Numerical modeling and experimental verification for anisotropic heat conduction process in velocity probe of the thermal mass flowmeter

Traditional models ignore the temperature gradients caused by anisotropic heat conduction process in the axial and radial directions of the velocity probe of a thermal mass flowmeter (TMF), essentially assuming constant wall temperature. Recently, a novel TMF with a large length-diameter ratio of the velocity probe and more evident temperature gradient was proposed; although this novel TMF is insensitive to the radial velocity profile, it leads to significant calculation errors. To reduce the error of this TMF, this study proposes a numerical model of pipeline flow heat transfer that considers the axial and radial heat conduction of the velocity probe. The velocity probe axial heat conduction numerical model is proposed, and the results of apparent thermal conductivity are verified using empirical formulas. A feedback adjustment convergence program is performed to maintain the average temperature of the velocity probe at 10 K above the temperature of the observed fluid. The simulation results showed that a temperature gradient forms in both the axial and radial directions of the velocity probe of the improved model. Moreover, the higher the flow velocity and the farther it is from its central axis, the lower the temperature. Experimental results revealed that, at a velocity rang of 1.0-7.0 m/s, the average relative error between the improved simulated results and current experimental data is 2.92 % and the maximum relative error is 10.91 %, whereas the average relative error between the traditional simulated results and original experimental data is 7.44 % and the maximum relative error is 19.45 %. Thus, the improved model better simulates the real process.

Automated summary

This study proposes a numerical model that considers both axial and radial heat conduction for a thermal mass flowmeter (TMF) to address the limitations of traditional models. By using a feedback adjustment convergence program, the improved model reduces the calculation errors compared to experimental data.