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Unsteady two-dimensional analytical model for a thermal time-of-flight flow sensor

机译:热飞行时间流量传感器的非稳态二维分析模型

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摘要

A thermal time-of-flight sensor consists of a resistive element that periodically delivers heat to a flow and two downstream thermocouples that detect the temperature change due to this heat addition. This study presents an analytical solution to the two-dimensional advection diffusion equation in cylindrical coordinates for an axially semi-infinite domain subjected to a time-dependent Neumann boundary condition. The results describe the propagation of heat in the thermal time-of-flight sensor. The finite Hankel transformation and the generalized integral technique are used to solve the governing equation. The analytical temperature profile shows dependence on the Peclet number and on the tube diameter. The derived temperature distribution is compared with measured data from an experimental setup using R134a as the working fluid. The model demonstrates good agreement with the experimental data, with an average relative error of 9%. (C) 2019 Elsevier Ltd. All rights reserved.
机译:热飞行时间传感器由一个电阻元件和两个下游热电偶组成,该电阻元件周期性地将热量传递到流中,两个下游热电偶检测由于这种热量增加而引起的温度变化。这项研究提出了一个二维半对流扩散方程在圆柱坐标系中的轴向半无限域受时间依赖的诺伊曼边界条件的解析解。结果描述了热量在热飞行时间传感器中的传播。用有限的汉克尔变换和广义积分技术求解控制方程。分析温度曲线显示了对Peclet数和管直径的依赖性。将导出的温度分布与使用R134a作为工作流体的实验设置的测量数据进行比较。该模型证明与实验数据吻合良好,平均相对误差<9%。 (C)2019 Elsevier Ltd.保留所有权利。

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