多声道超声气体流量计的建模与仿真

Modeling and simulating of multi-path ultrasonic gas flowmeters

基于时差式超声流量计测量原理和Gauss-Legendre数值积分方法,建立了多声道超声气体流量计的数学模型.在建模过程中,根据瞬时流速以流速分布函数按面积积分的公式,推导出在弦向声道处的平均流速按声线积分的表达式,然后推导出在弦向声道处的平均流速加权求和的瞬时流速公式;应用Legendre多项式求解出高斯节点值和加权系数,即确定了各个声道的分布位置.以四声道交叉布置方式的超声气体流量计为例,通过Matlab仿真与误差分析,结果表明:在考虑流速分布的影响下,模型的测量误差不大于0.1%,验证了模型的正确性,因而多声道超声气体流量计完全能满足油气、天然气等气体在输送和分配计量中的精度要求.

The measurement principle of transit time ultrasonic flowmeters and the method of Gauss-Legendre numerical integration were noticed. A mathematical model for multi-path ultrasonic gas flowmeters is built. Using the instant flow velocity formula in which flow velocity profile function was integrated by sectional areas, an acoustic linear integration of the mean velocity in the position of the chord path was expressed. The instant flow velocity formula of the weighted sum of the mean velocity in the position of the chord path is deduced. The Gauss nodes and the power coefficients are solved by Legendre polynomials, and the position of the paths is determined. A four-criss-cross-path ultrasonic flowmeter was stimulated and analyzed with Matlab. The result showed that the relative error of the flowrate is less than 0.1 % and the accuracy of the model is certificated. It was known that multipath ultrasonic gas flowmeters would meet the need of metering precision of these gases, such as oil vapour and natural gas, etc. , when they are transported and distributed.