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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 cylindrical acoustic resonance method is an important method to measure the Boltzmann constant and to study the acoustic thermometer.The thermal boundary layer and the viscous boundary layer are the most important factors affecting the acoustic resonance frequency of the cylinder. At present, the first order perturbation theory of acoustics can not satisfy the requirement of accurate measurement of Boltzmann’s constant by cylindrical acoustic resonance method (the uncertainty is less than 1 × 10 -6) .Based on the second order perturbation theory of acoustics, The results show that the second-order correction does not affect the resonant frequency of the cylindrical cavity compared with the first-order correction, but it has a non-negligible effect on the half-width of the frequency. With the acoustic resonance mode in the cylindrical cavity The effect of the second order correction on the half width of Ar (2,0,0) frequency is close to 7 × 10 at 273.16 K and 50 kPa for a cylindrical cavity with a length of 80 mm and a radius of 40 mm ~ (-6). The second-order correction model is more in line with the real physical laws to meet the needs of accurate measurement.