Application of Digital Fourier Analysis in Processing Dynamic Aerodynamic Heating Measurements

Abstract

APRACTICAL application of a digital Fourier analysis (fast Fourier transform) in processing fluctuating heattransfer data was utilized in a wind-tunnel test program at Mach number 8. A 4-deg, half-angle cone instrumented with conventional heat gages was oscillated in pitch at an amplitude of 2 deg and frequencies up to 15 Hz. The gages had a time constant of approximately 120 ms, which was not sufficiently responsive to follow the motion, and the Fourier analysis was used to correct the gage outputs. These measurements were used to map the location of the boundarylayer transition front. The purpose of this paper is to describe in some detail the technique used in processing these transient heat-transfer measurements. A more detailed presentation may be found in Ref. 1. The results indicate that the Fourier analysis was a very powerful method for correcting dynamic heat-transfer measurements. Contents The procedure for analyzing transient sensor data signals which are produced by undefined input signals is well documented. Any transient signal can be viewed in the frequency domain as a spectrum (amplitude distribution of the real and imaginary terms as a function of frequency), and the fast Fourier transform (FFT) algorithm provides the numerical procedure needed to transform digitally recorded transient data from the time domain into the frequency domain. Brigham2 has suggested that the FFT, in many respects, is analogous to using natural (or common) logarithms as a means of substituting simple arithmetic operations such as addition and subtraction for multiplication and division. In the frequency domain, certain numerical operations on a signal such as convolutions, correlations, energy content, and discrete digital filtering can be performed quite simply. In particular, the FFT can be used to determine the response or transfer function of a linear measuring system based on the distorted output of a sensor along with the known calibration pulse which caused the sensor response. A computer calculates the Fourier transforms of both the input and output time histories and ratios the two transforms to