Wall-pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder

Abstract

Measurements of the turbulent pressure field on the outer surface of a 3 in. diameter cylinder aligned with the flow were made at a point approximately 24 ft. downstream of the origin of the turbulent boundary layer in an air stream of 145 ft./sec. The boundary-layer thickness was 2·78 in. and the Reynolds number based on momentum thickness was 2·62 × 104. The wall-pressure measurements were made with pressure transducers constructed from 0·06 in. diameter lead–zirconate–titanate disks mounted flush with the wall. The measurements including root-mean-square, power spectrum, and correlations of the wall pressure are compared with the existing experimental results for the turbulent pressure field beneath a plane boundary layer. The streamwise convection speed deduced from longitudinal space-time correlation measurements was almost identical to that obtained in the plane boundary layer. The rate of decay of the maxima of the space-time correlation of the pressure produced by the convected eddies was double that in a plane boundary layer. The longitudinal and transverse scales of the pressure correlation were approximately equal (in a plane boundary layer the transverse scale is larger than longitudinal scale) and were one-half or less than the longitudinal scale in the plane boundary layer. It is concluded that the effect of the transverse curvature of the wall is an overall reduction in size of pressure-producing eddies. The reduction in transverse scale of the larger eddies is greater than that of the smaller eddies. In general, the smaller eddies decay more rapidly and produce greater spectral densities at high frequencies owing to the unchanged convection speed.

Predicting turbulence-induced vibration in axial annular flow by means of large-eddy simulations

“…In reasonable agreement with experimental results of flat-wall boundary layer flow by Bull (1967), the longitudinal correlation decreases strongly until a length of approximately ∆z/h = 4, with h being the half-height of the channel (= D h /4). The current results also agree reasonably with the measurements of Willmarth and Yang (1970) who measured a correlation length (the integral of the two-point correlation) of 1.31 times the boundary layer height on a body of revolution. Theoretically, the correlation should drop to zero at large distances.…”

“…Therefore, Equation 6 is plotted in Figure 3, using C1 = 2.5 and C2 = 5.5, which are the flat-plate constants. These constants are very close to the measured values of C1 = 2.5 and C2 = 5.1 (Willmarth and Yang, 1970). It can be observed that the computed velocity profile, at least for cases C and D, is indeed close to this logarithmic law, which was also observed in Moreno (2000).…”

Spanwise structure of wall pressure on a cylinder in axial flow

“…In this study we assume that when comparing the response of microphone pairs, the spanwise spacing of the microphones is the primary effect, while the axial spacing of microphones is secondary in importance based on the following arguments. First, Willmarth and coworkers 6,8 found that even for the maximum axial separation in our study, x ϭ1.65␦*, the maximum cross-correlation between axiallyspaced microphones for ␦/aϭ2 and 4 was nearly 0.5. Even higher correlations resulted for smaller axial separations.…”

“…At low frequencies the differences in the spectra are consistent with previous researchers. 6,8 Since the spectra were obtained at similar Reynolds numbers using microphones of similar size, the difference between the spectra can only be attributed to transverse curvature. A useful form in which to plot power spectra to answer this question is the first moment of the power spectrum ⌽ pp () versus log , as shown in Fig.…”

“…4,5,7 The majority of studies on cylindrical boundary layers have concentrated on the velocity field, while wall pressure measurements have been few. Only Willmarth and Yang, 8 Willmarth et al, 6 and Snarski and Lueptow 7 have made velocity-pressure cross-correlation measurements, and Nepomuceno and Lueptow 9 have made pressure-shear-velocity cross-correlation measurements.…”