The pulsed ultrasonic Doppler velocimeter has been used extensively in transcutaneous measurement of the velocity of blood in the human body. It would be useful to evaluate turbulent flow with this device in both medical and non-medical applications. However, the complex behaviour and limitations of the pulsed Doppler velocimeter when applied to random flow have not yet been fully investigated.

In this study a three-dimensional stochastic model of the pulsed ultrasonic Doppler velocimeter for the case of a highly focused and damped transducer and isotropic turbulence is presented. The analysis predicts the correlation and spectral functions of the Doppler signal and the detected velocity signal. The analysis addresses specifically the considerations and limitations of measuring turbulent intensities and one-dimensional velocity spectra.

Results show that the turbulent intensity can be deduced from the broadening of the spectrum of the Doppler signal and a mathematical description of the effective sample-volume directivity.

In the measurement of one-dimensional velocity spectra at least two major complicacations are identified and quantified. First, the presence of a time-varying, broad-band random process (the Doppler ambiguity process) obscures the spectrum of the random velocity. This phenomenon is similar to that occurring in laser anemometry, but the ratio of the level of the ambiguity spectrum to the largest detected velocity spectral component can be typically two to three orders of magnitude greater for ultrasonic technique owing to the much greater wavelength.

Secondly, the spatial averaging of the velocity field in the sample volume causes attenuation in the measured velocity spectrum. For the ultrasonic velocimeter, this effect is very significant.

The influence of the Doppler ambiguity process can be reduced by the use of two sample volumes on the same acoustic beam. The signals from the two sample volumes are cross-correlated, removing the Doppler ambiguity process, while retaining the random velocity. The effects of this technique on the detected velocity spectrum are quantified explicitly in the analysis for the case of a three-dimensional Gaussianshaped sample-volume directivity.

An extensive experimental programme in both laminar and turbulent flow was undertaken to examine the validity of all of the major implications of the model of the pulsed ultrasonic Doppler velocimeter for turbulent flow developed in part 1 of this investigation. The turbulence measurements were made in fully developed flow at the centre of a 6·28 cm diameter pipe. The Reynolds number of the flow ranged from 6000 to 40000. The carrier frequency of the ultrasonic velocimeter was 4·7 MHz.

Measurements of the turbulence intensity and of the one-dimensional velocity spectra made with the ultrasonic velocimeter are compared with the analysis and with the actual quantities as measured by a hot-film anemometer. The experimental results are in agreement with theoretical predictions.

Measurements of one-dimensional turbulence spectra with reduced ambiguity spectra made by the two sample volume methods described in part 1 are presented. The results verify the analysis and indicate that an improvement in the useful dynamic range of the velocity power spectrum of nearly three orders of magnitude can realistically be achieved.