Wall Pressure Correlations in Turbulent Airflow

Abstract

The correlation properties of turbulent wall pressure fluctuations are investigated experimentally with a view toward developing an adequate phenomenological model of the pressure correlation function for use in engineering calculations. It was found that both mean eddy sizes and mean eddy lifetimes determined by averaging over broad frequency bands did not contain sufficient information to accurately describe the high frequency end of the turbulent power spectrum. Thus, such gross quantities are of somewhat limited utility in detailed analysis, for instance, in predicting response of multimodal mechanical systems driven by flowing turbulence. However, by measuring eddy sizes and lifetimes over narrow frequency bands it appears possible to construct mathematical models for the turbulent pressure correlations which are successful in predicting the turbulent power spectrum over the frequency band of interest which could include the entire spectrum. In addition, measurements of rms pressure and space-time correlations are presented which supplement the data obtained by W. W. Willmarth [-NASA Memo. 3-17-59 W (1959)-] for a somewhat higher mach range.

Response of Bars and Plates to Boundary-Layer Turbulence

“…Details of the equipment and techniques were described in a previous work. 10 Parasitic acoustic noise in the wind tunnel presents difficulties in these measurements, since it has correlation maximums for zero time delay in lateral correlation measurements and very nearly zero time delay in longitudinal correlation measurements. The amount of acoustic noise was negligible at the highest frequencies for which measurements of L x and L y were obtained but was appreciable at the lowest frequencies and highest flow speeds.…”

“…In previous work, 10 where £ = x ~ x\ rj = y -y', T = t -t\ (p 2 ) is the mean square pressure, v is the mean eddy drift velocity, f is the mean eddy lifetime, and L x and L v are the longitudinal and lateral eddy sizes, respectively. Actually, in the work referred to above we treat in detail only the one-dimensional form of this spectrum, but pressure correlation measurements indicate that the pressure correlation falls off exponentially in the lateral direction.…”

“…10 The frequency range was restricted by frequency-response limitations in the pressure probes used to measure L x , L y , and f. Values of L x , L y , and f were obtained by averaging over narrow frequency bands since it was found that measurements of eddy sizes and eddy lifetimes obtained by averaging over broad frequency bands were not sufficiently accurate to predict the behavior of the turbulent power spectrum at high frequencies, say above 1,000 cps. Results of eddy-size and eddylifetime measurements in a subsonic wind tunnel are shown in Figs.…”

“…tively easy to interpret in terms of measurable pressure-correlation properties of the turbulent boundary layer. 10 It is the purpose of this investigation to determine whether or not a phenomenological model of the pressure correlations of boundary-layer turbulence is capable of predicting the absolute magnitude of the response of a bar (or plate) which forms the boundary. Lyon's measurements on the string were only relative, and so far as is known, no absolute response measurements on any simple mechanical system (string, bar, or plate) that can be compared with theoretical calculations have been made.…”

A Review of Flow Noise Research Related to the Sonar Self Noise Problem

“…The Minnesota studies were based on Dyer's model of the wall pressure correlation function R(r , ,). Tack, Smith and Lambert (1961) measured the properties of this function and found that U. U, the centerline velocity of the tunnel. but that the correlation lengths A. , A 3 and the decay time • were functions of U and of frequency L .…”