Asymmetric viscothermal acoustic propagation and implication on flow measurement

TL;DR

This paper develops a mathematical model for asymmetric viscothermal acoustic propagation in high-frequency flow measurement, revealing how viscothermal effects influence acoustic modes and measurement accuracy.

Contribution

It introduces a novel iterative method to analyze asymmetric acoustic modes considering viscothermal dissipation and shear flow effects.

Findings

Viscothermal dissipation affects the cut-on frequency of acoustic modes.

Shear convection nonlinearly couples with viscothermal effects at high Mach numbers.

Inherent measurement derivations can help compensate for flow measurement errors.

Abstract

In the application of high frequency acoustic flow measurement, viscothermal dissipation and asymmetric acoustic modes cannot be overlooked. Present paper mathematically formulates asymmetric linear disturbance dynamics in terms of velocity and temperature disturbances based on the conservations of mass, momentum and energy. An iterative calculation procedure, which is similar to Galerkin method, is presented. Numerical analysis of asymmetric acoustic features (phase velocity and attenuation coefficient) are comprehensively given under the effects of viscothermal dissipation and shear flow convection. In the end, flow measurement performance of asymmetric acoustic modes is literally discussed. Numerical study shows that viscothermal dissipation affects the cut-on frequency of acoustic modes and couples nonlinearly with shear convection when the flow Mach number is large. These parameters impose significant influences on measurement performance. Each acoustic mode has inherent measurement derivation which can be theoretically used to compensate the acoustic flow measurement error. Apparent prediction error may occur if the viscothermal dissipation is taken out of consideration