# A semi-analytical approach to characterize high-frequency three-dimensional wave propagation through clamp-on flowmeters

## TL;DR

This paper introduces a semi-analytical method combining FEA, ray tracing, and analytical modeling to efficiently analyze high-frequency 3D wave propagation in clamp-on ultrasonic flowmeters, overcoming computational challenges.

## Contribution

It develops a hybrid approach that separates the system into domains, analyzes them individually, and scales the results to accurately model 3D wave behavior in clamp-on flowmeters.

## Key findings

- Accurate 3D wave propagation modeling achieved with reduced computational cost.
- Enhanced clarity of fluid signals in the receiver output.
- Method applicable at multiple high frequencies (up to 1 MHz).

## Abstract

Wave propagation analysis at high frequencies is essential for applications involving ultrasound waves, such as clamp-on ultrasonic flowmeters. However, it is extremely challenging to perform a 3D transient analysis of a clamp-on flowmeter using standard tools such as finite element analysis (FEA) due to the enormous associated computational cost. In this study, we separate the clamp-on flowmeter into different domains and analyze them separately. Wave propagation in the fluid domain is analyzed via FEA at low frequencies (100 kHz, 200 kHz, and 500 kHz) and using ray tracing at high frequencies (1 MHz). The behavior in the solid domain (wedges and pipe wall) is analytically characterized via geometric projection. All these individual analyses provide us with different scaling factors with which the waves in the respective domains scale when 3D effects are considered. The complete clamp-on system is then analyzed in 2D via the Discontinuous Galerkin (DG) method to obtain the response at the receiver. The receiving signal is then scaled using the aforementioned scaling factors to accurately capture the wave propagation behavior of the clamp-on system in 3D. The output signal from the 2D analysis then becomes much clearer so that the fluid signal can be identified straightforwardly, which would be nearly impossible otherwise.

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Source: https://tomesphere.com/paper/2509.00020