Wall-bounded turbulence at high Reynolds numbers

Abstract

Measurements are reported that give new insight into the behavior of turbulent wall-bounded flows at high Reynolds number. Turbulent pipe and boundary layer flows are examined experimentally over a wide range of Reynolds numbers - up to Re&tau;=100,000 (ReD=6&times;10<super>6</super>) in pipe flow, and up to Re&tau;=73,000 (ReD=235&times;10<super>3</super>) in a flat plate zero pressure gradient boundary layer. A Nano-Scale Thermal Anemometry Probe (NSTAP) was developed for very high spatial and temporal resolution measurements. Sensors with wire lengths 30 and 60 &mu;m were fabricated, tested and validated in known flows, and then used to obtain single-point measurements at high Reynolds numbers in pipe and boundary layers.

The mean velocity data together with data from previous studies and extensive error analysis showed that the von K´arm´an's constant in the log-law is &kappa;=0.40&plusmn;0.02. It was shown that the streamwise Reynolds stress exhibits a logarithmic behavior in the inertial sublayer for Re&tau;&ge;20,000, in both pipes and boundary layers. Variances as well as higher order even moments were compared for pipes and boundary layers and it was shown that all even moments have a logarithmic behavior in the inertial sublayer, suggesting a true scale separation.

Streamwise turbulent spectra showed a clear k<super>-5/3</super> region for up to two decades in wavenumber. No k<super>-1</super> region was found to be present in any of the cases in the pipe or the boundary layer. The location of the outer spectral peak, associated with very large scale motions, was found to have only a weak dependence on Reynolds number. The loci of these peak occur at the same wall-normal distance where the streamwise stresses establish a logarithmic behavior and where the amplitude modulation coefficient has a zero value. This suggests that with Reynolds number increasing to infinity most of the energy is contained within a diminishing wall-layer in physical coordinates.