Estimating particle concentration using passive ultrasonic measurement of impact vibrations

A method of obtaining particle size and concentration information, from ultrasonic transducer measurements of particle-wall interactions in a particle laden fluid, is presented. A mathematical model of the flexural vibrations of the vessel wall due to the particle impact is constructed. The key component of this model is the derivation of an analytic expression for the impact force amplitude. An analytic expression for the power spectrum is then obtained that shows its explicit dependency on the system parameters. This spectrum is then integrated over a specific frequency range and a comparison with experimental results is reported.