Spectral Analysis of the Signal from the Laser Doppler Flowmeter: Time-Independent Systems

Abstract

A method for prediction of the spectrum observed with the laser Doppler flowmeter (LDF) is developed. A detailed analysis of the spectrum observed with steady flows is presented. The effects of diffusive motion of the scattering centers, spatially varying velocities, finite transit time of the centers through the sample volume, and uncertainty in scattering vector are computed. The latter two effects are shown to be identical. A computation of the sample volume size and shape is made using the optical parameters of the system. The calculated linewidths and shapes are in good agreement with data taken on two independent LDF systems. The general formalism is also applicable to measurements made on turbulent fluids and diffusely reflecting solid objects. The special case of a static fluid (zero velocity) is considered in detail and the low angle correction to the conventional expressions used in laser ``beat-frequency'' spectroscopy is developed.

The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy

“…By measuring the spectrum of the scattered light mixed with the incident light (heterodyne mode) it is possible to determine the mean velocity of the scattering centres in the scattering volume (Edwards et al 1971). The effect of velocity gradients and of random motionEI due to diffusion is to broaden the heterodyne spectrum, but these are second-order effects compared to the Doppler shift of the frequency which is cauf'ed by the mean motion of the particles in suspension.…”

Dynamic light scattering during shear: measurements of diffusion coefficients

“…Very little work has concerned the application of this technique in the presence of a flow [4][5][6]. Edwards et al [4] and Pike [5] showed that the mean velocity of the scattering centers can be accessed from the heterodyne mode of the scattering light whereas Fuller et al [6] showed that the homodyne mode leads to the determination of velocity gradients. A potential application is the determination of the transverse diffusion coefficient of polymer chains during flow.…”

Turbulent transport measurements with a laser Doppler velocimeter

“…Detailed calculations of the spectrum for laminar pipe flow have been presented in a previous paper [1]. A typical spectrum is shown in figure 3.…”

“…The instantaneous A.C. heterodyne current from the photodetector for a Laser Doppler Velocimeter may be written [1], assuming a constant ref-…”

“…The signal at the detector can be written Case Western Reserve University, Chemical Engineering Division, Cleveland, Ohio, 44106. f(t) = A cos [co Q t + 0(t)J (1) where A is an amplitude, o> is the laser frequency, and <£(t) is the resultant phase. 0(t) is the phase that results from properly adding the phase received from each of the particles.…”