Robert V. Edwards

Particle-sampling statistics in laser anemometers Sample-and-hold systems and saturable systems

The output statistics of a laser anemometer operating in a low particle density are discussed. A rigorous derivation is given for the influence of two popular data-handling algorithms on these statistics. In particular it is shown that the measured statistics can differ from those of the flow statistics and from the particle-arrival statistics. The variables that control the statistical regime are derived and quantitative estimates are given for their ranges of influence. The first system discussed is a sample-and-hold system where the output is a piecewise-continuous signal obtained by holding the last processor measurement until a new one is obtained. The second system is one where an attempt is made to store all the measurements for processing, but which contains a rate-limiting device. Because of this device, some measurements may be lost when the particle rate is high. This system is referred to as a saturable system. In both cases it is found that the statistics of the output depend on the product of the mean particle rate and the flow correlation time as well as the flow statistics. The statistics of the saturable system also depend on the ratio of the mean particle rate to the maximum rate at which measurements can be accepted by the system. Because of this, the statistics of both systems depend on the particle density. Attainable conditions are demonstrated, where the output velocity measurement statistics are essentially identical with the flow statistics.

Measurement of fluid velocity inside porous media with a laser anemometer

A successful measurement of fluid velocity inside porous media is presented. A laser anemometer was used to measure velocities in a packed bed of transparent spheres. The refractive index of the spheres was matched with that of the flowing fluid.

Surface fluctuation scattering using grating heterodyne spectroscopy

Heterodyne photon spectroscopy is used for the study of the viscoelastic properties of the liquid interface by studying light scattered from thermally generated surface fluctuations. A theory of a heterodyne apparatus based on a grating is presented, and the heterodyne condition is given in terms of the parameters of the experimental setup. Particular attention is paid to those conditions of the experiment that can cause systematic errors. An instrument function for the apparatus relating the measured output to the experimental parameters of interest is derived. It is shown that the instrument function is generally not Gaussian but that its functional form can depend strongly on the parameters of the experimental setup. In particular, it is shown that significant systematic deviations are expected from previous published analysis of the problem. This is primarily due to the nonlinear relation of the surface wave number to the frequency. An algorithm is suggested to arrive at the frequency and width parameters of the spectrum from a typical noisy experimental data set and applied to data obtained from ethanol surfaces.

Binary phase digital reflection holograms: fabrication and potential applications.

A novel technique for the fabrication of binary-phase computer-generated reflection holograms is described. By use of integrated circuit technology, the holographic pattern is etched into a silicon wafer and then aluminum coated to make a reflection hologram. Because these holograms reflect virtually all the incident radiation, they may find application in machining with high-power lasers. A number of possible modifications of the hologram fabrication procedure are discussed.

Surface fluctuation spectroscopy: Comments on experimental technique and capillary ripple theory

We comment on several aspects of the light scattering technology that have been developed in our laboratory. In particular we show that Shih’s [Rev. Sci. Instrum. 55, XXX (1984)] data is consistent once beam propagation is taken into account fully and a small error in the grating constants corrected. The result is that we can make a stronger statement concerning the correspondence between theory and experiment for both the center frequency and width of the spectrum of capillary wave fluctuations at the liquid/vapor interface. We discuss questions of optimal design of the optical system and detection system for these measurements. We collect a set of dimensionless groups that are useful for the design of experiments.

New space domain processing technique for pulsed laser velocimetry

Current pulsed laser velocimetry data processing techniques offer high precision (1%) velocity estimates, but can require several hours of processing time on specialized array processors. Under some circumstances, a simple, fast, less accurate (~5%), data reduction technique, which also gives unambiguous velocity vector information is acceptable. In this work, we examine a direct space domain processing technique. The direct space domain processing technique was found to be far superior to any other techniques known, in achieving the objectives listed above. It employs a new data coding and reduction technique, where the particle time history information is used directly. Further, it has no 180 degrees directional ambiguity. A complex convection vortex flow was recorded and completely processed in under 2 min on an 80386 based PC, producing a 2-D map of the flow field containing over 300 velocity vectors.

Analysis of a surface-scattering spectrometer

A general light-scattering spectrometer for measuring surface fluctuations is analyzed by using the methods of Fourier optics. Optical configurations can be designed so that the autocorrelation of the photocurrent is given by either the first- or the second-order correlation functions for the surface fluctuations. Fluctuations in capillary-wave amplitude and in surface density can be detected separately for a number of cases of practical interest. A method is proposed for unambiguous detection of capillary waves with amplitudes larger than the optical wavelength.

Laser velocimeters: lower limits to uncertainty

Laser velocimeters based on many-particle scattering or rough surface scattering are considered. It is shown that the established lower limits to the accuracy are not fundamental limits. Both linear and nonlinear signal processing may enhance the performance. Generic schemes for the processing are presented, and limitations are discussed.

A Look at the Multiphase Mixture Model for PEM Fuel Cell Simulations

Two-phase flows in polymer electrolyte membrane fuel cells (PEMFCs) are complex dynamic processes involving phase transitions and phase production due to concurrent processes. There have been attempts to simulate these phenomena using the multiphase mixture (M 2 ) model. The conjecture is that M 2 is mathematically equivalent to classical two-fluid models without invoking any additional approximations. We show that the M 2 model has a narrow applicability, limited to flows without phase transitions or phase production due to other processes. For more complex situations, including those encountered in PEMFCs, the M 2 model ceases to correctly reflect the conservation principles and may lead to predictions of unrealistic velocity and scalar fields.

Quantitative simulation of errors in correlation analysis

Bounding the errors of measurements derived from correlation functions of light scattered from some physical systems is typically complicated by the ill conditioning of the data inversion. Parameter values are estimated from fitting well-chosen models to measurements taken for long enough to look acceptable, or at least to yield convergence to some reasonable result. We show some simple numerical simulations that indicate the possibility of substantial and unanticipated errors even in comparatively simple experiments. We further show quantitative evidence for the effectiveness of a number of ad hoc aspects of the art of performing good light-scattering experiments and recovering useful measurements from them. Separating data-inversion properties from experimental inconsistencies may lead to a better understanding and better bounding of some errors, giving new ways to improve overall experimental accuracy.