An Improved Greenspan Acoustic Viscometer

An improved Greenspan acoustic viscometer (double Helmholtz resonator) was used to measure the viscosity of gases at temperatures from 250 to 400 K and at pressures up to 3.4 MPa. The improvements include a vibration damping suspension and the relocation of the fill duct. The fill duct, which is needed to supply gas to the resonator, was connected to the center of the resonator to eliminate acoustic coupling between the resonator and the manifold. In anticipation of handling corrosive gases, all surfaces of the apparatus that are exposed to the test gas are made of metal. The viscometer was tested with argon, helium, xenon, nitrogen, and methane. Isothermal measurements were carried out at 298.15 and 348.15 K and at pressures up to 3.2 MPa. Without calibration, the results differed from published viscosity data by –0.8% to +0.3% (0.47% r.m.s.). These results are significantly better than previous results from Greenspan viscometers. The measurements also yielded the speed of sound, which differed from literature data by +0.16% to +0.20% (0.18% r.m.s.). Adding empirical effective-area and effective-volume corrections to the data analysis decreased the r.m.s. deviations to 0.12% for the viscosity and to 0.006% for the speed of sound. No unusual phenomena were encountered when the viscometer was tested with a helium-xenon mixture between 250 and 375 K.     

A Capillary Tube Viscometer Designed for Measurements of Hydrogen Gas Viscosity at High Pressure and High Temperature

A capillary tube viscometer was developed to measure the dynamic viscosity of gases for high pressure and high temperature. The apparatus is simple and designed for safe-handling operation. The gas was supplied to the capillary tube from a high-pressure reservoir tank through a pressure regulator unit to maintain a steady state flow. The measurements of a pressure drop across the capillary tube with high accuracy under extreme conditions are the main challenge for this method. A differential pressure sensor for high pressures up to 100 MPa is not available commercially. Therefore, a pair of accurate absolute pressure transducers was used as a differential pressure sensor. Then the pressure drop was calculated by subtracting the outlet pressure from the inlet one with a resolution of 100 Pa at 100 MPa. The accuracy of the present measurement system is confirmed by measuring the viscosity of nitrogen as a reference gas. The apparatus provided viscosities of nitrogen from ambient temperature to 500 K and hydrogen from ambient temperature to 400 K and for pressures up to 100 MPa with a maximum deviation of 2.2 % compared with a correlation developed by the present authors and with REFPROP (NIST).     

近临界区二氧化碳声速的精密测量研究

基于圆柱声学共鸣法原理,开展了303.10～303.18 K,压力从3.855 MPa至7.534 MPa的近临界区CO2测量研究。二氧化碳声速测量的相对标准不确定度结果为:当压力低于7.1 MPa时为0.035%,当压力高于7.3 MPa时为0.15%。与CO2国际标准状态方程计算得到的声速相对偏差分布在0.005%～-0.4%范围。所获得的测量结果可为CO2国际标准状态方程的改进提供重要数据来源,建立的实验系统和方法可用于更宽广温区CO2及其他工质的声速精密测量研究。     

实用氦气声学温度计初步研究

对高温气冷堆堆芯温度的可靠测量是目前的技术难题之一。传统温度计依靠实验室标定的材料特性与温度的关系进行测温,然而,长期暴露在高温、高辐照环境中,其测温材料的性质会发生改变且得不到及时校准,温度传感器易发生漂移甚至失效。气体声学温度计通过测量单原子气体的声速可以直接获得热力学温度;由于气冷堆内氦气介质相对稳定,利用氦气声速获得温度具有较高的可靠性。针对实用氦气声学温度计开展了初步研究,基于圆柱声学共鸣法设计了实用声学温度计测试系统,采用声波导管声学传感器测量了488K至806K圆柱共鸣腔内氦气的声学共振频率,修正了热边界层和粘性边界层的影响;基于量子力学从头算得到的氦气声学维里状态方程,获得了热力学温度。对氦气共振频率的测量相对标准偏差小于0.07%,温度测量的信噪比可满足需求,声学温度计与热电偶测温结果差异小于1%。研究结果为未来持续开展极端环境下气体声学温度计的应用研究提供了支持。     

