圆柱声学共鸣腔边界层扰动的二阶修正模型
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摘要
圆柱声学共鸣法是测量Boltzmann常数和研究声学温度计的重要方法.热边界层和黏性边界层是影响圆柱声学共振频率的最主要因素。目前已有的声学一阶微扰理论已不能满足圆柱声学共鸣法精确测量Boltzmann常数的需求(不确定度小于1×10~(-6)).本文建立了基于声学二阶微扰理论的边界层扰动修正模型,计算结果表明,与一阶修正相比,二阶修正不影响圆柱声学腔的共振频率,但对频率半宽产生不可忽略的影响,且随着圆柱腔内的声学共振模式而变化,压力越低影响越大.对于长度80 mm、半径40 mm的圆柱腔,在273.16 K、50 kPa,二阶修正对Ar的(2,0,0)频率半宽的影响接近7×10~(-6).采用二阶修正模型,更符合真实物理规律,满足精确测量的需求.
The acoustic cylindrical resonator method is one of the most importmant methods to determine the Boltzmaim constant and acoustic thermometry.Thermal and viscous boundary layer cause the larg'cst perturbation to the resonance frequccics.The corrections for the boundary layers based on the first-order theory are not sufficient for the Boltzmaim constant determination towards1×10~(-6) The second-order correction for cylindrical resonator is presented here.The calculation shows that the second-order correction doesn't have effects on the resonance frequencies,but have effects on the half-widths.At each temperature,the perturbation to the half-widths varies with the acoustic modes and increases with pressure p~(-1).For a cylindrical resonator with length of 80 mm and radius of 40 mm,at temperature of 273.16 K and pressure of 50 kPa in argon,the second-order correction to the half-width can be high up to 7×l0~(-6).The second-order correction leads to a better understanding of the energy loss in a cylindrical resonator.
The acoustic cylindrical resonator method is one of the most importmant methods to determine the Boltzmaim constant and acoustic thermometry.Thermal and viscous boundary layer cause the larg'cst perturbation to the resonance frequccics.The corrections for the boundary layers based on the first-order theory are not sufficient for the Boltzmaim constant determination towards1×10~(-6) The second-order correction for cylindrical resonator is presented here.The calculation shows that the second-order correction doesn't have effects on the resonance frequencies,but have effects on the half-widths.At each temperature,the perturbation to the half-widths varies with the acoustic modes and increases with pressure p~(-1).For a cylindrical resonator with length of 80 mm and radius of 40 mm,at temperature of 273.16 K and pressure of 50 kPa in argon,the second-order correction to the half-width can be high up to 7×l0~(-6).The second-order correction leads to a better understanding of the energy loss in a cylindrical resonator.
引文
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[10]Trusler J P M.Physical Acoustics and Metrology of Fluids[M].New York:Adam Hilger,1991
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[2]BIPM.Report of the 20th Meeting of CCU to the International Committee for Weights and Measures[R].2010
[3]Pitre L,Moldover M R and Tew W L.Acoustic Thermometry:New Results from 273 K to 77 K and Progress towards 4 K[J].Metrologia,2006,43:142-162
[4]Ripple D C,Strouse G F and Moldover M R.Acoustic Thermometry Results from 271 to 552 K[J].Int J Thermophys,2007,28:1789-1799
[5]Lin H,Gillis K A and Zhang J T.Characterization of Piezoelectric Ceramic Transducer for Accurate Speed of Sound Measurement[J].Int J Thcrmophys,2010,31:1234-1247
[6]Zhang J T,Lin H,Sun J P,et al.Cylindrical Acoustic Resonator for the Re-dctcrmination of the Boltzmann Constant[J].Int J Thcrmophys,2010,31(7):1273-1293
[7]Zhang J T,Lin H,Feng X J,et al.Progress toward Redetermining the Boltzmann Constant with a Fixed-PathLength Cylindrical Resonator[J].Int J Thcrmophys,2011,32:1297-1329
[8]安保林.刘强,段远源.边界层效应对定程干涉法声速测量的影响[J].工程热物理学报,2012,33(4):561-564AN Baolin,LIU Qiang,DUAN Yuanyuan.The Influence of Boundary Layer Effect on the Measurement of Speed of Sound Using Fixed Path Acoustic Resonator[J].J Eng Thcrmophys,2012,33(4):561-564
[9]林鸿,冯晓娟.张金涛等.声波导管对圆柱型共鸣腔声场扰动的研究[J].工程热物理学报.2012,33(8):1291-1294LIN Hong,FENG Xiaojuan,ZHANG Jintao,et al.Investigation on the Waveguide Perturbation to the Cylindrical Resonator[J].J Eng Thermophys,2012,33(8):1291-1294
[10]Trusler J P M.Physical Acoustics and Metrology of Fluids[M].New York:Adam Hilger,1991
[11]Morse P M and Ingard K U.Theoretical Acoustics[M].New Jersey:McGraw-Hill,1986