Axially symmetric turbulent boundary layers on cylinders: mean velocity profiles and wall pressure fluctuations

Abstract

Experimental measurements of the mean velocity profiles produced by axially symmetric turbulent boundary layers on cylinders of various diameters are described. The profile measurements were made with very small hot wires developed for this investigation. Measurements of the wall shear stress on cylinders ranging from 0.02 to 2.0 in. in diameter are also reported. In the boundary layer on cylinders, well-defined regions exist in which the two-dimensional law of the wall and a three-dimensional wake law are valid. There was no evidence that the boundary layer was not fully turbulent even on the cylinders of smallest diameter. Measurements of wall pressure fluctuations beneath the boundary layer on a 1 in. diameter cylinder are also described. The results were much the same as those previously reported by Willmarth & Yang (1970) for a 3 in. diameter cylinder. The only difference was the discovery that the wall pressure was correlated in the transverse direction approximately half-way around the cylinder. This was not true on the 3 in. diameter cylinder.

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

“…The smaller slope is however consistent with the experimental results in Willmarth et al (1976). As the r i /r o ratio gets smaller, experimental (Willmarth et al (1976)) and DNS results (Chung et al (2002), Boersma and Breugem (2011)) indicate that the slope will decrease further. Figure 4 displays the sensitivity of the force power spectral density, which will be defined in Section 5, to the grid density.…”

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.…”

“…Small Preston tubes have been shown to provide accurate measurements of the wall shear stress on a cylinder based on a flat plate calibration. 6,27 The wall shear stress measured using the Preston tubes varied by less than 2.5% from the mean indicating that the boundary layer was essentially axisymmetric. The streamwise mean velocity profile in the boundary layer measured using a hot wire was slightly fuller than predicted by the cylindrical log law of Lueptow et al, 30 but it was within the expected range of variation.…”

“…The mean velocity profile is fuller and there is an increase in the coefficient of friction. 6 However, the maximum turbulence intensity and VITA detected events in a cylindrical turbulent boundary layer are similar to those of planar wall-bounded flows suggesting that the near wall structure of the boundary layer is similar to that of planar flows with the burst-sweep cycle being the underlying mechanism for the generation of turbulence. 4,5,7 The majority of studies on cylindrical boundary layers have concentrated on the velocity field, while wall pressure measurements have been few.…”

“…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.…”