Viscosity and Speed of Sound of Gaseous Nitrous Oxide and Nitrogen Trifluoride Measured with a Greenspan Viscometer

The viscosity and speed of sound of gaseous nitrous oxide and nitrogen trifluoride were measured using a Greenspan acoustic viscometer. The data span the temperature range 225–375 K and extend up to 3.4 MPa. The average relative uncertainty of the viscosity is 0.68% for N₂O and 1.02% for NF₃. The largest relative uncertainties were 3.09 and 1.08%, respectively. These occurred at the highest densities (1702 mol · m^-3 for N₂O and 2770 mol · m^-3 for NF₃). The major contributor to these uncertainties was the uncertainty of the thermal conductivity. The speeds of sound measured up to 3.4 MPa are fitted by a virial equation of state that predicts gas densities within the uncertainties of the equations of states available in the literature. Accurate measurements of the speed of sound in both N₂O and NF₃ have been previously reported up to 1.5 MPa. The current measurements agree with these values with maximum relative standard deviations of 0.025% for N₂O and 0.04% for NF₃.     

气体声学温度计中声波导管的优化设计研究

声波导管的设计是影响声学信号信噪比的关键因素,导管内径越大、长度越短,越利于声波传输,但同时对声学共鸣腔产生更大的扰动。提出了采用变径声波导管降低声波的能量损耗和扰动方法,建立了变径声波导管的衰减和扰动模型,对比分析声学信号在不同尺寸声波导管内的能量衰减和导管对圆柱轴向非缔合声学共振频率和半宽的扰动,获得了优化的导管尺寸,在声波传输能量损失较小的情况下对内长为80 mm圆柱腔体首个轴向非缔合声学共振频率产生的相对扰动在3×10^-5以内,该声波导管的优化设计可为高温气体声学温度计的深入研究提供理论支持。     

Progress Towards an Acoustic Measurement of the Molar Gas Constant at INRIM

Progress in developing an experiment for the determination of the molar gas constant R and the Boltzmann constant k at INRIM is reported. The experiment involves simultaneous measurements of the acoustic and microwave resonance frequencies of a stainless steel spherical resonator for which its hemispheres were deliberately misaligned. For the present work, these frequencies were measured in helium near 273.16 K, in the pressure range from 100 to 800 kPa. From microwave data, the radius of the resonator was determined as a function of pressure with an estimated uncertainty of 6.0 ppm. Using acoustic data and the microwave determination of the resonator radius, the speed of sound in helium was deduced, and these values were compared with those predicted by recent accurate ab initio calculations. Over most of the pressure range, the present values agreed with the ab initio values within the uncertainty of the measurements (standard uncertainty of approximately 7.0 ppm). Many suggestions for reducing the uncertainty are provided.     

Progress Report on NMIJ Acoustic Gas Thermometry at the Triple Point of Water

Herein, progress in the development of an acoustic gas thermometry (AGT) system at the National Metrology Institute of Japan is reported. This AGT system is an initial low-cost version that uses a 1-l quasi-spherical resonator (QSR) made of oxygen-free copper. The system was tested by measuring the speed of sound in argon at the temperature of triple point of water. Measurements were conducted at ten different pressures, ranging from 60 kPa to 420 kPa. The ideal gas limit of the squared speed of sound was obtained through extrapolation, and a preliminary calculation of the Boltzmann constant, which was 12 ppm below the CODATA2014 value, was made. Large inconsistencies among microwave and acoustic modes were observed, which are dominant sources of uncertainty in speed of sound measurements. The system will be improved by replacing the present QSR with another one that is more precisely fabricated.     

