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PDV Uncertainty Estimation & Methods Comparison

Several methods are presented for estimating the rapidly changing instantaneous frequency of a time varying signal that is contaminated by measurement noise. Useful a posteriori error estimates for several methods are verified numerically through Monte Carlo simulation. However, given the sampling rates of modern digitizers, sub-nanosecond variations in velocity are shown to be reliably measurable in most (but not all) cases. Results support the hypothesis that in many PDV regimes of interest, sub-nanosecond resolution can be achieved.

47 OTHER INSTRUMENTATION↗

Establishing precision and accuracy in PDV results

We need to know uncertainties and systematic errors because we create and compare against archival weapons data, we constrain the models, and we provide scientific results. Good estimates of precision from the data record are available and should be incorporated into existing results; reanalysis of valuable data is suggested. Estimates of systematic errors are largely absent. The original work by Jensen et al. using gun shots for window corrections, and the integrated velocity comparison with X-rays by Schultz are two examples where any systematic errors appear to be <1% level.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Limiting noise fraction in PDV measurements

The limiting frequency resolution of a PDV measurement is: σf = $\sqrt\frac{6 η}{fsτ^3π}$ where f s is the sample rate, τ is the analysis time duration, and 11 is the noise fraction. Although T is a strong lever for reducing uncertainty, this parameter must be kept small to preserve time resolution. Consider a PDV measurement with sampled at 80 GS/s and analyzed in 1 ns durations. A 1% noise fraction corresponds to 0.87 MHz of frequency uncertainty, which at 1550 nm works out to 0.68 m/s. A 10% noise fraction has a limiting velocity resolution of about 7 m/s; for comparison, a VISAR system with similar response time (0.5 ns delay, 532 m/s fringe constant) would have a limiting uncertainty of 5-6 m/s. Noise fractions of 10-20% or less are desirable for measurements at this time scale.

42 ENGINEERING↗

Planar Doppler Velocimetry for Large-Scale Wind Tunnel Testing

Recently, Planar Doppler Velocimetry (PDV) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike other optical means of measuring flow velocities, PDV is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDV have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDV in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDV capabilities for applications in large-scale wind tunnels that are intended primarily for the production testing of subsonic aircraft. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes and separations. To accomplish the objectives indicated, the PDV measurement process is first modeled and its performance evaluated computationally. The noise sources considered include those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with coherent illumination from pulsed lasers. The signal noise estimates are incorporated into the PDV signal analysis process and combined with computed scattering signals using a Mie scattering theory for polydisperse smoke particles. The relevant parameters incorporate a range of practical aerodynamic test conditions and facility sizes. The results define the optimum instrument configurations, show that the expected signal levels from a practical PDV system are sufficiently large to allow its useful application in large facilities, and show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing. Experimental studies using several experimental bench-top setups are then described that validate the physics of the PDV model and to calibrate its computed results. The validated model allows estimates of the uncertainties of PDV measurements and a complete definition of the PDV capabilities to be made with sufficient confidence to decide the viability of PDV for large-scale wind tunnel applications.

McKenzie, Robert L.↗