## High Reynolds Number Flows

Our research focuses on high Reynolds number turbulence. Most of the flows we experience in everyday life are turbulent, and many of these exhibit very high Reynolds numbers. For example, the flow in the earth’s atmosphere has an extremely large Reynolds number, and so do aircraft, submarines and large pipe flows. In order to design energy efficient applications, and understand meteorology and climate change, high Reynolds number turbulence needs to be better understood.

A higher Reynolds number means a larger ratio between the largest and the smallest scales in the flow. In a laboratory the largest scale is fixed by the size of the facility, thus high Reynolds number will unavoidably mean that the smallest scales become very small. Classically, there have been two main limitations on conducting quality high Reynolds number experiments: a lack of facilities capable of generating high Reynolds number turbulence, and poor resolution of available measurement techniques. Our research group, however, has shown that it is possible to reach very high Reynolds numbers in a laboratory-sized facility by using high-pressure air as the working fluid, and our laboratory now has two such wind tunnels, but their true potential has been limited by the size of our measurement sensors. Our solution to this has been to develop a velocity sensor with a sensing length of 20μm and diameter of 100 nm which is almost two orders of magnitude smaller than conventional probes.

The new probes have been designed so that they would be smaller than the smallest scales in the flow. However, it is actually not clear what the size of the smallest scale is. The classical length scale to describe the smallest scales is the Kolmogorov length scale, which is based on the rate of energy dissipation in the fluid. Because of the intermittent nature of the small-scale motions, the Kolmogorov scale only describes the rate of dissipation in a mean sense. We have showed that the true local dissipation scale is distributed around the Kolmogorov scale, with contributions from motions that are at least an order-of magnitude larger. We were also able to show that this scale distribution is universal, independent of both the Reynolds number and the degree of anisotropy of the large scales of turbulence (or flow type), indicating that the dynamics of turbulence at the smallest scales are already in an asymptotic state even at Reynolds numbers where the larger scale dynamics are not. This observation may also mean that there are scales in the flow even smaller than what the classical theory predicts, making the problem of turbulence even more difficult. However, the universality of the scale distribution may permit the formulation of an asymptotic model that will hold at all Reynolds numbers.

These new probes have been used to show that the near-wall turbulence in pipe-flow is invariant with Reynolds number when scaled in inner coordinates, in contrast to the behavior in a flat plate boundary layer, where it increases with Reynolds number. This is of great interest since many theories and models have assumed these two canonical flows to behave similarly when scaled with the appropriate scales.

References:

Hultmark, M. N., Leftwich, M. and Smits, A. J., “Flowfield measurements in the wake of a robotic lamprey.” Experiments in Fluids, Vol. 43, pp. 683-690, 2007.

Bailey S., Hultmark M., Smits A. J. and Schultz M. P., “Azimuthal structure of turbulence in high Reynolds number pipe flow”, Journal of Fluid Mechanics, Vol 615, pp. 121 – 138, 2008.

Bailey S., Hultmark M., Schumacher J., Yakhot V. and Smits A. J. “Measurement of Local Dissipation Scales in Turbulent Pipe Flow”, Phys. Rev. Lett., Vol. 103, 014502, 2009

Hultmark M., Bailey S. C., and Smits A. J, “Scaling near-wall turbulence in pipe flow”, Journal of Fluid Mechanics, Vol 649, pp. 103 – 113, 2010.

Jiménez, J., Hultmark, M. and Smits, A. J., “The wake of a body of revolution at high Reynolds number.” In Press, Journal of Fluid Mechanics.

Bailey, S. C., Kunkel, G. J., Hultmark, M., Hill, J., Meyer, K., Arnold, C. B. and Smits, A. J., “Development of NSTAP: a Nanoscale Thermal Anemometry Probe.” In Press, Journal of Fluid Mechanics.

Hultmark, M. and Smits, A. J., “Temperature corrections for constant temperature and constant current hot-wire anemometers.” Under Review, Meas. Sci. Tech.