Progress Towards an Acoustic/Microwave Determination of the Boltzmann Constant at LNE-INM/CNAM

The Boltzmann constant k will be re-determined by using the simple, exact connection between the speed of sound in noble gases (extrapolated to zero pressure) and the thermodynamic temperature T, the molar mass of the gas M, and the universal gas constant R. The speed of sound will be determined in a spherical cavity of known volume V by measuring the acoustic resonance frequencies. This acoustic method led to the CODATA-recommended value of k; however, the CODATA value of k came from measurements using an almost perfectly spherical, stainless-steel-walled cavity filled with stagnant argon. The steel cavity’s volume was determined by weighing the mercury of well-known density required to fill it. In contrast, a copper-walled, quasi-spherical cavity (intentionally slightly deformed from a sphere), filled with helium gas that is continuously refreshed by a small helium flow that will mitigate the effects of outgassing, will be used. The volume of the copper cavity will be determined by measuring the microwave resonance frequencies and/or by three-dimensional coordinate measurements. If the microwave method is satisfactory, the measurement of k will be based on the ratio of the speed of sound in helium—obtained by acoustic resonance measurements—to the speed of light, obtained by microwave resonance measurements. This method exploits the theorem that the frequency ratios are independent of the details of the shape of the quasi-spherical cavity. Here, progress at LNE-INM/CNAM towards a better mechanical design and better understanding of the excess of the half-widths of the acoustic and microwave measurements are reported.     

Virial equation of state and ideal-gas heat capacities of pentafluoro-dimethyl ether

A virial equation of state is presented for vapor-phase pentafluoro-dimethyl ether (CF₃−O−CF₂H), a candidate alternative refrigerant known as E125. The equation of state was determined from density measurements performed with a Burnett apparatus and from speed-of-sound measurements performed with an acoustical resonator. The speed-of-sound measurements spanned the ranges 260≤T≤400 K and 0.05≤P≤1.0 MPa. The Burnett measurements covered the ranges 283≤T≤373 K and 0.25≤P≤5.0 MPa. The speed-of-sound and Burnett measurements were first analyzed separately to produce two independent virial equations of state. The equation of state from the acoustical measurements reproduced the experimental sound speeds with a fractional RMS deviation of 0.0013%. The equation of state from the Burnett measurements reproduced the experimental pressures with a fractional RMS deviation of 0.012%. Finally, an equation of state was fit to both the speed-of-sound and the Burnett measurements simultaneously. The resulting equation of state reproduced the measured sound speeds with a fractional RMS deviation of 0.0018% and the measured Burnett densities with a fractional RMS deviation of 0.019%.     

大型压力输水管道泄漏监测方法的试验研究

为研究一种针对大型压力输水管道泄漏问题的在线监测方法,设计了4种不同压力工况(0.2 MPa、0.4 MPa、0.6 MPa、0.8 MPa)和4种不同泄漏孔直径工况(2 mm、4 mm、8 mm、14 mm)的管道模型试验。试验通过控制阀门开闭、阀门孔径大小和输水管压力变化来模拟实际运行管道的泄漏状态,并用水声检波器采集泄漏状态和非泄漏状态下的管道噪声数据来比较信号差异。经过分析,推导出了泄漏孔面积、管道压力与管道噪声信号振幅三者的关系。试验结果表明,通过利用水声检波器监测管道噪声变化进而监测管道泄漏是可行的,且泄漏信号主要由偶极子声源组成,泄漏状态下振幅随泄漏孔面积和管道运行压力均呈幂函数的关系增长。     

Thermodynamic Properties of Gases from Speed-of-Sound Measurements

A procedure for deriving thermodynamic properties of gases from speed of sound is presented. It is based on numerical integration of ordinary differential equations (ODEs) (rather than partial differential equations—PDEs) connecting speed of sound with other thermodynamic properties in the T-p domain. The procedure enables more powerful methods of higher-order approximation to ODEs to be used (e.g., Runge-Kutta) and requires only Dirichlet initial conditions. It was tested on gaseous argon in the temperature range from 250 to 450 K and in the pressure range from 0.2 to 12 MPa, and also on gaseous methane in the temperature range from 275 to 375 K and in the pressure range from 0.4 to 10 MPa. The density and isobaric heat capacity of argon were derived with absolute average deviations of 0.007% and 0.03%, respectively. The density and isobaric heat capacity of methane were derived with absolute average deviations of 0.006% and 0.09%, respectively.     

