independent variables.