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Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder

  • H. H. Fernholz (a1) and J.-D. Vagt (a1)


Measurements, including the six components of the Reynolds-stress tensor, have been made along three generators of a centre-mounted circular cylinder with an elliptical nose cone. The pressure distribution was axisymmetric upstream and asymmetric downstream. The streamwise adverse pressure gradient led to almost zero skin friction in the direction of the limiting streamline, and the circumferential pressure gradient led to skew angles up to 30° in the vicinity of the wall. Special emphasis was laid on measurements in the wall region (y+ > 4), on the repeatability of these measurements and on an estimate of error bounds. The turbulence level encountered (up to 60% close to the wall) was much higher than in other threedimensional boundary-layer measurements. It has been shown that available measuring techniques have to be improved considerably or even abandoned if used under these conditions. Previous measurements of collateral velocity profiles in three-dimensional boundary layers will probably now have to be corrected for severe aerodynamic interference effects.

It has been shown that the normal stresses $\overline{u^{\prime 2}_i}$ and the shear stress component $\overline{u^{\prime}v^{\prime}}$ behave qualitatively much as those in a two-dimensional adverse pressuregradient boundary layer. The other components, $\overline{v^{\prime}w^{\prime}}$ and $\overline{u^{\prime}w^{\prime}}$, both characteristic of three-dimensional flow and caused by the circumferential pressure gradient, are influenced in different ways by the streamwise and circumferential pressure gradients. Spectra of u′-fluctuations are again similar to those obtained from two-dimensional boundary layers.

Mean velocity profiles obey the linear and logarithmic law of the wall known from two-dimensional boundary layers both along a line of symmetry and in the threedimensional boundary layer. This may be because the streamwise pressure gradient dominates over the circumferential pressure gradient in this experiment.

Finally it has been found that the skew angle γ of the Reynolds shear stress vector leads the skew angle ζ of the resultant velocity gradient or ‘mean shear’, both having the opposite sign of the skew angle β of the mean velocity vector except close to the wall. The ratio of Reynolds shear stress and turbulent kinetic energy is no longer ‘approximately’ constant as is assumed for two-dimensional boundary layers.



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Turbulence measurements in an adverse-pressure-gradient three-dimensional turbulent boundary layer along a circular cylinder

  • H. H. Fernholz (a1) and J.-D. Vagt (a1)


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