Thermophysical Properties of Gaseous CF4 and C2F6 from Speed-of-Sound Measurements

A cylindrical resonator was employed to measure the sound speeds in gaseous CF₄ and C₂F₆. The CF₄ measurements span the temperature range 300 to 475 K, while the C₂F₆ measurements range from 210 to 475 K. For both gases, the pressure range was 0.1 MPa to the lesser of 1.5 MPa or 80% of the sample’s vapor pressure. Typically, the speeds of sound have a relative uncertainty of less than 0.01 % and the ideal-gas heat capacities derived from them have a relative uncertainty of less than 0.1%. The heat capacities agree with those determined from spectroscopic data. The sound speeds were fitted with the virial equation of state to obtain the temperature-dependent density virial coefficients. Two models for the virial coefficients were employed, one based on square-well potentials and the second based on a Kihara spherical-core potential. The resulting virial equations reproduce the sound-speed measurements to within 0.005 % and yield densities with relative uncertainties of 0.1% or less. The viscosity calculated from the Kihara potential is 2 to 11% less than the measured viscosity.     

Speed of sound in liquid R134a

The speed of sound for liquid R134a (1,1,1,2-tetrafluoroethane) has been measured along isotherms at temperatures from close to the triplee point to above the critical temperature (180–380 K) at pressures from near saturation to 70 MPa. The measurements were made by using a pulse-echo-overlap technique at 3 MHz. A rational approximant fits the data with a standard deviation of 0.45 m s⁻¹. Because the speed of sound depends on the molar volume and the adiabatic compressibility, these data may be used with density and heat capacity data to construct accurate thermodynamic property tables.     

Sound-velocity measurements for HFC-134a and HFC-152a with a spherical resonator

A spherical acoustic resonator was developed for measuring sound velocities in the gaseous phase and ideal-gas specific heats for new refrigerants. The radius of the spherical resonator, being about 5 cm, was determined by measuring sound velocities in gaseous argon at temperatures from 273 to 348 K and pressures up to 240 kPa. The measurements of 23 sound velocities in gaseous HFC-134a (1,1,1,2-tetrafluoroethane) at temperatures of 273 and 298 K and pressures from 10 to 250 kPa agree well with the measurements of Goodwin and Moldover. In addition, 92 sound velocities in gaseous HFC-152a (1,1-difluoroethane) with an accuracy of ±0.01% were measured at temperatures from 273 to 348 K and pressures up to 250 kPa. The ideal-gas specific heats as well as the second acoustic virial coefficients have been obtained for both these important alternative refrigerants. The second virial coefficients for HFC-152a derived from the present sound velocity measurements agree extremely well with the reported second virial coefficient values obtained with a Burnett apparatus.Paper dedicated to Professor Joseph Kestin.     

Speed-of-sound measurements in liquid and gaseous air

The speed of sound in air has been measured along isotherms for a standard air mixture (0.7811 N₂+0.2097 O₂+0.0092 Ar) in the gas and liquid phases at pressures to 14 MPa. A cylindrical resonator was used in the vapor and supercritical gas phases, and a time-of-flight system was used for measurements of the liquid phase. Data were obtained for the liquid phase at 90, 100, 110, 120, and 130 K. Data were taken at 110, 120, 130, 135, 140, 150, 200, and 300 K in the vapor and supercritical gas phases. These experimental results were compared to a predictive computer model, namely, AIRPROPS.     

Sound velocity and ideal-gas specific heat of gaseous 1,1,1,2-tetrafluoroethane (R134a)

A cylindrical, variable-path acoustic interferometer operating at 156.252kHz is developed for determining ideal-gas specific heats. Results of validation measurements with argon are very satisfactory, with the maximum deviation of the speed of sound equal to 3×10^–4. The sound velocity of gaseous R134a has been measured at low temperatures and low pressures. The specific heat was then calculated from the results. The experimental results corrected for various dispersions for the sound velocity of gaseous R134a match well with an earlier publication, with a room mean square deviation of 2.56×10^–4. A new relation for the ideal-gas specific heat as a function of temperature for R134a is obtained.