Error analysis of CASH method: computer-averaging of noisy periodic signals

Abstract

Computer-assisted synchronous hot wire, or “CASH,” method was developed to permit computer averaging of hot wire data when sampling oscillating velocity profiles. Using emitted sound pressure as phase reference, computer separates periodic component of hot wire signal from turbulent background by averaging over large number of acoustic cycles. So far technique has been utilized in two investigations: (1) interface oscillations of flow-excited cavities, and (2) growth of instability waves in laminar jets. Accuracy depends on the ability to match closely the reference source frequency. Any mismatch produces systematic error. For given amount of mismatch, however, error is minimized by dividing sample into subsets and performing the averaging at two levels. In the cavity resonator problem, random deviations from periodicity in the reference itself make frequency-matching difficult. Measured standard deviations show a predicted periodicity, with greatest amplitude discrepancy occurring 90° after signal maximum. To assure amplitude error of no more than 3% requires that frequency mismatch be kept to less than 0.1%. [Work sponsored by Naval Ship System Command, GHR program, administered by Naval Ship Research and Development Center.]