The Structure of the Doppler-difference Signal and the Analysis of its Autocorrelation Function

Abstract

The Doppler-difference optical arrangement is nowadays the one most commonly used for fluid flow investigations with a laser anemometer. In this review, the essential characteristics of the Doppler-difference signal and of the associated autocorrelation function, obtained in general by integrating over many successive particle transits, are considered for both laminar and turbulent flows. Experimental conditions under which it is known that the autocorrelation function can be analysed to yield reliable estimates of mean velocity and turbulence intensity are specified; the stated restrictions are sufficient but may not all be necessary. In particular, it is shown that the effect on the autocorrelation function of the total velocity-component in the plane normal to the included bisector of the beam-axes is usually inseparable from the contribution due to the component u normal to the fringe system.The various data-reduction methods which have been proposed are classified and briefly reviewed. For laminar flows data-processing is relatively straightforward, but we are led to the conclusion that unknown flows having relatively high levels of turbulence (greater than about 15%) can only be treated successfully if there are very many fringes within a beam diameter, or if frequency-shifting techniques are used to achieve an equivalent effect. Under these circumstances, the relationship between the autocorrelation function and the distribution of the u-component of velocity reduces immediately to that of a simple Fourier cosine transform. When the measuring volume contains only a small number of fringes, certain approximations must always be made if interpretation of the data is to be possible in the general case, and it is shown that the Fourier transform relationship again arises in a natural way. However, the estimation of turbulence intensity in low-turbulence flows presents special difficulties, since truncation of the data at a finite number of channels causes broadening of the distribution in the transform plane. In these cases, it is often possible to assume that the velocity-distribution is approximately Gaussian in form, and curve-fitting methods can be used. An alternative procedure which uses information already available in the transform plane is described. Finally, the analysis of the autocorrelation function arising from a single transit in the presence of background radiation is briefly considered.